Kinematics modeling and trajectory optimization for precision grinding of variable-parameter helical grooves

End mills with variable helix angles in a certain range can suppress the cutting vibration, and the change of the core radius can improve the cutting rigidity and realize the best match between the rigidity and the chip removal performance. However, the existing process cannot accurately realize the continuous variable helix angle along the cutting edge. Moreover, the change in helix angle and core radius increases the difficulty of calculating the grinding trajectory and makes it difficult to control the rake angle accurately, and that results in the performance of this end mill cannot be accurately guaranteed. Therefore, this paper proposed a kinematics modeling and trajectory optimization method for the precision grinding of variable-parameter helical grooves. Firstly, a general grinding kinematics model is established by geometric analysis. Secondly, with the rake angle, helix angle, and core radius as constraints, models are constructed to solve the location and direction parameters of the grinding wheel. Then, the calculation and optimization method of the grinding trajectory for variable-parameter helical grooves is developed. Finally, the experimental verification is carried out and the results show that the maximum rake angle error is 0.09°, the maximum helix angle error is 0.08°, and the maximum core radius error is 0.053 mm. It indicates the grinding kinematics model and the trajectory optimization are correct. This process can also be used to grind complex helical grooves on custom cutting tools such as drills and screw taps.