External force sensing is essential for enabling robot manipulators to perform force control tasks in industrial applications. However, the use of force sensors increases costs and requires additional calibration tasks, such as gravity compensation. This study proposes a sensor-less force estimation strategy to develop a virtual force estimator for n-link industrial robot manipulators. A model-based identification scheme is used to determine dynamic parameters and construct an inverse dynamics model for external force estimation. Neural learning-based semi-parametric friction compensation model further enhances joint friction estimation, mitigating uncertainties during low-speed motion. The proposed method is validated through experiments on the industrial robot manipulator HIWIN RT605–710. A surface interaction experiment demonstrated a mean absolute error of 4.7388 N of contact force estimation in the Z-direction during a 12-s contact process with an applied force of approximately 40 N using the proposed force estimator.