Measurement Systems And Calibration .Engineering Math Problem

Measurement Systems And Calibration .Engineering Math Problem Measurement Systems And Calibration .Engineering â€" Math Problem Example > Experiment 1: Strain gauge measurements1. Summary: This report aims at describing the strain gauge measurement using Quarter, half and Full Wheatstone bridge configurations. Their respective response for same load conditions and respective sensitivity of the circuits compared. 2. Table of contents: Sl noContentsPage no1Introduction 12Theory13Experimental Apparatus and Procedure34Results and Discussion65Conclusions93. Introduction: The objective of this experiment is to measure strain and output voltage of quarter, half and full bridge circuit configurations for varying loads and prove that the measured output voltage is more linear and approximately double for the same applied load in half bridge compared to quarter bridge and full bridge compared to half bridge configurations. Sensitivities of the respective circuits to external load are also compared. 4. Theory: An external force applied on a body causes deformation, specifically along its length resulting in change in length. Th e ratio of change in length (?L) to the actual length (L) of the body is called Strain (?) [1]. This change in length can be positive (tensile) or negative (compressive). Strain is dimensionless, often expressed as micro strain (??). ?????L/LStrain gauge is a device used to measure strain. This gauge works on the principle that due to applied load, the amount of strain developed in the body is proportional to change in its resistance[1]. Strain gauge materials are thermally sensitive. To compensate thermal sensitivity strain gauges are used in a bridge configuration. Characteristics or behavior of a circuit depends of its components. Characteristics of a components change with time and no two identical components exhibit exactly the same characteristics. The actual value of component may be slightly different from its specified value due to tolerances in manufacturing. All these factors affect the behavior of a circuit. Sensitivity is the measure of change in the characteristic of a circuit for a given change in the value of a particular component [9]. A Wheatstone bridge consists of four resistive arms with an excitation voltage applied across the bridge. Output voltage is zero in the balanced condition where (R2/R1) = (R3/R4) [1]. Bridge enters an unbalanced condition when a resistance change happens in any arm of the bridge resulting in a non zero output voltage. If resistance in one arm is replaced with a strain gauge in compression (Rg - ?R) to the applied load, output voltage will be non zero due to the change in the ratio of resistances (R3/(Rg - ?R)) when external strain is applied. The following figure shows the schematic of a Quarter bridge circuit [2]. Half bridge circuit contains two strain gauges in one leg one gauge mounted in tension and another in compression. Full bridge circuit contains all strain gauges instead of resistances two gauges in tension and two in compressionFigure (1). Wheatstone bridge configurationIn a Half bridge, resistanc es in two arms can be replaced with strain gauges, one gauge mounted in tension (Rg + ?R) and the other one in compression (Rg - ?R) where ?R is the change in resistance. Hence for the same applied load the ratio (Rg + ?R)/ (Rg - ?R) in Half bridge configuration is more compared to the ratio (R3/(Rg - ?R)) in Quarter bridge configuration. Unbalance is more in half bridge configuration compared to Quarter bridge configuration. Hence, half bridge configuration yields an output voltage that is linear and approximately double the output of the Quarter bridge configuration. Similarly Full bridge configuration output voltage will be more linear and approximately double the output of the Half bridge configuration.