Torsion Test

DESIGN AND DEVELOPMENT OF AN ECONOMICAL

TORSION TESTING MACHINE

by

GLENN E. VALLEE

ASSISTANT PROFESSOR

MECHANICAL ENGINEERING

and

ROBERT SHORT

WESTERN NEW ENGLAND COLLEGE

SPRINGFIELD MASSACHUSSETS

Session 1C Mechanical Engineering

Proceedings of the ASEE New England Section 2006 Annual Conference. Copyright ©2006 1

ABSTRACT

A low cost torsion testing machine capable of determining the shear properties of

materials according to ASTM specifications is developed. The machine provides

an economical means of performing the standard ASTM torsion experiment

which is integrated into the Mechanical Engineering laboratory sequence to

augment the usual ASTM tensile test. Developed as part of a capstone

Mechanical Engineering senior design project, the torsion tester provides students

with the means to observe and study the internal drive mechanism, torque load

cell and rotational potentiometer within the machine, thus allowing students to

calculate the performance characteristics of the machine prior to using it in an

actual experiment. The result is a more comprehensive understanding of the

laboratory experience, as the technology behind the testing apparatus, the test

methodology and the response of materials loaded in torsion are explored. The

machine provides a low cost solution for engineering and engineering technology

programs that wish to expand their material testing capabilities but are not capable

of funding the acquisition of commercially available torsion testing machines.

I. INTRODUCTION

The shear stress-strain response of materials can be extremely important in the design, analysis

and manufacture of a wide variety of products and components which are loaded primarily in

shear or torsion. When the applied loadings are primarily shear in nature, the shear modulus of

elasticity and shear yield strength must be known in order to apply the usual closed form

equations commonly used in engineering design and analysis. These properties are determined


from the shear stress-strain diagram which is most commonly measured according to an ASTM

torsion test [1], where a material specimen of solid or hollow round cross section is twisted in a

torsion testing machine as the applied torque and angle of twist are recorded simultaneously.

The torque-twist diagram is constructed from these data, and elementary mechanics theory is

then used to construct the shear stress-strain diagram.

Unfortunately, many engineering and engineering technology programs do not include an ASTM

torsion test in their lab sequences, often due to insufficient funding required to purchase a torsion

testing machine which typically costs between $10,000 and $25,000 depending on capacity and

instrumentation. The ASTM tensile test is then the only test performed to characterize material

behavior, which implies that the shear response of materials may be neglected without

consequence. The Mechanical Engineering Department at Western New England College saw

the value of giving students exposure to the ASTM torsion experiment but was not in a position

to purchase the required equipment. The capstone senior mechanical engineering design project

was therefore used as an alternative approach to solving this problem. A senior mechanical

engineering student [2] was asked to design and fabricate a torsion testing machine capable of

reliably duplicating test results measured using more expensive machines, but at a fraction of the

cost. The design was to allow students access to view and study the major internal components,

such as the gear drive system, torque load cell and rotational potentiometer, so they could predict

the performance of the machine and its limitations. The student involved in the project gained

valuable experience in a number of areas, including ASTM test methods, mechanical design and

analysis, manufacturing processes, assembly and instrumentation.


II. DESIGN OF THE TORSION TESTING MACHINE

A. Performance Parameters

1. Torque Requirements

The torsion testing machine was designed to test engineering materials typically studied at the

undergraduate level, such as steel, aluminum and other common metals. Considering first the

upper range of shear strength to be measured, a commonly available C1018 steel having a shear

yield strength of 31.1 kpsi and an ultimate shear strength of 42.7 kpsi [3] was considered. Using

elementary mechanics theory [4], the maximum shear stress is developed at the outer surface of

the test specimen and is related to the applied torque using equation (1):

J

Tc=

max! (1)

where:

max! = maximum shear stress in shaft J = polar moment of inertia of the cross section

T = torque acting on the cross section c = radius of cross section

In order to use equation (1) to calculate the torque requirements of the machine, the test

specimen dimensions needed to be selected. A specimen diameter of 0.375 inches was selected

to provide a failure surface of adequate size for viewing by students and a specimen length of 6

inches was selected to meet the minimum length to diameter ratio requirement set forth by

ASTM. This length also provided easy insertion of the test specimen into the machine. Now,

equation (1) is only valid for linear elastic material behavior and its use in calculating the torque

required to fracture the steel specimen results in an overly conservative value of 442 in-lb.


However, this value was used as the minimum threshold for the machine in order to include a

factor of safety in the design.

