A new computationally efficient model of the non-linear dynamics in harmonic drive reducers

Harmonic drives, known for their high precision and compactness, are widely used in applications such as robotics and aerospace. Due to their design, harmonic drives exhibit complex nonlinear dynamics that cannot be described through the traditional equations employed for conventional gear transmissions. Such non-linearities heavily impact both the static and the dynamic performances of the system, requiring in-depth investigation to predict and optimize its expected behavior. This paper presents an accurate and computationally efficient dynamic model able to capture non-linear dynamic effects such as the kinematic errors, hysteresis, internal friction and tooth meshing behavior. Additionally, the proposed model incorporates non-ideal factors such as the internal defects, wear, erroneous assembling and improper lubrication conditions, allowing for a comprehensive simulation of real-world conditions. Results demonstrate the model’s ability to replicate the response of the real component across diverse operational scenarios, validated against literature data. The accuracy of the results together with the reduced computational burden make this model a valuable tool for those applications requiring a good fidelity and computational efficiency, such as model-based design applications or prognostic and health management systems.