Engineering Science

Guidance Notes

TORSION KIT ES5

© TecQuipment Ltd 2012

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DB/bw/1121

Guidance Notes Page 1 of 24

 ES5 Guidance

Guidance Notes Page 2 of 24

 Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

The ES5 Kit - What is it and what can it do? . . . . . . . . . . . . . . . . . . . . 6

List of Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6

General Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

The Work Panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7

Weights, Masses, Weight Hangers and Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8
Fitting a Specimen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9
Zeroing the Rotating Chuck . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10
Testing The Zero . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10
Accurate Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11

Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13
Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15
Factors that Affect Twist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16
The Torsional Load or "Torque" T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17
The Shear Modulus G . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20
The Shaft Dimensions and J . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21
Shaft Length L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22
Relationships - Angle of Twist and Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
Relationships - Twist and Modulus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
Relationships - Twist and J . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24
Relationships - Twist and Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24

Guidance Notes Page 3 of 24

Guidance Notes Page 4 of 24
Introduction ES5 Guidance

Introduction
These Guidance Notes introduce you to the theory for a set of experiments in an engineering science topic.
You fit different parts of your kit to a Work Panel to do an experiment. Figure 1 shows a typical experiment.

Work Panel

Parts of
your Kit

Figure 1 A Typical Experiment

Each kit can do one or more experiments and each experiment has Worksheets that tell you how to do the
experiment. You must use the Worksheets with the Guidance Notes as they:

• Introduce the parts in the kit, and list the experiments that it can do.

• Give you important information you need to do the experiments or complete your Worksheet.

Your tutor may decide to ask you to do all the experiments or just a few. You must be sure what you need
to do. To help you, Table 1 shows a list of the experiments for your kit.

24 Guidance Notes Page 5 of 24

The ES5 Kit - What is it and what can it do? ES5 Guidance

The ES5 Kit - What is it and what can it do?

This kit helps you understand rods and shafts. It shows what they are, what factors affect how much they
twist, and why this is important to scientists and engineers.

The kit comes in a plastic box with a lid and contains all the parts you need to do the experiments shown in
Table 1. Refer to the Parts List in your kit to see what parts are included.

Your tutor may decide to ask you to do all the experiments or just a few. You must be sure what you need
to do.

List of Experiments

Does my teacher need

me to do this Have I got the
Experiment experiment? Worksheet?

1. Torque and Diameter

2. Specimen Rod Material

3. Specimen Rod Length

Table 1 List of Experiments

Guidance Notes Page 6 of 24

General Notes ES5 Guidance

General Notes
The Work Panel

Thumbscrews

Supports

Figure 2 The Work Panel Mounted in Two Typical ways (Portrait and Landscape)

The Work Panel mounts on its Supports in different ways as needed by each experiment. The Worksheets
show you which way TecQuipment recommends you to fit the Supports but you may find an alternative
that fits better on your desk. To change how the Supports hold the Work Panel, ask your Teacher or a
classmate to help you hold the Work Panel while you change the Supports around. However you mount
the Work Panel, you must always use two Thumbscrews and Thumbnuts to hold each Support to the Work
Panel.

24 Guidance Notes Page 7 of 24

General Notes ES5 Guidance

Weights, Masses, Weight Hangers and Forces

Figure 3 A Weight Hanger

The masses supplied with the Engineering Science Kits have markings in grams (or grammes). For your
calculations, you use the unit of force (Newton - N) caused by the pull of gravity (downward) on the
masses.

1 kg = 9.81 N or 100 g = 0.98 N

Note: Each weight hanger itself weighs 10 g, so you only need to add 9 x 10 g masses to get 100 g.

