static fixturing and testing of torsional shafts in combined loading

8/12/2019 Static Fixturing and Testing of Torsional Shafts in Combined Loading

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Rochester Institute of TechnologyManufacturing & Mechanical Engineering Technology

& Packaging Science

American Society of Engineering EducatorsMid-Atlantic Section

Static Fixturing and Testing of

Torsional Shafts in Combined Loading

By: Robert Aldi

Advised by: Professors Carl Lundgren and Hany Ghoneim

Date: April 10, 2009


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Table of Contents

Robert Aldi 4/22/09

Rochester Institute of Technology, ASEE

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1.0 ABSTRACT...............................................................................................................................................3

2.0 INTRODUCTION AND PURPOSE .............. .............. .............. ............... .............. .............. .............. ....4

3.0 COMPOSITE TEST SAMPLE SHAFTS...............................................................................................4

4.0 TESTING METHOD ...............................................................................................................................6

4.1 FIXTURE DESIGN AND MANUFACTURING ................................................................................................6

4.2 LOADING SCENARIO ................................................................................................................................7

5.0 TEST PROCEDURES AND DATA COLLECTION............................................................................7

6.0 RESULTS .............. ............... .............. .............. .............. .............. ............... .............. .............. .............. ....8

7.0 CONCLUSIONS ............. .............. .............. .............. ............... .............. .............. .............. .............. .......13

8.0 APPENDIX..............................................................................................................................................14

8.1 FEAFRINGE PLOTS ...............................................................................................................................14


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1.0 Abstract

This project was out of necessity while in the process of developing composite drive-shafts and

the need to be capable of creating test scenarios with combined bending and torsional loading. The

new processing technique and novel fiber orientation for composite shafts aim to produce mechanical

properties with high torsional stiffness while allowing angular misalignment. The shafts should allow

for a similar result as a constant velocity shaft or universal joint except that the angular misalignment

capabilities are provided through fiber orientation. In order to then analyze these shafts a test fixture

was created to modify a torsion tester so that one side can be moved off alignment like a universal

joint thus inducing a bending moment. This bending load is then in conjunction with torque applied by

the torsion tester to create a combined static loading scenario.

Aluminum rods were then tested to analyze the legitimacy of the fixture and loading scenario.

Each shaft was first loaded into one end of the tester chuck-jaws so that the other end floated as a

cantilever beam. A load was applied to which the resultant deflection was measured with a dial indi-

cator. This deflection was then recreated with the new test fixturing by having curved faces that

matched the radius of creating a bending moment on the axially fixed end of the tester with out the

need for load cells along that face. This then helps to minimize fixed end conditions that would alter

the loading as a cantilever beam versus pinned-pinned end conditions. The test results were then

compared to a Finite Element Analysis (FEA) model to determine the legitimacy of the loading sce-

nario. Comparison of the test results to the FEA model did not confirm the setup and experimental

data only matched the FEA data typically by 20 or 25%. The results of the FEA and experimental

testing confirm the need to continue to refine the loading scenario in the FEA model. Consequently

the composites test samples were tested under a pure torsional situation with out any misalignment.

These initial results indicated the need for better design and manufacturing of the samples in addition

to the FEA model situation. Generalizations about the composite fiber orientations were justified to

conclude that:

A fiber orientation that creates a steeper central diameter with a length to diameter ratio

favoring the length will have decreased torsional properties but larger allowable mis-

alignment capabilities.

An orientation that is less steep with a similar length to diameter ratio favors higher tor-

sional stiffness as well as bending stiffness.


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2.0 Introduction and Purpose

Approximately one year and 2 months ago as part of a composites design and manufacturing course, I had

built a composite drive-shaft for my car to transmit engine power from the transmission to the rear differential.

It was manufactured utilizing an existing steel drive-shaft where the center tubular steel section was replaced

with a composite tube made of carbon fiber and epoxy. The method however did no yield the proper weight re-

duction desired in a carbon drive-shaft (only approximately 15%) due to the fact that the majority of the weight

was residual in the steel yokes, differential flange and splines at the ends of the tube. Considering this issue,

thoughts lead to the possibility of creating composite shafts that have the ability to rigidly transmit torque while

permitting a certain amount of misalignment. In order to gain experimental information to form valid character-

istics of different composite tubes a test method had to be created that combines a torsional and bending load

while constraining both ends of the test member. If it were possible to eliminate universal or constant velocity

(CV) joints from existing drive-trains, there is potential to reduce losses, weight and improve efficiency.

