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i want it with in 6 hours.
and i need perfect work only.
my input/lab_13.xlsx
Sheet1
w1= 9.0 g w2= 9.5 g w3= 9.3 g
w Mean
0 -1.81329
w1 9 -2.08293
w1+w2 18.5 -2.37752
w1+w2+w3 27.8 -2.65388
Bridge measurements
length = 20.5 mm
width = 2.5 mm
t = .34
Weight vs. Mean
0 9 18.5 27.8 -1.8132900000000001 -2.0829300000000002 -2.3775200000000001 -2.65388 Weight (g)
Mean (mV)
my input/lab13.lvm
LabVIEW Measurement
Writer_Version 2
Reader_Version 2
Separator Tab
Decimal_Separator .
Multi_Headings No
X_Columns Multi
Time_Pref Absolute
Operator ecslogon
Date 2013/11/24
Time 17:56:45.6681595499425889578
***End_of_Header***
Channels 1
Samples 5000
Date 2013/11/24
Time 17:56:45.6681595499425889578
Y_Unit_Label Strain
X_Dimension Time
X0 0.0000000000000000E+0
Delta_X 0.001000
***End_of_Header***
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my input/labview.PNG
my input/Mansour_week_13_lab.vi
my input/origin.PNG
my input/strain.xlsx
Sheet1
0 weight w1 w1+w2 w1+w2+w3
X_Value Strain X_Value Strain X_Value Strain X_Value Strain
0 -0.000183 0 -0.000218 0 -0.000224 0 -0.000276
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0.977 -0.000164 0.977 -0.000205 0.977 -0.000259 0.977 -0.000276
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0.979 -0.000168 0.979 -0.000186 0.979 -0.000229 0.979 -0.000282
0.98 -0.000174 0.98 -0.000212 0.98 -0.000225 0.98 -0.000281
0.981 -0.000179 0.981 -0.000202 0.981 -0.000224 0.981 -0.000256
0.982 -0.000188 0.982 -0.000214 0.982 -0.00024 0.982 -0.000246
0.983 -0.000179 0.983 -0.000215 0.983 -0.000249 0.983 -0.000259
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0.985 -0.000216 0.985 -0.000215 0.985 -0.000257 0.985 -0.000279
0.986 -0.000191 0.986 -0.000218 0.986 -0.000238 0.986 -0.000263
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1.002 -0.000167 1.002 -0.000213 1.002 -0.00025 1.002 -0.000287
1.003 -0.000174 1.003 -0.0002 1.003 -0.000239 1.003 -0.000277
1.004 -0.000183 1.004 -0.000223 1.004 -0.000226 1.004 -0.000271
1.005 -0.000196 1.005 -0.000215 1.005 -0.000225 1.005 -0.000256
1.006 -0.000198 1.006 -0.000218 1.006 -0.00023 1.006 -0.000249
1.007 -0.000192 1.007 -0.00022 1.007 -0.000245 1.007 -0.000255
1.008 -0.000193 1.008 -0.000218 1.008 -0.000242 1.008 -0.000263
1.009 -0.00018 1.009 -0.000215 1.009 -0.000246 1.009 -0.000274
1.01 -0.000177 1.01 -0.000201 1.01 -0.000246 1.01 -0.000281
1.011 -0.00016 1.011 -0.000201 1.011 -0.000237 1.011 -0.000275
1.012 -0.000177 1.012 -0.000208 1.012 -0.000228 1.012 -0.000261
1.013 -0.000177 1.013 -0.000196 1.013 -0.000228 1.013 -0.000249
1.014 -0.00018 1.014 -0.000209 1.014 -0.000225 1.014 -0.000244
1.015 -0.000186 1.015 -0.000205 1.015 -0.000238 1.015 -0.000239
1.016 -0.000204 1.016 -0.000219 1.016 -0.000251 1.016 -0.000249
1.017 -0.000196 1.017 -0.000223 1.017 -0.000256 1.017 -0.000265
1.018 -0.000194 1.018 -0.000212 1.018 -0.00025 1.018 -0.000278
1.019 -0.000187 1.019 -0.00022 1.019 -0.000233 1.019 -0.000296
1.02 -0.000175 1.02 -0.000218 1.02 -0.000221 1.02 -0.00027
1.021 -0.000167 1.021 -0.000191 1.021 -0.000224 1.021 -0.000256
1.022 -0.000172 1.022 -0.000205 1.022 -0.000235 1.022 -0.000248
1.023 -0.000155 1.023 -0.000191 1.023 -0.000238 1.023 -0.000251
1.024 -0.000174 1.024 -0.00019 1.024 -0.000245 1.024 -0.000262
1.025 -0.000188 1.025 -0.000191 1.025 -0.000251 1.025 -0.000264
1.026 -0.000164 1.026 -0.000217 1.026 -0.000256 1.026 -0.000302
1.027 -0.000197 1.027 -0.000212 1.027 -0.000246 1.027 -0.000262
1.028 -0.000195 1.028 -0.000195 1.028 -0.000229 1.028 -0.00026
1.029 -0.000205 1.029 -0.00024 1.029 -0.000216 1.029 -0.000254
1.03 -0.00018 1.03 -0.000221 1.03 -0.000231 1.03 -0.000241
1.031 -0.00017 1.031 -0.000209 1.031 -0.000229 1.031 -0.000284
1.032 -0.000171 1.032 -0.000223 1.032 -0.000238 1.032 -0.000253
1.033 -0.000179 1.033 -0.000193 1.033 -0.000251 1.033 -0.000269
1.034 -0.000165 1.034 -0.000192 1.034 -0.000259 1.034 -0.000275
1.035 -0.000171 1.035 -0.000204 1.035 -0.000238 1.035 -0.000284
1.036 -0.000226 1.036 -0.000203 1.036 -0.000242 1.036 -0.000257
1.037 -0.00022 1.037 -0.000197 1.037 -0.000235 1.037 -0.000257
1.038 -0.000199 1.038 -0.0002 1.038 -0.000227 1.038 -0.000229
1.039 -0.00019 1.039 -0.000216 1.039 -0.000231 1.039 -0.000241
1.04 -0.000187 1.04 -0.000218 1.04 -0.00023 1.04 -0.000291
1.041 -0.000201 1.041 -0.00022 1.041 -0.000254 1.041 -0.000281
1.042 -0.00015 1.042 -0.000215 1.042 -0.000234 1.042 -0.000267
1.043 -0.000146 1.043 -0.000207 1.043 -0.000252 1.043 -0.000272
1.044 -0.000154 1.044 -0.000191 1.044 -0.000237 1.044 -0.000274
1.045 -0.000166 1.045 -0.000201 1.045 -0.000225 1.045 -0.000243
1.046 -0.000171 1.046 -0.000209 1.046 -0.000223 1.046 -0.000245
1.047 -0.000183 1.047 -0.000193 1.047 -0.000234 1.047 -0.00026
1.048 -0.000191 1.048 -0.000207 1.048 -0.000244 1.048 -0.000276
1.049 -0.000189 1.049 -0.000221 1.049 -0.000251 1.049 -0.000278
1.05 -0.000196 1.05 -0.00022 1.05 -0.000254 1.05 -0.000276
1.051 -0.000191 1.051 -0.000218 1.051 -0.000232 1.051 -0.000255
1.052 -0.000182 1.052 -0.000214 1.052 -0.00024 1.052 -0.000253
1.053 -0.000191 1.053 -0.000218 1.053 -0.000231 1.053 -0.000262
1.054 -0.00017 1.054 -0.000213 1.054 -0.000213 1.054 -0.000267
1.055 -0.000172 1.055 -0.000196 1.055 -0.000242 1.055 -0.00028
1.056 -0.000187 1.056 -0.000199 1.056 -0.000274 1.056 -0.000277
1.057 -0.000156 1.057 -0.000196 1.057 -0.000249 1.057 -0.00026
1.058 -0.000193 1.058 -0.000208 1.058 -0.000265 1.058 -0.000246
1.059 -0.000217 1.059 -0.000207 1.059 -0.000256 1.059 -0.000252
1.06 -0.000184 1.06 -0.000221 1.06 -0.000231 1.06 -0.000257
1.061 -0.000193 1.061 -0.00022 1.061 -0.000245 1.061 -0.000284
1.062 -0.000204 1.062 -0.000221 1.062 -0.00023 1.062 -0.000273
1.063 -0.00019 1.063 -0.00022 1.063 -0.000216 1.063 -0.000273
1.064 -0.000177 1.064 -0.000205 1.064 -0.000235 1.064 -0.000268
1.065 -0.000176 1.065 -0.000194 1.065 -0.000242 1.065 -0.000255
1.066 -0.000173 1.066 -0.000193 1.066 -0.000238 1.066 -0.000259
1.067 -0.000169 1.067 -0.000196 1.067 -0.000262 1.067 -0.000259
1.068 -0.000154 1.068 -0.000199 1.068 -0.000227 1.068 -0.000261
1.069 -0.000172 1.069 -0.000212 1.069 -0.000226 1.069 -0.000274
1.07 -0.000193 1.07 -0.000205 1.07 -0.000219 1.07 -0.000283
1.071 -0.000182 1.071 -0.000238 1.071 -0.000228 1.071 -0.000259
1.072 -0.000199 1.072 -0.000224 1.072 -0.00023 1.072 -0.000254
1.073 -0.000188 1.073 -0.000226 1.073 -0.000241 1.073 -0.000246
1.074 -0.000203 1.074 -0.00022 1.074 -0.000249 1.074 -0.000276
1.075 -0.000193 1.075 -0.000214 1.075 -0.000243 1.075 -0.000268
1.076 -0.000159 1.076 -0.000204 1.076 -0.000239 1.076 -0.000278
1.077 -0.000179 1.077 -0.000199 1.077 -0.000222 1.077 -0.000279
1.078 -0.000173 1.078 -0.000191 1.078 -0.000229 1.078 -0.000276
1.079 -0.000168 1.079 -0.000203 1.079 -0.000224 1.079 -0.000265
1.08 -0.000171 1.08 -0.000201 1.08 -0.000232 1.08 -0.00025
1.081 -0.000187 1.081 -0.000216 1.081 -0.000245 1.081 -0.000249
1.082 -0.000191 1.082 -0.000213 1.082 -0.00024 1.082 -0.000257
1.083 -0.000196 1.083 -0.00022 1.083 -0.000248 1.083 -0.000273
1.084 -0.000194 1.084 -0.000214 1.084 -0.00024 1.084 -0.000285
1.085 -0.000185 1.085 -0.000213 1.085 -0.000227 1.085 -0.000293
1.086 -0.000162 1.086 -0.00021 1.086 -0.000222 1.086 -0.000275
1.087 -0.000172 1.087 -0.000197 1.087 -0.000216 1.087 -0.000251
1.088 -0.000169 1.088 -0.000187 1.088 -0.000231 1.088 -0.000248
1.089 -0.00017 1.089 -0.000204 1.089 -0.000242 1.089 -0.000263
1.09 -0.000185 1.09 -0.000202 1.09 -0.000265 1.09 -0.000279
1.091 -0.000185 1.091 -0.000204 1.091 -0.000259 1.091 -0.00027
1.092 -0.000181 1.092 -0.000217 1.092 -0.000242 1.092 -0.000278
1.093 -0.000196 1.093 -0.000224 1.093 -0.000243 1.093 -0.000269
1.094 -0.000188 1.094 -0.000223 1.094 -0.000221 1.094 -0.000257
1.095 -0.000196 1.095 -0.000223 1.095 -0.000245 1.095 -0.000262
1.096 -0.000172 1.096 -0.000214 1.096 -0.000224 1.096 -0.000255
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1.098 -0.000171 1.098 -0.000187 1.098 -0.000259 1.098 -0.000274
1.099 -0.000168 1.099 -0.000187 1.099 -0.00025 1.099 -0.000275
1.1 -0.000177 1.1 -0.000194 1.1 -0.000232 1.1 -0.000289
1.101 -0.00016 1.101 -0.000203 1.101 -0.00023 1.101 -0.000264
1.102 -0.000144 1.102 -0.000204 1.102 -0.000222 1.102 -0.000251
1.103 -0.000196 1.103 -0.000215 1.103 -0.000229 1.103 -0.000248
1.104 -0.000194 1.104 -0.000221 1.104 -0.000232 1.104 -0.000266
1.105 -0.000194 1.105 -0.00022 1.105 -0.00025 1.105 -0.000271
1.106 -0.000193 1.106 -0.000209 1.106 -0.000253 1.106 -0.000269
1.107 -0.000183 1.107 -0.00021 1.107 -0.000249 1.107 -0.000277
1.108 -0.000164 1.108 -0.000203 1.108 -0.000234 1.108 -0.000278
1.109 -0.000175 1.109 -0.000204 1.109 -0.000227 1.109 -0.000256
1.11 -0.00016 1.11 -0.000182 1.11 -0.000234 1.11 -0.00026
1.111 -0.000152 1.111 -0.000201 1.111 -0.000231 1.111 -0.000247
1.112 -0.000189 1.112 -0.000227 1.112 -0.000257 1.112 -0.000257
1.113 -0.000187 1.113 -0.000196 1.113 -0.000246 1.113 -0.000268
1.114 -0.000188 1.114 -0.000215 1.114 -0.000246 1.114 -0.000276
1.115 -0.000204 1.115 -0.000218 1.115 -0.000251 1.115 -0.000303
1.116 -0.000198 1.116 -0.000232 1.116 -0.000238 1.116 -0.00031
1.117 -0.000173 1.117 -0.000198 1.117 -0.000221 1.117 -0.000265
1.118 -0.000175 1.118 -0.000201 1.118 -0.000207 1.118 -0.000265
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1.12 -0.000158 1.12 -0.000204 1.12 -0.000235 1.12 -0.000268
1.121 -0.000177 1.121 -0.000209 1.121 -0.000238 1.121 -0.000265
1.122 -0.000176 1.122 -0.000184 1.122 -0.000246 1.122 -0.000275
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1.124 -0.000196 1.124 -0.000221 1.124 -0.000248 1.124 -0.000277
1.125 -0.000198 1.125 -0.000236 1.125 -0.000236 1.125 -0.000253
1.126 -0.000201 1.126 -0.000243 1.126 -0.000212 1.126 -0.000252
1.127 -0.00019 1.127 -0.000218 1.127 -0.000225 1.127 -0.000262
1.128 -0.000204 1.128 -0.000182 1.128 -0.000223 1.128 -0.000292
1.129 -0.000161 1.129 -0.000204 1.129 -0.000247 1.129 -0.000267
1.13 -0.000154 1.13 -0.000242 1.13 -0.000247 1.13 -0.000267
1.131 -0.000128 1.131 -0.000199 1.131 -0.000251 1.131 -0.000296
1.132 -0.000173 1.132 -0.000187 1.132 -0.000249 1.132 -0.000268
1.133 -0.000183 1.133 -0.000201 1.133 -0.000224 1.133 -0.000237
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1.136 -0.000167 1.136 -0.000233 1.136 -0.000244 1.136 -0.000271
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1.138 -0.00019 1.138 -0.000216 1.138 -0.000242 1.138 -0.000288
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1.14 -0.000147 1.14 -0.000218 1.14 -0.000218 1.14 -0.000257
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1.159 -0.000187 1.159 -0.000227 1.159 -0.000219 1.159 -0.000265
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1.174 -0.000166 1.174 -0.0002 1.174 -0.00024 1.174 -0.000261
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1.19 -0.000196 1.19 -0.00021 1.19 -0.000226 1.19 -0.000267