2. Rotational Requirements

The next parameter to be calculated was the total angular displacement to be recorded. The

angle of twist, θ, may be calculated for a linear elastic material according to equation (2):

JG

TL=! (2)

where:

J = polar moment of inertia of the cross sectional L = specimen length

T = torque acting on the cross section G = shear modulus of elasticity

However, the maximum angle of twist at failure for materials is difficult to calculate using closed

form equations as material plasticity must me considered and equation (2) is no longer valid.

Experiments were therefore observed using commercial machines which fractured torsion

specimens made from a variety of materials. It was then decided that the measurement of the

angle of twist over three revolutions would be adequate for most materials up to failure.

Measurement of the torque applied to the specimen and the corresponding angle of twist could

then be used in equation (2) to calculate the shear modulus of the material in the linear elastic

range.

B. General Design Layout

The basic concept for the operation of the machine is shown in figure 1. The specimen was

mounted between a non-rotating fixed hub assembly and a rotating hub assembly which was


connected to a drive train. The non-rotating hub was mounted on a T-slide to allow motion

along the axis of the specimen to prevent axial loads from developing as the length of the

specimen decreased during twisting. The non-rotating hub would also include a strain gauge

torque sensor used to measure the applied torque. The rotating hub would be driven using a

drive sprocket connected to the drive train. The specimen angle of twist would be determined by

measuring the rotation of the rotation hub.

FIXED HUB

SPROCKET

ROTATING HUB

T-SLIDE

STRAIN GAGE

CHUCKS

UNIFORM BASE PLATE

SPECIMEN

Figure 1 – Schematic of the torsion machine layout

C. Drive Train

Several motors and drive systems were considered based on the required torque and specimen

geometry. A DC motor having an integral gear reduction and an external speed control was

selected based on cost, size, performance, and reliability. The speed controller was selected to

provide a means of adjusting the speed of the test as it was difficult to select commercially

available sprocket sets which could develop the exact rotational speed desired in the test. This

motor developed an output torque of 500 in-lb at a speed of 13 rpm.


A sprocket and chain drive was selected as a durable connection between the motor output shaft

and the rotating hub which loaded the test specimen. A single gear set comprised of a 2 inch

diameter driving sprocket and a 12 inch diameter driven sprocket was found which would

achieve a gear ratio of 6:1. This resulted in a rotational speed of 2.2 rpm which falls within

ASTM specifications, and a driving torque of 3000 in-lb. This torque was well above the 442 in-

lb threshold established earlier and was considered to be more than capable of maintaining a

constant angular velocity during all tests. The torque developed by the machine was transferred

to the specimen using grips which were threaded onto the fixed and rotating hubs. Standard 1/2

inch drill chucks proved to be an inexpensive means of holding the specimens and were very

effective provided that flats were machined on the specimen ends to prevent slippage.

D. Frame

A frame was designed to support the hub assemblies, drive train and controller. The frame was

made from 1 ¼ inch square steel tubing with a 1/8 wall thickness and had overall dimensions of

24 inches long by 18 inched wide by 24 inches high. The frame was welded together and the

motor and drive train were bolted to the frame. The frame was then covered with 1/16 inch

galvanized steel plating. Two common 110V light switches were inserted into an electrical box

which was mounted to the frame. These switches controlled power to the entire machine and the

motor alone. The torsion machine was then placed on a four wheel movable cart. The

completed machine is shown in figure 2.


Figure 2 - Torsion Testing Machine

E. Measurement of Torque and Angle of Twist

1. Torque Measurement

The torque applied to the test specimen was measured using a strain gauge which was mounted

to the non-rotating hub, as shown in figure 3. This hub was fabricated from 4340 steel and

consisted of a 4 inch diameter mounting flange, a 0.625 inch diameter reduced section on which

a strain gauge was mounted, a section of increased diameter used for insertion into a bearing and

a threaded section used for attaching a specimen grip. Equation (1) was used to determine the

diameter of the reduced section of the hub required to prevent yielding under the maximum

torque developed by the machine. The hub was encased in a sheet metal housing with a clear

plastic top cover which was used to facilitate viewing of the torque gauge and for positioning of

the strain gauge connector terminals.

Torque Load Cell Assy’

Power Switches

Speed Control

Potentiometer Connections

Rolling Cart

T-Slide

Potentiometer 12 Inch Sprocket

Hub Bearing

Strain Indicator


Figure 3 – Top View of Torque Load Cell Assembly

It is well known that the maximum principle stress occurring in a shaft loaded in pure torsion

occurs at a 45° with respect to the torsional axis. This principle stress is equal in magnitude to

the maximum shear stress in the shaft. Accordingly, a single element strain gauge having a 1/8

inch gauge length was mounted on the reduced section of the non rotating hub at a 45° angle in

order to record the maximum principal strain which, when multiplied by the elastic modulus of

the material, would yield a measurement of the maximum in-plane shear stress occurring in the

gauge. The torque applied to the hub, and therefore the specimen, could then be solved for using

equation (1). A single strain gauge was selected for simplicity and provided adequate resolution

for strain measurements. Multiple gauges were not used as temperature compensation would not

be needed and bending of the specimen was prevented by proper alignment of the grips. The

strain gauge was connected to a micromeasurements strain indicator having a digital display, and

the torque cell was calibrated by applying a series of torques using a torque wrench and

recording the resulting strain. This indicator was then connected to channel 1 of a digital storage

oscilloscope.

