Introduction to Torsion

HNC in Engineering- Mechanical ScienceEdexcel Unit: Engineering Science (NQF L4)

Author: Leicester CollegeDate created:Date revised: 2009

Abstract: Torsion or twisting is a common concept in mechanical engineering systems. This section looks at the basic theory associated with torsion and examines some typical examples by calculating the main parameters. Further examples include determination of the torque and power requirements of torsional systems.

ContentsTorsion...........................................................................................................................................................3Transmission of power..................................................................................................................................4Credits............................................................................................................................................................5

These files support the Edexcel HN unit – Engineering Science (mechanical)

Unit outcome

Key words

Stress introduction

1.1 Stress, strain, statics, young’s modulus

BM, shear force diagrams

1.1 Shear force, bending moment, stress

Selecting beams

1.2 Beams, columns, struts, slenderness ratio

Torsion introduction

1.3 Torsion, stiffness, twisting

Dynamics introduction

2.1/2.2 Linear motion, angular motion, energy, kinetic, potential, rotation

For further information regarding unit outcomes go to Edexcel.org.uk/ HN/ Engineering / Specifications

© Leicester College 2009 This work is licensed under a Creative Commons Attribution 2.0 License.

Introduction to Torsion

Torsion

Torsion is the term used for the twisting of a structural member when it is acted upon by TORQUE so that rotation is produced about the longitudinal axis at on end of the member with respect to the other.

Torque - Fr - Twistingmoment

Fixed end

The amount of twist ( torsion) that the shaft experiences will increase as we move away from the fixed end of the shaft.

Assumptions;

The shaft has a uniform cross section

The shaft material is uniform throughout and the shear stress is proportional to the shear strain (Elastic region)

The shaft is straight and initially unstressed

The axis of twisting moment is the axis of the shaft

Plain transverse sections remain the same after twisting

General equation for torsion of cross sectioned circular shafts;

T = τ = Gθ Where T = torque (Nm)J r L J = polar 2nd moment of area

τ = Max. shear stress (MPa) r = radius of shaft (m) G = Modulus of Rigidity (GPa) θ = Angle of twist (radians) L = length of shaft (m)

Torsional stiffness - T/ θ (Applied torque per radian)

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Introduction to Torsion

Transmission of power

P = 2πnT (n = revs/sec, T = applied torque

Example 1

Calculate the torsional stiffness of a 0.5m long shaft, 15mm diameter. G = 90GPa.

Using;T = Gθ so that T/θ = GJ / LJ L

And J = πd4 / 32 for a shaft

J = (π x 0.0154)/ 32 = 4.97 x 10-9

T/θ = (90 x 109 x 4.97 x 10-9 ) / 0.5 = 894.62Nm / rad

Example 2

A solid steel shaft is 2.5m long and 40mm in diameter. The maximum stress in the shaft must not exceed 60 MPa. Determine the maximum torque that can be applied and the angle of twist at this torque (in degrees)Assume G = 80 GPa

J = (π x 0.044)/ 32 = 2.514 x 10-7

Using T = τ J r

Therefore T = J τ = (2.514 x 10-7 x 60 x 106) / 0.02 r

= 753.98 Nm

Using;

τ = Gθ (NOTE we can neglect one term) r L

θ = τ L = (60 x 106 x 2.5) / (0.02 x 80 x 109)r G

=0.09375 rads

Change radians to degrees ;

0.09375 x 57.3 = 5.372 degrees

Note – Conversion Rads to degrees - multiply by 57.3

(360/2π ) = 57.3

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Introduction to Torsion

Credits

This resource was created Leicester College and released as an open educational resource through the Open Engineering Resources project of the Higher Education Academy Engineering Subject Centre. The Open Engineering Resources project was funded by HEFCE and part of the JISC/HE Academy UKOER programme.

© 2009 Leicester College

This work is licensed under a Creative Commons Attribution 2.0 License.

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