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1.202 -0.000195 1.202 -0.000209 1.202 -0.000255 1.202 -0.000254
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1.205 -0.00018 1.205 -0.000221 1.205 -0.000231 1.205 -0.000251
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1.207 -0.000142 1.207 -0.000216 1.207 -0.000223 1.207 -0.000289
1.208 -0.000175 1.208 -0.000209 1.208 -0.000232 1.208 -0.000235
1.209 -0.000182 1.209 -0.000193 1.209 -0.00024 1.209 -0.000284
1.21 -0.000199 1.21 -0.000202 1.21 -0.000248 1.21 -0.000252
1.211 -0.00019 1.211 -0.000197 1.211 -0.000248 1.211 -0.000248
1.212 -0.000183 1.212 -0.000195 1.212 -0.000235 1.212 -0.00026
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4.979 -0.000187 4.979 -0.000196 4.979 -0.000227 4.979 -0.000283
4.98 -0.000187 4.98 -0.000221 4.98 -0.000223 4.98 -0.000278
4.981 -0.000193 4.981 -0.000197 4.981 -0.000232 4.981 -0.000266
4.982 -0.000188 4.982 -0.000194 4.982 -0.000237 4.982 -0.000249
4.983 -0.00019 4.983 -0.000194 4.983 -0.000254 4.983 -0.000265
4.984 -0.00018 4.984 -0.00019 4.984 -0.000298 4.984 -0.000265
4.985 -0.00018 4.985 -0.000197 4.985 -0.000247 4.985 -0.000263
4.986 -0.00016 4.986 -0.000215 4.986 -0.000231 4.986 -0.000284
4.987 -0.000167 4.987 -0.000248 4.987 -0.000232 4.987 -0.000273
4.988 -0.000179 4.988 -0.000229 4.988 -0.000215 4.988 -0.000258
4.989 -0.000167 4.989 -0.000224 4.989 -0.000229 4.989 -0.000251
4.99 -0.000187 4.99 -0.000185 4.99 -0.000221 4.99 -0.000254
4.991 -0.00018 4.991 -0.000203 4.991 -0.000252 4.991 -0.000269
4.992 -0.000174 4.992 -0.000192 4.992 -0.000248 4.992 -0.000271
4.993 -0.000191 4.993 -0.000202 4.993 -0.000244 4.993 -0.000281
4.994 -0.000195 4.994 -0.000201 4.994 -0.00023 4.994 -0.000271
4.995 -0.000193 4.995 -0.000199 4.995 -0.000221 4.995 -0.000273
4.996 -0.000194 4.996 -0.000223 4.996 -0.000213 4.996 -0.000252
4.997 -0.000182 4.997 -0.000215 4.997 -0.000225 4.997 -0.000249
4.998 -0.000171 4.998 -0.000216 4.998 -0.000235 4.998 -0.000238
4.999 -0.000173 4.999 -0.000237 4.999 -0.000245 4.999 -0.000266
my input/w1.PNG
my input/w1andw2.PNG
my input/w1andw2andw3.PNG
my input/zero gram.PNG
needed/Lab Manual-2013-Spring-V1 (1)
Copyright 2013 by Sinha 1
Laboratory Manual*
for
Experimental Measurements
and Instrumentation
ME 3600/5600
Dr. S. Sinha
Wright State University
Dayton, OH 45435
Phone (937) 775-5146
E-mail: sanjiv.sinha@wright.edu
*Note that some changes may be made to these lab write-
ups during the course of the quarter.
Copyright 2013 by Sinha 2
ME3600/5600
WEEK 1 LAB : No Lab
EXPERIMENTAL MEASUREMENTS AND INSTRUMENTATION LABORATORY
WRIGHT STATE UNIVERSITY
ME3600/5600
Copyright 2013 by Sinha 3
ME3600/5600
WEEK 2 LAB : No Lab
EXPERIMENTAL MEASUREMENTS AND INSTRUMENTATION LABORATORY
WRIGHT STATE UNIVERSITY
Copyright 2013 by Sinha 4
ME3600/5600
EXPERIMENTAL MEASUREMENTS AND INSTRUMENTATION LABORATORY
WEEK 3 LAB : Group Statistics Lab
WRIGHT STATE UNIVERSITY
Objective: The objective of this laboratory is to gain a greater understanding of statistics: what
they mean and why we need them.
References: Chapter 4 of Figliola, R. S. and Beasley, D. E, Theory and Design for Mechanical
Measurements, 5
th
Edition, Wiley, 2011. There is also a great deal of information on the web.
Information: This lab will be done as a group and all directions will be given in laboratory
class.
Report: Nothing needs to be turned in.
Copyright 2013 by Sinha 5
ME3600/5600
EXPERIMENTAL MEASUREMENTS AND INSTRUMENTATION LABORATORY
WEEK 4 LAB: Individual Statistics Lab
WRIGHT STATE UNIVERSITY
Objective: The objective of this laboratory is to analyze supplied data sets using statistics.
Averages, standard deviations, confidence intervals, histograms, chi-squared goodness of fit test,
plotting, linear regression, correlation coefficient, and standard error are included. This lab will
be done using the software EXCEL.
References: Chapter 4 of Figliola, R. S. and Beasley, D. E, Theory and Design for Mechanical
Measurements, 5
th
Edition, Wiley, 2011. There is also a great deal of information on the web.
Information: An EXCEL spreadsheet file has been produced for you that includes three sets of
data. This file can be obtained off of the course PILOT site in the folder Laboratory>Lab
Handouts. The data set can be found in the file named “Week 4 Lab Data”. There are three sets
of data in this file. The first two sets, “Strain Measurement using 11 data points” and “Strain
Measurement using 1001 data points” are measuring a single strain for an aluminum bar. Both
data sets are measuring the exact same conditions and thus should produce the same strain. The
only difference between these two data sets is the number of points taken. The third data set,
“Pressure Measurement using 1001 data points”, is for measurements made of a single pressure
in a vacuum chamber. The first column in each of these data sets is time in seconds and the
second column is the desired measured value in the appropriate units.
When you try to draw conclusions from these results realize you are simply analyzing the
signals. No information is given on the way these measurements are made. Thus do not draw
conclusions on the measurement technique. Assume the measurement technique is correct. The
only piece of information you are given about the measurement is that one single value is being
measured. Thus you are to interpret the data as if you are simply analyzing a signal. You are
simply doing signal analysis.
Theory: This lab deals with a number of statistics on a finite set of data. A number of
techniques discussed in class and in our book are used.
Equipment:
1. The data set is on the ME3600 lecture class PILOT web site in Laboratory>Lab
Handouts> Week 4 Lab Data. This file is an Excel spreadsheet with the extension
.xlsx.
2. You will need the software Microsoft Excel 2007 or 2010. You may perform this work
in the lab, 142RC, or on any computer you wish.
Caution!
1. Make sure you save your work to your thumb drive. The computers in the lab wipe out
all unoriginal files after the computer is shut down.
Copyright 2013 by Sinha 6
Experimental Procedure: The student should use the software EXCEL to obtain the required
results.
Report: Your program with all the required results asked for below and answers to the
questions below needs to be submitted. Highlight all required numerical results in yellow.
Submit your program to the DROP BOX on PILOT for your lab section. Do not submit your file
to the lecture PILOT web site. Name your EXCEL file with your last name and Week 4 Lab. For
example:
Sinha_week_4_lab.xlsx
Required Results: Obtain the following results for each of the data sets:
1. Plot of each data set.
2. Sample average.
3. Sample standard deviation.
4. Standard deviation of the averages.
5. The 95% confidence interval of each data point in the sample.
6. The 95% confidence interval of the sample mean. Realize this is our attempt to specify
the population mean.
7. The 95% confidence interval of the sample standard deviation. Realize this is our
attempt to specify the population standard deviation.
8. Plot a Histogram.
9. Perform chi-squared goodness of fit test between your histogram and a Normal
distribution.
10. Place an appropriate polynomial curve fit of the results on your plots. You should place
the equation for the curve fit on the plot as well as a plot of the curve fit.
11. Determine the correlation coefficient and the standard error of your polynomial curve
fit.
12. Finally, give me your best estimate of the true value being measured for the strain and
the true value for the pressure. I want two numbers even though you have three data
sets. Realize the first two data sets are measuring the exact same thing. Explain your
choice to me. Write this next to your answer in the EXCEL spreadsheet.
13. Put each data set on a separate sheet of your EXCEL file.
14. Answer the questions below on a fourth sheet of your EXCEL file. Merge a number of
cells to give yourself a place to write.
Questions to Answer:
1. Why do the data in each of these three data sets behave the way they do if I am
measuring the exact same thing? Why do the 11 measurements in the first data set
vary? Why do the 1001 measurements in the second data set vary? Why do the 1001
measurements in the third data set vary?
2. Why might there be differences in the results from the “Strain Measurement using 11
data points” and “Strain Measurement using 1001 data points” if I am measuring the
same thing? Remember the measurements are correct, so do not tell me the
measurement was done wrong.
3. How did you choose your curve fit? What do these curves fits indicate?
4. Is there anything interesting happening in any of these data sets?
Copyright 2013 by Sinha 7
ME3600/5600
WEEK 5 LAB : Lab View Orientation,
Tutorials and Problems
EXPERIMENTAL MEASUREMENTS AND INSTRUMENTATION LABORATORY
WRIGHT STATE UNIVERSITY
Objective: The objective of this lab is to introduce the student to the software from National
Instruments called LabVIEW.
References:
1. Bishop, Robert H., Learning with LabVIEW 8, Pearson, 2007.
2. LabVIEW help menu and the web site
http://zone.ni.com/devzone/cda/tut/p/id/5054
3. There is also a great deal of help within the LabVIEW software such as “Getting Started
with LabVIEW”, “LabVIEW Fundamentals”, “Guide to LabVIEW Documentation”, and
“LabVIEW Help.”
Information: LabVIEW is a powerful graphical development environment for acquiring,
manipulating, analyzing, and presenting experimental data. LabVIEW stands for Laboratory
Virtual Instrumentation Engineering Workbench and was developed by the National Instruments
Corporation. LabVIEW makes use of icons (subroutines) or groups of icons it calls virtual
instruments (VIs) because they have the look and feel of real instruments. These icons can also
called functions or subroutines. LabVIEW has a large number of VIs and library functions
available to the user for performing many types of tasks. LabVIEW uses graphical programming,
G programming, that makes its use intuitive in many situations. LabVIEW also makes use of a
programming idea called data flow programming. In data flow programming an icon does not
execute until it has received all required input data. Icons are joined together by wires that dictate
how the program flows from one icon to another icon.
Theory: LabVIEW programming.
Equipment:
1. Computer
2. LabVIEW Software
Lab View Documents:
1. Getting Started with Lab View
2. ME3600 – LabView – Week5 LAB – Tutorials
3. ME3600 – LabView – Week5 LAB – Problems
http://zone.ni.com/devzone/cda/tut/p/id/5054
Copyright 2013 by Sinha 8
CAUTION!!!
1. Make sure you save your work to your thumb drive.
Experimental Procedure and Required Results: The student will write LabVIEW programs to
complete the tutorials and problems as described in the documents listed above.
