Abstract
The paper presents a novel geometrical stability analysis of centerless grinding that takes into account the nonlinearity associated to wheel-workpiece detachment during lobes formation. Even though the rounding mechanism in centerless grinding has been studied since more than fifty years, stability analysis has been carried out applying stability criteria for linear systems (e.g., Nyquist) on a process model that neglects actual removal “clipping” due to wheel-workpiece detachment. This model limitation is usually overcome by considering only an integer number of lobes, supporting the restriction by the claim that a non-integral number of waves is less likely to build up since the waviness must be constantly removed and replaced by a succeeding wave, which is constantly moving around the workpiece. In this work, the nonlinearity entailed by removal clipping is explicitly taken into account and, by harmonic linearization, represented by a double input describing function (DIDF). Applying the Nyquist criterion on the resulting equivalent delayed system, the paramount instability associated to a quasi-integer number of lobes emerges naturally, without requiring additional assumptions. Moreover, it is shown that the nonlinearity due to wheel-workpiece detachment does not produce a limit cycle in a reasonable operation time. The results delivered by the proposed approach are verified by numeric simulations and positively compared to the relevant literature. The proposed formulation can be easily extended to consider also machine structure dynamics, thus increasing, even in this case, the accuracy of the stability analysis provided by the standard approach.
Highlights
Centerless grinding is a broadly used manufacturing process because of its unique workpiece (WP) holding system which leads to high-productivity and high accuracy
A quasi-linear approximation can be obtained by the Describing Function (DF) approach, which is a widely known technique to study frequency response and limit cycles of nonlinear systems[23]
In this work we demonstrated that, dealing with pure geometrical instability, the formation of an integer number of lobes can be ascribed to clipping nonlinearity, occurring when the theoretical wheel/WP intersection is negative, without invoking other additional assumptions
Summary
Centerless grinding is a broadly used manufacturing process because of its unique workpiece (WP) holding system which leads to high-productivity and high accuracy. Gallego[17], Lizarralde[18], Hashimoto[19] and Madariaga[20] have applied similar approaches to guide set up and optimization of centerless plunge grinding processes, in order to reduce set-up time and avoid geometric instabilities as a function of WP height and blade angle, taking into account machine-WP dynamic interaction. These techniques lead to models that quantitatively predict the evolution of profile error for each geometric configuration[18].
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