Helical springs to test position vs force.2. Materials

Helical Springs LabEGGN 350: MEL II Sec CSteven Ripple and Thomas HallBench: 31/23/18 1. Introduction: Background Information: Springs are an unavoidable part of engineering, and can be found in almost all mechanical systems. The purpose of the spring may also vary; the primary job of springs in car suspension is to resist compression, springs are placed in something to resist tension, and the mainspring in a watch exists in torsion. The functionality of springs remains relatively similar though: resist change.What makes a spring a spring is that it has some rigidity such that as it is deformed it exerts a force to restore itself to its initial position insert citation number. This restorative force may be used in combination with the change in length of the spring to acquire the force per length value of the spring for that amount of stretch:k(y) = lim?y?0  (?F/?y) = (dF/dy)This relationship may be simplified further for springs in one directional loading by treating the k value as a constant:k = F/y Experiment Description Lab objectiveThe goal of this lab is to become familiar with the Mini Tini and its manual data collection system as well as with the operation of the MEL II classroom and project schedule. In addition students explored hooke’s law using springs to test position vs force.2. Materials and Equipment: Material Description (pictures of setup if we have any) Equipment List1 x Mini Tini1 x Mini Tini Control Box1 x Digital Multimeter1 x BK Precision DC power source1 x GW instek power source1 x Yellow Multimeter2 x Tension Springs 3. Procedure: Put on safety goggles! The first step of the helical springs exercise is the proper wiring of the equipment. The Mini Tini will be used to measure both the restorative force of our springs and the displacement of the springs in terms of voltage, this will require two different multimeters to be attached to our circuits. The multimeter that reads Voltage to a higher precision is the one that should be set up to record Force as the load cell outputs in mV, whereas the lower precision multimeter should be placed in the circuit so that it may measure displacement which outputs in full on Volts. Follow the wiring diagram provided on canvas 1 and in Appendix 1 below to properly hook up the Mini Tini. For the calibration of the Mini Tini, it may also prove helpful to attach a ruler or a tape measure to one side of the device (see picture?) such that when the jaws are expanded or contracted it is easy to observe their traveled distance. Begin calibration of the Mini Tini by noting the minimum and maximum jaw separation lengths, and then dividing this difference into approximately 12 equal increments. Record the voltage at either the min or max separation, and move the clamps in the opposite direction in the increments that were just calculated, recording the voltage at every increment. The clamps should be moved through every increment at least twice to help account for hysteresis. These measurements may then be used to create a voltage vs. displacement equation (Graph 1) to be used in this exercise and future exercises. Once the Mini Tini has been calibrated, acquire one of the springs to be tested. Before clamping the spring it is pertinent to take a few necessary measurements. Record the number of coils, outer spring diameter, wire diameter, and the length of the spring while it is unstretched. While attaching the spring to the Mini Tini it is important to use a washer in between the spring attachment loop and the bolt head to prevent the spring from slipping off of the device while it is under load. Once the spring is properly secured, progressively increase the tension by expanding the jaws of the Mini Tini. Make sure to collect voltage data at a variety of points during the expansion, the more data points collected the more accurate the k value calculation will be. There should be two voltages being recorded: the voltage being produced by the load cell, and the voltage being produced by the linear motion sensor.  