Report: Submit hardcopies of the tutorial and problems as described in the Lab View tutorial
and problems documents listed above. Your final programs are also required for this lab. Submit
your programs to the DROP BOX on PILOT for your lab section. Name your file with your last
name and Week 5 Lab. For example:
Sinha_week_5_lab_tutorial_1.vi
Sinha_week_5_lab_tutorial_2.vi
Sinha_week_5_lab_problem_1.vi
Sinha_week_5_lab_problem_2.vi
Required Results:
1. See Experimental Procedure and Required Results section.
Questions to Answer:
1. None
Copyright 2013 by Sinha 9
ME3600/5600
EXPERIMENTAL MEASUREMENTS AND INSTRUMENTATION LABORATORY
WEEK 6 LAB: Lab VIEW Problem
WRIGHT STATE UNIVERSITY
Objective: This is a continuation from Week$5 lab and the objective of this lab is to further
introduce the student to the LabVIEW software from National Instruments.
References:
4. Bishop, Robert H., Learning with LabVIEW 8, Pearson, 2007.
5. LabVIEW help menu and the web site
http://zone.ni.com/devzone/cda/tut/p/id/5054
6. There is also a great deal of help within the LabVIEW software such as “Getting Started
with LabVIEW”, “LabVIEW Fundamentals”, “Guide to LabVIEW Documentation”, and
“LabVIEW Help.”
Information: LabVIEW is a powerful graphical development environment for acquiring,
manipulating, analyzing, and presenting experimental data. LabVIEW stands for Laboratory
Virtual Instrumentation Engineering Workbench and was developed by the National Instruments
Corporation. LabVIEW makes use of icons (subroutines) or groups of icons it calls virtual
instruments (VIs) because they have the look and feel of real instruments. These icons can also
called functions or subroutines. LabVIEW has a large number of VIs and library functions
available to the user for performing many types of tasks. LabVIEW uses graphical programming,
G programming, that makes its use intuitive in many situations. LabVIEW also makes use of a
programming idea called data flow programming. In data flow programming an icon does not
execute until it has received all required input data. Icons are joined together by wires that dictate
how the program flows from one icon to another icon.
Theory: LabVIEW programming.
Equipment:
3. Computer
4. LabVIEW Software
CAUTION!!!
2. Make sure you save your work to your thumb drive.
Experimental Procedure and Required Results: The student needs to write a LabVIEW
program that does the following:
1. Generate and plot on its own graph a 60 Hz sine signal that has an amplitude of 0.1 volts.
This will be looked at as 60 Hz noise present in the measurement. Put a control on this 60
Hz signal so the frequency can be changed. Generate this signal from 0 to 0.2 seconds.
You should use a different y-axis plotting range to see the signal better.
http://zone.ni.com/devzone/cda/tut/p/id/5054
Copyright 2013 by Sinha 10
2. Generate and plot, on its own graph, white noise with amplitude of 0.08 volts. Place a
control on your front screen that will allow you to change the amplitude of the white
noise. Plot this signal from 0 to 0.2 seconds. You should use a different y-axis plotting
range to see the signal better.
3. Generate and plot, on its own graph, a signal that has the following form:
{ ]
Plot this signal from 0 to 0.2 seconds.
4. Generate and plot on its own graph a signal that has the following form:
{ ]
Plot this signal from 0 to 0.2 seconds.
5. Add all four signals together, multiple the sum by 0.333, and plot the resulting signal on a
separate graph. Call this the combined signal.
6. Display the number for the maximum voltage, minimum voltage, DC mean voltage, and
RMS voltage for the combined signal generated in step 5.
7. Write the numbers for all five of your signals to a data file. Make the data file such that
the name of the file to which the data is saved can be entered in the front panel.
8. Make all these plots run continuously and plot on the scale from 0 to 0.2 seconds until a
stop button on your front panel is pressed.
9. Make sure you label all graphs and numerical outputs so they can be identified easily.
Report: Only your final program is required for this lab. Submit your program to the DROP
BOX on PILOT for your lab section. Name your file with your last name and Week 6 Lab. For
example:
Sinha_week_6_lab.vi
Required Results:
2. See Experimental Procedure and Required Results section.
Questions to Answer:
2. None
Copyright 2013 by Sinha 11
ME3600/5600
EXPERIMENTAL MEASUREMENTS AND INSTRUMENTATION LABORATORY
WEEK 7 LAB: Data Acquisition
WRIGHT STATE UNIVERSITY
Objective: The objective of this project is to use LabVIEW for data acquisition and explore the
effects of sample rate. Offshoots of the sampling rate the student will be expected to explore are
the Nyquist frequency, aliasing, and amplitude accuracy.
References: LabVIEW help and Sections 1 and 2 of Chapter 7 of Figliola, R. S. and Beasley, D.
E, Theory and Design for Mechanical Measurements, 5
th
Edition, Wiley, 2011. There is also a
great deal of information on the web.
Theory: There are four theories (ideas) that are pertinent for this lab:
1. Sampling Theorem
2. Nyquist Frequency
3. Aliasing
4. Amplitude accuracy (this is different than the amplitude ambiguity discussed in the book)
Equipment:
1. Computer
2. LabVIEW Software
3. Waveform Generator – see class web site for manual
4. Data Acquisition Card – see class web site for manual and performance statistics
5. Connector Box – see class web site for manual
6. Short Wires
7. Voltmeter – see class web site for manual
Caution!
1. Note that the data acquisition cards are only capable of measuring -10 to +10 volts!
2. Save your programs and results to your thumb drive!
Experimental Procedure:
1. Write a program to sample an analog signal produced by a waveform generator.
2. Set the offset on your waveform generator to zero. This can be done crudely with your
voltmeter. Fine tuning can be done with your DAQ.
3. Set the amplitude of your waveform generator to about half the full scale.
4. Use your program to sample a 120 Hz sine wave at 96 Samples/s (fs = 96 Hz). Save the
discrete numerical data to a file so that you may work with it latter if you need to. Try to
obtain at least two periods of the measured wave.
5. Use this program to sample a 120 Hz sine wave at 240 Samples/s, (fs = 240 Hz). Save the
discrete numerical data to a file so that you may work with it latter if you need to. Try to
obtain at least two periods of the wave.
Copyright 2013 by Sinha 12
6. Use this program to sample a 120 Hz sine wave at 12000 Samples/s, (fs = 12000 Hz). Save
the discrete numerical data to a file so that you may work with it latter if you need to. Try
to obtain at least two periods of the measured wave.
7. Use this program to sample a 120 Hz square wave at 12000 Samples/s (fs = 12000 Hz).
Save the discrete numerical data to a file so that you may work with it latter if you need to.
Report: A formal lab report is required which is due in two weeks at your lab session time.
Submit your report to the DROP BOX on PILOT for your lab section. Name your file with your
last name and Week 7 Lab. For example:
Sinha_week_7_lab x
Do not send me your raw data or your program. Your program should be presented in your report
and the required results should be presented there as well. Save your raw data should I request it
from you at a later date.
Required Results:
1. Plot of discrete results of a 120 Hz fundamental frequency sine wave using a sampling
frequency of 96 Samples/s.
2. Plot of discrete results of a 120 Hz fundamental frequency sine wave using a sampling
frequency of 240 Samples/s.
3. Plot of discrete results of a 120 Hz fundamental frequency sine wave using a sampling
frequency of 12000 Samples/s.
4. Plot the discrete results of a 120 Hz fundamental frequency square wave using a sampling
frequency of 12000 Samples/s.
5. Determine the amplitude of the sine wave and square wave signal.
6. Do an uncertainty analysis on the amplitude measurement of your square wave. See the
data acquisition card specification sheet to help you with this uncertainty analysis. The
connector block does not add any uncertainty to your measurement. Include the random
uncertainty of the system as a whole by doing some statistics on the measurements made
for the square wave. Because you are doing the random uncertainty this way you should
not include random uncertainty for the DAQ card in the analysis. You should only use the
data for the flat portions of the square wave. Note that there is no bias uncertainty injected
from the waveform generator; this is our measurand. We do want to include the random
variations of the measurand because we are looking for the values without noise present.
This is included in your system uncertainty just discussed. For the data acquisition card
uncertainty use 20
o
C for the use temperature and 25
o
C for all required calibration
temperatures.
Questions to think about while writing your lab report:
1. What happens to the measured signals as the sampling frequency is increased?
2. Why would the sampling theorem be important for data acquisition?
3. Of what importance is the Nyquist frequency?
4. Why do your measured waves look the way they do?
5. How accurately can you discern the rise time of your square wave?
6. What is the real rise time of your square wave?
Copyright 2013 by Sinha 13
ME3600/5600
WEEK 8 LAB : No Lab
EXPERIMENTAL MEASUREMENTS AND INSTRUMENTATION LABORATORY
WRIGHT STATE UNIVERSITY
Copyright 2013 by Sinha 14
ME3600/5600
WEEK 9 LAB : No Lab
EXPERIMENTAL MEASUREMENTS AND INSTRUMENTATION LABORATORY
WRIGHT STATE UNIVERSITY
Copyright 2013 by Sinha 15
ME3600/5600
EXPERIMENTAL MEASUREMENTS AND INSTRUMENTATION LABORATORY
WEEK 10 LAB: Fourier Transforms
WRIGHT STATE UNIVERSITY
Objective: The objective of this laboratory exercise is to use a Fourier Transform to obtain the
frequency spectrum of five different input signals
References: LabVIEW help and Chapter 2 of Figliola, R. S. and Beasley, D. E, Theory and
Design for Mechanical Measurements, 5
th
Edition, Wiley, 2011. There is also a great deal of
information on the internet that can be obtained by doing a search for Fourier transforms.
Information: This lab uses the software LabVIEW to perform the Fourier transform of five
different signals produced by the LabVIEW VI simulate signal. The primary goal of this lab is to
give the student a deeper appreciation for the frequency domain view of waveforms. This lab
also demonstrates one of the many abilities of LabVIEW to process experimental data. The
Fourier transform used by LabVIEW is a DFT (Discrete Fourier Transform). This topic has been
discussed in class and is discussed somewhat in Chapter 2 of our textbook.
Theory: There are two ways to look at a measured signal that varies with time. The first way is
to simply look at the signal as a function of time. This will be called the time domain. The
second way of looking at a signal is as a function of frequency. This will be called the frequency
domain. There are advantages to both of these domains. This lab deals with signals generated in
the time domain and then transformed to the frequency domain using a Fourier transform
technique.
When doing a Fourier transform it is important to obtain an integer number of wavelength
intervals. This is especially important if only one waveform is used to do the Fourier transform.
Remember in class that we always integrated over one period of the signal to obtain the Fourier
series or the Fourier transform. This problem diminishes if a very large number of waveforms are
obtained. In this lab you should sample an integer number of waveforms. You should try
performing the Fourier transform using a non-integer number of waves and see what happens to
your frequency domain results. This problem will be the most obvious on the sine wave you have
to simulate.
In class we have written the Fourier series as
( ) ∑ [ ( ) ( )]
(1)
where , , and are coefficients to be determined. Once these coefficients are determined
the Fourier transform of the signal can be obtained by specifying the amplitudes, at each
frequency
(2)
√
(3)
√
(4)
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√
(5)
In LabVIEW the s are provided as well as a phase angle. The way to write Equation (1) to
recapture the time dependent signal, ( ), from the frequency domain results obtained from
LabVIEW is
( )
√
∑ [ ( )]
(6)
where is a phase angle obtained from the LabVIEW Fourier transform. Note that LabVIEW
will give a phase angle for every frequency calculated, even if the amplitude at this frequency is
zero. The number of frequencies calculated will be N/2+1.This number includes the DC
frequency, which is zero.
Equipment:
1. Computer
2. LabVIEW Software
Caution!
1. Make sure you save your program often so that you do not lose any of your work.
2. Save your programs and results to your thumb drive!
Experimental Procedure:
1. The student should use the software LabVIEW to obtain and graph the required results.
2. Write a LabVIEW program that is capable of simulating a sine wave, a square wave, and
a triangle wave. All these waves should be generated on one run of your program. The
amplitude of all of these waves should be set to 20 volts. The fundamental frequency of
all of these waves should be set to 130 Hz. Make sure you use the proper sampling rate
and the right number of total samples. You need to obtain an integer number of waves
exactly. Make sure you set the default values of any controls you use to the inputs
required. If you do not do this the inputs are reset when you reopen the program.
Put your cursor over the control and right click. Then select “data Operations” and
click “Make Current Value Default”.
3. Do the same thing (Fourier Transform) as stated in step two for a pure white noise signal.
This noise should have an amplitude of 20 volts. Use a frequency resolution of 100 Hz
and an upper frequency of 2000 Hz in the frequency domain plot.
4. In addition to simulating the waves above the student should simulate the arbitrary wave
{ ] .
Simulate this signal from 0 to 0.2 seconds.
5. Add to this program the ability to perform a Fourier transform of each one of the five
simulated signals.
6. Add to this program a graph for each of the five signals simulated. You should have one
graph for each signal. These five graphs are the time domain graphs. These five graphs
will be continuous and should be line plots. Make sure you label the axes with names and
units.
7. Add to each of the Fourier transformed signals two graphs, one that plots the amplitude
of the signal versus frequency and the other that plots the phase angle of the signal versus
frequency. These ten graphs are the frequency domain plots. The frequency domain
Copyright 2013 by Sinha 17
signal is obtained by a discrete Fourier transform and will be treated as being discrete.
Plot the frequency domain signals using a bar graph. Make sure you label the axes with
names and units. Make sure you use unwrap phase when doing the Fourier analysis.
8. Run your program to obtain the five time domain plots and the ten frequency domain
plots. Study your results. While you do not have to write a lab report on these results
there is a good chance that you will be asked questions on the final exam to see if you
understand these results.
