DOCSLIB.ORG

An Introduction to Stress Analysis and Transducer Design Using Strain Gauges

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
An Introduction to Stress Analysis and Transducer Design Using Strain Gauges Karl Hoffmann An Introduction to Stress Analysis and Transducer Design using Strain Gauges The definitive work on strain gauge measurement www.hbm.com Contents IX Contents Page 1. Introduction ...................................................................................................... 1 1.0.1 Metal strain gages............................................................................................... 2 1.0.2 Semiconductor strain gages ................................................................................ 7 1.0.3 Vapor-deposited (thin-film) strain gages............................................................ 8 1.0.4 Capacitive strain gages ....................................................................................... 9 1.0.5 Piezoelectric strain gages.................................................................................. 10 1.0.6 Photoelastic strain gages................................................................................... 11 1.0.7 Mechanical strain gages.................................................................................... 11 1.0.8 Other systems ................................................................................................... 11 1.1 The operating principle of the strain gage ........................................................ 12 1.1.1 Metal strain gages............................................................................................. 12 1.1.2 Semiconductor strain gages .............................................................................. 14 1.2 The measurement system.................................................................................. 15 2 Terms and units of measurement used in strain gage technology ............. 17 2.1 Strain: Definition and unit of measurement ..................................................... 17 2.1.1 Absolute change of length ................................................................................ 17 2.1.2 Relative change of length or strain ................................................................... 18 2.1.3 Unit of measurement for strain [2-1]................................................................ 19 2.2 Mechanical stress: Definition and unit of measurement................................... 21 2.2.1 Normal stress.................................................................................................... 21 2.2.2 Shear stress....................................................................................................... 22 2.2.3 Residual stress, thermal stress .......................................................................... 24 2.2.4 Stress states....................................................................................................... 25 2.3 Material parameters .......................................................................................... 26 2.3.1 Modulus of elasticity, definition and units ....................................................... 26 2.3.2 Shear modulus .................................................................................................. 28 2.3.3 Poisson's ratio................................................................................................... 29 2.3.4 Thermal expansion........................................................................................... 31 2.4 Strain gage loading ........................................................................................... 32 2.4.1 Static measurements (zero referenced)............................................................. 32 2.4.2 Quasi-static measurements ............................................................................... 33 2.4.3 Dynamic measurements (non-zero referenced)................................................ 33 3 Selection criteria for strain gages.................................................................. 34 3.1 Range of application......................................................................................... 36 3.1.1 Stress analysis, model measurement techniques, biomechanics ...................... 36 3.1.2 Transducer construction................................................................................... 36 3.2 Types of strain gages ........................................................................................ 37 3.2.1 Length of measuring grid ................................................................................. 37 3.2.1.1 Homogeneous field of strain............................................................................. 38 3.2.1.2 Inhomogeneous strain field .............................................................................. 40 3.2.1.3 Dynamic strain conditions ................................................................................ 42 3.2.2 Multiple strain gages, their advantages and fields of application..................... 42 3.2.2.1 Strain gage chains for the determination of stress gradients ............................ 42 3.2.2.2 Strain gage rosettes for the determination of stress conditions ........................ 44 3.2.2.3 Strain gage rosettes for the investigation of residual stress.............................. 46 3.2.3 Special strain gages.......................................................................................... 48 HBM Test and Measurement www.hbm.com X Contents 3.2.3.1 Weldable strain gages....................................................................................... 49 3.2.3.2 Free-grid strain gages, high-temperature strain gages...................................... 49 3.2.3.3 Weldable high-temperature strain gages .......................................................... 50 3.2.4 Electrical resistance.......................................................................................... 