Once the data has been collected, the spring travel may be discovered using the previously acquired correlation between distance and voltage. FINISH THIS 4. Results and Discussion: Calculating Theoretical Spring ConstantsThe theoretical k constants of the springs can be calculated using the equations provided by the Introduction to Helical Springs video 4. The equations take into regard the springs length (L), wire diameter (d), coil radius (R), Modulus of Rigidity (G), and Modulus of Elasticity (E). Further information on the derivations of the equations used and a deeper dive into the mechanics surrounding helical springs can be found in the Helical Spring Reference 5 on canvas. The theoretical spring constants for both springs 1 and 2 separately and in parallel: L = N*d     N = Ld=5.0”0.091”=54.9455 coils2R + d = 0.75”R = 0.75”-d2=0.75 – 0.0912=0.3295”k1,2 = G*d464*N*R3= 11.5*106*0.091464*55*0.32953=6.2625 lb/in The two springs separately should both theoretically have a k constant of 6.2625 in/lb. For two springs in parallel the effective k constant is calculated below:kparallel=k1+k2 =6.2625+6.2625=12.525 lb/in     Theoretically the two k constants should add together to obtain a value of 12.525 lb/in. Calculating Experimental Spring ConstantsTo calculate the experimental spring constants the Mini Tini was utilized to create a plot of position vs linear potentiometer voltage as described in graph 1 below. This data reveals the linear relationship between the position of the Mini Tini’s jaws and the output voltage from its potentiometer, allowing for accurate position readings. The raw data used can be seen in Appendix 2 below.Graph 1: Describes the Linear relationship between Mini Tini #3’s jaw position and potentiometer voltage.Using excel, an equation depicting the relationship was created, where y = 0.602*x -0.092. Using this equation it is possible to determine the distance each spring was stretched. For the purposes of the lab a position of 0 indicates the closest the Mini Tini jaws can get to one another. This means that at a position of 0 the output voltage should be 0.155 V. The other half of the spring puzzle is determining how much force each springs exerts at a stretched position. To do this the MEL II professors provided a calibration sheet for the bench 3 Mini Tini as seen in Graph 2 6. Graph 2: Displays the calibration curves for both Tension and Compression for Mini Tini #3This data is essential as it provides the needed relationship for the load sensor of the specific Mini Tini that was used. It was mentioned that each Mini Tini had a different calibration curve due to the specific history of the machine, making a calibration curve for the machine used to be very important. As the springs are only in tension the tension calibration curve was used, y = 23.66*x + 0.0488. Now that both position and force can be measured from the setup both values were recorded for springs 1 and 2 in series and parallel. Spring 1’s graph is shown as Graph 3 below. The data points used to calculate Graph 3 can be found in Appendix 3Graph 3: Increasing and decreasing force vs position data for Spring 1 indicates hysteresis is small. Springs were loaded in tension.Data was taken while the load on the spring increased and decreased in order to determine if hysteresis was present, the data proves that the k constant of the spring does depend slightly on its history. The increasing values of the data will be used. The k constant of the spring is the slope of the curve, in this case a y = mx+b equation means the value in front of the x is the slope, the equation is y = 6.6636*x + 7.9158. Since prior to data collection the spring was stretched a small amount to unwind the coils, a position of 0 on this graph means very little, the only important piece of information is how the change in position and change in voltage relate to one another as that is the slope.Spring 1 Experimental k constant k1 = 6.6636 lbfinSpring 1 Theoretical k constant: k1 = 6.2625 lbfinThe same data was collected for spring 2 as evidenced by Graph 4 below. In a similar fashion to spring 1, there was a small amount of hysteresis but the k constants ended up similar to spring 1. Appendix 4 holds the data points used for Graph 4.Graph 4: Increasing and decreasing force vs position data for Spring 2 indicates hysteresis is small. Springs were tested in tension.Spring 2 equation: y = 6.6449*x+8.0727Spring 2 Experimental k constant k2 = 6.6449 lbfinSpring 2 Theoretical k constant: k2 = 6.2625 lbfinThe springs were then placed in parallel and readings for position and voltage were taken once more. Graph 5 below holds the results. Appendix 5 contains the data used for Graph 5.Graph 5: The experimental Values of Springs 1 and 2 in parallel plotted against the Theoretical values of springs 1 and 2 in parallel.The two springs in parallel add their k constants together yielding a experimental value of Experimental Spring 1,2 equation: y = 13.432*x+12.624Spring 1,2 Experimental k constant k1,2 = 13.432 lbfinSpring 1,2 Theoretical k constant: k2 = 12.525 lbfinData Analysis and DiscussionIn order to set a standard to gauge the results it is necessary to decide with what accuracy