9. Save this version of your program. This is the version that you should submit to the
DROP BOX on PILOT for your lab section.
10. For your understanding, set your total number of samples on the sine wave, square wave,
sawtooth wave, and triangle wave to measure 1.5 waveforms of each signal. Compare
these results to the results where you sampled an integer number of waveforms. What do
you notice? Do not send this version of your program to me. This is for your
understanding. This will provide Dr. Sinha with good material for the course’s final
exam.
Report: Submit your LabVIEW program to the DROP BOX on PILOT for your lab section.
Name your file with your last name and Week 9 Lab. For example:
Sinha_week_9_lab.vi
Required Results:
1. Time and frequency domain plots for a 130 Hz sine wave, a 130 Hz square wave, and a
130 Hz triangular wave with amplitudes of 20 volts. The frequency domain plots should
include amplitude versus frequency and phase angle versus frequency plots.
2. Time and frequency domain plots for the white noise with an amplitude of 20 volts. The
frequency domain plots should include amplitude versus frequency and phase angle
versus frequency plots.
3. Time and frequency domain plots for the arbitrary signal defined in step 4 of the
Experimental Procedure. Again, your frequency domain plots should include amplitude
versus frequency and phase angle versus frequency plots.
4. Make sure that your program is capable of displaying all the results requested with one
run of the program. I will not change any of your inputs so they need to be locked into
your program. You are required to have a graph for each of the results requested. You
should have 15 graphs on your front panel.
5. Answer the questions below on your front panel, below your program, in text boxes.
Questions to Answer:
1. Do the time and frequency domain plots for a given type of waveform look the same?
Why or why not?
2. What are some of the differences of each of the frequency domain plots for the sine
wave, square wave, and triangle wave at an amplitude of 20 volts?
3. What do you think would happen to your frequency domain plots if you were to change
the amplitude of your signals?
4. Why do you have more phase angles than you have amplitudes in your frequency domain
plots?
5. Why is the sine wave frequency domain plot the way it is?
Copyright 2013 by Sinha 18
6. What is the frequency increment between the bars in your frequency domain plots of the
square wave and triangle wave?
7. Is there anything different between the frequency domain plots for the white noise and
the other waveforms you have sampled?
8. Do you think you would get a different result for the frequency domain plots of the white
noise if you sampled it at a higher or lower rate?
9. Is there any useful information that can be gained from the frequency plots of the five
signals in regards to making measurements of a system that produces these types of
signals?
10. What are the lowest frequencies seen in each of your frequency domain plots?
11. What happened to your frequency domain plots for the sine wave, square wave, and
triangular wave when you sampled a non-integer number of waveforms?
Copyright 2013 by Sinha 19
ME3600/5600
EXPERIMENTAL MEASUREMENTS AND INSTRUMENTATION LABORATORY
WEEK 11 LAB: Dynamic Response
WRIGHT STATE UNIVERSITY
Objective: The objective of this laboratory is to study the dynamic response of a 2
nd
order
system. Specifically we will measure the amplification ratio and phase shift characteristics of a
second order system.
References: Chapter 3 of Figliola, R. S. and Beasley, D. E, Theory and Design for Mechanical
Measurements, 5
th
Edition, Wiley, 2011 and LabVIEW help. There is also a great deal of
information on the web.
Theory: The primary theory important for this lab is that on second order measurement systems.
For this lab we are using a second order electrical system. The reason we are using an electrical
system instead of a mechanical system is the difficulty and expense in driving a mechanical
system with a sinusoidal driving function. The electrical system we are looking at can be taken
as a general second order system. It will behave just like a second order measurement system.
A few of the important equations for a second order RLC circuit are given. The second order
equation for an RLC circuit is
dt
ftEd
CI
dt
dI
RC
dt
Id
LC in
2sin
2
2
The cyclical natural frequency of this system is
LC
1
2
1
f n
,
the critical resistance is
C
L
2Rc ,
and the static sensitivity is
CK .
Note that the forcing function in this case is the derivative of the electrical potential. This is
reasonable because a DC input for an RLC circuit simply results in zero current. In these
equations L is the inductance of the inductor, C is the capacitance of the capacitor, and R is the
resistance of the resister. You should use henrys, farads, and ohms as units in these equations to
be consistent. The quantity Ein represents the amplitude of the voltage input to the circuit.
ftEin 2sin represents the magnitude of the voltage at a given time. The output from the circuit
is the voltage across the capacitor.
Copyright 2013 by Sinha 20
Note that we are not concerned with the transient response of this 2
nd
order device to the
sinusoidal driving function. We are looking for the steady state temporal response. For this
reason you should turn on the waveform generator a few seconds before you start acquiring data.
Equipment:
1. Computer
2. LabVIEW Software
3. Waveform Generator
4. Data Acquisition Card
5. Connector Box
6. Four short wires
7. Four alligator clamp wires
8. Breadboard
9. One 550 ohm resister
10. One 1.1 microfarad capacitor
11. One 15 millihenry inductor
12. Ohm/Inductance/Capacitance meter
Caution!
1. Save your programs and results to your thumb drive!
Experimental Procedure:
1. Make the circuit shown in Figure 1.
Figure 1. Electrical schematic of RLC circuit.
2. You should measure the values of your resister, inductor, and capacitor with the provided
ohm/inductance/capacitance meter. Take the reading at a frequency of 1000 Hz and in the
series mode. The resisters, inductors, and capacitors that you are using are not high
tolerance. We do not require a high tolerance on these components for this experiment.
However, you should accurately identify them by measurement with the provided
ohm/inductance/capacitance meter. You should use the measured values in your report.
3. Obtain a LabVIEW data acquisition program that can take data on two channels. You need
to measure the input voltage and the output voltage as shown in Figure 1. The only way
you can determine the amplification ratio and the phase shift is by comparing the two
Waveform
Generator
0 or 550 Ohm Resister
15 mH Inductor
1.1 F
Capacitor
Vout Vin
Copyright 2013 by Sinha 21
waves. Write both the acquired waveforms to a data file so that they can be looked at latter
if needed. Be careful that you sample the waveforms correctly.
4. The input waveform should be a sine wave.
5. Set your sampling rate and number of samples to numbers that provide good
representations of the waveform. Make sure you set the default values of any controls you
use to the inputs required as was done for Fourier Transforms Week#10 Lab.
6. Measure the input and output voltages as shown in Figure 1 for three different frequencies
for 2 different size resistors. Thus a total of 6 data sets should be taken. The three input
frequencies are 10, 1000, and 6000 Hz. The two resistances are 0 and 118 ohms.
7. Use LabVIEW to obtain plots of the input and output waveforms as a function of time.
Note that the input and the output waveform should be on the same plot. This will make it
easier for you to see the amplitude ratio and the phase shift. Thus you will have 6 different
graphs, each with two curves, in your report. It would help if the input waveform and the
output waveform were plotted with different types of lines. On the computer screen two
different colors does the best job; however, on paper in black and white make sure the
coloring shades are vastly different.
Report: Submit your Lab View program and an informal MS-Word report with results and
answers to the DROP BOX on PILOT for your lab section. Name your file with your last name
and Week 10 Lab. For example:
Sinha_week_10_lab x
Sinha_week_10_lab.vi
The informal MS Word document report will also contain the answers to the requested results
and questions below.
Required Results:
1. Turn in a MS WORD document with all the results requested below.
2. Provide graphs of all 6 of the resistor/frequency combinations. Both the input and the
output should be plotted on the same graph. These can come directly from LabVIEW.
Paste them into your MS WORD document.
3. Provide the phase shift and the amplification ratio for each of the 6 cases. Provide a table
of these results in your MS WORD document.
4. For each resistor plot the amplification ratio as a function of the frequency. There will be
three data points on each curve and there will be two curves. Do this on one graph. You
probably will want to do this in EXCEL. Copy this plot into your MS Word document.
5. For each resistor plot the phase shift as a function of the frequency. There will be three
data points on each curve and there will be two curves. Do this on one graph. You
probably will want to do this in EXCEL. Copy this plot into your MS Word document.
6. Answer the questions below in your MS WORD document.
Questions to Answer:
1. What types of second order behavior do you see: filtering, transmission, or resonance?
2. How does the system behave in response to the changing frequency?
3. What effect does the changing resistance have?
4. Do you really have zero resistance in your circuit when you take the resistor out?
Copyright 2013 by Sinha 22
ME3600/5600
WEEK 12 LAB : No Lab
EXPERIMENTAL MEASUREMENTS AND INSTRUMENTATION LABORATORY
WRIGHT STATE UNIVERSITY
Copyright 2013 by Sinha 23
ME3600/5600
EXPERIMENTAL MEASUREMENTS AND INSTRUMENTATION LABORATORY
WEEK 13 LAB: Strain Gage Measurement
WRIGHT STATE UNIVERSITY
Objective: There are three objectives to this lab: 1) to use a strain gage including the
Wheatstone bridge, 2) to calibrate a cantilever beam to measure weight using the strain gage as
the sensor, and 3) determine the ringing frequency (natural damped frequency) of your newly
made measurement device.
References: LabVIEW help and Chapters 3 and 11 of textbook. Two other references are the
National Instruments web site: http://zone.ni.com/devzone/cda/tut/p/id/4179 and the How
Sensors Work website http://www.sensorland.com/HowPage002.html . See also the links
presented on this web site.
Theory: The theory for strain gages is given in Chapter 11 of your book. The ringing frequency
(natural damped frequency) is discussed in Chapter 3 of your book. For purposes of this lab, I
would like to remind you of a few concepts and give you a few items that are special to this lab.
Strain gages measure the stretch in a material by sensing a resistance change. For the most
part we are interested in stretch caused by mechanical strain. When the stretch is caused by
mechanical strain this stretch per unit length of the member is called strain. You should be aware
that stretch can be caused by thermal expansion as well. In general, this resistance change caused
by the stretch in the strain gage is sensed as a voltage change across a Wheatstone bridge. The
bridge used in this experiment is a Half Bridge, Type II, Wheatstone bridge. This type of
Wheatstone bridge is shown in Figure 1. The half bridge refers to the fact that two active strain
gages are in the bridge circuit and not one, three, or four active strain gages. The Type II implies
the gages only sense bending strain in a manner that is additive. One gage is on the top of the
cantilever beam and one gage is on the bottom of the cantilever beam. Thus one strain gage is in
tension and one is in compression. This causes one to increase its resistance and one to decrease
its resistance. Because the strain gages are placed in adjacent legs of the Wheatstone bridge the
increase in resistance and the decrease in resistance are additive, instead of cancelling one
another out. This doubles the sensitivity of the measurement. This arrangement also helps to
eliminate temperature effects in the strain gages themselves and within the beam. Note that
temperature effects in the two resister legs of the Wheatstone bridge may still show up in your
measurements if they are not equal.
http://zone.ni.com/devzone/cda/tut/p/id/4179
http://www.sensorland.com/HowPage002.html
Copyright 2013 by Sinha 24
Figure 1. Electrical schematic of Wheatstone bridge circuit
(From How sensors work: strain gage web site:
http://www.sensorland.com/HowPage002.html).
From our book the equation relating output voltage to the resistance changes in four strain
gages placed in a Wheatstone Bridge arrangement is
3421
4
GF
E
E
i
o
,
(1)
where all strain gages are the same. For a half bridge arrangement this can be written as
42
4
GF
E
E
i
o
.
(2)
Since one of our strain gages is in compression and one is in tension (they are equal and
opposite) this can be written as
2
GF
E
E
i
o
.
(3)
Solving for strain gives
i
o
EGF
E
2
.
(4)
To be more precise, more effects can be included in this equation, such as the effect of the
lead resistances and the fact that the Wheatstone bridge may need to be zeroed before the strain
measurement is taken. In this case Equation (4) becomes
g
Lr
R
R
GF
V
1
)(
2
(5)
where
GND
Copyright 2013 by Sinha 25
Ex
CHCH
r
V
unstrainedVstrainedV
V
)()(
, (6)
Rg = the strain gage resistance,
R1= R3 = the resisters in the circuit which should be as close as possible
to Rg
RL = Rwire 1 = Rwire 2 = Rwire 3 = the lead wire resistance
GF = the gage factor
VEx = the excitation voltage
VCH = the measured voltage
In this lab the strain gages have been mounted to register a bending moment strain. Because
two are used, one measuring tension and one measuring compression, the signal is doubled. For
purposes of this lab we do not have to relate this strain to a stress. We simply have to record the
strain for different conditions. However, it would be very interesting to compare your stress
determined from your strain gage measurements to an analytical result.
With this strain gage you are required to do two things: calibrate it so that it can measure the
weight of a light object and then measure the ringing frequency of this measurement device. The
calibration of a measurement device can be performed by putting known weights on the
cantilever beam and recording the measured output. Since the device is linear, only two points
should be required. However, it is always a good idea to obtain a few other points. I am requiring
four points and one of these is the no load point. Make sure you mark and measure the position
of where you put the weights. This position needs to be put in your lab report. You should also
measure the size of your beam and state it in your report. The critical length is the distance from
the table to the end of your beam, not the total length of the beam.
The ringing frequency can be obtained by perturbing the system and watching its time
response. The formula for the ringing frequency is
2
1 nd ff . (5)
You cannot calculate the ringing frequency from this formula because you do not know the
damping ratio or the natural frequency. You need to get the ringing frequency by measuring the
response of the beam to a step perturbation.
