Appendix – Torsional Prototype

Performed by Hyungsuk Kang, Jason Whyte and Daniel BowersMultidisciplinary Senior Design

Rochester Institute of Technology

Abstract—The goal of this test was to determine that capability of generating torsional load and vibrating to the unit under test with minimal damping. We designed a simplified engineering system to validate the mechanism of the final design. Various static load and vibration were applied to during the test. Overall the test was a successful proof-of-concept for torsional load and vibration that we have designed.

Keywords—torsional load; torsional vibration; dynamic stiffness; natural frequency

I. INTRODUCTION In the design of this test, we needed to develop a simplified

engineering system that is capable of creating torsional static load with vibration and affordable with allowed budget. The prototype system maintained the same aspect ratio as the proposed final design, and had significantly reduced loads to prevent mechanical failure. The purpose of the prototype were to determine if our system was capable of generating torsional load and vibration independantly to the unit under test. An air spring was used to generate various static load, and an electromagnetic shaker was used to generate vibration. We ran frequency sweep of vibration with various static load conditions. We then compared the magnitude of input and output vibration ratio of the system to compare the effects.

II. ASSUMPTIONS

In order to run this test, we needed to make the following assumptions:

Static load generated from air spring is consistent and vertical to the ground.

Lever arm and supporting parts will not deform before the unit under test.

III. DESIGN

In the prototype system we are testing, it is important to transmit static and dynamic loads effectively to the unit under test. Among the various prototype design, we chose airspring and electromagnetic shaker motor method to perform the test.

A. Unit under testThe material of unit under test(UUT) in prototype is 1.2”

diameter x 13” long 6061-T6 aluminum while the actual UUT is ¾” diameter x 36” long steel. The purpose of the change in material is to reduce the required amount of load for the same behavior during the test.

The UUT is machined from 2” diameter aluminum rod in order to have sufficient area on one end to insert pin to install the UUT to the sleeve fixture on the frame. We created fillet to reduce the concentration of stress on the edge of UUT and tap drilled the other end to connect UUT with lever arm. According to the simulation on Solidworks, the maximum stress was 402ksi when we apply 200lb-ft of torque to the UUT.

B. FrameThe frame sturcture of prototype is made of steel in order to

ensure the capability of handling the load and vibration applied during the tests. 1” width square tube and steel sheet are welded together at the machine shop. Overall size of the frame is 24” x 24” x 22”.

This test is sponsored by LORD and by RIT Multidisciplinary Senior Design. Project assisted by Mr. Gary Werth, Dr. Deth Debartalow, Dr. Marca Lam, Mr. Keith Ptak, Mr. Zach Butler, Ms. Robin Chapman.

Fig. 1. Stress simulation of the unit under test

In order to ensure the capability of handling the load, we designed the frame with factor of safety of 10. The static force of 2000 pounds generates 76.88 ksi which is under the yield strength 89.98 ksi.

C. Static load and vibration applicationWe chose an air spring 1S3-011 from GoodYear to generate

static load to the lever arm since it is capable of 400 pounds of force at 100 psi. The air spring is mounted straight on the metal sheet with a ¾” nut. We used a regulator attached to the air hose to vary the air pressure to generate various static force during the test. We used Tovey SW10-300-0082 to monitor the static load applied from the air spring. In order to generate torsional vibration, 2025E Modal Exciter from The Modal

Shop TMS was used which was available at LORD facility. It was capable of creating 13 pounds of peak force with 0.7 inches of displacement and frequency range of 0-9000 Hz. The shaker was mounted on the separated support structure with bungee cords and 2150G12 stinger was connected between the shaker and lever.

IV. EXPERIMENTAL SETUP

The most of the frame sturcture and lever were assembled prior to the test and data measuring equipment were install at the LORD facility.

The load cell is installed between the air spring and the bearing mount as Fig 4. We adjusted air pressure of air spring to set the initial location of the lever arm is horizontal to the ground.

Fig. 2. CAD design of torsional prototype

Fig. 3. Stress simulation of prototype frame

Fig. 4. Test setup of torsional prototype

Fig. 5. Accelerometer installation location

Two triaxial accelerometer PCB 339B10 were installed on the lever and the top bearing mount as Fig 5. We used z-axis to control the vibration of lever, and used x and y axis of secondary accelerometer to ensure whether the vibration is occuring on the right direction.

V. RESULT

We ran the test with three different static load conditions and three different acceleration conditions; 50 lbs, 60 lbs, 75 lbs, 0.1 g, 0.25g, 0.5g. During the test, we were able to observe resonace at the frequency of 51 Hz. In order to analyze the collected information, we imported data into Matlab and created graphs of Bode plot on each axis. The shaker motor aborted test with 0.25g and 0.5g due to the significant vibration at the natural frequency of the system.

According to the analysis by using the equations,

J=( π D4 ) /32

K t=G ∙J / L f n=√K t /m Dcg2

we were able to determine theoretical torsional stiffness of the system and natural frequency based on the information in Table 1.

TABLE 1. PARAMETERS

G, shear modulus 3770 ksi

L, length of rod 13 in

D, diameter of rod 1.2 in

J, polar moment of inertia 0.2035 in4

m, mass of lever arm 19.5 lbsDc, distance from center of rotation 6 in

From the given information we determined torsional stiffness of 59036.8 in-lb/deg and natural frequency of 9.17 rad/sec which is 57.62 Hz. Compare to the observed natural frequency it is within 11.5% error range.

VI. CONCLUSION

In order to determine that capability of generating torsional load and vibrating to the unit under test with minimal damping, we designed a simplified engineering. Various static load and vibration were applied to during the test. We were able to produce torsional load from an air spring, and torsional vibration from an electromagnetic shaker. Through the test we determined that the natural frequency of the system was consistent with various torsional load and vibration conditions, which means the stiffness of the system was consistent during

Fig. 6. 50 lbs 0.1 g 10-200 Hz Test Result

Fig. 7. 60 lbs 0.1 g 10-200 Hz Test Result

Fig. 8. 75 lbs 0.1 g 10-200 Hz Test Result

the test. Overall the test was a successful proof-of-concept for torsional load and vibration that we have designed.

REFERENCES

[1] Beer, Ferdinand P., E. Russell Johnston, John T. DeWolf, and David F. Mazurek. Mechanics of materials. New York, NY: McGraw-Hill Education, 2015.

[2] Madweb,“http://www.matweb.com/search/datasheet_print.aspx?matguid=1b8c06d0ca7c456694c7777d9e10be5b,”