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ANALYSIS OF A SIMPLE GEARBOX

Based on a simple project, we found out the most vulnerable regions in a gearbox, considering a helical gearbox, 2-stage, supported by ball bearings and used in an agitator drive.

# Static analysis of Geared pairs:

The power transmitted between geared pairs exerts a force on the point of contact. The point at which the forces are the maximum and a general trend of the variation of forces with the tooth profile is necessary for determining backlash.

EQUIVALENT STRESS DISTRIBUTION

EQUIVALENT STRAIN DISTRIBUTION

# Static analysis of Output shaft:

This is the shaft subjected to maximum torque. Hence it is subjected to maximum bending moment due to the weight of the gears as well as torsional force due to the gear fixed to it. This is the most critical shaft and is more prone to failure.

EQUIVALENT STRESS DISTRIBUTION

EQUIVALENT STRAIN DISTRIBUTION

# Load analysis on bearings:

The bearings are responsible for housing rotating shafts. The overhang, the revolution speed and the weight of the shafts and the gears being housed influence the bearing life and chances of bearing failure.

EQUIVALENT STRESS DISTRIBUTION

EQUIVALENT STRAIN DISTRIBUTION

In the Gear analysis, the maximum stress is at the tooth profiles which are at immediate contact for a short instant. The maximum stress is less than permissible values [evident from the absence of red regions]. The other regions have lesser stresses.

Similarly, the maximum deformation is at the point of contact at the teeth. This proves that the maximum stress and strain is experienced at the instantaneous point of contact at the gear mesh.

In the output shaft, the torsional stress dominates bending stress due to output shaft and gear. The yellow regions at the bearing supports are due to the bending moment at those points due to the overhang. The blue regions at the centre regions are due to the self weight of gears and the torque of the gear.

The deformation is maximum at the centre regions, marked by red zones. This proves that the most critical region portion of the shaft is the gear portion due to torsional stresses.

In case of bearings, the stress is within permissible limits. The stress is more at the inner ring due to a less diameter. However in case of deformation, the backward region of the bearings is marked by red regions. This indicates that more balls are needed for the ball bearing, or that the ball bearings must be replaces with cylindrical rolling contact bearings.

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