Equipment:
1. Computer
2. LabView Software
3. Data Acquisition Card
4. Connector Box
5. Breadboard
6. Two 350 ohm resisters. Note that this inaccuracy will be handled by adjusting the zero
point of our data acquisition system.
7. Two SKF-28899 KYOWA linear strain gage with a nominal resistance of 350 ohms, a GF
= 2.1, and tolerance of ±1%
Copyright 2013 by Sinha 26
8. One aluminum bar with strain gage attached
9. One C-clamp
10. Four alligator clamp wires
11. Small connector wires
12. Voltmeter
13. A vernier caliper
14. Three weights
15. One OHAUS CS2000 Compact Scale balance scale for entire class with ±1.0 gram
accuracy
Caution!
1. Be very careful with the strain gages and the bars. The gages are somewhat delicate. Do
not hold these aluminum bars by the strain gage wires.
2. Do not put your C-clamp on the strain gage or its wires.
3. Make sure you have a good connection between the alligator clamps and the wires they
are connected to.
4. Be careful that the voltmeter is not set to resistance when measuring a powered
component. There cannot be any voltage present when measuring resistance.
5. Be careful when placing your hands at the back of the Strain Gage Panel Meter. The 110
volt connection is made back here. These cord connection sometimes comes loose.
6. Do not bend the aluminum bars too far. This can bend the bar permanently and break the
glue bond between the strain gage and the bar.
7. Save your programs and results to your thumb drive!
Procedure:
1. Make the circuit shown in Figure 1.
2. Write a LabVIEW program to measure strain.
3. Set your sampling rate and number of samples to numbers that provide good
representations of the waveform. You will need to use two different sampling rates that do
not change your results to make sure you are obeying the sampling theorem. Note that you
do not know what the ringing frequency is, and therefore you need to make sure your
results do not change as you change your sampling rate.
4. Perturb the beam downward with your finger and let it go. Make measurements during this
time to determine the ringing frequency. This will give you an idea of the time response
characteristics of your device. While we will only do a static calibration of this system, it
is nice to have an idea of its dynamic response. Do a Fourier transform on this signal.
5. Because you essentially have a linear system for measuring weight, over a limited range,
you only need two points to do your calibration. I am requiring that you have three
nonzero points and a zero point for a total of four points. The additional two points will
help you to realize errors in your measurement, or if your system is not responding
linearly. You need to give me an equation that will provide the weight of an object placed
on your beam as a function of the reading from the strain gage. Use a regression analysis
to do this. To calibrate your beam you should be using a numerical output from the
computer as opposed to the plotted output.
6. You need to do an uncertainty analysis on your new weight measurement device so that
you may specify a 95% confidence interval for your device. I do not want an uncertainty
Copyright 2013 by Sinha 27
analysis of the strain gage; I want an uncertainty analysis of your measurement device,
which is mainly from the calibration process. Give me the confidence interval for the
largest weight measurement that you used to calibrate. On the other hand, you can use
results for one of your single weight measurements to determine the precision uncertainty.
Make sure you use a significant number of points to do this. With your LabVIEW
program you should be taking several points at each calibration point and averaging. In
this uncertainty analysis you do not need to account for the bias uncertainty of the
excitation voltage or the resisters in the bridge. We will assume we can zero these out.
There are some uncertainties here but we will ignore them. The part that we are not able to
zero out will be present in your random uncertainty. Only include the uncertainties that
affect your weight measurement device. You need to do some thinking about this.
7. Measure your beam thickness, width, and length with the veneer calipers or a ruler so that
you can quantify it in the “Experimental Apparatus” part in your report. Also measure the
distance from the location of the weight on your beam to the location of the strain gage.
8. Make sure answer or discuss all questions below in the “Results and Discussion” part in
your lab report.
Report: A formal lab report is required which is due in two weeks at your lab session time.
Submit your report to the DROP BOX on PILOT for your lab section. Name your file with your
last name and Week 13 Lab. For example:
Sinha_week_13_lab x
Do not send me your raw data or your program. Your program should be presented in your report
and the required results should be presented there as well. Save your raw data should I request it
from you at a later date.
When you write this lab report does not go back and give me a great deal of theory on topics
we have dealt with in your other formal lab report. For example, you do not need to discuss the
sampling theorem, just tell me what your sample rate was and if it obeys the sampling theorem.
Focus on the topics new to this lab.
Required Results:
1. Provide plots of the data used to determine the ringing frequency.
2. Provide plots of the raw data used to do your calibration. You should have four plots here.
3. Provide a table of your calibration data.
4. Provide an equation that converts the reading that you get from the strain gage to the
appropriate weight. Make sure you give me the units you are using. You should plot this
line as well as the data points used to determine the line.
5. Give me the uncertainty present in your new weight measurement device for the largest
weight measured.
Questions to think about while writing your lab report:
1. Is your measurement device a zeroth, first, or second order system? Does it depend on
whether you are looking at the system from a static perspective or a dynamic perspective?
2. Is a strain gage a zeroth, first, or second order system? Again, does this answer depend on
the frequency at which the strain gage is used?
3. What makes the ringing frequency slightly different from the natural frequency?
4. Did you use a high enough sampling frequency to determine the ringing frequency?
Copyright 2013 by Sinha 28
5. Why do we use a Wheatstone bridge with a strain gage?
6. Over what weight range would you recommend your new scale be used?
7. What is the uncertainty in your new weight measurement system?
8. Are there any peculiarities in your new weight measurement device that you should pass
on to someone who uses it?
Copyright 2013 by Sinha 29
ME3600/5600
EXPERIMENTAL MEASUREMENTS AND INSTRUMENTATION LABORATORY
WEEK 14 LAB: No Lab
WRIGHT STATE UNIVERSITY
Copyright 2013 by Sinha 30
ME3600/5600
EXPERIMENTAL MEASUREMENTS AND INSTRUMENTATION LABORATORY
WEEK 15 LAB: No Lab
WRIGHT STATE UNIVERSITY
needed/Logan Korosei – Nov 15, 2011 1018 PM – korosei_week_9_lab x
90/100
Wright State University
Department of Mechanical Engineering
ME-314L-04
Week 9 Lab: Strain Gage Measurement
Logan Korosei
Lab Performed: 11/1/11
Report Due: 11/15/11
James A. Menart
Abstract
In this experiment, a strain gage was used to find a calibration equation. This equation is used to find the weight of an object if the strain caused by that object was known. This was done by first using a scale to find the weight of some washers followed by finding the strain caused by these washers and doing a regression analysis. By doing this, the strain gage can be used as a measurement device. The ringing frequency of the strain gage was also calculated and found to be equal to 8 Hz.
Nomenclature
fd ringing frequency
fn natural frequency of the system
ζ damping ratio of the system
Td period of the ringing behavior
εa axial strain
δL change in length
L original unloaded length
σa normal stress
Em Young’s modulus
GF gage factor
δR resistance change
R electrical resistance
δE0 change in voltage
Ei input voltage
εi strain in the i coordinate direction
Vr voltage across the resistors
Rg strain gage resistance
RL lead wire resistance
VEx excitation voltage
VCH measured voltage
ux total uncertainty
B measurement systematic uncertainty
tv student t value
P standard random uncertainty
Wm maximum weight measured
u1 uncertainty in weight scale
Syx random error between data and best fit linear equation
N number of measurements taken
Introduction
The objectives of this lab are to use a strain gage such as a Wheatstone bridge, calibrate a cantilever beam to measure weight using this strain gage as a sensor, and find the ringing frequency of the measurement device being used. This can be done by a regression analysis. The data used for the regression analysis are measurements of weights by way of a weight scale and strain measurements of the weight by way of the Wheatstone bridge. This allows for the cantilever beam to be used as a measurement device. The equation will take an inputted x value, strain, and produce an outputted y value, weight. This is important because it allows for a measurement device originally only used to find strain to also be used to find the weight of objects. An uncertainty analysis is also done to find the uncertainty of this new weight measurement device.
Theory
There are two important theories that are pertinent to this lab. They are the ringing frequency (also known as the natural damped frequency) and the idea of strain. The ringing frequency is the free oscillation frequency of a system displaced from its equilibrium1. This phenomenon occurs for underdamped systems and also is not dependent of the input signal. It is a property of the measurement system being used. The formula used to find the ringing frequency is
, (1)
where 0 ≤ ζ < 1. The ringing frequency can also be found if the period of the ringing behavior is known by
. (2)
Ringing frequency can be measured by applying a step input to the second-order measurement system and recording the response with time1. Determining the ringing frequency of a measurement system is important because this value is used in the equation solving for the motion of the system2. A Fast Fourier Transform in LabVIEW will be used to find this ringing frequency.
Strain is defined as the ratio of elongation with respect to the original length3, or
. (3)
This is a dimensionless quantity (length divided by length) that is given in either the units of strain or microstrain. For this experiment, the measurements are found in strain, which is reported in units of m/m. Strain can be used to find the normal stress of a material if the modulus of elasticity is known
(4)
The normal stress is not important in this experiment, but can be useful for comparing measured results to analytical results. The strain is being measured for different weights in order to determine a linear relationship between the two.
A strain gage measures the stretch in a material by way of a resistance change. This resistance change is sensed as a voltage change; in this case a voltage change across a Wheatstone bridge. An example of a very simple Wheatstone bridge is shown in Figure 1. The schematic for the Wheatstone bridge used for this experiment is shown in Figure 2.
Figure 1: Basic Wheatstone bridge circuit4.
Figure 2: Wheatstone bridge, half bridge, Type II5.
As noted, a half bridge, type II, Wheatstone bridge is used for this experiment. The half bridge indicates that two strain gages are active, instead of four. The type II indicates that only bending strain in a manner that is additive is being sensed. One strain gage is in tension while the other is in compression which doubles the sensitivity of what is being measured. Temperature can also affect strain gages, but this can be eliminated due to the arrangement of the gages which is further explained in the next section.
For a full Wheatstone bridge, the equation relating the output voltage to the changes in resistance of four strain gages is given as
(5)
Because a half Wheatstone bridge is being used for this experiment, equation 5 can be rewritten as
. (6)
The strain gages ε2 and ε3 are equal and placed on adjacent legs of the Wheatstone bridge. Knowing this is true and knowing one is increasing in resistance (tension) and the other is decreasing in resistance (compression), they are additive instead of cancelling one another. Equation 6 can be rewritten as
(7)
and rearranged to solve for the strain as
(8)
Other factors affecting the measurement such as lead resistances and the need to zero the Wheatstone bridge can be taken into account and equation 8 can be written as
(9)
where
(10)
The uncertainty must also be calculated for this experiment at a 95% confidence interval. The overall uncertainty can be found by
(11)
where
(12) This equation is not right. You do not multiply the given weight uncertainty by the weight. Only do this for percentage uncertainties.
You also need the DAQ card uncertainty.
and
(13)
Experimental Apparatus and Procedure
The equipment needed to carry out this experiment include a computer, LabVIEW software, a data acquisition card, a connector box, a breadboard, four resistors (two 118.2 ohm resistors and two 1.6 ohm resistor), an Omega DP25B-S strain gage panel meter, two Kyowa type KFG-10-120-C1-11LIM3R linear strain gages, an aluminum bar with the strain gages attached, a C-clamp, four alligator clamp wires, small connector wires, a voltmeter, a vernier caliper, three weights, and a Metler A550 weighing balance.
The strain gage panel meter is manufactured by Omega. The DP25B-S model used for this experiment can be bought for a cost of $245. The accuracy given for this type of meter is ±0.03%.
Figure 3: Omega DP25B-S strain gage panel meter6.
The linear strain gage is manufactured by Kyowa. They manufacture many different types of strain gages which can be used in various fields such as civil engineering, electrical equipment, chemicals and medicine7. The model used for this experiment is a type KFG-10-120-C1-11LIM3R. It has a nominal resistance of 120 ohms with a tolerance of ±1.3% and a gage factor of approximately 2.09.
The aluminum bar used is very similar to the size of an average ruler. The dimensions are 0.045 inches for the thickness, 1.008 inches for the width, and 9 inches for the length from where the strain gage is attached to the end of the bar. It should be noted that the weights were placed 8.5 inches from the strain gage, very close to the end of the bar.
The weights used were washers. Three different washers were used, all similar in weight but slightly different. A Metler A550 weighing balance was used to measure the weight of the washers. This scale has a maximum weight limit of 51 g and an uncertainty of 1.0 mg. The weights of the three washers were found to be 9.4102, 9.5023, and 9.2532 g.
A basic set up of this experiment can be found in Figure 4.
Figure 4: Experimental Set-up.
Figure 4 is not a perfect diagram of the equipment set-up, but Figure 2 good. should be examined and used to do the actual set-up of the Wheatstone bridge. Here are the steps taken to perform the experiment:
1. Use the C-clamp to fasten the aluminum bar with the strain gage attached to the end of the table as shown in Figure 5.
Figure 5: Strain gage set-up.
2. Plug in the panel meter and measure the voltage across the wires sticking out of the back using the voltmeter. This value should be around 5 volts.
3. Use the breadboard to construct the circuit for the Wheatstone bridge as seen in Figure 2. This includes the four resistors, wires from the strain gage, alligator clips, and small connector wires. This circuit should resemble Figure 6.
Figure 6: Breadboard circuit.
4. The green wires shown in figure six are connected to the connector block, one going to the connector numbered 56 and the other going to the connector right below that numbered 23. There should also be a small wire connecting connector number 23 and connector number 56. The red wires shown in Figure 6 are connected to the panel meter. This is where the input voltage for the system comes from.
