# 9. Force Measurement with a Strain gage Bridge

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1 9. Force Measurement with a Strain gage Bridge Task 1. Measure the transfer characteristics of strain-gage based force sensor in a range 0 10 kg Determine the mass of an unknown weight. 3. Check whether it is possible to obtain more precise measurement by polarity commutation of the bridge excitation voltage. 4. (optional) Measure the mass of other objects (back-pack, notebook...) 5. Connect the sensor to the Omega measurement module and determine in which unit it presents the output (with the use of known weight). 6. (optional) Measure the force you are able to develop with your arms (use handrails, max. force 1000N). 7. Measure the resistance of the bridge with an ohmmeter and check whether the resistance changes while the applied load is changed. Explain the results. 8. Determine the base value of resistance of each strain-gage element in the bridge. Determine the change of resistance for applied load of 100kg. Calculate the prolongation of the strain gage element if you know the coefficient of deformation sensitivity k = 2 (gage factor) and the length of the strain-gauge is 5 mm. Questions 1. What is the principle of a resistance based strain-gage? What is the definition of the deformation sensitivity coefficient k? 2. What are the advantages of using full-bridge circuit (with 4 active elements)? 3. Make a simple chart showing a flexible support in a bended position with a four active elements bridge; indicate which of the strain-gages are stressed in strain and which in compression ; relate them to an electrical circuit. 4. What is the resolution in weight you are able to achieve with this sensor? What is the corresponding change of resistance of a single element strain-gage? In case you would measure the resistance change without the use of a bridge circuit, how many digits would have to have the used ohmmeter? How many effective bits it corresponds to? Theoretical and practical background Force sensors with flexible elements of different shapes are often used as weight scales. The advantages are relatively high accuracy and flexibility of measurement ranges the range can be adjusted by changing the shape or size of the flexible element. The mechanical stress in the flexible element is sensed by resistive strain-gages. The strain-gages are typically glued on spots where the stress is maximal (highest sensitivity). Let s consider a conductor with length l and cross-section S which is stressed in strain by force F, the force causes the prolongation of the length and cross section reduction and also micro-structural changes in the material which alters the material s resistivity ρ. The total resistance of a conductor with cross section S and length l is given by following equation: 1 The unit of force is Newton. The manufacturer uses a unit KgF, 1 KgF = 9.8 N, 9.8 m.s -2 is a normal gravity.

2 l R = ρ S The total change of resistance can be expressed with the use of total differential: R l S ρ = + R l S ρ Coefficient of deformation sensitivity (gage factor): l R k = l 0 R 0 A typical strain-gage is shown on Fig.1. The dimension of the strain-gage is maximized in the direction of applied stress, in order to get the highest sensitivity and to suppress the sensitivity in the perpendicular direction. Fig. 1 Resistance based strain-gage The set of four resistance based strain-gages forms full Wheatstone bridge (Fig.2). The set is glued on to a flexible element. One of the most often used elements is an S shaped support (Fig. 3). If there is a tension applied to the support, the strain-gages 1 and 4 are strained (R is increased), while the 2 and 3 strain-gages are compressed (R is decreased). The output voltage is given by following equation, where U EXC is the bridge excitation voltage and R/R 0 is the relative change of resistance of each strain-gage. U out U = EXC R 0 R

3 Fig. 2 Full Wheatstone bridge F R 1 R 2 R 3 R 4 F Fig. 3 Strain-gage based force sensor Instructions 1) Measure the output voltage U OUT (bridge diagonal voltage) by DMM. Power up the sensor with a 10VDC stabilized power supply U EXC. Use the available weights to load the sensor. Important! The pinout of the sensor is: U EXC + red U EXC - black U OUT + green U OUT - white

4 Fig. 4 Circuit for tasks 1-3 4) The Omega module uses 10VDC excitation voltage and measures the diagonal voltage. The voltage is scaled with pre-programmed calibration constant and shown on display. Fig. 5 Circuit for tasks 4 and 5 Attachment: calibration datasheet of the used load cell sensor

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