This paper proposes a CAE-based method to predict the maximum load at which bolts start to loosen. The qualitative validity of this method was confirmed using the fastening bolts between the differential case and ring gear.

In general, the differential case and ring gear are fastened with bolts. Therefore, it is essential to estimate the maximum load of bolt loosening when designing these bolts. Moreover, prototypes found that tightening bolts are more likely to loosen as the thickness of the differential case or ring gear decreases and becomes easier to deform. This indicates that the deformation of the differential case and ring gear must be considered in bolt design. However, predicting the maximum load is relatively difficult because the behavior of both the screw and the contact surface between the differential case and ring gear is complicated.

In contrast, recent transmissions require further weight reduction without sacrificing reliability. Consequently, a method of predicting the maximum load of bolt loosening is required.

First, this paper describes a CAE model for estimating the pressure and friction generated at the contact surface between the differential case and ring gear, as well as at the screw surface and bolt seating surface. Furthermore, a method for determining bolt loosening is described that incorporates the pressure and friction on the bolt seating surface into friction circle theory. This method was used to derive the maximum load of bolt loosening. In addition, it was also confirmed that the results qualitatively agree with actual cases of bolt loosening.

Second, this paper identifies the relative sliding of the screw surface and contact surface when the load increases. In this case, it was verified that the sliding on the contact surface between the differential case and ring gear induces relative sliding of the screw, followed by sliding of the bolt bearing surface and loosening of the bolt.

Finally, this paper refers to design guidelines for reducing the weight of the differential case using an experimental design method. Certain ribs cause non-uniform bolt bearing surface pressure distribution, which likely affects bolt loosening.

Through this research, the validity of the method was confirmed and the bolt behavior was clarified when a differential case and ring gear are loaded in one direction. Based on these results, it should be possible to apply this method to more complicated load cases in the future.

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