5. Open a blank VI in LabVIEW and set up the block diagram as shown in Figure 7.
Figure 7: Block diagram.
6. Under the DAQ assistant window set the gage factor to 2.09, gage resistance to 120, initial voltage to 3.5m, vex source to external, vex value to your measured voltage across the panel meter (5.08 V for this experiment), and strain configuration to half bridge II.
7. Set the number of samples and rate to values that will allow for good representations of the waveform. Use two different sampling rates in order to obey the sampling theorem.
8. Perturb the beam downward so the ringing frequency can be determined. This will be found on the frequency domain plot created by the Fast Fourier Transform. The ringing frequency is the frequency where the strain is the greatest. Take screenshots of these plots.
9. Use the weighing scale to measure the weight of three different washers. Record these values for future use.
10. Choose one of the two sampling rates used before for the calibration measurements. First, determine the strain of the gages with no weight on the end of the bar. This should be a numerical indicator on the front panel found by taking the average strain over a period of time for the filtered signal. Take a screenshot of the filtered signal plot.
11. Now add the first weight to near the end of the aluminum bar and record the average strain. Once again take a screenshot of the filtered signal plot.
12. Repeat step 11 with one more weight added and then two weights added (two and three weights total, respectively). You now have four data points that can be used to find the linear relationship between the weight and the strain.
13. Through regression analysis, find an equation that will find the weight of an object placed on the bar as a function of strain gage reading.
Results and Discussion
Here are the plots of the data used to find the ringing frequency:
Figure 8: Un-filtered/filtered time domain plots, rate=200,000. You need your y-axis labeled better than zeros.
Figure 9: FFT plots, rate=200,000.
The plots for the sampling rate of 250,000 are extremely similar so they will not be included here. From Figure 9 it can be seen that the ringing frequency is equal to about 8 Hz Should give me two significant figures here. Look at the numerical data instead of the plot. for the measurement system being used. Because the ringing frequency is determined by creating a dynamic response, the measurement device is a second order system here. The ringing frequency differs from the natural frequency because it is actually the damped natural frequency. The difference is the damping ratio is used to find the ringing frequency. The sampling rate was set very high to make sure the ringing frequency was an accurate measurement.
Here are the plots for the data used to do the calibration of the measurement system:
Units.
Figure 10: No weight on beam.
Figure 11: One weight on beam.
Figure 12: Two weights on beam.
Figure 13: Three weights on beam.
Here is a table of the calibration used to do the regression analysis (from filtered plot):
Weight (g)
Strain (strain)
0
0.00054525
9.4102
0.00062894
18.9125
0.000753788
28.1657
0.000850021
Table 1: Calibration data.
It was determined to use the filtered plot data because the un-filtered plot was not giving consistent strain readings due to the noise in the system. This should not be the case. They should be similar. Filtering the data eliminates this noise. Figure 14 shows the calibration data plotted as weight vs. strain.
Figure 14: Calibration data.
A linear trend line was added into Figure 14, which was used to find the equation that converts a measured strain to the appropriate weight. This equation is
(14)
The weight range that should be used for this measurement device should be between 0 to 30 grams due to the fact that the highest weight used to calibrate the device was around 28 grams.
The data used to find the uncertainty at a 95% confidence interval is shown in Table 2.
B
yi
yci
(yi-yci)
sum(yi-yci)
P
0.02817
0
0.68995475
0.476037557
2.187854343
0.522954867
9.4102
8.22197106
1.411888014
Syx
ux
tv
18.9125
19.45816621
0.297751615
1.045909734
2.250451055
4.303
28.1657
28.11903998
0.002177158
I thing you are using the wrong data to get your random uncertainty.
Table 2: Uncertainty analysis
The uncertainty using the highest weight measurement was solved to be equal to ±2.25 grams. This is too large. How many points did you use in your random uncertainty?
Conclusions
The experiment carried out in this lab is very important due to the fact that it has real world applications. The measuring of weights is something that is done very often in engineering and creating new devices to find this weight can be very useful. The new measurement device created in this lab is not of an extremely high accuracy, but still a good device to find the weights of small objects. The uncertainty was calculated to be ±2.25 grams, which is somewhat high, but not a number that indicates that this device should not be used. It should be noted that this uncertainty is present when using this device to measure weights. The ringing frequency was found to be around 8 Hz, with the second order system of the oscillating to be under damped. In the future, a device like this Wheatstone bridge could be used to not only measure strain but also measure the weight of objects, a very useful tool if an actual weight scale is not present. You should give you calibration equation here.
References
1Figliola, Richard and Beasley, Donald., Theory and Design for Mechanical
Measurements Fourth Edition, John Wiley & Sons, Inc., United States, 2006.
2“Damping.”, Wikipedia. 25 October 2011. Web. 13 November 2011.
< http://en.wikipedia.org/wiki/Damping>
3“Global 1D Strain,” efunda. Web. 13 November 2011.
< http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/strain.cfm>.
4”Bridge Circuits,” All About Circuits. Web. 14 November 2011.
< http://www.allaboutcircuits.com/vol_1/chpt_8/10.html>
5”The Strain Gauge.”, how they work. Web. 14 November 2011.
< http://www.sensorland.com/HowPage002.html>
6Pilot course website, ME-314L content section
7”Strain Gages,” Kyowa. Web. 15 November 2011.
< http://www.kyowa-ei.co.jp/english/products/gages/index.htm>
Appendix A
Measured data available upon request from the author, korosei.2@wright.edu
Weight vs. Strain
5.4525000000000005E-4 6.2894000000000003E-4 7.5378800000000003E-4 8.5002099999999996E-4 0 9.4101999999999997 18.912500000000001 28.165700000000001 Strain, strain
Weight, g
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needed/Nathan Hornback – Nov 15, 2011 1023 PM – lab9_report x
98/100
Lab 9 Report: Strain Gauges
Wright State University
ME 314L-05
Professor: Dr. James Menart
Student: Nathan Hornback
Performed: 1 Nov 2011
Due: 15 Nov 2011
Abstract
In order to create an indirect weight measurement process through the use of strain gauges, a strain-weight instrument consisting of an aluminum beam, strain gauges, Wheatstone bridge, and necessary data acquisition devices was constructed, calibrated, and tested. Initially the cantilever beam was zeroed yielding a strain value of 0.00012 microstrain. Three weights were applied to the end of the beam of 9.396, 19.132, 28.528 grams resulting in a strain in the beam of 0.000236, 0.000329, and 0.000438 microstrain respectively. From this data a strain vs. weight relationship was created in order to give a relationship for input strain to a specific weight. Using this curve and instrument the weight of an object can be determined by strain in the beam verifying that this indirect measurement instrument is valid with an overall uncertainty of .102 grams.
Nomenclature
A- Area
B- Systematic error
E- Young’s Modulus
Eo- Excitation voltage
Ei- Bridge voltage
F- Force
GF- Gauge Factor
R- Resistance
L- Length
– Stress
– Strain
Κ- Bridge constant
Introduction
Often natural phenomena can be quantified and measured by indirect measurement processes. One can probe nature through the understanding of the relationships nature present. In the case of the strain gauge as presented in chapter eleven of Theory and Design of Mechanical Measurements by Beasley and Figliola the relationship of the change in resistance of a wire with a change in cross sectional area due to strain is used to quantify the amount of strain present in an object. Strain is not directly measure but indirectly by its relationship to resistance1. In this lab, the theory, construction, use, and application of the strain gauge will be explored as well as its relation to force inputs. Through this lab, the behavior of force input on a beam as it relates to strain will be analyzed and used to extrapolate behavior of measurements yet undone. With this end, the concept of stress and strain will be reinforced as well as signal amplification and data acquisition, analyses, and presentation processes put into practice in weight measurement. Through this lab a strain instrument will be constructed and used to measure the unknown weight of an object.
Theory
Strain and the Strain Gauge
When force is applied to a material it causes a resulting stress in the material. The magnitude of stress present is proportional to the force applied and inversely proportional to the cross sectional area.
(1)
This force and resulting stress also causes strain in the material. Strain is measure of a change in length of a material relative to its original length and is define by1:
(2)
where E is the modulus of elasticity in the material. As can be deduced from these relationships, the strain is relative to the stress of the material and varies according to the elasticity of the material. It is important to be able to quantify strain in a specific material under a specific stress in order to define the Young’s modulus and to understand the behavior of the material in reaction to an applied force.
A strain gauge generally defined is a device that measures the strain present in an object. That is, it measures the relative change in length of an object or part of an object compared to its original length. There are many forms of strain gauges all of which convert a relative unit of distance and convert it into a readable unit of strain. In the case of a resistance strain gauge, it comprised of series of resistive foils that are wound back and forth and create the platform for the strain measure. The gauge device takes advantage of the change in electrical properties a conductor such as a wire experiences resulting from a change in physical geometry caused by strain. Mechanically, when the wire undergoes strain and is stretched, the wire reduces in cross sectional area due to a constant amount of material being required to occupy a larger amount of space. This change in cross sectional results in a change of resistance in the wire,.
. (3)
Because the strain gauge is adhered directly to the object being measured, the deformation in the strain gauge is exactly equal to the deformation in the object over the area that the gauge is adhered to. Therefore the change in resistance in the strain gauge due to its deformation can be directly compared to the deformation in the object. The strain gauge translates a change in length of an object to a change of resistance across the gauge.
A. Wheatstone Bridge
Resistance change produced by strain in a strain gauge is extremely sensitive (10-6 Ω/(kN m2)) and can be very hard to measure if measureable at all with standard equipment. Because of this, it is necessary to use a measuring device such as a Wheatstone which capable of measuring very slight differences in resistance on top of a large resistance1.
Figure 1: Wheatstone bridge
This is done by taking differential resistance signal then amplifying/converting it to a deferential voltage signal. By using a Wheatstone bridge the change in resistance of the strain gauge can be measured even though it is small and the unstretched resistance is large.by a larger but proportional change in voltage. From this change in voltage, strain in the measurand can be quantified. The governing equation for this relationship (relating to the bridge configuration in fig 1) is
(4)
In practice however, a single strain gauge may not be able to properly define the behavior of an object under stress. In reality, strain is not perfectly uniform and is not in a single direction. The use of multiple strain gauges simultaneously compensates for some of these effects. Multiple strain gauge configurations are listed on page 484 of Theory and Design for Mechanical Measurements, each of which having a specific measurement capability. For a bending measurement such as the one performed in this lab, two strain gauges can be used – one on the top and bottom of the beam in bending1.
Figure 2: Strain measurement in bending
The Wheatstone bridge configuration should also be adjusted accordingly to produce correct measurement and to take advantage of the compensatory effects of this type of measurement. For this lab, a type II half bridge is used. The half bridge term signifies that half of the resistances present in the Wheatstone bridge are strain gauges. Type II means that the strain measurements are additive and a bridge constant should be used.
Figure 3: Wheatstone bridge
B. Strain Measurement and Apparent Strain
Under bending, the gauges experience equal and opposite strain – one gauge in tension and the other in compression. Using a Wheatstone bridge configuration like in figure 3, the difference of the two measurements can be taken to find the true value of the strain. However, because the measurements are equal and opposite, the value for the strain given by the Wheatstone bridge is actually twice that of the true value of strain. This factor of two is referred to as the bridge constant for this strain gauge configuration and can vary depending how strain gauges are aligned and how they are measured by the Wheatstone bridge (see Figliola and Beasley p. 484 for common configurations and corresponding bridge constants). Because of this, when using this configuration, the change in voltage from the bridge should be divided by the bridge constant to compensate for the addition of the two strain measurements5.
(5)
Outside conditions such as temperature can influence a strain measurement by adding excess strain that is not related to the measurement at handmechanical force. This unrelated strain is referred to as apparent strain. As the term implies, apparent strain appears to be a true strain measurement but it is actually a measurement of strain caused by components of strain that are outside of the experiment. A common form of apparent strain is strain produced by fluctuations in temperature resulting from the current flowing through the strain gauges.
By using a strain gauge configuration like the one in figure 3, these changes in temperature can be compensated for. The reason for this is the additive nature of the configuration. As stated, in bending the gauges experience equal and opposite strain. The difference of the two gives a value twice that of the magnitude of the true strain. By taking a difference measurement, apparent strain caused by fluctuation in temperature can be compensated for. If strain exists due to temperature change, it will cause a strain that is equal in both magnitude and direction between the gauges. The resulting difference causes the strain produced by temperature to be negated. I am not sure how this equation fits in?
(6)
Figure 4: Temperature effects on strain Nice figure.
You should put the equation used by LabVIEW to determine the strain in your report. This is in the lab handout.
Weight Measurement with a Strain Gauge
Below measurements of weight will be taken with a strain gauge and beam measuring device. The measurement device consists of a cantilevered aluminum beam with a strain gauge on the top and bottom connected to a Wheatstone bridge. The change in voltage from the Wheatstone bridge will then be converted from a voltage signal to a strain readout which will be correlated to a weight which is on the beam. It is obvious that this measuring device makes an indirect comparison giving a weight readout with an initial force and subsequent strain input.
Figure 5: Experiment layout
By applying the principles found in chapter three of the Theory and Design for Mechanical Measurements the components of this instrument can be identified. The input or measureand in this case is a force. It could be argued that the input is some strain but unless the strain is caused by a force it should be neglected in the procedures below. Either way it is to be considered, the force and strain inputs are simultaneous and related by Hooke’s law. The sensor in this case is the aluminum bar and metal foil in the strain gauge. The sensor is what experiences the resulting strain from the force input and the reaction of this sensor to the input is what will be measured and quantified.
