In the spring of 2011, as the final project for my Control Theory course, I developed a Simulink model to simulate the dynamics of thread-cutting on a lathe. The rationale behind this was to lay the groundwork for the eventual development of an “electronic leadscrew” for my Ames lathe, which does not have a geared connection between its headstock and its Z-axis drive. Implementing this system electronically rather than mechanically creates a far more flexible thread-cutting system, but which is also affected by a wide variety of control problems. One problem particularly of concern with the Ames lathe, which is belt-driven rather than geared, is belt slippage under both heavy cutting and normal operating conditions: the leadscrew system must respond quickly enough to belt slippage to keep thread profiles within acceptable tolerance.
My model was derived from the model developed by Ward, Ralston and Stottman in “Continuous-Time Simulation of Metal Cutting On A Lathe” (Computers & Industrial Engineering, vol. 20, iss. 3, 1991). In addition to simulating the interaction between the cutting tool and the workpiece, the model also determines resultant thread errors. The input to the lathe spindle was simulated as a constant velocity input with random smaller step inputs, to simulate belt slippage. Encouragingly, the model showed that pitch error was negligible even when a zero-feedback system was used. However, significant refinement of the model – especially in terms of accurately determining system parameters such as component masses, damping coefficients and stiffnesses – is needed before the model can be said to be representative.