Differential Case Imbalance Calculation Using Monte Carlo Simulation

A driveline differential gear housing or diff-case is the heaviest component of a driveline that rotates at high velocities. core shift during diff-case casting is a major source of imbalance as casting cores can never be placed at the exact intended location. Core shift in the present case is defined as combination of pure translation along the parting plane and tilting about two orthogonal axes. Given the ranges of variation of these shift parameters, large numbers of random sampling of these variations are generated through Monte Carlo method where normal distribution of each of the core shift parameters is assumed. Static unbalance values of the diff-case from each of the instances of core shift is calculated using Boolean operation in MSC Adams View and a nonlinear data set is created. Next, a statistical model is created based on a neutral network-based fitting method to appropriately represent the set. The validity of the model is checked based on specific core shift cases to gain confidence on the model. Main effects plot is generated to show the key core shift parameters influencing the static unbalance. The benefit of the above automated process is the ability to predict the maximum imbalance values, its main influencers, and accordingly control the manufacturing operation, effectively. Also, dynamic unbalance is calculated at the diff-case bearing planes based on the inertia tensor of the diff-cases. This is useful in determining the mass and orientation of the balancing masses. It was found that imbalance due to translational core shift is highest. In addition, imbalance in the direction perpendicular to the diff-case window was highest followed by that in the orthogonal lateral direction along the window. The maximum dynamic unbalance value was high and above the requirement.