Virtual Model of Gear Shaping-Part I: Kinematics, Cutter-Workpiece Engagement, and Cutting Forces

Title Virtual Model of Gear Shaping-Part I: Kinematics, Cutter-Workpiece Engagement, and Cutting Forces
Author
Abstract

Gear shaping is, currently, the most prominent method for machining internal gears, which are a major component in planetary gearboxes. However, there are few reported studies on the mechanics of the process. This paper presents a comprehensive model of gear shaping that includes the kinematics, cutter-workpiece engagement (CWE), and cutting forces. To predict the cutting forces, the CWE is calculated at discrete time steps using a tridexel discrete solid modeler. From the CWE in tridexel form, the two-dimensional (2D) chip geometry is reconstructed using Delaunay triangulation (DT) and alpha shape reconstruction. This in turn is used to determine the undeformed chip geometry along the cutting edge. The cutting edge is discretized into nodes with varying cutting force directions (tangential, feed, and radial), inclination angles, and rake angles. If engaged in the cut during a particular time-step, each node contributes an incremental force vector calculated with the oblique cutting force model. Using a three-axis dynamometer on a Liebherr LSE500 gear shaping machine tool, the cutting force prediction algorithm was experimentally verified on a variety of processes and gears, which included an internal spur gear, external spur gear, and external helical gear. The simulated and measured force profiles correlate closely with about 3-10% RMS error.

Year of Publication
2018
Journal
Journal of Manufacturing Science and Engineering
Volume
140
Number of Pages
071007
ISSN Number
1087-1357
URL
https://asmedigitalcollection.asme.org/manufacturingscience/article-abstract/140/7/071007/473193/Virtual-Model-of-Gear-Shaping-Part-I-Kinematics
DOI
https://doi.org/10.1115/1.4039646
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