Testing
The final task in the CSUS ME191 course is to verify the original theoretical analysis by testing. There are many reasons that testing results may not math theoretical calculations, such as: bad or inappropriate assumptions, material proprieties not matching the calculation value, imperfections in materials, change of design, and a whole host of other factors.
Dynamic Motion Testing: Jake Abe
My analysis consisted of the dynamic motion of the staircase, including the velocities and accelerations of the steps as well as a quantitative analysis on the parallelogram design to ensure it would work. The calculations of the velocity and accelerations was based upon rigid body calculations which hold true for the system which was a rigid body. I has originally assumed that the acceleration of the linear actuators was 0 which meant VB = speed of actuators (0.98 In/s). Additionally, the rigid body equations stipulate that ω and α as reliant upon the speeds of VB and VA which is a proven theory. Therefore, the
To test the velocity of point A I used a Bosch laser tape measure that could measure 1/16 inch increments in real time. I used 3M double sided tape and affixed the device to the structure at point A, I then used a 90 degree piece of sheet metal and affixed it to the other side of the telescoping tubing and in a position that interrupted the laser. In this arrangement the laser would be measuring the displacement of point A. I used a camera and recorded the display of the Bosch laser while the transforming staircase transitioned from flat to staircase. I then used a program to slow that video down by a factor of 8 so I could record the measurements as it changed increments.
main thing to test is the velocity of VA and then the rest are dependent upon that and the known VB
The velocity and acceleration tabulation are shown with the important data being the maximum linear velocity of VA = 0.70520 In/s.
The recorded data and calculated data for VA are tabulated below. The main thing to take from the data is that the maximum velocity in the actual system is 0.3116 In/s., unfortunately, the maximum velocity VA of the theoretical calculations does not match that of actual testing of 0.70520 In/s. There are many reasons as to why the theoretical calculations to not match, the largest being that of friction, in the theoretical calculations friction is nonexistent – in the real world there are eight 4x4 steel telescoping tubes that have approximately 170 lbs of friction (according to Eric). The friction is actually quite substantial to the system and caused the actuators to move slower than the 0.98 In/s as originally thought. Another reason for a slower real world velocity is the control system, which had to slow the actuators to accommodate the slowest actuator.
The curve (right) illustrates how as the system rises the frictional forces do in fact slow down the Velocity, the high arc at the beginning is deceptive, because the velocity is actually very slow and takes a while to get moving – before 10 seconds the amount that the telescoping tubing has retracted is only about 2 inches out of a total 12 in displacement. However, the actual velocity has a percent error from the theoretical value of 55.8%.
If this testing were to be done again, it would have been more effective to take the measurements while the staircase was moving downwards so that the actuator would not have been having to fight as much friction or the weight of the steps and support structures. It also would have been good to use the same process to measure the actual velocity of point B - the velocity of the actuators.
Dynamic motion analysis reminder
Stringer Deflection Testing: Miguel Gonzalez
The testing method for the stringers involved the use of linear strain gauges. According to ADA and ASME regulations, the platform of the elevator lift must not deflect a certain amount. The important part of this analysis comes down to loading the platform with weight and analyzing the stringers to see if they maintain structural integrity. Since our system does not have a uniform platform, the stringers become the most critical component to analyze deflection. The approach to the theoretical analysis was to apply a load to each step and divide it in half to accommodate what force is applied to one stringer. Taking this these loads across the span of the beam results in a distributed load that is used alongside the simply supported beam deflection equation. Figure M1 below displays the free body diagram of the stringer followed by the theoretical calculations.
The testing method of the stringers involved placing two linear strain gauges at the bottom center of the stringer. Having these strain gauges connected to a readout mechanism and loading each step with weight produced a few strain gauge readings to work with. Since the load and the corresponding strain is known, the values are then used to determine the deflection of the stringer using the beam deflection equation. Since the equation involves the length of the beam, for each loading case, the corresponding change in length was added to the original length of the beam, and that length is used to calculate the beam deflection. Strain gauge recordings were taken loading the stringer as well as unloading it.
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The Table below displays the testing data for the strain gauge. The difficulty encountered during testing was access to a substantial amount of weight to load the steps. Comparing the results to the theoretical required a similar magnitude of the distributed load placed on the stinger. A linear relationship between the load and the deflection was used to produce the results. Stresses acting on the stringer are below the yield strength of the material, which allowed me to assume a linear relationship with the unit loads and their corresponding deflections.
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Assuming a linear relationship with the known distributed load and the calculated deflections that incorporated the strain recordings, a linear interpolation produced a deflection value close the theoretical results. Setting W equal to 6.05 lb./in results in a deflection of 0.177152269 inches. Comparing this value to the theoretical value of 0.1880 inches results in a percentage error of 5.8%.
To improve the analysis, there are a few things I would do differently. First, I would make sure to have access to a substantial amount of weight to load onto the steps producing far more data points. Second, to produce even better results, I would test the stinger as an individual component. Lastly, with a substantial amount of load, I would use dial indicators to get an actual measurement of the stringer deflection
Stringer Deflection analysis reminder
Friction Testing: Eric Berger
Our project has four structural L components that must slide apart as the staircase transforms into a platform. I chose to go with polycarbonate as a friction reduction material as well as it gives the columns a tight fit to each other. For my testing, I inserted one side floating off the table. I then used an inline scale to measure the force it took to move the beam from rest. The center of mass is 10 inches from the reaction of the plastic. There is a 20-inch slider that is inserted when the structure of fully collapsed. The 90 pounds that each column weight not creates a torque of 75 lb-ft. when the tube is compressed fully. As the tube is extended the torque increases and thus the friction force increases.
Friction analysis reminder
From this graph I can assume that the coefficient of friction is actually 0.4. The theoretical coefficient of friction of polycarbonate on steel is 0.3, our steel is not polished, so having a larger coefficient was expected.