The transducer stage in this instrument is actually through the application of voltage to the strain gauge. The transducer is the bar and strain gage. The Wheatstone Bridge is signal conditioner. I would consider the DAQ card to be a signal conditioner as well. This voltage takes the natural resistance changes in the strain gauge caused by the input and converts them into voltage changes which can be more easily measured. This analogue voltage signal is then transduced again by the DAQ card so that it can be processed in LabVIEW. LabVIEW then becomes the final transducer and signal conditioner by taking this digital voltage input and converting it to a value of strain as well as filtering the data. LabVIEW also becomes the readout by displaying the data in a neat form such as graphs and tables. I would agree that LabVIEW is a signal conditioner. At least the computer is and LabVIEW is used to contrl the computer. The readout would be the screen of the computer.
Still yet, this is a weight measurement device. One last conversion must take place in order to get a weight measurement from a strain reading. The strain response must be compared to a standard and then calibrated such that the correct, standard weight correlates with the relative strain input. This is the final step in transducing and reading the data.
In application, the strain gauge is limited in its measurements by the material of which it is measuring. Depending on the material that the strain gauge is adhered to the gauge will be limited by the maximum amount of strain that the material can withstand. For this study, the strain measurement from the bending beam is used to make a weight measurement of the item set on the end of the beam. If the weight on the end of the beam causes a permanent deformation in the beam then the strain gauge can no longer be used to measure weight. For this case the strain gauge is limited by the elastic modulus of the aluminum beam.
On the converse, the strain gauge is also limited in sensitivity depending on the rigidity of the aluminum beam. The weight of a feather for example may not be enough to cause a strain in the beam rendering this strain gauge useless for weighing applications. The weight being measured must be enough that the cantilevered beam actually responds to the weight input. This sensitivity varies with the material properties of the beam that is used.
Natural Response of the Strain-Weight Instrument
Often in instruments such as the one used in this lab there is an oscillatory behavior referred to as ringing. This ringing is a property solely of the instrument itself and is independent of the input. Ringing can be observed in the cantilever beam by “pinging” the beam. That is striking or displacing the end of the beam and then leaving it free to respond to the ping. The end of the beam will respond with oscillatory motion with a frequency exactly that of the ringing frequency. Mathematically the ringing frequency is described as
(7)
(8)
where ζ is the damping ratio of the system.
Notice that the ringing frequency is dependent on the amount of damping that is present in the instrument. A large damping ratio produces a small ringing frequency and vice versa. This is easily understood in the extreme cases. If there was no damping the instrument would ring freely at its natural frequency. On the contrary, if the damping ratio was one, there would be no ringing at all.
Experimental Apparatus
An aluminum bar with strain gauges adhered in the configuration seen in fig 6 is used as the base measurement instrument.
Figure 6: Bar dimensions Good.
The strain gauges are Kyowa type KFG-10-120-CI-11LIM3R linear strain gauges having a nominal resistance of 120 ohms, a gauge factor of 2.09 and a tolerance of ±1.3%. The strain limit at room temperature is about 5% and the fatigue life is about 1.2×10-7 cycles making this gauge more than capable for the testing in this lab.
The strain gauge is wired to a Half Bridge, Type II Wheatstone bridge according to the figure below2.
Figure 7: Wheatstone bridge configuration used
The resistances needed for R3 and R4 are 120 Ohms each. However, the combination of a 118.6 Ohm resistor (nominally 120 Ohm) and a 1.6 Ohm resistor were used in series to approximately produce the necessary 120 Ohms of resistance needed in each leg. A few extra wires and alligator clips are needed to complete the Wheatstone bridge and make it capable of connection with other measurement devices.
Excitation voltage is produced by an Omega DP25B-S Strain Meter/Controller. The DP25B can be used from standard wall power supply and can produce a 0-10 V voltage. This device is ideal for strain gauge measurement because of its steady output voltage. The maximum error in this device is ±0.03% of the reading. It should be noted that when using the DP25B caution should be taken in order to avoid electric shock. It is possible that live wires could be exposed at the rear of the device3.
The Wheatstone bridge is measured is connected to a National Instruments SCC-68 connector block. Because a differential measurement is desired, the voltage measurement should be conducted through pins 57 and 23. Using wires and alligator clips connect the two nodes corresponding to the voltage measurement in the Wheatstone Bridge (see figure 7) to the pins 57 and 23 respectively. As time passes, charge will build on the DAQ card so it may be necessary to ground the DAQ. This can be done by bridging a small wire across pins 23 and 56. However, when making a measurement, this ground can cause some unwanted noise so it may be necessary to ground the DAQ just before the measurement is taken to relieve the card of any charge and then remove the ground to ensure no extra noise is produced.
The connector block is connected as mentioned to is a National Instruments 6221 DAQ card. Uncertainty in this device is prescribed in the National Instruments user’s manual. A pertinent specification in this card is its sampling rate. The DAQ card can sample no faster than 250,000 samples per second. As noted above, the DAQ card can build charge in it that could skew results of a measurement so it may be necessary to follow the procedure above in order to rid the card of this charge. The DAQ card is housed in a Hewitt-Packard Compaq dc7900 that uses Windows XP operating system and is equipped with LabVIEW and Microsoft Excel. Other necessary equipment for this lab is include a C-clamp, Vernier calipers, three weights, multimeter, and a tape measure.
Weight measurements are taken using a Metler A550 weighing balance. The maximum weight weighed on this device is 51 grams and this device has an uncertainty of .001 grams for the purposes of this lab. When operating the scale it is important to use care as the device is very sensitive, expensive, and old.
Experimental Procedure
With the strain gauges adhered to the aluminum bar as prescribed above, clamp the aluminum bar with the C-clamp to the table such that it cantilevers over the edge with the strain gauges closest to the table. Be sure that the strain gauges do not rest on the table and that the clamp is not pressing on any part of the gauges or protruding wires.
Create a Wheatstone bridge using the wires, resistors, and breadboard. Configure the Wheatstone bridge as described above in order to make the proper measurements. Using the alligator clamps and wires, connect the strain gauges to the Wheatstone bridge as well as the Wheatstone bridge to the connector block (Pins 57 and 23). Be sure that all other connections between the equipment are properly made as is listed above and that all devices are powered up.
On the computer open the LabVIEW software and create a visual Interface that will measure, filter, and graphically display the inputs produced by the strain gauge. Include controls for the front panel to change the sampling rate, and number of samples needed. Use a LabVIEW’s Fourier transform capabilities to display the data in the frequency domain. Be sure that the data is written to a file such that analyses can be performed at a later time. Use the following figure to aid in the construction of the wire diagram.
Figure 8: Wire Diagram
Under the DAQ assistant block be sure that a strain measurement is being made from a voltage input from ai7. In the DAQ assistant pop-up window set the vex voltage to 5.12V, the gauge factor to 2.09, and the initial voltage to .002 volts. Also, be sure that the correct type of Wheatstone bridge is selected in the dropdown box corresponding to the Wheatstone bridge that is being used. For this lab a Half Bridge, Type II bridge is used.
In labVIEW set the sampling rate to the maximum 250,000 and prepare to “ping” the aluminum bar. By setting the sampling rate extremely high the chance of getting an alias frequency is greatly reduced. Although there is no way to know the ringing frequency of the bar before it is measured this sampling rate will be extremely more than twice of the ringing frequency and will satisfy the sampling theorem. Set the number of samples to 2,500,000 so that 10 seconds of data is measured. Press run and immediately ping the bar by displacing the end of the bar and then letting it go such that I it sways back and forth freely. After the 10 seconds is over the filtered time domain data should appear oscillatory in nature with amplitudes moving towards zero. Save the data to a file. Repeat this process with a sampling rate of 100,000 and a number of samples of 1,000,000 just to prove there is no aliasing. Notice in both cases the oscillation returns to zero in about 10 seconds. This is a good approximation of time to wait for the instrument to settle.
Choose three weights, in this case washers, then weigh and record the weights of each individual weight using the weigh scale. These weights are used to calibrate the strain gauge in order to use it for weight measurement. With no weight on the bar, set the sampling rate very high and then number of samples high enough to produce a second of data, run the LabVIEW program, and record the data in order to get a “zero” value for the instrument. Place the first weight on the bar, wait about 10 seconds, and run the program. Add the second weight to the first, wait the allotted amount of time and then measure the corresponding strain. Be sure that the second weight is in the exact same place as the first weight. An easy way to accomplish this is to measure all weights against the very end of the beam. Repeat this step with all three weights on the bar. This will result in 4 separate groups of data each pertaining to a certain amount of weight on the bar. Note, if there is a lot of noise present in the data try to ground the DAQ and repeat the measurement.
Use this data for analyses in order to create a calibration scale that correlates strain to weight. With this scale strain should then be able to be used to predict an unknown weight placed on the bar.
Results
When the end of the bar was displaced and then left to move freely it becomes apparent that this instrument behaves as a second order system with some damped oscillation eventually settling to its starting position. This follows exactly the behavior outlined in chapter three of Theory and Design for Mechanical Measurements (Beasley p97).
Figure 9: Filtered ringing at 250,000 samples per second Very nice data. You should also show the uflitered time domain plot.
This strain-weight instrument behaves as a second order system because it contains inertia in its oscillatory movement. Mathematically this inertia is described as a second derivative component in the governing model.
(9)
When an input force is applied to this system and then it is allowed to move freely the system tries to move with its natural frequency but the damping in the second slowly stifles the movement eventually bringing it to rest.
From this data the ringing frequency can be discovered. The ringing frequency will always be less than or equal to the natural frequency. As the name implies, the system naturally moves at the natural frequency but because of the damping in the system the frequency at which it truly moves is reduced and is less than the natural frequency. This damping is caused by a number of things such as gravity, material properties, temperature, friction, wind resistance, etc. This new frequency resulting from the damping of the natural frequency is exactly the ringing frequency. The ringing frequency is calculated by observing the period of the wave- that is the time between two peaks.
The time between the peaks gives a period of about .125 seconds. This gives a ringing frequency of about 8 Hz. The original sampling rate used proves to be much much greater than what is necessary to measure this oscillation. This calculation can be confirmed by examination of the data in the frequency domain as is seen below.
8 Hz Ringing
60 Hz Noise
Figure 10: Ringing Frequency very nice.
When the bar was measured with no weight, as was expected the result was nearly a horizontal line over one second. There were slight fluctuations in the data due to noise present in the measurement. The mean value of the data present showed that the initial strain in this system was approximately .00012 microstrain. This value represents the zero point of the measurements taken with this device. Should show this plot.
A weight of 9.396 grams was placed on the end of the bar causing a corresponding strain in the bar and strain gauge. The 9.396 grams produced a mean of .000236 microstrain . Using the unfiltered data is probably a little better for this. The average removes the noise and you do not have to deal with that nasty jump in the data at the start.
Figure 11: Weight Measurement 1
The second weight was added to the first making a combined 19.132 grams on the end of the bar. This induced a strain of .000329 microstrain.
Figure 12: Weight measurement 2
Lastly the third weight was added to the first two and again the strain was measured. The weight on the bar was 28.528 grams with a corresponding strain of .000438 microstrain.
Figure 13: Weight Measurement 3
These four values make a linear scale such that if the value of strain on the bar is known then it can be known how much weight is on the bar. In essence this scale is what makes this instrument a weight measurement device. However, it can also be used to predict the amount of strain that a specific weight will exert on the bar.
Weight
Strain
0.00012
0
0.000236
9.3956
0.000329
19.1323
0.000438
28.5279
Figure 14: Strain vs Weight calibration curve Just use data points for the experimental results.
The equation for this relationship is
good. (10)
Where X is the amount of strain and Y is the corresponding weight. In what units?
Although this equation is true for this weight measurement device, in practicality this device is limited in the weights that it can measure. On the high end, it is limited by the aluminum’s modulus of elasticity. If a weight is set on the end of bar causing a stress that exceeds the yield stress of the bar, the measurement instrument will not only be inaccurate but will also be rendered useless for further measurement. On the low end, there is a sensitivity limit to this scale. The aluminum bar may not react to extremely small weights. For example, the weight of a feather may cause no strain at all. If a weight is measured that causes a reaction smaller than the noise present in the system then it may be impossible to detect a measurement. Even though this instrument measures weight it cannot measure all weights. I would limit the upper weight to the range for which the instrument was calibrated.
Another factor to consider when operating this instrument is the behavior of the instrument under a large deformation. Because the bar is cantilevered it reacts to a force that is normal to its surface by bending. When the bar is completely straight gravity causes the force of the mass to me be normal to the surface of the beam but as the beam bends and the angle of force application changes gravity maintains its force causing two components of force: one that is normal to the face and another perpendicular. The normal force contributes to the bending but the perpendicular force contributes to axial deformation. This is true, but you calibration accounts for this.
Axial deformation in the strain gauge is counted as an apparent stress and is negated from the measurement. The Wheatstone bridge is configured such that it takes a difference measurement. This will eliminate effects from expansion due to temperature, but will also eliminate any axial loading. Axial deformation will cause a slight non-linearity in the measurements. Very slight.
Practically speaking, the largest amount of weight that can be weighed with this instrument is the maximum weight that can sit on the end of the bar without sliding off. This is limited by the friction coefficient between the aluminum and the weight. This amount of friction is also the largest amount of axial loading that can exist in the weight measurement. Again, axial loading will not be accounted for by the strain gauge as it is accounted as apparent strain so it does not help to try to improve the frictional coefficient of the surface in any way. This may in fact skew the results.