50 3.2.5 Useful temperature range ................................................................................. 51 3.3 Technical data................................................................................................... 52 3.3.1 Strain gage sensitivity (gage factor) for metal strain gages ............................. 53 3.3.2 Gage factor for semiconductor strain gages..................................................... 54 3.3.3 Transverse sensitivity....................................................................................... 56 3.3.4 Temperature response of a mounted strain gage.............................................. 59 3.3.4.1 Temperature compensated strain gages............................................................ 61 3.3.4.2 Thermal drift..................................................................................................... 67 3.3.5 The dependence of sensitivity on temperature................................................. 67 3.3.6 Static elongation............................................................................................... 69 3.3.7 Dynamic strain measurement ........................................................................... 70 3.3.7.1 Continuous vibration characteristics................................................................ 71 3.3.7.2 The cut-off frequency....................................................................................... 74 3.3.8 Electrical loading.............................................................................................. 79 3.3.9 Creep ................................................................................................................ 80 3.3.10 Mechanical hysteresis.......................................................................................87 3.4 Environmental influences................................................................................. 90 3.4.1 Temperature...................................................................................................... 90 3.4.2 Humidity........................................................................................................... 90 3.4.3 Hydrostatic pressure......................................................................................... 91 3.4.4 Vacuum ............................................................................................................ 96 3.4.5 Ionizing radiation............................................................................................. 99 3.4.5.1 The effects of ionizing radiation on strain gage measuring points................. 100 3.4.6 Magnetic flelds............................................................................................... 104 3.4.7 Storage............................................................................................................ 107 4 Materials used for mounting strain gages.................................................. 108 4.1 Strain gage bonding materials ........................................................................ 108 4.2 Mounting materials......................................................................................... 112 4.2.1 Cleaning agents.............................................................................................. 112 4.2.2 Soldering agents............................................................................................. 113 4.2.2.1 Soldering devices........................................................................................... 113 4.2.2.2 Solders and fluxing agents ............................................................................. 114 4.2.3 Connection methods......................................................................................
Load more

Recommended publications
  • Electromechanical Piezoresistive Sensing in Suspended Graphene
    This document is the unedited Author’s version of a Submitted Work that was subsequently accepted for publication in Nano Letters, copyright © American Chemical Society after peer review. To access the final edited and published work see http://pubs.acs.org/articlesonrequest/AOR-kGn5XaTPGiC7mYUQfih3. Electromechanical Piezoresistive Sensing in Suspended Graphene Membranes A.D. Smith1, F. Niklaus1, A. Paussa2, S. Vaziri1, A.C. Fischer1, M. Sterner1, F. Forsberg1, A. Delin1, D. Esseni2, P. Palestri2, M. Östling1, M.C. Lemme1,3,* 1 KTH Royal Institute of Technology, Isafjordsgatan 22, 16440 Kista, Sweden, 2 DIEGM, University of Udine, Via delle Scienze 206, 33100 Udine, Italy 3University of Siegen, Hölderlinstr. 3, 57076 Siegen, Germany * Corresponding author: [email protected] Abstract Monolayer graphene exhibits exceptional electronic and mechanical properties, making it a very promising material for nanoelectromechanical (NEMS) devices. Here, we conclusively demonstrate the piezoresistive effect in graphene in a nano- electromechanical membrane configuration that provides direct electrical readout of pressure to strain transduction. This makes it highly relevant for an important class of nano-electromechanical system (NEMS) transducers. This demonstration is consistent with our simulations and previously reported gauge factors and simulation values. The membrane in our experiment acts as a strain gauge independent of crystallographic orientation and allows for aggressive size scalability. When compared with conventional pressure sensors, the sensors have orders of magnitude higher sensitivity per unit area. Keywords: graphene, pressure sensor, piezoresistive effect, nanoelectromechanical systems (NEMS), MEMS 2 Graphene is an interesting material for nanoelectromechanical systems (NEMS) due to its extraordinary thinness (one atom thick), high carrier mobility 1,2, a high Young’s modulus of about 1 TPa for both pristine (exfoliated) and chemical vapor deposited (CVD) graphene.3,4 Graphene is further stretchable up to approximately 5 6 20%.
