Constant-Cutting-Force Circumferential Feed Optimization in Gear Shaping Using an Element-Based Force Model

Interstroke fluctuations in the main cutting force in gear shaping cause uneven tool loading and localized overloading. This study develops a stroke-by-stroke circumferential feed optimization method for constant-cutting-force gear shaping. An element-based cutting-force model treats the top and side cutting edges as orthogonal and oblique cutting, respectively, and a reduced-order power-law surrogate between cutting area and force enables rapid feed evaluation. A multi-objective particle swarm optimization (MOPSO) algorithm minimizes the weighted deviation from a target force, the number of effective strokes and the maximum adjacent-stroke force difference, subject to constraints on the force band, feed range, smoothness and interstroke variation. Validated against five repeated experiments, the model gives a root mean square error (RMSE) of 44.8 N over ten representative strokes and a mean absolute percentage error (MAPE) of 1.9% for the seven strokes with a theoretical force above 300 N, with the relative error growing at small uncut chip thickness. The optimized feed reduces the peak-to-valley difference, stroke number and standard deviation by 70.2%, 24.4% and 78.8%, and the measured force stays near-constant, matching theory to an RMSE of 19.65 N and MAPE of 0.69%. The method suppresses periodic force fluctuation, improves load uniformity and raises machining efficiency.