When this instrument is used in a dynamic setting it behaves as a second order system with oscillatory movement. Now, when this instrument is used in a static condition, as is seen in figure XX 14 above, the system behaves linearly. This linear behavior matches a zero order system. In fact, the governing equation of stress versus weight is just the equation of a line. This indicates that it is a zeroth order system that reacts directly to the input force by some scaling constant.
The change in behavior however is solely due to the properties of the aluminum bar. A wire foil strain gauge is always a zero order system. No, it is a second order system for dynamic measurements. It just take a higher frequency to see the bad effects. It has a static response due to an input. Its governing equation is also linear. In the first case the output from the strain gauge appeared to be of second order but it was actually being influenced by the metal bar. The zero order strain gauge can be used to measure a second order system.
The uncertainty in this device is defined by
Where B is the systematic uncertainty and is the random uncertainty in the measurements. Together these yield a total uncertainty of .102 grams. What makes up the systematic uncertainty? How to you determine the random uncertainty?
Conclusion
Strain gauges mounted to an aluminum bar created a weight measuring device that was calibrated using four specified weights. The four weights were 0, 9.396, 19.132, and 28.528 grams and corresponded to resulting strains 0.00012, 0.000236, 0.000329, and 0.000438 microstrain respectively. These data points were used to create a linear relationship between weight on the bar and strain in the bar with a total uncertainty of .102 grams. You should state your linear equation. Using this relationship an unknown weight can be quantified by observing the amount of strain that it produces in the bar. This instrument is a great example of an indirect measurement device that was calibrated by a standard weight. State the ringing frequency here as well.
References
1) Figliola, R. S., and Donald E. Beasley. “Sampling, Digital Devices, and Data Acquisition.”Theory and Design for Mechanical Measurements. Hoboken, NJ: John Wiley, 2011. Print.
2) Menart, James. “Data Acquisition.” ME 314 Lab. Wright State University, Dayton. 11 Oct. 2011. Lecture.
3) B&K Precision Corporation. Models 4001A and 4003A Function Generators. Yorba Linda: B&K Precision Corporation. Print.
4) National Instruments Coporation. NI 622x Specifications. National Instruments Coporation. Print.
5) Menart, James. Chapter 11 Strain Gauges. Dayton, 2009. Print
Appendix A: Data
Measured data available upon request from the author: hornback.4@wright.edu
Strain vs Weight
1.2012E-4 2.3603701518185816E-4 3.2913906924855599E-4 4.3783318120141671E-4 0 9.3956 19.132300000000001 28.527900000000002 Strain, microstrain
Weight, grams
[
]
4
2
4
e
e
d
+
–
=
GF
E
E
i
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needed/Zachary Hafner – Nov 14, 2011 302 PM – Hafner_Week_9_Lab x
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Wright State University
ME 314 – 05
Lab 9
Strain Gauge Investigation
Zachary Hafner
Experiment 11/1/11
Report 11/15/11
Instructor: Dr. Menart
Abstract
The experimental focus was on the configuration and testing of a Wheatstone bridge set up of two strain gauges. Using a LabVIEW program to measure the strain and perform signal analysis, a cantilever beam with two strain gauges attached can be used for different applications. Due to the use of two strain gauges, the sensitivity of the measurement increases, along with an added resistance to fluctuations of the measurement due to temperature. Following calibration, the cantilever beam can be used to measure the weight of different objects. This cantilever beam will also display a naturally damped ringing frequency when excited.
Nomenclature
= Cross Sectional Area
DAQ= Data Acquisition Card
= Modulus of Elasticity
= Input Voltage
= Output Voltage
= Ringing Frequency
= Natural Frequency
GF= Gauge Factor
L= Length
= Voltage Change
= Change in Length
= Resistance Change
R=Electrical Resistance
Axial Strain
= Strain on Gauge 1
= Strain on Gauge 2
= Piezoresistance Coefficient
= Electrical Resistivity
Introduction
The objective of this lab is to configure, test, and analyze two strain gauges configured in a Wheatstone bridge. A strain gauge is a device that will predictably change in resistance when subjected to a stress. “The majority of strain gauges are foil types, available in a wide choice
of shapes and sizes to suit a variety of applications.” (Sensorland) It is this foil within the gauges that will change in resistance. The use of strain gauges coincides with the use on a Wheatstone bridge, which provides set up configurations based on the number and use of the gauges.
The Wheatstone bridge, invented by Hunter Christie, was popularized by Charles Wheatstone. The original arrangement consisted of a battery, four resistors, and a galvanometer. (Greenslade) The Wheatstone bridge is used to gather a differential measurement, and can be adapted for numerous uses. In this lab, the strain gauges are used to measure stress on a cantilever beam. With the use of a direct current power supply and LabVIEW to measure the values, a change in resistance will occur, representing the stress.
I would indent new paragraphs. At least leave a space.
In addition to measuring a constant stress, the set up will be pinged and the oscillation of the device will be recorded in LabVIEW. From this data, the ringing frequency of the cantilever beam can be determined.
Theory
The use of resistance strain gauges was pioneered in the late 1800s through the understanding of how metals will react while a stress is applied. This innovation led to the development of the modern strain gauge in the 1930s by Edward Simmons and Arthur Ruge. (Figliola and Beasley, 2011) The modern strain gauge is the basis for numerous measurement devices, such as the load cell, torque meter and pressure transducers.
The basis for a metallic strain gauge is a relationship between the change in electrical resistance due to an applied load, where resistance
(1)
showing the relationship between a change in the cross sectional area and length of the wire. Note there are three things that change the resistance. Piezoresistance is one of the reasons for the resistance change. This relationship between resistivity and mechanical strain is also known as piezoresistance. When expressed as a piezoresistance coefficient, is defined as
The construction of a strain gauge is tailored for each application and the main consideration when deciding on the correct gauge for the application is a proper gauge length. This length will minimize the error from the measurements. Another consideration is the material used to attach the gauge to the sample. This bond is used to transmit the strain from the sample to gauge while also allowing similar thermal expansion qualities, reducing the initial error of the device.
Each strain gauge has a gauge factor, GF, where
When equation 3 is related to equation 2, it is apparent that the Poisson ratio is a determining factor for the gauge factor. “For metallic strain gauges, the Poisson ratio is approximately 0.3 and the resulting gauge factor is ~2.” (Beasley)
In order to properly measure the change in resistance from the strain gauges, a Wheatstone bridge set up is utilized. Due to the nature of the Wheatstone bridge, the set up can be zeroed for no strain by changing resistors within the circuit before any loads are applied. In addition, multiple gauges can be used in place of resistors, allowing for an accurate system that will detect and account for changes in temperature and other undesired effects.
The equation relating output voltage to resistance change for the half bridge arrangement used in this lab is
The set-up of the system uses one gauge in tension while the other is in compression, and since they are equal and opposite, equation 4 can be written as follows
When this equation is solved for strain, is
When additional effects are compensated for, equation 4 converts to
in which
In addition to gathering strain data for calibration of the cantilever beam, the ringing frequency must also be gathered from the system. If the damping ratio or natural frequency are known, then the formula is as follows
In this work the ringing frequency will have to be determined by measurement.
Experimental Apparatus and Procedure
The experiment was completed using 6 main components. These are the computer, the data acquisition card, the connector box, the breadboard/circuit, the strain gauges/cantilever beam and a 5 volt power supply. The computer used was an HP mid tower model containing an Intel Core 2 Duo processor running at 3.33 GHz along with 3.5 GB of RAM and a 230 GB hard drive. This system runs the Windows XP Professional operating system with the Service Pack 3 update installed. Installed in the computer is the data acquisition card, a National Instruments 6221 m-series card, which has 8 differential or 16 single channels. The card also features a maximum sampling rate of 250,000 samples per second, a timing resolution of 50 nanoseconds and a voltage range of ± 10 Volts. Attached to this data acquisition card is a National Instruments SCC-68 connector block which includes 84 screw terminals to attach wires and assorted devices. The power supply will allow a constant 5 volt output for power of the circuit and allow LabVIEW and the DAQ card to read and analyze the output signals.
The experimental procedure presents a step by step guide on how to set up and subsequently perform the experiment. A properly explained procedure will allow the user to follow the exact steps along with giving reference points to enable troubleshooting if necessary.
1. Create a LabVIEW program to sample, display, and analyze an analog input signal produced by the Wheatstone bridge set up (see Figure 1).
Figure 1: LabVIEW Block Diagram
2. Ensure the SCC-68 connection block is properly connected to the NI 6221 DAQ
3. Assemble the Wheatstone bridge circuit as shown in figure 2
Figure 2: Wheatstone Bridge Circuit
a. are each a 118.2 ohm resistor and a 1.6 ohm resistor in series
b. Connect the red striped leads from the strain gauges to the opposite nodes (top/bottom)
c. Connect the remaining leads together in pairs of 2 (corresponding wires together)
d. Connect a lead wire to one set of corresponding wires and another between the two resistor series
e. Attach these wires to Ai7 and Ai15 in the connector box
f. Attach a set of wires to the top and bottom nodes
g. Attach these wires to the 5 V output from the power supply
4. Power on the 5 V power supply
5. Record 3 weights of washers using a scale accurate to 1 milligram
6. Record 3 values for the strain, ensuring no vibration is occurring (zeroing value)
7. Place 1 washer 6 inches from the center of the gauges, record 3 values and graphs.
8. Place washer 2 onto washer 1, and record 3 values and graphs
9. Place washer 3 on the stack of 1 and 2, record 3 values and graphs
10. Remove all washers from cantilever beam
11. Start recording, and pluck the end of beam gently
12. Record the filtered plot and ensure values can be determined.
Results/Discussion
An analysis and comparison of the gathered data allows for a calibration of the measurement device. Due to the fact that the calibration range is from 0 grams up to 28.9 grams, the cantilever beam will provide the most accurate measurements of weight in that range. Good. Along with use in this specified range, the cantilever beam should also be the same, to ensure the same physical properties and subsequent reactions to applied loads. Good. The aluminum beam was 12 inches long, 1 inch wide, and had a thickness of 0.039 inches. The washers are also placed 6 inches from the center of the strain gauges.
Weight (g)
Mean Strain (m/m)
0
0.000168
0
0.000158
0
0.000161
9.7006
0.000251
9.7006
0.000247
9.7006
0.000226
19.5607
0.00031
19.5607
0.000319
19.5607
0.000318
28.9342
0.000394
28.9342
0.000387
28.9342
0.000383
Table 1: Calibration Data
The calibration data from table 1 is plotted using Microsoft Excel. This plot will allow a linear regression line to be inserted through the data. This line is the representation of the calibration curve, and the equation of this line can then be used to convert the strain measurement from the cantilever beam into a weight measurement of grams.
Figure 3: Calibration Chart with Linear Trend line Very nice.
As viewed in figure 3, the data represents a very linear relationship between the strain and the weight applied. The resulting calibration equation is
where x is the value for strain in m/m and y is the weight in grams.
In addition to calibrating the cantilever beam for use as a weight scale, the ringing frequency must also be determined. When the end of the beam is plucked, the beam will display a damped oscillation, with the amplitude decreasing over time. To ensure a good measurement, the data was recorded at a sampling rate of 250,000 samples per second over 10 seconds. This allows enough time to show the entire oscillation and display the damping effect. From this data, two sequential data points are gathered from the oscillation graph. The time value of these were recorded, and the period and frequency were then determined.
Figure 4: Damped Oscillation of Cantilever Beam
Using the graph in figure 4, the first point is estimated to have a time of 1.29 seconds while the second has a time of 1.41 seconds. This results in a period of 0.12 and a frequency of 8.333 Hz. A quick check using the graph confirms this number, showing just over 7 points between 1.2 and 2 seconds. Where is your frequency domain plot. You should also show your unfiltered data.
Conclusions
The analysis of the strain gauge set up and subsequent conversion into a measurement device for weighing objects reveals the vast amount of uses for not only strain gauges, but also for Wheatstone bridge set ups. While the strain gauge itself can be considered a zeroth order system due to its linearity, The strain gage is a second order system. the overall measurement device acts as a second order system. The measurement device can act as a zeroth order device, but only for a static load, reverting to a second order with a dynamic load. The use of a Wheatstone bridge enabled a higher sensitivity of the cantilever beam, with both strain gauges acting together while also cancelling out any undesirably changes due to temperature.
The ringing frequency is independent of the input force and is a property of the measurement system. State the ringing frequency here. Contrary to this, the natural frequency is the rate which the system vibrates when not disturbed by an outside force. You should also state your curve fit here.
References
Ekelof, Stig. “The Genesis of the Wheatstone Bridge.” Engineering Science and Education Journal. 10.1 (2001): 37-40. Print.
Figliola, Richard, and Donald Beasley. Theory and Design for Mechanical Measurements. 5th ed. John Wiley & Sons, Inc, 2011. Print.
“How They Work: The Strain Gauge.” Sensorland. N.p., n.d. Web. 11 Nov 2011.
“NI 622x Specifications.” National Instruments, Print.
Thomas B. Greenslade, Jr., “Nineteenth Century Textbook Illustrations (XXIII) The Rheostat”, Phys. Teach., 16, 301-302 (1978)
Appendix A:
Measured data and LabVIEW program available upon request
Hafner.2@wright.edu
Lab View Block Diagram
Sample LabView Front Panel, with 2 washers, 3rd sample Where are these plots for the ringing frequency?
