ECE5320 Mechatronics Assignment#01: Literature Survey on Sensors and Actuators Topic: Electrical Resistance Strain Gaug

1. ECE5320 MechatronicsAssignment#01: Literature Survey on Sensors and Actuators Topic: Electrical Resistance Strain Gauges Prepared by: Antoine Rousseau Dept. of Electrical and Computer Engineering Utah State University E: info@ece.usu.edu; T: (435)797-2840; F: (435)797-3054 W: http://www.engineering.usu.edu/ece March 11, 2005

2. Outline • Reference List • To Explore Further • Major Applications • Why Use Strain Gauges? • Stress and Strain Theory • Metallic Strain Gauges • Gauge Factor • Grid Patterns • Strain Gauge Measurements • Apparent Strains • Sources and Prices “www.vishay.com” ECE5320 Mechatronics. Assignment#1 Survey on sensors and actuators

3. Reference list • John G. Webster, “The Measurement, Instrumentation, and Sensors Handbook” • Richard S. Figliola, Donald E. Beasley, “Theory and Design of Mechanical Measurements” • Robert H. Bishop, “The Mechatronics Handbook” • Warren C. Young, Richard G. Budynas, “Roark’s Formulas for Stress and Strain” ECE5320 Mechatronics. Assignment#1 Survey on sensors and actuators

4. To Explore Further • Strain gauge manufacturers: • Vishay • Omega • SMD Sensors • HBM • Strain gauge tutorials: • Measuring Strain With Strain Gauges • The Strain Gauge • Strain Gauges ECE5320 Mechatronics. Assignment#1 Survey on sensors and actuators

5. Major Applications • Used to measure the deflection or strain of mechanical components for stress analysis • Static or dynamic analysis possible • Can be used as a component in other sensors • Load cells for measuring large forces • Transducers for measuring pressure, force, or torque ECE5320 Mechatronics. Assignment#1 Survey on sensors and actuators

6. Why Use Strain Gauges? • Design of critical load-bearing members • information is needed about distribution of forces, stresses, and strains within the member • Theoretical analysis is usually not sufficient • experimental measurements of physical displacements are required to validate theoretical models and to achieve final design • Strain gauges are used to measure the deformation of a member under load • stresses can then be calculated from the measured deformation ECE5320 Mechatronics. Assignment#1 Survey on sensors and actuators

7. Stress and Strain Theory • Stress is defined as a force per area: • Strain is defined as the ratio of the change in length to the original length: • The relationship between uniaxial stress and strainin the linear-elastic region of the stress-strain curve is given by Hooke’s Law: where E is the modulus of elasticity of the material. Linear-elastic region “Theory and Design for Mechanical Measurements” ECE5320 Mechatronics. Assignment#1 Survey on sensors and actuators

8. Stress and Strain Theory • In a two-dimensional stress field, a ratio exists between axial strain and lateral strain. • This ratio is called Poison’s ratio and is defined as: “The Measurement, Instrumentation, and Sensor Handbook” ECE5320 Mechatronics. Assignment#1 Survey on sensors and actuators

9. Stress and Strain Theory • For a two-dimensional member loaded in both the x and y directions, a biaxial state of stress exists. The strains and stresses are given as follows: “Theory and Design for Mechanical Measurements” ECE5320 Mechatronics. Assignment#1 Survey on sensors and actuators

10. Metallic Strain Gauges • Ideal sensor for the measurement of strains would • have good spatial resolution, stress would be measured at a point • be unaffected by changes in ambient conditions • have a high-frequency response for dynamic strain measurements • Bonded resistance strain gauge closely meets these characteristics • resistance of strain gauge changes when it is deformed • change in resistance is easily related to the local strain • History • 1856—Lord Kelvin lays the foundation for understanding the changes in the electrical resistance of metals subjected to loads • Late 1930s—Edward Simmons and Arthur Ruge develop bonded metallic wire strain gauges ECE5320 Mechatronics. Assignment#1 Survey on sensors and actuators

11. Metallic Strain Gauges • Construction and terminology of typical bonded metallic wire strain gauge: “Theory and Design for Mechanical Measurements” ECE5320 Mechatronics. Assignment#1 Survey on sensors and actuators

12. Metallic Strain Gauges • For a metallic conductor of uniform cross-sectional area A, resistivity ρe, and length L, the resistance is given by: • Change in resistance of strain gauges is caused by two effects: • change in value of resistivity, ρe, under strain • dependence of resistivity on mechanical strain is called piezoresistance • change in geometry as length and area change under strain • normal stress along the axis of the conductor will cause a reduction in cross-sectional area and an increase in length, producing a corresponding increase in resistance ECE5320 Mechatronics. Assignment#1 Survey on sensors and actuators

