The measurement of static deflections in spur gear teeth

The problem of measuring deflection of spur gear teeth has been considered by several investigators. Attia (11) in 1959 measured tooth deflections using an unbonded strain gage as an extensometer. The combined deflection of the gear tooth and the gear body was measured. More than one tooth-pair was in contact during which of the arc of contact. Timoshenko and Baud (1) in 1926 and Wulker (5) in 1938 measured deflection of gear teeth using a dial indicator. Timoshenko and Baud proposed that a rigidly fired, tapered cantilever beam be used to approximate the actual tooth, and derived equations to predict deflection of that equivalent tooth. They were not specific in how the equations were to be applied.

Therefore, the object of the investigation was to design, develop and fabricate equipment for accurately measuring the deflection of a single spur gear tooth loaded at any point along the line of action. A secondary objective was to propose a specific manner in which to apply the equations of Timoshenko and Baud.

The test fixture designed for this investigation was used in conjunction with the load and deformation measuring circuitry of the lnstron Universal Testing Machine. The test specimens were models of the spur gear tooth machined from acrylic plastic.

The test apparatus was then used to measure deflection in test specimens which simulated various tooth number combinations.

It was concluded that the equations of Timoshenko and Baud give an accurate approximation of gear tooth reflection when applied as proposed. It was also concluded that the experimental data is in close agreement with the analytical and experimental work of Timoshenko and Baud, Walker, Weber (6) and Attia. It was concluded that gear tooth test specimens of acrylic plastic give accurate deflection data when properly generated, machined and tested.

Finally, it was concluded that the test apparatus developed for this investigation provides deflection measurements accurately and, therefore, fulfills the object of this work.