Mechanical Investigation and Optimization of Foil Strain Gauge byFEM by jennyyingdi

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									 Mechanical Investigation and Optimization of Foil Strain Gauge
                            byFEM



                               dem Fachbereich Maschinenbau

                           an der Technischen Universität Darmstadt

                                             zur

                    Erlangung des Grades eines Doktor-Ingenieurs (Dr.-Ing.)

                                         genehmigte



                                      Dissertation



                                        vorgelegt von

                                       M.Sc. Yu Tao

                                          aus Beijing




Berichterstatter:                                                Prof. Dr.-Ing. C. Tropea

Mitberichterstatter:                                             Prof. Dr.-Ing. Hanselka

Tag der Einreichung:                                             O6.Dec 2005

Tag der mündlichen Prüfung:                                      25. April 2006



                                       Darmstadt 2006

                                             D17
Contents




Contents

Contents                                                                        I
Symbols                                                                       III
1 Introduction                                                                  1
2 Strain Gauge Basics and Research Motivation                                   3
  2.1     Principles and Known Problems                                         4
     2.1.1 Working Principle of Strain Gauge                                    4
     2.1.2 Working Principle ofaTransducer                                      9
     2.1.3 Faced Problems and State of Research                               10
  2.2     Research Tool and Goal                                              18
3 Characteristics of Strain Gauges                                            23
  3.1     Important Data of Strain Gauges                                     23
     3.1.1 Strain Gauge Factor                                                24
     3.1.2 Transverse Sensitivity                                             29
  3.2     Strain Gauge Resistance Change under Strain Loading                 34
     3.2.1 Geometrie Effect of Strain Gauge Resistance Change                 34
     3.2.2 Piezo Resistive Effect                                             35
4 Investigation of Strain Gauges by FEM                                       41
  4.1     Finite Element Method                                               41
        .1 FEM for Stress/Strain Analysis                                     41
        .2 Conditions for Stress/Strain Analysis                              42
        .3 FEM for Electrical Analysis                                        43
        .4 FEA Precision                                                      45
       1.5 Limitations of FEA                                                 45
  4.2 , FEA for Strain Gauge                                                  46
     4.2.1 Strain/Stress Analysis                                             46
     4.2.2 Electrical Analysis                                                50
     4.2.3 Resistance Calculation                                             51
  4.3     Strain Gauge Simulation                                             51
     4.3.1 Strain Gauge Factor                                                52
     4.3.2 Transverse Sensitivity                                             54
     4.3.3 Strain Gauge Stress/Strain Analysis under Temperature Change       55
     4.3.4 Accuracy of Analysis Result                                        56
     Mechanical Investigation of Strain Gauge                                 57
  5.1     Stress and Strain Analysis                                          57
     5.1.1 Analysis Results of Strain Gauge under Axial Strain Loading        57
     5.1.2 Analysis Results of Strain Gauge under Transverse Strain Loading   63
     5.1.3 Analysis Results of Layers under Axial Strain Loading              67
     5.1.4 Results of Electrical Analysis                                     70
     Parametric Analysis                                                      73
  6.1     Parametric Analysis of Layers: Young's Modulus                      75
     6.1.1 Influence to Gauge Factor                                          77
     6.1.2 Influence of Young's Modulus Change to the Stress Level             77
  6.2     Parametric Analysis of Layers: Thickness                            77
     6.2.1 Influence of Layer Thickness to Strain Gauge Factor                77
     6.2.2 Influence of Thickness on the Stress Level of Every Layer          77
  6.3     Parametric Analysis: Young's Modulus of Strain Gauge Grid            78
  6.4     Parametric Analysis: Thickness of Strain Gauge Grid                 79
                                                                             Contents


6.5     Parametric Analysis: Dimensions of Strain Gauge Layout                           81
   6.5.1 Grid Length                                                                     82
   6.5.2 End Loop Length                                                                 82
   6.5.3 Gridline Width                                                                  85
   6.5.4 Gridline Distance                                                               85
   Optimization of Strain Gauges                                                         89
7.1     Optimization Regarding Gauge Factor and Transverse Sensitivity                   90
   7.1.1 Definition of End Loop Influence Area under the Axial Strain                    91
   7.1.2 Gauge Factor Analysis                                                           94
   7.1.3 Definition of End Loop Influence Area under the Transverse Strain               98
   7.1.4 Transverse Sensitivity Analysis                                                 99
7.2     Optimization regarding the Stress Gradient                                      105
   7.2.1 Optimization regarding the Stress Concentration                                105
   7.2.2 Optimization regarding the Stress Gradient and Electrical Current              107
7.3     Conclusion of the Optimized Strain Gauge Layout                                 111
   Summary                                                                              113
8.1     Research summary                                                                113
8.2     Outlook                                                                         114
   References                                                                           115

								
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