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Wc - we weighed to be 50 lb each
Wtot - we are unable to weigh at the school. So it was guessed by solidworks and teammates to be roughly 200 lbs.
ΣFx = 0 = Fx + (Wtot)(2*Wc)Sin θ°
ΣFx = 0 = Fx + 300Sin θ° = 175 lbs.
Ffriction = (µk)(Nx) = 70 lbs.
ΣFy = 0 = Fy + (Wtot)(2*Wc)Cos θ°
ΣFy = 0 = Fy + (300)Cos θ° = 243.5 lbs.
Ffriction = (µk)(Ny) = 97.4 lbs.
ΣFfriction = (µk)(Nx+Ny) = 167.6 lbs. of friction in the system as it is transforming.
Due to the predicted loading applied, only defection in the elastic range will be produced. A linear strain gauge rosette will be attached to the bottom of both long support beams of the step. Then 4 separate loads were applied up to the max amount of weights in the shop which was 340 pounds. I then had Jake, my partner stand on the weights to get a max of 672.5 pounds on the tread. This will produced data plots where a trend line was fit to. Then through interpolation, a predicted max strain on the bars can be determined at a max 1000 pound load case to predict the maximum deflection of the steps.
Two strain gauges on the front and back bars in the middle measuring micro strain in the length wise direction recorded similar results. The data was recorded using a live data readout and the results varied within 1 to 2 micro strain. The theoretical results for deflection of -0.0949 inches at 1000 pounds are extremely close to the interpolated data of -0.0943 inches. This gives a percent error for deflection of 0.6%. This percent error could result from the top wood structure adding to the moment of inertia of the total system or the way that the tread was supported on either end of the step.
Tread Deflection analysis reminder
Tread Deflection Testing: David Sarver
Circuit Testing: Laake Scates-Gervasi
Circuits analysis reminder
There were several discrepancies that had to be overcome for the electrical analysis of this project. The first being that the electrical components chosen during the design phase changed when the manufacturing phase began. The first key change was that the actuators peak current dropped from 15 amps to 12 amps. The second key change was choosing completely different motor controllers to incorporate a full stop and reverse function. Both changes affect the initial theoretical analysis seen in the table below. The second discrepancy involved the tool chosen to perform the analysis, the multimeter, and the fact that most multimeters can test a max of 10 amps. Although I located a multimeter that could test a max of 15 amps, but it had a separate port to plug the test wires into and this plug was disabled from being used. I decided to test the circuit when it was running the actuators at 50% speed using the 10-amp multimeter. The picture to the right is a photograph taken during the testing in my left-hand I am holding the multimeter and applying the testing wires to the output terminals on Motor Controller 1.
The table to the left shows the raw data received while testing the actuators in 2 separate functions, front up and back up. Due to the over sizing of the AC-DC transformer it is safe to assume that the same values would be seen no matter how many actuators were running at once.
The motor controller voltage in The table above confirms the theoretical result, which used Kirchhoff’s voltage law as seen in the equations below, that the voltage will remain the same across elements in parallel. Although the voltage that was expected in the theoretical analysis is 13.8VDC and the average voltage in testing is 13.66VDC, we can assume that this is due to the output of the transformer and has no overall effect on the ability for the system to run. With the system running at 50% speed we can see in the table that the current into the actuators is slightly below half of the peak current, which makes sense since the peak current will only be applied at full load. However, since we were running the system in a 2-actuator motion case, the actuators pulled the same amount of current which confirms the theoretical analysis. Which used Kirchhoff’s current law, shown in the equations below and states that the current going into each node must equate to the current leaving the same node. After all other testing was completed I decided to test the current going into the motor controllers. As I touched the test wires to the terminals sparks flew and the wires started to get extremely hot, at this point I will say that I do not recommend anyone attempt this test without full safety gear. Although the multimeter states that it reads 10 amps, the screen went above 10 amps and wavered around 12.63 amps. Since the current going out of the motor controllers and into the actuators was roughly 5.70 amps I decided not to test the input terminals of the other motor controllers and assumed that they would show the same current. The motor controllers 12.63 amps was taken while 50% speed was being applied to the actuator. Which means that the motor controllers H-Bridge MOSFET is always pulling the max current and voltage that would be required, and therefore the overall power consumption of the system will be based on the max of the motor controllers and will not rely on the speed of the actuator. Taking the raw data and applying Ohms law, as seen in the equations below, to calculate the power we can find that if all actuators were running there will be a power draw of 690.1032 Watts. The table below shows the current, voltage and power draw based on how many actuators are being run.
The table above does contain some errors, such as the 0.1 current being applied to each motor controller when it is not running. This is not a measured value but is the value given by the manufacturer for the motor controller. The data for the motor controller can be seen in Table-L4 to the right. We can then plot the theoretical and tested data together with Actuator count being the X value and Power Draw being the Y value. This will allow us to compare the Theoretical Power Draw and the Actual Power Draw. Figure-L2 shows this plot with the slope equations for each set of data. The data for both the theoretical analysis and the testing follow a perfect linear line as expected but due to the discrepancies talked about before we are using up less power. This is due to the current and voltage both being smaller than expected.
However, even with the discrepancies the electrical system still followed the same guidelines that were assumed in the theoretical analysis. Kirchhoff’s voltage law was proven with each motor controllerreceiving the
same voltage. Along with Kirchhoff’s current law which proved that the current going into each motor controller would be the same for each actuator that is running. Although if this testing were to be performed again, I would recommend using a multimeter capable of large currents and preforming the test at multiple speeds and motion cases. All theoretical assumptions motor controllers and actuators
were proven with this electrical system and with choosing different
we lowered the power draw and preforming the needed action.