Exponential and sigmoid-interpolated machining trajectories

In single-point metal turning and boring processes, a chip nest can often be created that is a hazard to part and operators alike. In order to mitigate this, a process called modulated tool path (MTP) machining was developed that superimposes a sinusoidal motion tangent to the feed direction onto the tool feed path to break chips. The sinusoidal motions are created under CNC control in the part program. In the current implementation, the sinusoidal motion is approximated as a series of short linear moves. Linear interpolation is currently used to create position and velocity commands to the axis servomotors at each control loop closure. Linear interpolation is a computationally heavy and dated method that is not well tailored to a sinusoidal trajectory. In this paper a new method called the sigmoidal interpolator is introduced that honors all physical constraints of a machining system while offering better tracking performance and lower accelerations than the linear interpolator, all while reducing the number of possible state transitions of the implemented software from approximately 17 to 4.