Torsion Report

TORSION TEST

1. OBJECTIVES

To understand and determine the elastic, plastic and yielding behaviours of three (3) different materials when subjected to twisting moment or torsional load (torque).

1. INTRODUCTION

The purpose of a torsion test is to determine the behaviour a material or test sample exhibits when twisted or under torsional forces as a result of applied moments that cause shear stress about the axis. Measurable value include the modulus of elasticity in shear, yield shear strength, torsional fatigue life, ductility, ultimate shear strength, and modulus of rapture in shear. Torsion test is not widely accepted as much as tensile test.

        The three common forms that torsion testing take include failure, proof and operational. A torsion test for failure requires that the test sample be twisted until it breaks and is designed to measure the strength of the sample. A proof test ids designed to observe the material under a specified torque load over a test period of time. Finally operational testing is measures the materials performance under the expected service conditions of its application. All of three forms of tests may be performed with either torsion only loading or a combination of torsion and axial (tension or compression) loading depending upon the characteristics to be measured.

1. THEORY

Torsion refers to the twisting of a shaft loaded by a torque, also commonly known as twisting couples or twisting moments. For example, in the generation of electricity shafts carry torque from the turbine to the generator. In this example the shaft is loaded by two equal and opposite forces P acting on a bar (moment arm) perpendicular to the shaft. The moment generated by these forces is sometimes called a couple. The magnitude of the moment due to this couple is given by P times d, where P is the applied forces and d is the distance between the lines of action of the forces. This twisting couple is also called the 'Torque' or 'Twisting Moment'. In the left-hand figure the torque is shown as a loop with an arrow depicting its direction. In the right hand figure the torque is shown as a vector moment.

The derivation and interpretation of the theory of torsion of circular shafts can be reviewed by looking at a small section of length dx of a circular shaft under torsion. During twisting, one end of the shaft will rotate about the longitudinal axis with respect to the other end. The magnitude of this rotation is measured in terms of the angle in radians by which one end rotates in relative to the other. This is called 'angle of twist' and denoted by ∅ (radian).

For a linear elastic material, using Hooke's Law, we can write the relationship between shear stress , Modulus of Rigidity, G and shear strain  as:[pic 1][pic 2]

                                                           (1)[pic 3]

The shear strain , on a small area of a material situated at a distance  from the centre  to be:

                                                             (2)[pic 4]

Thus using Hooke's Law, shear stress can be expressed as:

                                                           (3)[pic 5]

The torque, T is found by integrating over the cross section the product of shear stress, τ and the distance, ρ from the center of the shaft.

                                                  (4)[pic 6]

Using shear stress from previous relations, we get

                         (5)[pic 7]

Where   is called the polar moment of inertia for the solid bar specimen.[pic 8]

Using the Eq.(5), the relation between the twist and the torque is given by:

                                         (6)[pic 9]

Generally, based on the torsion theory and combining Eqs. (3) and (6) the following torsion formula may be obtained;

                                 (7)[pic 10]

1. PROCEDURES

1. To fit the Torsiometer

1. A hexagon tool has been used to loosen the hexagon fixings to the specimen
2. The distance from the holder has been set to the measurement arm as approximately 3 mm and the large locking ring has was tightened.
3. The specimen was fitted to the torsion machine.

1. Mount the specimen

1. The specimen was mounted between the loading device and the torque-measuring unit.
2. 13 mm of hexagon socket has been used.
3. The shifting specimen holder of the load device has been make sure in the mid position.
4. There is no pre load on the specimen.
5. Both indicators was set up at the input and the output shaft of the worm gear to zero.

1. Loading the specimen

1. The ‘ Peak Holder ‘ button of the Load Meter Hs been press so that it records the maximum torque in the test.
2. The hand wheel at the input of the gear was turned clockwise to load the specimen.
3. The specimen was stresses in its elastic region only, so the angle was increases twist in 0.50 radian steps up to a maximum of 0.80 radians.
4. The torque was recorded at each step.

1. Continue the experiment until break

1. The torsiometer was removed.
2. The angle of twist was increases twist in small steps of 1 degree and the data has been recorded.
3. After 30 degrees the angle size was increases between measurements to larger increments until the specimen break.
4. The equipment will return to the original condition.

5.0        RESULTS

RESULTS

Specimen Type                         :         Brass

Socket Size                        :        13 mm

Initial Dimension of specimen

Original Length, Lo                        :        74.45 × 10-3 m[pic 11]

Average Original Diameter, Do        :        6.018 × 10-3 m

Average Original Area, Ao                :        0.0293 × 10-3 m2

Final Dimension of specimen

Final Length, Lf                        :        79.933 × 10-3 m[pic 12]

Average Final Diameter, Df        :        5.94 × 10-3 m