Weights Force (N)

1 x 10 g = 10 g 0.098

10 x 10 g = 100 g 0.98

20 x 10 g = 200 g 1.96

30 x 10 g = 300 g 2.94

40 x 10 g = 400 g 3.92

50 x 10 g = 500 g 4.90

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General Notes ES5 Guidance

Fitting a Specimen

Figure 4 Fitting a Specimen

1. Use the hexagon tool supplied to loosen the screws of the fixed and rotating chucks.

2. Carefully slide the specimen into the right hand side of the Fixed Chuck.

3. Push it fully through the Fixed Chuck and into the Rotating Chuck as far as it will go.

4. Tighten the screws of the Fixed Chuck.

5. Zero the Rotating Chuck as described in Zeroing the Rotating Chuck.

24 Guidance Notes Page 9 of 24

General Notes ES5 Guidance

Zeroing the Rotating Chuck

Before you start your experiment, you must set the Rotating Chuck assembly to zero degrees (see Figure
5). To do this:

1. Fit the specimen as shown in Fitting a Specimen.

2. Loosen the screws at the Rotating Chuck, so the Torque Arm can move without twisting the specimen.

3. Carefully align the 0° mark on Torque Arm scale with the mark on the transparent cursor.

4. Hold the Torque Arm steady at 0° while you tighten the screws of the Rotating Chuck.

5. Now if necessary, you can use the small thumbscrews that hold the transparent cursor to adjust its
position even more accurately.

Figure 5 To Set the Scale on the Rotating Chuck to Zero

Testing The Zero

Put the maximum load that the experiment suggests onto the cord for few seconds, then remove the load
and check that the mark on the cursor still shows 0°. If not, then the specimen has probably slipped in one
of the chucks. You will then need to rezero the Rotating Chuck and retighten the screws on both chucks.

Guidance Notes Page 10 of 24

General Notes ES5 Guidance

Accurate Results
For best results:

• Do not rush your experiment.

• Double-check each reading.

• Repeat the experiment if you are not sure of your results.

• Unless the instructions say otherwise, gently tap the Work Panel before taking a reading.
Sometimes, mechanical parts ‘stick’ against each other (caused by friction). This is often called
‘stiction’ or static friction. Tapping the Work Panel helps to reduce this.

Do not expect your results to be exactly as shown in the theory. Theory always shows
‘perfect’ or ‘ideal’ results, based on perfect scientific conditions. Your ‘actual’ results will be
slightly different to theory, based on the accuracy of the equipment and how carefully you
do your experiment.

You may learn more about your experiments by making and finding mistakes than getting
things right first time!

24 Guidance Notes Page 11 of 24

General Notes ES5 Guidance

Guidance Notes Page 12 of 24

Theory ES5 Guidance

Theory
Introduction
Torsional or twisting loads can appear in many structures and parts of machines, sometimes by design or
as a by-product of some loading on the structure that causes a twisting action. Before structures were as
well understood as they are today structural failure, due to unexpected twisting loads caused problems and
accidents, especially in the early days of aeroplanes and their wings.

Even a simple looking aeroplane wing is a relatively complicated structure and far beyond what this kit aims
to study. This kit studies simple round section members subject to a twisting action. This needs to be
understood before you study more advanced structures (like aeroplane wings). These simple members are
often called shafts or rods. Although what the kit studies is a simple example, it is very commonly found in
all sorts of machines and mechanisms.

Figure 6 Twisting a Rod

Figure 7 Using the Twist of a Shaft as a Spring - a Torsion Bar Suspension in a Car

24 Guidance Notes Page 13 of 24

Theory ES5 Guidance

As with any load carrying part or structure, it is unacceptable for the part to break by applying loads we
expect them to carry. What is also equally unacceptable is that they should deflect too much when we
apply the loads. In the case of a drive shaft, it can be undesirable for the input and output of the shaft to
be at a significantly different angle dependant on the load. However, in some shafts, the twist may be
desirable - for example a twisting rod or shaft is a form of spring. In any case it is important to know how
to predict the angle of twist for a given load and what factors affect the amount of twist.

If you have used other Engineering Science kits, you may have looked at the deflection of beams and used
the ES4 Deflection of Beams and Cantilevers kit. There are a lot of similarities between the ES4 and ES5 kits
as you will see.

