Design of Gear

What is the Design of Gear?

Gear is defined as a toothed element that is used for transmitting rotary motion from one shaft to another with a constant velocity ratio. The concept of gear is come from the friction wheels, to increase the friction and avoid slipping between the wheels proper teeth are cut over it. The profile of the tooth should follow the law of gearing, then only we can say it as gear. General involute and cycloidal profiles are most used and suitable for gear.

A combination of two or more gears, which are arranged in such a way that power is transmitted from a driving shaft to the driven shaft, is known as a gear train. The gear train consists of the main driver known as the pinion, the main drive known as the gear, intermediate gear, and some in some cases arms. ​As the gear has the advantage that there is no slip condition, it is used in the application where accurate and precise motion is required like watches, lathe machines, etc. 

Forces Analysis in Design of Gear

As far as concerns the design of gear the first thing that comes into the picture what are the forces acting on the gear tooth. According to the gear tooth profile type, gears have a different tooth profile. As the mashing gear starts rotating and transferring the power and torque force are applied normally to the face and shank of the gear, according to their tooth profile the resultant forces are resolved into two components at a pitch point.

1. Tangetial components F_t
2. Radial components F_r

In the design of gears, we have to consider the following assumptions:

• As the point of contact moves, the magnitude of the resultant force Fn changes. This effect is neglected in the analysis. ​
• It is assumed that only one pair of teeth takes the entire load. At times there are two pairs, which are simultaneously in contact and share the load. This aspect is neglected in the analysis. ​
• The analysis is valid under static conditions, i.e., when the gears are running at very low velocities. In practice, there is a dynamic force, in addition, to force due to power transmission. The effect of this dynamic force is neglected in the analysis.

The tangential force responsible for transmitting the torque is given by

F_t  = (2 M_t)/d 

Where,

M_t = [60 * 10⁶ (kW)]/2πn    

The radial force or separating force is given by

F_r = F_t tanα

The resultant force normal to the surface is given by 

F_N = F_t/cosα

Where,

• M_t = Torque transmitted by gears
• α = Pressure angle
• d = Dimeter of gear
• n  = Speed of rotation (rpm)

Stress Analysis in Design of Gear

While doing design analysis of spur gear, we consider the teeth of gear as a cantilever beam. As we see that two forces acting on the tooth, the radial component results in the compressive stress and tangential components result in the bending stress in the gear tooth, as the magnitude of radial force is less than that of the tangential component. Therefore we considered only bending moment while doing the stress analysis in the design of gear.

In stress analysis of the design of gear following assumptions have to be considered:

• The effect of the radial component (F_r), which induces compressive stresses, is neglected.
• It is assumed that the tangential component (F_t) is uniformly distributed over the face width of the gear. This is possible when the gears are rigid and accurately machined.
• The effect of stress concentration is neglected.
• It is assumed that at any time, only one pair of teeth is in contact ​and takes the total load.

The beam strength of the gear tooth is given by the equation:

F_t = m b σ_b Y

Y = t²/(6 h m)

S_b ≥ m b σ_b Y

S_b ≥ F_t ……………(For the safe design of gears)

Where,

• S_b= Beam strength of gear tooth (N)
• σ_b = Permissible bending stress (N/mm²)
• m = Module of gear
• b = Width of gear tooth
• Y  = Lewis form factor
• h  = Effective length of gear tooth
• t  = Thickness of gear tooth 

For the safe design of gears beam strength of the gear is should be greater than  or equal to the tangential force applied to the gear