In the machining industry, there is a constant need to increase productivity while also maintaining dimensional tolerances and good surface quality. For many classical machining operations (e.g. milling, turning, and broaching), research has been established that is able to predict the part quality based on process parameters, workpiece material, and the machine’s dynamic characteristics. This allows process planners to design their programs virtually to maximize productivity while meeting the specified part quality. To accomplish this, it is necessary to predict the cutting forces during the machining operation. This can be done using analytical equations for a lot of operations;​ however, in more recent research for complicated processes (e.g. 5-axis milling, gear hobbing), this is done by calculating the cutter-workpiece engagement with geometric CAD modellers and calculating incremental cutting forces along the cutting edge. With knowledge of the cutting forces, static deflections and dynamic vibrations of the tool and workpiece can be calculated which is one of the most prominent contributors to dimensional part inaccuracies and poor surface quality in machining. The research presented in this thesis aims to achieve similar goals for the gear shaping process.

Gear shaping is one of the most prominent methods of machining cylindrical gears. More specifically, it is the most prominent method for generating internal gears which are a major component in planetary gear boxes. The gear shaping process uses a modified external gear as a cutting tool which reciprocates up and down to cut the teeth in the workpiece. Simultaneously, the tool and workpiece are also rotating proportionally to their gear ratio which emulate the rolling of two gears. During the beginning of each gear shaping pass, the tool is radially fed into the workpiece until the desired depth of cut is reached. In this study, the three kinematic components (reciprocating feed, rotary feed, and radial feed) are mathematically modelled using analytical equations and experimentally verified using captured CNC signals from the controller of a Liebherr LSE500 gear shaping machine.

To predict cutting forces in gear shaping, the cutter-workpiece engagement (CWE) is calculated at discrete time steps using a discrete solid modeller called ModuleWorks. From the CWE in dexel form, the two-dimensional chip geometry is reconstructed using Delaunay triangulation and alpha shape reconstruction which is then used to determine the undeformed chip area along the cutting edge. The cutting edge is discretized into nodes with varying cutting directions (tangential, feed, and radial), inclination angle, and rake angle. If engaged in cutting during a time step, each node contributes an incremental three dimensional force vector calculated with the oblique cutting force model. Using a 3-axis dynamometer, 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 very closely (about 3-10% RMS error) with the most error occurring in the external helical gear case. These errors may be attributable due to rubbing of the tool which is evident through visible gouges on the finished workpiece, tool wear on the helical gear shaper, and different cutting speed than the process for which the cutting coefficients were calibrated. More experiments are needed to verify the sources of error in the helical gear case.

To simulate elastic tool deflection in gear shaping, the tool’s static stiffness is estimated from impact hammer testing. Then, based on the predicted cutting force, the elastic deflection of the tool is calculated at each time step. To examine the affect of tool deflection on the final quality of the gear, a virtual gear measurement module is developed and used to predict the involute profile deviations in the virtually machined part. Simulated and measured profile deviations were compared for a one-pass external spur gear process and a two-pass external spur gear process. The simulated profile errors correlate very well with the measured profiles on the left flank of the workpiece, however additional research is needed to improve the accuracy of the model on the right flank. Furthermore, the model also serves as a basis for future research in dyamic vibrations in gear shaping.

The above-mentioned algorithms have been implemented into a tool called ShapePRO (developed in C++). The software is meant for process planners to be able to simulate the gear shaping operation virtually and inspect the resulting quality of the gear. Accordingly, the user may iterate the process parameters to maximize productivity while meeting the customer’s desired gear quality.