    [Show full text]
  • A Field Guide to Understanding Pressure Transducers
    A Field Guide to Understanding Pressure Transducers Section I Basic Theory of Pressure Transducers A pressure transducer is a device which converts an applied pressure into a measurable electrical signal which is linear and proportional to the applied pressure. A pressure transducer consists of two main parts: an elastic material which will deform when exposed to a pressurized medium and an electrical device which detects the deformation and converts it into a usable electrical signal. The elastic material can be formed into many different shapes and sizes depending on the sensing principle and range of pressures to be measured. This often involves a diaphragm combined with an electrical device that uses a resistive, capacitive, or inductive principle of operation. Resistive Pressure Transducer (Strain Gauge) A resistive pressure transducer has strain gauges bonded to the surface of the non-media contacted side of the diaphragm so that any change in pressure will cause a momentary deformation of the elastic material resulting in a change of the resistance of the strain gauge that is converted into a useable electrical signal. Capacitance Pressure Transducer A variable capacitance pressure transducer has a capacitive plate (diaphragm) and another capacitive plate (Electrode) fixed to an unpressurized surface gapped a certain distance from the diaphragm (Cs - starting capacitance). A change in pressure will widen or narrow the gap WWW.TEESING.COM | +31 70 413 07 50 between the two plates which varies the capacitance (ΔC). This change in capacitance is then converted into a usable signal for the user. ΔC Inductive Pressure Transducer An inductive pressure transducer uses the principle of inductance to convert the flexing of a diaphragm into the linear movement of a ferromagnetic core.
    [Show full text]
  • Bmt 18Bm45 Module 3
    BMT 18BM45 MODULE 3 MODULE 3: PRESSURE MEASUREMENT 3.1 Pressure Transducers 3.1.1 LVDT pressure transducers 3.1.2 Strain gauge pressure transducers 3.2 Physiological pressure ranges and measurement sites 3.3 Direct pressure measurement-catheters for pressure measurement 3.4 Diaphragm Displacement Transducers 3.5 Catheter Tip Pressure Transducers 3.6 Implantable Pressure Transducers and Pressure Telemetering Capsules. 3.7 Indirect Pressure Measurement-Indirect Measurement of Systolic, Diastolic, And Mean Blood Pressure 3.8 Detection of Korotkoff sounds. Mr. Hemanth Kumar G, Assistant Professor, Department of BME, ACSCE BMT 18BM45 MODULE 3 3.1 Pressure Transducers 3.1.1 LVDT pressure transducers An extremely useful phenomenon frequently utilized in designing displacement pick up units is based upon variations in coupling between transformer windings, when the magnetic core of the transformer is displaced with respect to the position of these two windings. Generally, a differential transformer (Fig. 3.1) designed on this principle is employed for the measurement of physiological pressures. The central coil is the energizing or primary coil connected to a sinewave oscillator. The two other coils (secondary coils) are so connected that their outputs are equal in magnitude but opposite in phase. With the ferromagnetic core symmetrically placed between the coils, and the two secondary coils connected in series, the induced output voltage across them would be zero. When the core is moved, the voltage induced in one of the secondary windings exceeds that induced in the other. A net voltage output then results from the two secondaries. Figure 3.1: Principle of LVDT pressure transducer.
    [Show full text]
  • Guide and Usage of Resistive Bridges for Pressure Measurement with The
    AN296202 APPLICATION INFORMATION MCO-0001002 AP-1067 GUIDE AND USAGE OF RESISTIVE BRIDGES FOR PRESSURE MEASUREMENT WITH A17700 By Nevenka Kozomora Allegro MicroSystems ABSTRACT The A17700 is the first Allegro interface IC designed for Wheatstone bridge configurations located on elastic carriers for pressure measurements. The A17700 interface chip condi- tions the signals from the Wheatstone bridge into an accurate output message dependent only on the measured pressure. This application note explains the science behind the strain gauge used for pressure sensing, most common strain gauges on the market, sensing solutions presented by differ- ent strain gauge configurations, and A17700 input specifica- tions. Figure 2: Vertical semiconductor strain gauge between metal pads. In the appendix, there is a market example of strain gauge bridge specifications interpreted into A17700 input specifi- The resistance of the strain gauge can be described in the cations. following equation (Roylance): STRAIN GAUGE = × Strain gauges consist either of conductor tracks folded back and forth on themselves or a single semiconductor track where R is the resistance of the strain gauge, L is the length, bonded to the sample surface. Typical conductive materi- A is the cross sectional area, and is the material resistivity. als include wires as Constantan (copper-nickel alloy) and If the circular wire is assumed such that A = 2, then after Nichrome V (nickel-chrome alloy), metallic foils, and metallic ρ applying a logarithm to both sides and simplifying: thin films. The semiconductor gauge is cut from a single crys- πr tal of silicon or germanium doped with impurities to obtain N ln = ln + ln (ln + 2 ln ) or P type.
    [Show full text]