The material properties of the surface layer caused by deep rolling are closely related to the degree of strain hardening. It is of great significance to establish the prediction model of strain distribution to realize the surface strain control and improve the service performance of deep rolling parts. In this study, the analytical models of elastic-plastic strain based on the Hertz contact theory were established by two different methods. The accuracy of the analytical prediction model of elastic-plastic strain was examined by deep rolling simulation. Then, the influence of deep rolling parameters, such as rolling force, the ball diameter, and material on the elastic-plastic strain along the depth was studied and validated by the microhardness profiles along the depth. The results indicate that the analytical model established by the first method is more accurate, and the error between maximum elastic-plastic strain obtained by the first method and finite element (FE) simulation is 12.6%. The elastic-plastic strain along the depth increases with the increasing rolling force and decreases with the increasing ball diameter, and its effective depth increases with the increasing rolling force. The tungsten carbide ball generates more elastic-plastic strain than balls of the other two materials (silicon nitride and steel). In addition, the elastic-plastic strain profiles are in accordance with the change of microhardness along the depth. In a word, the model can be used to predict the strain distribution along the depth induced by deep rolling.

深滚压引起的表层材料性能与应变硬化程度密切相关。建立应变分布预测模型对实现表面应变控制、提高深轧件使用性能具有重要意义。本研究通过两种不同的方法建立了基于赫兹接触理论的弹塑性应变解析模型。弹塑性应变解析预测模型的准确性通过深轧模拟检验。然后，通过沿深度的显微硬度分布研究并验证了深轧参数，如轧制力、球直径和材料对沿深度的弹塑性应变的影响。结果表明，第一种方法建立的解析模型精度更高，第一种方法得到的最大弹塑性应变与有限元（FE）模拟的误差为12.6%。沿深度的弹塑性应变随着轧制力的增大而增大，随着球径的增大而减小，其有效深度随着轧制力的增大而增大。碳化钨球比其他两种材料（氮化硅和钢）的球产生更大的弹塑性应变。此外，弹塑性应变曲线与显微硬度沿深度的变化一致。总之，该模型可用于预测深轧引起的沿深度的应变分布。第一种方法得到的最大弹塑性应变与有限元（FE）模拟的误差为12.6%。沿深度的弹塑性应变随着轧制力的增大而增大，随着球径的增大而减小，其有效深度随着轧制力的增大而增大。碳化钨球比其他两种材料（氮化硅和钢）的球产生更大的弹塑性应变。此外，弹塑性应变曲线与显微硬度沿深度的变化一致。总之，该模型可用于预测深轧引起的沿深度的应变分布。第一种方法得到的最大弹塑性应变与有限元（FE）模拟的误差为12.6%。沿深度的弹塑性应变随着轧制力的增大而增大，随着球径的增大而减小，其有效深度随着轧制力的增大而增大。碳化钨球比其他两种材料（氮化硅和钢）的球产生更大的弹塑性应变。此外，弹塑性应变曲线与显微硬度沿深度的变化一致。总之，该模型可用于预测深轧引起的沿深度的应变分布。沿深度的弹塑性应变随着轧制力的增大而增大，随着球径的增大而减小，其有效深度随着轧制力的增大而增大。碳化钨球比其他两种材料（氮化硅和钢）的球产生更大的弹塑性应变。此外，弹塑性应变曲线与显微硬度沿深度的变化一致。总之，该模型可用于预测深轧引起的沿深度的应变分布。沿深度的弹塑性应变随着轧制力的增大而增大，随着球径的增大而减小，其有效深度随着轧制力的增大而增大。碳化钨球比其他两种材料（氮化硅和钢）的球产生更大的弹塑性应变。此外，弹塑性应变曲线与显微硬度沿深度的变化一致。总之，该模型可用于预测深轧引起的沿深度的应变分布。弹塑性应变分布与显微硬度沿深度的变化一致。总之，该模型可用于预测深轧引起的沿深度的应变分布。弹塑性应变分布与显微硬度沿深度的变化一致。总之，该模型可用于预测深轧引起的沿深度的应变分布。