3.0 Composite Test Sample Shafts

Currently in the College of Engineering here at RIT, Dr. Hany Ghonheim is doing research work with tor-

sional composite couplings. Using his new idea for fiber orientation was the source of inspiration for this drive-

shaft. Essentially Dr. Ghonheims method involves wrapping fiber reinforcements directly from one end of the

shaft to the other with a radial transverse of less than 180 degrees. An example of this orientation can be seen

in Figure 1. The thick rectangular areas in the two-dimensional representations indicate the shaft ends and

where the fibers are anchored. The line between the two circles (tube ends) is the fiber and goes straight from

one point at the disc to a predetermined position on the other. The position on the other can be located by an

angle relative of transverse to each end as seen by the side view below the top view. Orientating fibers in this

manner should not allow the shaft to easily deflect under a torsional load. Fibers would then also be wrapped

in both positive and negative transverse directions to keep symmetry in the wrap. In creating an orientation in

this manner, the diameter at the middle of the shaft becomes smaller and forms a tapered shape. It can be

seen that as the angle between the start and end points increases, the diameter at the center reduces. An an-

gular transverse of 90 degrees reduces the

diameter of the discs by 50% at the mid-

dle.

Manufacturing was accomplished with

the aid of Professor Carl Lundgren through

creating a mandrel similar to the one used

for the initial drive-shaft process seen in

Figure 2. It was capable of aligning fibers

at the desired shaft ends with notches

around the circumference of a high density


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polyethylene (HDPE) flange. HDPE was used because epoxy is incompatible with it and thus the mandrel can

be cleaned in between laminations. The notches were CNC cut on a mill and were spaced accordingly to the

width of the carbon fiber strands to be wound. In the case of the mandrel that produced this presentations

samples the notches were 10 degrees apart. The new mandrel is approximately one third the size of the origi-

nal mandrel with a crucial improve-

ment, a fiber pre-tensioning mecha-

nism. The new mandrel (Figure 2)

incorporates our improved ideas and

has one of the flanges floating axially

yet is located tangentially to prevent

twisting. The ability to increase the

flange gap by 0.38mm and put a faint

amount of pretension in the fibers

made great strides in retaining the in-tended fiber orientation as compared

to the original mandrel which was

susceptible to operator skill and fiber

sag. The device worked well enough so that rotating the mandrel during curing was no longer necessary as in

the case of the original mandrel.

Fibers were hand wound onto the mandrel dry once in each direction and the slack would be removed with

the tensioning mechanism. In order to approximate the necessary amount of epoxy resin required to ade-

quately wick out the carbon fiber (and obtain the optimum 50/50 ratio between resin and fiber weight), a weight

of the fiber was determined per length. Since the mandrel had 36 notches and one circumferential transverse

per direction it was a simple calculation to approximate the fiber length used. Based on this a fiber weight was

determined. The calculated amount was then increased by approximately 3 grams for consideration of contact

losses on the mixing and application components as well as to simplify the measuring of the portions of resin

and hardener for the resin system used.

The samples were then cut off the mandrel with a band saw and sanded to length. In order to anchor the

sample shafts to the chuck-jaws of the tester, steel inserts were post secondary bonded to the ends. Since the

samples ends were not perpendicular to the circular ends of the shaft due to the parabolic shape, a taper was

turned on a lathe into the inserts originating from plain carbon steel hexagon bar stock. The same laminating

epoxy resin was used to bond the shafts to the inserts except it was thickened with amorphous silica (cab-o-sil)

to increase the viscosity and mechanical properties of the resin. Details of the materials used for the samples

are located below in Table 1.


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4.0 Testing Method

4.1 Fixture Design and Manufacturing

Inherently there exists a necessity to develop a testing method for quantifying the properties of these novel

fiber orientations in combined bending (misalignment) and torsion. In order to accomplish this, a fixture was

designed that essentially locates one end of a Tinius Olsen torsion tester off axis. Pictures of the fixture can be

seen below in Figure 3. It is

made of one inch thick steel

plate (1018) in order to mini-

mize cost and simplify manu-

facturing. However as one

can see there is a radius ma-

chined into the edge of the

two side plates accompanied

by two concentric slots. There

are also two adjoining shoes

that fit into the plates and as-

semble with the load cell to

guide the load cell on the ra-

dius. These features were

created using CNC machining. All other machining was performed with a manual vertical mill. Figure 4 below

shows the assembly as separate components of the fixture. The floating assembly with the load cell is kept in

place against the rigid assembly through the use of a lock bar that fits in the slot machined concentrically to the

mating curved face of the side plate. A through hole in the lock bar tightens into a threaded hole in the center

of the square plate that butts against the load cell flange in order to pull the two assemblies together tight.