Guidance Notes Page 14 of 24

Theory ES5 Guidance

Notation

Symbol Meaning Units

 Angle of Twist Radians

R or r Radius m

G Modulus of Rigidity Pa or N.m-2

J Polar Second Moment of Area m4

T Torque Nm

L Length m

m Mass g

W Load N

Table 2 Notation

Degrees and Radians

Figure 8 The Radian

Many trigonometrical calculations use the angular unit of a ‘degree’, but a degree is not a scientific unit.
Instead, scientists and engineers use the SI Derived unit of a ‘radian’.

The radian is a part of a circle which as an arc length equal to the radius of the circle. It is approximately
equal to 57.3 degrees.

24 Guidance Notes Page 15 of 24

Theory ES5 Guidance

Factors that Affect Twist

For the simple case in Figure 6 there are four main factors that affect twist:

1. The torsional load - or what is called the ‘torque’

2. The material the shaft is made from

3. The shaft diameter

4. The length of the shaft

These four factors combine together to form the torsion equation for a circular shaft:

T
--- = G
------- (1)
J L

This can be rearranged to make the angle of twist the subject of the equation as this is the most important
variable during our experiments.

LT
 = ------
- (2)
JG
Worked Example:

T = 0.098 Nm
L = 0.34 m
J = 9.07 x 10-12 m4
G = 38 GPa (brass specimen) = 38000000000 Pa or 38 x 109 Pa

So:

0.34
 = 0.098  ------------------------------------------------------------
– 12 9
 9.07  10   38  10 

and

0.34
 = 0.098  -------------------
0.34466

and

 = 0.098  0.986

So  = 0.0966 radians or 0.1 radians

0.1 x 57.3 = 5.7 degrees

Guidance Notes Page 16 of 24

Theory ES5 Guidance

The Torsional Load or "Torque" T

Torque is simply a twisting force. It is the product of a force and the distance from that force to a pivot.
This is the same definition as a moment, but the term torque is often used instead of moments when we
talk about shafts. Figure 9 shows this in simple form and Figure 15 shows this as applied to the ES5 kit.

Torque T = Torque Arm Length x W

Figure 9 Torque

The torsion equation used in the experiments is only applicable for rods or shafts that are in pure torsion.
It will not work for rods that are being bent and twisted at the same time, so you must be careful how you
apply torque to the shaft.

Torque applied to the end of the shaft as shown in Figure 10 would also create an additional force tending
to bend the shaft.

As shown in Figure 11 we could have two torque arms, putting the shaft in pure torsion. But, it could still
bend, either by an imbalance of the force, or the position of the end. This is also quite difficult to do
practically.

Figure 10 Bend and Torsion

Figure 11 Two Torque Arms

24 Guidance Notes Page 17 of 24
Theory ES5 Guidance

By using a rotating bearing that restricts the vertical reaction but allows rotation of the shaft end, the shaft
cannot be bent, and a simple arm can apply the torque. This is how the torque arm on the equipment is
designed.

Figure 12 Using a Bearing

Figure 6 shows the rod with an equal and opposite torque at each end causing the twisting action. Since
this reaction is equal and opposite it is simpler to hold the end of the rod in an encastré (built in) fixing.

This can be represented diagrammatically as in Figure 14 which may look familiar to you if you have looked
at the ES4 Deflection of Beams kit.

Figure 13 Twisting Equivalent

Figure 14 Idealised Diagram

Guidance Notes Page 18 of 24

Theory ES5 Guidance

Torque Arm on the ES5 Kit

Figure 15 Torque and the Torque Arm

In the kit, you calculate the torque from the product of the torque arm length and the downward force
from the weight. So, from Figure 15:

T = Force (in Newtons) x Torque Arm Length (in metres)

or T = W x 0.1

From this, you can see the torque is in Newton Metres (Nm).

Figure 15 shows the torque arm length is the distance (100 mm) from the centre of the rod to the position
of the downward pull from the weights. It also shows that the torque arm shape keeps a constant radius
through the angles of twist printed on its scale.

Worked Example:

Weight = 100 g = 0.98 N

so T = 0.98 x 0.1 = 0.098 Nm

24 Guidance Notes Page 19 of 24

Theory ES5 Guidance

The Shear Modulus G

The material property used in the torsion equation is its stiffness. Different materials have different
stiffness.

