76 J. Koutsoupakis et al. Fig. 2 Cross-section of a gear tooth profile. Here, the subscript i denotes the pinion (1) and driven (2) gear and j denotes the tooth pair up toNmeshed tooth pairs. In literature, there is a multitude of models which can be used to estimate the normal force between to contacting bodies, such as two gears in mesh. The general expression of the contact normal force is given as: FN =Kδ n + χδn˙δ (12) where Kdenotes stiffness, δ and ˙δ are the indentation depth between the contacting bodies and the respective indentation velocity, n is the nonlinear exponent and χis the hysteresis damping coefficient which, based on the formulation used, is given in Table 1. In the equations shown in the table, cr is the coefficient of restitution. The formulation described in Equations (1) - (11) describes the TVMS for spur gears, where the contact angle is constant for the whole width of a gear tooth. In helical gears, however, due to the helix angle of the gear teeth, the contact angle changes along the width of the gear teeth. To account for this, the slicing method is used to split the gear tooth into subsections and the stiffness is estimated for each slice individually [12]. Then, the total stiffness of a tooth pair can be estimated as the sum of the individual slice stiffnesses as: Ktot = MX i=1 Ki (13) where Ki denotes the stiffness of each slice. Table 1 Hysteresis damping factor χwith respect to the contact force model. Aiming to improve the accuracy of the MBD model developed on this work, the Covariance Matrix Adaptation Evolution Strategy (CMAES) was employed. The CMAES algorithm is a powerful population-based method, which is well suited for
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