The curved mating faces are also machined with a raised section that inter-lock so that the torque applied

to the floating assembly is not transferred through the lock bar but rather through the thick steel plates of the


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fixture providing for a very rigid setup. The radi-

uses of the mating faces were dictated by the dis-

tance from the non-movable chuck-jaw to the back-

side of the steel plate that mounts to the load cell

flange. The purpose for this was to create a mo-

ment at the point near the non-movable end of the

tester and minimize end conditions. The goal of

this design feature was to recreate a scenario that

made the setup equivalent to a cantilevered beam

in combined bending and torsional loading.

4.2 Loading Scenario

Before testing of the carbon fiber samples could

begin, a verification of the above mentioned loading

scenario was performed with aluminum samples in

conjunction with a Finite Element Analysis (FEA).

In order to properly apply the bending load, initial

assumptions suggested that measuring the deflec-

tion of the fixture would be equivalent to a resultant

deflection of a bending load applied to a cantile-

vered beam. An aluminum sample was loaded at

the end with weights and the resultant deflection

was measured with a dial indicator. A test run was performed then at that deflection and the resultant peak

torque was recorded. These values were then applied in the FEA model for a cantilevered aluminum rod which

indicated a combined stress value far above the limits of the material. Also the cantilevered FEA model did not

accurately indicate the location of stress concentrations of where the sample was actually beginning to fracture.

The aluminum samples were simple ! (~12mm) in diameter and did not have raised end diameters to elimi-

nate the stress concentrations of the end conditions. Consequently the majority of samples would break at the

end of the chuck-jaw teeth. Iterations of the solid model, loading and constraints for the FEA model eventually

closely approximated what was occurring in the experimental setup.

5.0 Test Procedures and Data Collection

For the samples (aluminum and carbon), testing began by first ensuring the fixturing was properly located.

An angle gauge was used to level the assembly so that its centerline was concentric with the unmovable chuck-

jaw. A dial indicator with a magnetic base was then set on the fixture and zeroed so that if testing required

misalignment, the deflection could be accurately measured. The samples were tightened into the jaws at no

deflection with the lock bar snug. Once the jaws were tight, the lock bar was slowly loosened so that soft taps

with a scrap piece of wood would move the fixture to the appropriate misalignment. The lock bar would then be


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tightened and the torsion testers reading for load and angular deflection would be zeroed out. All torsional

data was collected in real time using LabView 8.5 through a serial port cable directly out of the Tinius Olsen

machine. The data rate was set to collect every 100 milliseconds. The angular speed on the tester was set at

20 degrees per minute prior to yielding. Once the curve began to level out, the speed was slowly increased to

the maximum of 360 degrees per minute. Once the sample broke the machine was stopped and the fixture end

of the tester was moved away to clear and remove the sample.

6.0 Results

Seen below is a summary of the results for the Aluminum testing. Since the number of carbon samples

was limited, testing was performed on the Aluminum first in order to become familiar with the new method and

equipment. The Al. samples were applied with different bending loads to try and form a trend between increas-

ing bending load and the maximum torque load. Since the measuring point of the fixture deflection is greater

than the length of the samples, a quick conversion factor was calculated to determine the percent increase of

deflection for the increased radius. As seen in Table 2 these deflections and experimental peak torques at

breaking show little correlation to changes in the applied bending load. The reason for this is likely either due

to the fixed-fixed end conditions or the fact that the bending loads are relatively small and may be too little to

create a noticeable difference. The FEA results are summarized in Table 2 as well and depict the Von Mises

combined stress value for each sample. Stress fringe plots depicting the graphical results of the FEA model

are located in Appendix 8.1. Unfortunately the values are approximately 10 Ksi (~70MPa) from the ultimate

tensile strength of the aluminum which likely indicate that further refinement of the FEA model is required to get

a full understanding of the loading scenario. This is especially necessary in the future to truly ensure that a

measured deflection on the fixture is similar to applying a bending load with the fixed-fixed end conditions.

Graphical displays of the data summarized in Table 2 are shown on Figure 7 depicting torque vs. angular de-

flection. The vertical gridlines of Figure 6 indicate divisions of 1 complete rotation of the test apparatus.

