Geometric error modeling and compensation of horizontal CNC turning center for TI worm turning

•TI worm turning method based on the variable pitch thread turning instruction is firstly proposed.•Geometric error compensation for shaped surface turning with the spatial accuracy prediction model is presented. The basic compensation method can be applied to any other turning process.•The TI worm turning and compensation method had been applied to the field of solar power generation.•Simulation and turning experiment are conducted to verify the efficient of proposed method.