Shear modulus is the stiffness for a material in torsion. It is the ratio of shear stress to shear strain. When
bending a beam, one side is in tension and the other is compression. If you have used the ES4 kit, you will
have used Young's Modulus in the bending Equation. In torsion, instead of bending, the material is subject
to ‘shear’. This is where the material tries to slide over itself. You can visualise this by using a pack of cards.

Figure 16 Pushing a Pack of Cards

How the shear appears in the shaft is quite hard to visualise but your tutor may have some simple models
to show this.

In exactly the same way as Young's Modulus is a constant until we apply too much load to a part and it
deforms (bends or stretches) permanently (Hookes law), the shear modulus is the same until we apply too
great a torque and the part says permanently twisted.

The shear modulus for a particular metal alloy is fairly constant within a relatively small band of tolerance,
even though the strengths of the alloy might be dramatically different. Table 3 shows the textbook values
used for the shaft materials in the kit.

Material Value
(GPa or GN.m-2)

Aluminium 25.5

Brass 38.0

Mild Steel 79.6

Table 3 Nominal Textbook Values for Modulus of Rigidity

Guidance Notes Page 20 of 24

Theory ES5 Guidance

The Shaft Dimensions and J

It is fairly intuitive that if you were to take a thin rod or shaft and twist it, that it would twist more than a
larger diameter one of the same material and length. So, the larger diameter rod would be stiffer.

Figure 17 Twisting Rods of Different Diameter

However, it is less intuitive that this stiffness is not simply proportional to the diameter, it is in fact
proportional the diameter to the power of four.

This dimensional property of the rod is called its Polar Second Moment of area "J". This is similar to the
second moment of area "I" for a beam, but uses different variables, shown in Equation 3:

4
J = D
---------- (3)
32
Worked Example:

D = 3.1 mm (0.0031 m)
4
J = 3.142  0.0031
-------------------------------------- So J = 9.07 x 10-12 (m4)
32

NOTE Note that in this equation, the diameter multiplies to the power 4. If you make
an error measuring the diameter, the error also gets multiplied to the power 4.

24 Guidance Notes Page 21 of 24

Theory ES5 Guidance

Shaft Length L
The final factor is the length of the rod or shaft. The experiments use the distance between the point of
torque application and the fixed end. Again it is fairly intuitive that a shorter rod or shaft will be stiffer and
twist less than a longer one of the same diameter and material.

Figure 18 Twisting Long and Short Rods

Guidance Notes Page 22 of 24

Theory ES5 Guidance

Relationships - Angle of Twist and Load

W

Figure 19 Twist and Load Relationship

As Figure 19 shows, for the torsion tests used in this kit, any charts of twist against load should give linear
results (a straight line). The line should pass through the origin (0, 0) of the chart. This shows that when
everything else remains constant in the torsion equation, the angle of twist is directly proportional to
load.

Relationships - Twist and Modulus

1
  ----
G

Figure 20 Deflection Modulus

As Figure 20 shows, for the torsion tests used in this kit, charts of twist against the inverse of the Modulus
of Rigidity value should give linear results (a straight line). The line should pass through the origin (0, 0) of
the chart. This shows that when everything else remains constant in the torsion equation, the angle of
twist is directly proportional to the inverse of the Modulus of Rigidity.

24 Guidance Notes Page 23 of 24

Theory ES5 Guidance

Relationships - Twist and J

1
  ---
J

Figure 21 Twist and 1/J Relationship

As Figure 21 shows, although you cannot test for it with the kit (as specimen diameters are constant) a
chart of twist against 1/J should give linear results (a straight line). The line should pass through the origin
(0, 0) of the chart. This shows that when everything else remains constant in the torsion equation, the
angle of twist is directly proportional to 1/J.

Relationships - Twist and Length

L

Figure 22 Twist and Length Relationship

As Figure 22 shows, for the torsion tests used in this kit, any charts of twist against length should give linear
results (a straight line). The line should pass through the origin (0, 0) of the chart. This shows that when
everything else remains constant in the torsion equation, the angle of twist is directly proportional to
length.

Guidance Notes Page 24 of 24