Experimental and Theoretical Study of Radial Force Component Effects on Spur Gear Teeth Design to Resist Failure

The Lewis equation in gear design is always used to determine spur gear tooth dimensions, i.e., face width tooth (b), based on the pushing force tangential component during engagement between gear and pinion. The radial pushing component force was neglected due to its insignificant value. The present study depends on the high radial component force along a tooth caused by the longitudinal vibration. The tooth was regarded as a cantilever. The Timoshenko equation was used to produce dynamic force. Then, the dynamic pushing component of tooth face width in the second case can be calculated. All the results were obtained from the Auto desk inventor program in the case of the Lewis equation depending on machine power. The Timoshenko equation for longitudinal vibration with different gear rotation speeds showed the same results as the theoretical ones. An inverse relationship was found between the speed increase and the tooth face width. The strain gauge technique, receiver, and transmitter (wireless) were experimentally used to record the dynamic strain readings and calculate (b). The importance of longitudinal vibration in tooth gear design in avoiding failure was highlighted.