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[Display omitted] • Using an existing metal worm drive dynamic model and adapt it to a polymer-metal one. • The use of generalized Maxwell model to simulate the viscoelastic behaviour of POM. • An optimization procedure based on Nelder-Mead simplex method is introduced to improve the numerical results. • The sidebands at the meshing frequency are the result of the creep phenomena occurring in the polymer gear teeth. • An accuracy of 94% is reached between numerical and experimental results. Polymer-metal worm drives are common in automotives and mechatronic systems. Despite this, there is a lack of studies on this type of transmission, especially when it comes to their dynamic behaviour. With the modern orientation of Industry 4.0 towards advancing technology in predictive maintenance, it is of a great importance to consider the study of the dynamic behaviour of this mechanism. It is first proposed to introduce an appropriate dynamic model to correctly simulate, by numerical means, the behaviour of a non-defective polymer-metal worm drive. For this purpose, it is necessary to correctly model the Gear Mesh Stiffness (GMS) of the gearing system. The GMS depends on the nature of the worm and worm gear materials. It is assumed that no deformation occurs in the steel worm, in contrast to the polymer worm whose viscoelastic behaviour must be accurately modelled. Generalized Maxwell Model (GMM) is chosen to model this behaviour. Eventually, the vibration signals from the numerical model are compared with those determined by the experimental tests. To obtain more similarities between the numerical and experimental signals, it is proposed to perform an optimisation. The procedure consists in using the Nelder-Mead simplex method to obtain a minimum residual objective function. After optimisation, an accuracy of 94% between the experimental and numerical results is achieved. [ABSTRACT FROM AUTHOR]