Prediction of lobe growth and decay in centreless grinding based on geometric considerations

Harrison, A J L; Pearce, T R A

Abstract

The growth and decay of lobes during centreless grinding have been studied by previous researchers using physical tests, time-domain simulation and identification of the roots of the Laplace transform of the characteristic equation. In this paper, the authors have extended these latter two methods to generate complete stability diagrams encompassing the entire practical range of machine set-up angles. These diagrams indicate that by varying the set-up angles in a prescribed manner during grinding, rapid rounding of arbitrarily lobed components can be achieved. This is verified via time-domain simulation. Secondly, a novel and arguably more intuitive method of predicting the lobe growth and decay during centreless grinding is presented. The method considers the locations of the three points of contact between a lobed workpiece and the regulating wheel, the support plate and the grinding wheel. Axial symmetry is assumed. A unique circle can be drawn through these three points. The centre and radius of this circle vary continually as the workpiece rotates, in a manner dependent upon the workpiece's profile and the set-up angles. An above-average instantaneous radius leads, via machine stiffness, to a correspondingly larger grinding force and so to an increased instantaneous depth of cut. If this occurs when the trough of a lobe is being ground, the trough will become deeper and lobe growth will result. By contrast, if the instantaneous radius is below average when the trough is being ground, the lobe will decay. From this simple geometric consideration, the authors have calculated the rates of decay and growth of a range of numbers of lobes, across a wide range of set-up angles. The results are shown to agree well with those given using the previous methods.

Citation

Harrison, A. J. L., & Pearce, T. R. A. (2002). Prediction of lobe growth and decay in centreless grinding based on geometric considerations. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 216(9), 1201-1216. https://doi.org/10.1243/095440502760291763

• Journal Article Type: Article
• Publication Date: Oct 12, 2002
• Journal: Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture
• Print ISSN: 09544054
• Publisher: SAGE Publications
• Peer Reviewed: Peer Reviewed
• Volume: 216
• Issue: 9
• Pages: 1201-1216
• DOI: https://doi.org/10.1243/095440502760291763
• Public URL: https://uwe-repository.worktribe.com/output/1079676
• Publisher URL: http://dx.doi.org/10.1243/095440502760291763
• Additional Information: Additional Information : Research arose as a more detailed analysis of a common industrial problem. Confirms the importance in centreless grinding of machine settings on roundness and demonstrates the effect of incoming roundness errors. The modelling technique has been used to directly help one company. Courses demonstrating the benefit of the research have been run for AAVF Ltd, Bideford (A Moore) and Morgan Advanced Ceramics, Stourport-on-Severn (MMoore). A course for Delphi Diesel Systems Ltd, Stonehouse (C Tanner) demonstrated that particular lobing errors encountered in production are predicted by the theory. The model also predicts the remedies to eliminate this lobing.