13. Metallic Strain Gauges • A typical strain gauge uses Constantan (45% nickel, 55% copper) which has a resistivity of 49x10-8 Wm “The Measurement, Instrumentation, and Sensor Handbook” ECE5320 Mechatronics. Assignment#1 Survey on sensors and actuators

14. Metallic Strain Gauges • Change in resistance can be expressed in terms of Poisson’s ratio where: fractional change in resistance fractional change in length fractional change in resistance Poisson’s ratio ECE5320 Mechatronics. Assignment#1 Survey on sensors and actuators

15. Gauge Factor • The change in resistance of a strain gauge is usually expressed in terms of a gauge factor, GF, that is supplied by the manufacturer • The gauge factor is expressed as: • Strain is therefore: ECE5320 Mechatronics. Assignment#1 Survey on sensors and actuators

16. Gauge Factor ECE5320 Mechatronics. Assignment#1 Survey on sensors and actuators

17. Grid Patterns • Strain gauges are available in a variety of grid patterns to meet specific measurement requirements • Uniaxial: gauge with a single grid for measuring strain in the grid direction (1) • Biaxial Rosette: gauge with two perpendicular grids used to determine principal strains when their directions are known (2) • Three-Element Rosette: gauge with three independent grids in three directions for determining the principal strains and their directions (3) • Shear Pattern: gauge having two chevron grids used in half-bridge circuits for direct indication of shear strains (4) (1) (2) (3) (4) “www.vishay.com” ECE5320 Mechatronics. Assignment#1 Survey on sensors and actuators

18. Grid Patterns • Strain gauges are often available in planar or stacked grid patterns • Planar Patterns • thin, flexible, and conform well to curved surfaces; have minimal reinforcing effect • cover a large surface area, may not fit, may sense different strain fields in steep gradient • Stacked Patterns • small, more nearly approach measurement of strain at a point, good for steep gradients • noticeably stiffer and less conformable than planar patterns, inferior heat dissipation “www.vishay.com” ECE5320 Mechatronics. Assignment#1 Survey on sensors and actuators

19. Strain Gauge Measurements • Circuit must be able to measure very small changes in resistance • A typical strain gauge measuring installation on a mild steel specimen will have a sensitivity of 10-6 Ω/(kN m2) • A Wheatstone bridge is generally used to detect the output of strain gauge measurements • Bridge can be balanced so that the output of the bridge is zero under a zero load conditions “Theory and Design for Mechanical Measurements” ECE5320 Mechatronics. Assignment#1 Survey on sensors and actuators

20. Strain Gauge Measurements • Output of a simple strain gauge Wheatstone bridge is given by: • If all resistors and the strain gauge resistances are initially equal and the bridge is balanced: where δEo is the bridge deflection and δR is the strain gauge resistance change “Theory and Design for Mechanical Measurements” ECE5320 Mechatronics. Assignment#1 Survey on sensors and actuators

21. Strain Gauge Measurements • Measurement devices are commercially available • Designed for use in a wide variety of physical test and measurement applications • Features of Vishay Model P3 (shown) • Direct reading LCD display • Intuitive, menu-driven operations • Portable, lightweight and rugged • Four input channels • Built-in bridge completion • On-board data storage • Automatic zero-balancing and calibration • Battery, USB or line-voltage power “www.vishay.com” ECE5320 Mechatronics. Assignment#1 Survey on sensors and actuators

22. Apparent Strains • Apparent strain is defined any change in strain gauge resistance that is not due to the components of strain being measured • Examples: • Temperature change of a specimen will cause a change in the resistance of a strain gauge • Bending strain will affect axial strain measurements in a beam • Axial strain will affect torsional strain measurements in a shaft “Roark’s Formulas for Stress and Strain” ECE5320 Mechatronics. Assignment#1 Survey on sensors and actuators

23. Apparent Strains • Gauges can be arranged to compensate various apparent strains “Theory and Design for Mechanical Measurements” ECE5320 Mechatronics. Assignment#1 Survey on sensors and actuators

24. Apparent Strains • Bridge can be arranged to compensate for temperature effects “Theory and Design for Mechanical Measurements” ECE5320 Mechatronics. Assignment#1 Survey on sensors and actuators

25. Sources and Prices “The Measurement, Instrumentation, and Sensors Handbook ” ECE5320 Mechatronics. Assignment#1 Survey on sensors and actuators