Strain Gauge

Bearing

Mounting Flange

Specimen Grip Strain Gauge Connectors


2. Angle of Twist Measurement

The angle of twist was measured using a variable potentiometer which operated off a 5V DC

power supply. The potentiometer was connected to a rotating disk which contacted the hub on

the driven sprocket, as shown in figure 4. The potentiometer was capable of making ten

complete rotations with a full range output of 5 volts. The potentiometer was fixed to a swing

arm to allow it to be moved away from the hub and manually rotated back to the zero position

before the start of a test. If the potentiometer rotation were to exceed 10 turns, the rotating disk

would simply slip on the hub and no damage to the potentiometer would result. The

potentiometer circuit was connected to channel 2 of the storage oscilloscope and was calibrated

by recording the output voltage at every 10 degrees of the fixed hub rotation over 10 revolutions

of the potentiometer.

Figure 4 – Potentiometer Assembly used for measurement of angle of twist

Rotating Hub

Potentiometer Disk

Potentiometer

Weighted Swing Arm


E. Performance

In order to quantify the performance of the machine, five samples of two common engineering

materials were tested: C1018 steel and 2014 aluminum. The average shear modulus for steel

was measured as 10.7E6 psi, or about 3% lower than the published value, and the shear modulus

for the aluminum was measured as 3.7E6 psi, or about 5% lower than the published value.

Errors in the measurements were most likely due to slight slipping of the test specimen in the

drill chucks, as test specimens observed following the tests displayed some gouging in the grip

areas. However, the machine was considered accurate enough to allow a comparison between

experimental results and published data.

F. Cost

The cost of the purchased components used in the torsion machine was $534. The DC motor and

controller, along with the 12 inch sprocket, amounted to 80% of the total costs. The drill chucks,

2 inch sprocket and chain accounted for the remainder of the costs. Materials used for the frame,

fasteners and steel plate used to cover the machine were freely available in the college machine

shop and were not included in the final cost.

III. INTEGRATION INTO THE MECHANICAL ENGINEERING CURRICULUM

The torsion machine has been integrated into the mechanical Engineering curriculum in two

ways. The mechanical engineering laboratory experience begins in the fall semester of the junior

year and continues through three consecutive semesters. The torsion test has been included in

the beginning of this sequence where students are exposed to mechanical testing. A typical

junior class size ranges from 20 to 35 students, so in order to most effectively utilize the limited


laboratory resources, a rotating schedule is used whereby teams of 4 to 6 students perform

different experiment each week. This allows each student the opportunity to become familiar

with the equipment, experimental procedures and data collection. The torsion laboratory

experience is discussed in section IV below.

The torsion machine was also utilized in the sophomore level mechanics of materials class.

Students were introduced to the machine as they studied members loaded in torsion. The

machine served as the centerpiece for the discussion of the ASTM torsion test and its procedures.

An actual ASTM torsion test was performed by the course instructor and the students observed

brittle and ductile failures of materials loaded in torsion. These results were revisited when the

students studied Mohr’s circle for pure torsion. Students were required to calculate the limiting

strength of the torque load cell, and these values were compared with values calculated by the

junior lab teams.

IV. LABORATORY EXPERIENCE

The torsion machine was used by junior mechanical engineering students to perform the ASTM

torsion test. The test began with a discussion of the goals of the testing and the ASTM test

method itself. The design of the torque load cell was then addressed and the students were

required to use the mechanics of materials theory discussed in section II.A.1 to calculate the

maximum torque which may be applied to the specimen based on the limiting strength of the

torque load cell. The students then created a calibration curve for the torque load cell by

applying a torque to the cell using a torque wrench and measuring the resulting strain from the


strain indicator box. The deviation from the theoretical values of strain were discussed and the

implications to the test method were addressed.

The potentiometer was then calibrated by recording the output voltage at predetermined rotation

angles, and a second calibration curve was created. The potentiometer disk and drive sprocket

hub were measured to develop the relationship between the potentiometer circuit output voltage

and the rotation of the hub, which correlated to the rotation of the specimen. The speed of

rotation was then measured using a stopwatch to determine the time required to complete three

revolutions of the rotating grip.

