Exercise 2: Bending Beam Load Cell
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1 Transducer Fundamentals The Strain Gauge Exercise 2: Bending Beam Load Cell EXERCISE OBJECTIVE When you have completed this exercise, you will be able to explain and demonstrate the operation of a board, by measuring voltages, and by making calculations. DISCUSSION electronic scales and other force measurement devices. To understand the use of the load cell in force measurement, it is necessary to understand certain properties of the beam and the strain gauge. Strain ( length: = If the length were measured in inches (in), what unit is measured in? a. in b. in 2 c. d. None of these parameter. Since strain is a ratio of change in length to the original length, it is sometimes expressed as a percent change. Because the change in length is usually very small relative to the original length (typically less than or x 10 3 ) or microstrain ( or x 10 6 ). For example, if you apply enough tension to a 1-inch long solid to increase its length by in, the strain is: = FACET by Lab-Volt 243
2 The Strain Gauge Transducer Fundamentals You can convert this value to microstrain by multiplying by 10 6 : x 10 6 = 5000 e (or 5000 microstrain) What is the strain on the solid for the parameters shown? L = 1.75 in L = in = = x 10 6 = (Recall Value 1) Elasticity is a property by which a solid deformed by stress returns to its original shape when the stress is removed (think of stretching and then releasing a rubber band). Although all solids have some degree of elasticity, none of them are perfectly elastic. There is a stress point called the elastic limit, beyond which the solid will either break or become permanently deformed. E = Where (the lower-case Greek letter sigma) = stress, modulus of elasticity. The modulus of elasticity is a force per unit area and depends on the material of which the solid is composed. The beam used on your circuit board is bronze, whose modulus of elasticity is E = 15 x 10 6 pounds per square inch (psi). factor is the ratio of the fractional resistance change to the fractional change in length: GF = N What strain gauge parameter equals a. b. c. E The gauge factor can therefore be expressed as GF = ( N 244 FACET by Lab-Volt
3 Transducer Fundamentals The Strain Gauge A force (F) is applied to the end of the beam. Y). The strain caused by this stress is detected by the strain gauge, whose resistance changes in proportion the a. applied force. b. c. strain gauge resistance change. d. All of the above FACET by Lab-Volt 245
4 The Strain Gauge Transducer Fundamentals pounds, grams, psi, etc. On your circuit board, you can simulate the application of force to the end of the beam by rotating the by rotating the knob any number of turns (n) can therefore be calculated as follows. 1 inch = = 28 turns Y = inch (Recall Value 2) F = Y x 1.92 = F x 4934 V AMP OUT = x where F is the force (in pounds) applied to the free end of the beam; is the strain (in microstrain) at the strain gauge; and V AMP OUT is the circuit output voltage (in volts). 246 FACET by Lab-Volt
5 Transducer Fundamentals The Strain Gauge The parameters were derived from the physical dimensions and modulus of elasticity of the beam, as well rotations. inserting this value into the force equation, you can determine the force applied. F = Y x 1.92 F = x 1.92 F = pound In turn, you can insert the force value into the strain equation to determine the strain caused by 1.5 knob revolutions. = F x 4934 = x 4934 = Insert this value into the output voltage equation to determine the voltage resulting from 1.5 knob rotations. V AMP OUT = x V AMP OUT = x V AMP OUT = V (Recall Value 3) PROCEDURE In this PROCEDURE, you will demonstrate the operation of the bending beam load cell in a practical force measurement application. Rotate the knob to place the beam in its unstressed position. FACET by Lab-Volt 247
6 The Strain Gauge Transducer Fundamentals Set your multimeter to read Vdc and connect the leads to AMP OUT (+) and GND (-). Insert a two-post connector to complete the bridge circuit. Adjust the multi-turn ZERO pot for a reading of 0 ±50 mv at AMP OUT. 248 FACET by Lab-Volt
