Chip geometry, cutting force, and elastic deformation prediction for gear hobbing
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Date
2023-08-08
Authors
Azvar, Milad
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
The machining industry is constantly challenged through increasing demands for productivity and stringent part quality requirements such as dimensional accuracy and surface quality. Physics-based models are becoming more commonly employed in the manufacturing industry for traditional machining processes like turning, milling, and drilling. By utilizing such models, machining process planners can optimize productivity while preserving or improving part quality, through virtual manufacturing of the components ahead of time via realistic simulations. In this context, cutting force prediction models are essential for machining process simulations. For traditional machining operations, where the cutter and workpiece geometries and kinematics are simple, cutting forces can be calculated via analytical equations. However, in complex processes like 5-axis milling, turn-milling and gear machining, the cutter-workpiece engagement is very complex and is best calculated using geometric CAD modelers. This engagement information allows for cutting forces along the cutting edge of the tool to be computed and summed up. Modeling the cutting forces also provides insight into the torque/power requirement, elastic deformation, vibrations, and machining stability (chatter) during the process, which are the primary factors that contribute to dimensional inaccuracies, surface location errors, and poor surface finish. By integrating these models, a comprehensive physics-based approach to machining processes can be developed, allowing for accurate simulation, prediction, and optimization of part quality. The main objective of this thesis is to establish the very first steps of such an integrated simulation environment for the gear hobbing process, by investigating the efficient prediction of cutting forces and elastic deformations.
Hobbing is a high-speed and accurate gear cutting process used extensively to produce external gears – which are essential components in power transmission, automotive, aerospace, and automation (e.g., robotics) applications. The hobging process involves feeding a rotating cutting tool (known as a ‘hob’) into a workpiece (referred to as blank gear) that is rotating while the two are meshed together, as would be in worm-gear mechanism. This results in the continuous removal of chips during the process. Unlike conventional machining operations, hobbing has complex tool and workpiece geometries, and complicated kinematics with multi-axis motions. In this thesis, a mathematical model of the hobbing kinematics is developed and validated through collected CNC signals obtained using the Siemens 840D controller of Liebherr LC500 hobbing machine.
The cutter-workpiece engagement is calculated using an efficient discrete geometric modeler in tri-dexel format. Using Delaunay triangulation and alpha shape reconstruction, the 2D cross-section of the uncut chip is created from its internal data. This cross-section is then utilized to approximate the local chip geometry along the discretized cutting edge of the tool. Each node along the cutting edge represents a generalized oblique cutting force model with specific rake and inclination angles, and principal directions (i.e., tangential, feed, and radial). At each time step, the incremental forces for the engaged cutting edge nodes are computed and ultimately integrated to obtain the total cutting forces.
Using a rotary dynamometer, the proposed cutting force model has been validated through cutting trials on a Liebherr LC500 CNC hobbing machine. The tests involved cutting of several spur and helical external gears with varying process parameters in single and two-pass processes. The model reasonably captures the overall behavior of the measured forces, min/max force envelopes and cutting strokes with the RMS error being 7-21% for roughing passes and 24-36% for finishing passes throughout the tests, which is reasonable for machining process planning. In the finishing cut, due to the forces being smaller, the signal-to-noise ratio and apparent prediction accuracy are worse.
The elastic deformation is modeled based on the static stiffness of the tooling and workpiece assemblies. The stiffness is approximated from experimentally-measured mechanical frequency response functions (FRFs). The expected elastic deformations are computed by dividing the cutting forces by the static stiffness values. The calculated deflections are then used to superpose the tool’s nominal position in the time-domain simulation of the gear machining operation, thereby gears to be ‘virtually-machined’ with errors originating both from the kinematics of the hobbing feeding process, as well as the mechanical elastic deformations. The virtually-produced gears are then measured according to the ANSI/AGMA standard for gear inspection, using the integrated gear cutting simulation and metrology software developed at the University of Waterloo, and the prediction results are compared with the quality inspection measurements taken from physically machined gears, using a GLEASON 300GMS Lead & Involute Checker. The lead deviation predictions showed good correlation, while profile deviations require further research.
Overall, this thesis has achieved a detailed physics-based model for hobbing, which focuses on the kinematics, chip geometry, cutting forces, and elastic deformation. Future research will explore error sources in the cutting force model prediction, enhancing the elastic deformation model, and developing models for vibrations and chatter.
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Keywords
gear, machining, hobbing, cutting force, gear metrology, physics based modeling