Three specimens of C1018 steel and 2114 aluminum were tested by the students. The

potentiometer voltage and the voltage measured using the strain indicator were recorded

simultaneously during the entire test using the digital storage oscilloscope. Students then used

the calibration factors determined earlier to create torque vs. twist diagrams for each material.

An average of these data for each material was then used to develop a shear stress vs. shear strain

diagram, and the slope of the linear region was used to calculate the shear modulus. Students

were then required to research the shear modulus of the test materials for comparison to the

experimental results. A comprehensive lab report was written and included a discussion of the

possible causes of discrepancies between the measured and published results, and the

implications of these discrepancies.


V. CONCLUSIONS

The torsion testing machine developed in this work has proven to be a valuable and cost effective

tool for enhancing understanding of the shear properties of materials and methods of determining

these properties. The design of the torque load cell and rotational potentiometer provided a

means of analyzing the function of the machine which in turn provided students with insights

into its function. Students indicated that this made the experiment more interesting than the

more typical experiment where the design and internal function of the testing machine is never

addressed.

Future plans involve including the machine as a component of the machine design course, as the

design of the torque load cell would fit well into the mechanics of materials review, and the

chain drive could be studied as part of the drive mechanism portion of the course. The

Biomedical Engineering Department has also expressed an interest in using the machine to study

shear failures of bone and other biomechanical materials. This would fit well within the

Biomechanical Engineering lab sequence. Finally, the project has been so successful that the

author has offered a similar senior design project which involves the design and fabrication of a

Charpy Impact testing machine. It is expected that this practical method of designing affordable

yet accurate test equipment will continue to expand the mechanical testing capabilities at

Western New England College.


REFERENCES

[1] American Society for Testing and Materials, “Standard Test Method for Shear Modulus at Room Temperature”, ASTM Designation E143-61, 1986, 1986 Annual Book of ASTM Standards, Vol. 03.01, 1986, pp 338-342.

[2] Short, Robert, “Design and Construction of a Torsion Testing Apparatus”, Senior Project, Western New England College, 2005. [3] Shigley, Joseph E. Mechanical Engineering Design. 7th ed. New York: McGraw Hill, 2004. [4] Hibbeler, R.C. Mechanics of Materials. 5th ed. New Jersey: Prentice, 2003.

AUTHOR BIOGRAPHIES Glenn Vallee, Ph.D., P.E., Assistant Professor of Mechanical Engineering Western New England College, 1215 Wilbraham Rd, Springfield, MA 01119 (ph) (413) 782-1334, e-mail [email protected] Dr. Glenn Vallee, Ph.D., P.E., is currently an Assistant Professor of Mechanical Engineering at Western New England College in Springfield, MA. Dr. Vallee currently teaches graduate and undergraduate courses in engineering mechanics, experimental mechanics and machine design, and has published in the areas of nonlinear finite element analysis, experimental mechanics and the experimental determination of dynamic material properties. Dr. Vallee received a BS in Mechanical Engineering from the University of Rhode Island in 1985 and began working for the Fastening Systems Division of the Stanley Works in East Greenwich Rhode Island soon after. Beginning as an Engineering Lab Technician, he received a number of promotions, serving as a Test Engineer, Design Engineer, Product Development Engineer and finally as the Manager of the largest Engineering Laboratory at Stanley. He received both a Masters degree and Ph.D. in Mechanical Engineering from URI while working at Stanley, and served as an Adjunct Assistant Professor of Engineering at the University of Rhode Island and the Community College of Rhode Island. In 1997, Dr. Vallee accepted a position as Director of Engineering and Quality Assurance, Worldwide, with Remington Products Company in Bridgeport CT. Dr. Vallee was the senior corporate manager responsible for customer satisfaction and developed Quality Assurance and Engineering offices in both Hong Kong and mainland China. He also managed the Quality Assurance departments and Engineering Laboratories for Remington in the UK, Australia, and the Bridgeport Manufacturing facility. He accepted the position of Assistant Professor of Mechanical Engineering at Western New England College in 2002.


Robert Short, Design Engineer GL&V USA, 141 Burke Street, Nashua, NH 03060 Robert Short received a BS in Mechanical Engineering from Western New England College in 2005 is currently is working for GL&V USA, a leading manufacturer and producer of pulp and paper processing equipment as well as several other areas such as liquid/solid separation, mining, water treatment and energy. Robert works for the engineering department designing pulp washing and handling equipment. He designed the torsion testing machine as part of his capstone senior design project under the supervision of Dr. Glenn Vallee.

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Torsion Test