The induction hardening process imposes strict requirements on high-precision relative motion control. As the primary motion actuator for this process， the servo control precision of the ball screw drives directly determines the quality of the heat treatment. To address the issues of large steady-state error and high-frequency chattering in the trajectory tracking of sliding mode control （SMC）， this paper proposes a simplified-model control strategy for ball screw drives， combining time-delay estimation with a PID-nonsingular fast terminal sliding mode （PID-NFTSM） control method. Simulation results demonstrate that under the same desired trajectory， the proposed strategy achieves high-precision position tracking， with the maximum tracking error significantly reduced from 68.2 μm in traditional SMC and 28.4 μm in variable power reaching law control， down to 13.8 μm. Simultaneously， this method effectively suppresses high-frequency chattering in the control input， yielding a smoother and more continuous control signal. This study effectively enhances the servo precision and operational smoothness of the ball screw feed system， providing a reliable control-theoretic reference for high-precision induction hardening processes.