7 Transducer Fundamentals The Strain Gauge The strain gauge circuit is now calibrated; do not change the ZERO pot setting for the remainder of this PROCEDURE. In the following steps, you will calculate the force applied to the beam by one revolution of the knob. You will then determine the resulting strain, stress, and output voltage. Y = inch (Recall Value 1) Calculate the force applied to the end of the beam due to one turn of the knob (you calculated a value of inch [Step 6, Recall Value 1] for Y). F = Y x 1.92 F = pound (Recall Value 2) Calculate the strain produced by one turn of the knob (F = pound [Step 7, Recall Value 2]). = F x 4934 = (Recall Value 3) Calculate the output voltage resulting from one turn of the knob ( = [Step 8, Recall Value 3]). V AMP OUT = x V AMP OUT = V (Recall Value 4) You can simplify your calculation by combining the design parameter equations to derive a direct relationship between applied force and output voltage for one knob rotation. Start with the output voltage equation and substitute F x 4934 for. V AMP OUT = x V AMP OUT = x (F x 4934) V AMP OUT = F x FACET by Lab-Volt 249
8 The Strain Gauge Transducer Fundamentals force applied by one turn of the knob. (You determined that one rotation produces pound of force.) V AMP OUT = F x V AMP OUT = V (Recall Value 5) Is this value about equal to the longer method? a. yes b. no V (Step 9, Recall Value 4) you calculated by using the Since the strain gauge response is fairly linear, you should be able to rotate the knob one turn from any starting position and measure the same voltage difference of V (Step 9, Recall Value 4). You will prove this theory in the following steps by measuring the voltage difference between one, two, and three knob rotations. does not apply stress to the beam. the free end of the beam just touches the upper surfaces of the slot in the guide block. 250 FACET by Lab-Volt
9 Transducer Fundamentals The Strain Gauge starting position = Recall Value 6) Rotate the knob exactly one turn counterclockwise and measure the output voltage. V O = V (Recall Value 7) Rotate the knob exactly one turn counterclockwise (two turns from your starting position). The dot on the top of the knob should be at the Recall Value 6) position. Measure the output voltage produced by two turns of the knob. V O = V (Recall Value 8) Rotate the knob exactly one turn counterclockwise (three turns from your starting position). The dot on top of the knob should be at the Recall Value 6) position. Measure the output voltage produced by three turns of the knob. V O = V (Recall Value 9) FACET by Lab-Volt 251
10 The Strain Gauge Transducer Fundamentals This table shows your output voltage measurements at one, two, and three turns of the knob. Turns V AMPOUT 1 (Step 13, Recall Value 7) 2 (Step 15, Recall Value 8) 3 (Step 16, Recall Value 9) V = V(2 turns) V(1 turn) V = V (Recall Value 10) Calculate the voltage difference between the second and third turns. V = V(3 turns) V(2 turns) V = V (Recall Value 11) Are the V values about the same as the value you calculated for a one-turn voltage change? a. yes b. no CONCLUSION A bending beam load cell consists of a strain gauge bonded to a metal beam to measure the surface strain at that point in the beam. A bending beam load cell can be used as the basic element of an electronic scale or other force measurement device. On your circuit board, you can simulate applying a weight to the free end of the beam by turning a You can prove that the bending beam load cell has a linear response over the measurement range by demonstrating that the output voltage difference is the same over several one-turn intervals. 252 FACET by Lab-Volt
11 Transducer Fundamentals The Strain Gauge REVIEW QUESTIONS 1. a. to convert the strain gauge resistance change to a voltage b. to increase the relatively low strain gauge output c. Both a. and b. d. None of the above 2. How much tensile strain in a 4-inch-long solid causes a length increase of in.? = = x 10 6 a. 200 b. 400 c. 500 d A 2-inch-long solid has a modulus of elasticity of 10.5 x 10 6 psi. How much stress is required to cause the length to increase to inches? a. 2,625 psi b. 26,250 psi c. 262,500 psi d. cannot be determined 4. In the bending beam load cell on your circuit board, the strain gauge output represents the a. surface strain of the beam at the point where the transducer is located. b. surface strain at the free end of the beam. c. L). d. FACET by Lab-Volt 253
12 The Strain Gauge Transducer Fundamentals 5. How much force is applied at the free end of the beam by three rotations of the knob? a pound b pound c pounds d pounds 254 FACET by Lab-Volt
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