the data should be held to. A spring manufacturing industry standard appears to be ± 10% accuracy of the k constant of mass produced springs 7. This standard accounts for variability in batches of spring material and manufacturing processes as not every spring will be equal. Dimensions of springs may be slightly different from  one another due to their history. With that in mind our results are as follows. Spring 1 measured an experimental k value of 6.6636 (lb/in) where the theoretical value was 6.2625 (lb/in). This is a difference of 6.4%, well below the industry standard of 10%. This means the data likely approximates the actual spring 1 k constant. Spring 2’s experimental k value was 6.6449 (lb/in) while its theoretical value remained the same as spring 1’s at 6.2625 (lb/in) as both springs should have identical properties. The difference between the experimental and theoretical values of spring 2 are 6.1%, also well below 10%, leading to When placing two springs in parallel it was derived by materials on Canvas 4 that the two spring constants are added together. Doing so provides a theoretical value of 12.525 (lb/in) for the combined spring system. In actuality the springs produced a k constant of 13.432 (lb/in) yielding a percent difference of 7.2%. This value is still within the manufacturing specifications for mass produced springs and as such should provide an accurate approximation for the actual springs. The linear potentiometer position vs voltage equation on Graph 1 has an R^2 value of 0.9999 meaning the trendline very closely approximates the collected data. As the data is linear and should be linear confidence in the results is high. In order to collect the voltage values, position points were eyeballed using a regular tape measure, not the most accurate method in the world. The smallest increments on the tape were 1/16 of an inch, therefore we had a measurement uncertainty of 1/32 in going by the MEL I rule of ½ the smallest readable increment. To try and combat any inaccuracy involved over 24 points of data were taken every half inch up and down the Mini Tini’s range creating a data pool large enough to average together accurately. Hysteresis was tested for and determined to be minimal. The data up was plotted separately from the data moving down the Mini Tini’s range and resulted in two equations, the increasing data with a slope of 0.602 and the decreasing data with a slope of 0.601 totalling a percent difference of 0.17%. This demonstrates that the Mini Tini’s movement history does not have a large impact on its data values. The setup for the Mini Tini and the lab was relatively straight forward but error could have been introduced at various points. The day after lab an email was sent out explaining that two sets of batteries in the yellow multimeters were found to be low. The yellow multimeter was used to measure the linear potentiometer voltage and if they were low the resulting calibration curve may have been shifted as the batteries began to die. This would have changed the position readings and potentially offset the resulting k constant calculations. Human error is always present, in this lab it may have presented itself as%%%%%%ADD MORE5. Conclusion:The k constant coefficients for two springs on their own and in parallel was predicted theoretically and then proven experimentally through the use of the Mini Tini tension device.This lab introduced the Mini Tini and its operation and data collection system, providing experience for upcoming labs where its successful operation will be necessary. The linear potentiometer was tested to ensure that voltage values can be converted into position readings. Students were introduced to the format for MEL II and in lab expectations ChangesTo improve this lab it would helpful to make a point to check the batteries in the yellow multimeter before starting the lab and explain to students what the low battery indicator looks like. This would prevent garbage data and save everyone’s time.%%%More?6. References Budynas, Richard G., et al. Shigley’s Mechanical Engineering Design. 10th ed., McGraw-Hill, 2011.1 Canvas Mini Tini Wiring Diagram4 Intro to Helical Springs video5 Helical Springs Reference6 Mini Tini Calibration Document7 https://us.misumi-ec.com/vona2/detail/110302288760/ spring k constant accuracy7. AppendixAppendix 1 – – – – Mini Tini Wiring DiagramAppendix 2 – – – – data for Graph 1 Linear PotentiometerAppendix 3 – – – – – data for Graph 3 Spring 1Appendix 4 – – – – – data for Graph 4 Spring 2Appendix 5 – – – – –  data for Graph 5 Spring Parallel

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