The drive shaft system with a tripod joint is known to cause lateral vibration in a vehicle due to the axial force generated by various contact pairs of the tripod joint. The magnitude of the generated axial force, however, is related to various operating factors of the drive shaft system in a complex manner. The generated axial force due to a drive shaft system with a tripod joint and a ball joint was experimentally characterized considering ranges of operational factors, namely, the input toque, the shaft rotational speed, the articulation angle, and the friction. The data were analyzed to establish an understanding of the operational factors on the generated axial force. Owing to the observed significant effects of all the factors, a multibody dynamic model of the drive shaft system was formulated for predicting generated axial force under different operating conditions. The model integrated the roller–track contact model and the velocity-based friction model. Based on a quasi-static finite element model, a new methodology was proposed for identifying the roller–track contact model parameters, namely, the contact stiffness and force index. To further enhance the calculation accuracy of the multibody dynamic model, a new methodology for identifying the friction model parameters and the force index was proposed by using the measured data. The validity of the model was demonstrated by comparing the model-predicted and measured magnitudes of generated axial force for the ranges of operating factors considered. The results showed that the generated axial force of the drive shaft system can be calculated more accurately and effectively by using the identified friction and contact parameters in the paper.
Contact forces and transmission efficiency of an automotive ball joint constitute important design goals of an automotive drive shaft system, which affect transmission performances of the ball joint and the drive shaft system. In order to analyze contact forces and transmission efficiency more comprehensively, a multi-body dynamic model for calculating contact forces and transmission efficiency of a ball joint is established. The effectiveness of the multi-body dynamic model is validated through experiments of contact forces and transmission efficiency of a ball joint. Based on the developed multi-body dynamic model, influences of the articulation angle, the ball number and the track offset on contact forces between the ball and the cage, and between the ball and the track are analyzed. To enhance the analysis and optimization efficiency of transmission efficiency, a proxy model for the transmission efficiency loss late is established on the basic of the multi-body dynamic model. Influences of the ball radius, the articulation angle, the friction coefficient, the central angle of the cross section of the cage rib, and the contact stiffness and the force exponent of contact pairs on the transmission efficiency loss late are analyzed. Using Sobol’ global sensitivity analysis method, the sensitivity of the proxy model is analyzed and influences of various factors on the transmission efficiency loss late are further determined. According to sensitivity analysis results, the articulation angle, the friction coefficient and the force exponent are selected as design parameters, and the transmission efficiency loss late is optimized through a numerical example.
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