A gear grinding allowance stochastic simulation model

Abstract

The paper proposes a method and technique that allow, using a minimum sample (3 units) from a batch (30 units) of real gears, to obtain stochastic information about the actual distribution of the gear grinding allowance both on the left and right flanks of the gear gaps for all gears in the batch. The proposed gear grinding allowance stochastic model is based on the representation of the distribution of the gear grinding allowance along the gear periphery as a superposition of a sinusoidal component with a random amplitude and a random component of the white noise type. The conditions for the equivalence of the stochastic characteristics of real (measured) and virtual (not actually measured) gears are formulated, namely the ratio between the amplitude of the sinusoidal component and the average amplitude of the high-frequency harmonic components of the gear grinding allowance distribution along the gear periphery. The gear grinding allowance stochastic model adjusted according to the proposed method makes it possible to predict the distribution of the gear grinding allowance on the left and right flanks of the gear gaps for a batch of gears and, taking into account the information obtained (replacing the experimental data), both evaluate the existing technology and optimize the gear grinding allowance value. As a result, it becomes possible to assess the quality of the technological process of manufacturing the gear, taking into account the effect random deformations to gear grinding allowance at the stage of their heat treatment (hardening), which is performed before the gear grinding operation. In turn, optimization of the grinding allowance (based on its actual distribution along the periphery of the gear) makes it possible to reduce both defects in burns (with increased allowance) and defects in unground teeth (with insufficient allowance).