Module 3. Stress

Lesson 14

14.1 Introduction

Power transmission is the movement of energy from its place of generation to a location where it is applied to performing useful work. Power transmission is normally accomplished by belts, ropes, chains, gears, couplings and friction clutches.They are subjected to twisting and bending moments.

Power is defined formally as units of energy per unit time. In SI units:

Watt = joule/second = (newton × meter) / second

14.2 Modes of Power Transmission

14.2.1 Belts

A belt is a loop of flexible material used to link two or more rotating shafts mechanically. Belts may be used as a source of motion, to transmit power, or to track relative movement. Belts are looped over pulleys. In a two pulley system, the belt can either drive the pulleys in the same direction, or the belt may be crossed, so that the direction of the shafts is opposite. As a source of motion, a conveyor belt is one application where the belt is adapted to continually carry a load between two points.

14.2.2 Ropes

Ropes were used as belts for the transmission of power before belts became common. Because of the low coefficient of friction between the rope and the pulleys, multiple loops were usually used, either as a single rope passing several times around the pulleys, or multiple ropes on the same pulleys. The advantage of multiple ropes is that if one fails, the others will continue to transmit power; however, it is difficult to get equal tension. A single rope will distribute the tension evenly, but the tension will also have to take the rope leaving the last groove on one pulley, pass it back over the other loops of the rope, and place it on the first groove of the other pulley, to keep the rope from moving off the end of the pulleys.

14.2.3 Chains

A chain drive can be used in a variety of machines such as bicycles and motorcycles. In addition to these machines, there are also many other vehicles which also have requirements for the chain drive. It is a basic way of transmitting mechanical power from one place to another. As we can see, one of its main uses is to convey power to the wheels of a vehicle.

14.2.4 Gears

A gear is a rotating machine part having cut teeth, or cogs, which mesh with another toothed part in order to transmit torque. Two or more gears working in tandem are called a transmission and can produce a mechanical advantage through a gear ratio and thus may be considered a simple machine. Geared devices can change the speed, magnitude, and direction of a power source. The most common situation is for a gear to mesh with another gear; however a gear can also mesh a non-rotating toothed part, called a rack, thereby producing translation motion instead of rotation.

14.2.5 Couplings

A coupling is a device used to connect two shafts together at their ends for the purpose of transmitting power. Couplings do not normally allow disconnection of shafts during operation.

14.3 Shafts

A shaft is a rotating machine element which is used to transmit power from power from one place to another. The power is delivered to the shafts by some tangential force and the resultant torque (or twisting moment) set up within the shaft permits the power to be transferred to various machines linked up to the shaft. In order to transfer the power one shaft to another, the various members such as pulleys, gears etc. are mounted on it. These members along with the forces exerted upon them causes the shaft is used for the transmission of torque and bending moment. The various members are mounted on the shaft by means of keys or splines.

14.3.1 Types of shafts

The following two types of shafts are important from the subject point of view

  1. Transmission shafts: These shafts transmit power between the source and the machine absorbing power. The counter shafts, line shafts, over head shafts and all factory shafts are transmitting shafts. Since these shafts carry machine parts such as pulley, gears etc., therefore they are subjected to bending in addition to twisting.
  2. Machine Shafts: These shafts from an integral part of the machine itself. The crank should be examples of machine shaft.

14.3.2 Stresses in shafts

The following stresses are induced in the shafts

  1. Shear stress due to the transmission of torque(i.e. due to torsional load)
  2. Bending stresses (tensile or compressive) due to the forces acting upon machine elements gears, pulleys est.’s well as due to the weight of the shafts itself.
  3. Stresses due to combined torsional and bending loads.

14.3.3 Maximum permissible working stresses for transmission shafts

According to American Society of Mechanical Engineers(ASME) code for the design of transmission shafts, the maximum permissible working stresses in tension or compression may be such as

  1. 112 MPa for shafts without allowances for key ways.
  2. 84 MPa for shafts with allowance for key ways.

For shafts purchased under definite physical specification, the permissible tensile stress t) be taken as 60 per cent of the elastic limit in tension el), but not more than 36 per cent of the ultimate tensile strength u). In other words, the permissible tensile stress,

σt=0.6 σel or 0.36 σu , whichever is less.

The maximum permissible shear stress may be taken as

a. 56 MPa for shafts without allowances for key ways.

b. 42 MPa for shafts with allowance for key ways.

For shafts purchased under definite physical specification, the permissible shear stress (τ) be taken as 30 per cent of the elastic limit in tension el), but not more than 18 per cent of the ultimate tensile strength u). In other words, the permissible tensile stress,

τ =0.3 σel or 0.18 σu , whichever is less.

14.3.4 Design shafts

The shafts may be designed on the basis of

  1. Strength
  2. Rigidity and stiffness.

In designing shafts on the basis of strength, the following cases may be considered:

    1. Shafts subjected to twisting moment or torque only,
    2. Shafts subjected to bending moment only,
    3. Shafts subjected to combined twisting and bending moments, and
    4. Shafts subjected to axial loads in addition to combined torsional and bending loads.

Last modified: Thursday, 18 October 2012, 4:39 AM