A summary of the carbon fiber data as specific as the aluminum would unfortunately be premature. Below

in Figure 7 are results for the aluminum samples and Figure 8 displays results for the carbon fiber samples. As

can be seen by the graph in Figure 8, there are many jagged drops during the testing from zero to 30 degrees.

Also 9 samples were made and only results for seven are being presented. All the jagged drops in the torque-


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deflection curves indicate spots where the epoxy bridging between the fibers broke. The general consensus for

all the carbon samples was a failure in the

epoxy and not the carbon. In fact, instead of

the carbon fibers snapping, they started to

buckle in on themselves as depicted to the

left in Figure 5. Another failure was the de-

lamination of the tubes to the steel inserts in

the case of two tubes. If one looks at the

data in Figure 8 for the failed insert data, it

can be seen that the strength of its bonded

counterparts were much greater.

Also in accordance with the buckling

issue, the carbon fiber did not physically

break thus it is hard to determine the tor-

sional and misalignment capacities of the

shafts. Consequently none of the carbon samples were tested in combined loading, only pure torsion. How-

ever considering the fact that the fibers are still continuous, it may be possible to reinforce the samples with

carbon fiber biaxial sleeves secondarily bonded to the outside surface. A separate sample could then be made

of the sleeve alone to determine the strength of the sleeve. This strength could then be subtracted from the

cumulative strength of the sleeve reinforced samples to relatively approximate the strength of the fiber orienta-

tion. Despite the varied results of the carbon testing, the results did at least support the premonition that the

tubes with greater angles of transverse on the opposite side were stiffer in torsion and resisted bending. The

tubes with steeper wrap angles however produced

more torsionally flexible shafts yet increased the

ability to deflect from the central axis. This justifi-

cation was based on hanging a 100 Newton lab

weight from all the different shafts and measuring

the deflection. Although the results were not re-

corded (measurements used to confirm hypothe-

sis), they did allow for a general confirmation of

expected sample properties. A picture of this

measurement can be seen below in Figure 6.


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7.0 Conclusions

Many different issues and realizations were discovered in the process of exploring this new test method.

The first main topic is the verification of determining the bending load. As presented earlier, the FEA results for

the test data do not strongly correspond with known information (UTS of 6061-T6 approx. 49 ksi). The reason

for this could again simply be a mistake in the loads and constraints applied to the FEA model. In a situation

where it is difficult to determine the static conditions, there needs to first be a way to confidently induce a de-

sired bending load. The main issue is that a cantilevered beam has a slope at the deflection side. Even though

the fixture side moves to meet this deflection angle, the slope (relative to the chuck jaws) is ultimately zero

(fixed end condition). Considering the FEA model is still based on the mathematics used to determine a resul-

tant deflection for a given load by hand calculation, it is easy to understand how a wrong scenario in the FEA

model can create skewed answers. The refinement of the FEA model to ensure assumptions is surely the sub-

ject of future attention and work.

Another key area for improvement is the manufacturing and assembly of the carbon fiber test sections.

Work is currently underway to further improve the mandrel and manufacturability of the shafts because with the

current tooling it can become rather tedious and time consuming. Design changes will likely include biaxial

carbon fiber sleeving to create a shell that keeps the fibers of interest in the proper orientation with fiber and

resin instead of mainly resin. Also for the inserts it may be wise to mill low depth keyways into the tapered

surface of the inserts so that epoxy and filler mechanically lock the sample to the insert. In addition to changing

the construction process and materials, it may be beneficial to alter sample geometry as well. A ratio can be

created that relates the distance from tube end to end and the diameter of the end. A sample such as present

in the paper would then have a large length:diameter ratio and would clearly more suited for a bending stiffness

with some torsional stiffness. Better torsional properties with increased flex properties could be created if this

ratio shifts more towards the diameter and thus a greater parabolic shape in the sample.

Regardless of the numerical results, it can be demonstrated that this testing method presented in this paper

is a potentially viable way of performing combined torsion and bending. If further development is successful,

the idea may have the potential to readily become a fatigue tester which would insert a friction brake at the un-

driven end of the shafts. Ultimately if composite shafts are to confidently be made with out universal or CV

joints, a way to ensuring their performance must be developed and is worth continued effort. I also appreciate

particularly the aid and effort of Carl Lundgren and Hany Ghoneim who have supported my undergraduate

scholastic endeavors. Thank you.


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8.0 APPENDIX

8.1 FEA Fringe Plots

static fixturing and testing of torsional shafts in combined loading

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