Study on Residual Stress and Optimum Hardening Condition of Induction Hardened Gears

采用有限元电磁场分析和热传导分析相结合的方法，考虑磁导率和电阻率随温度的变化，对等截面轴类零件感应加热过程中的温度进行了计算和测量。通过计算温度与实测值的比较，验证了该有限元计算程序的有效性。考虑磁导率、电阻率、热膨胀系数和屈服应力随温度的变化，用有限元方法对等截面轴、带肩圆角的轴、厚壁圆筒内表面、蜗轮、正齿轮内外齿轮感应加热和水冷过程进行了电磁场分析、热传导分析和弹塑性应力分析。功率和频率对…过程中温度和应力的影响在此基础上，研究了感应淬火过程和淬火过程中产生的残余应力。利用本文开发的有限元程序对等截面轴类零件感应加热过程中的温度进行了计算，计算结果与实测温度吻合较好。2.高频感应加热时，带圆角的轴大直径部位的表面热量大于小直径部位的表面热量，低频加热时小于小直径部位的表面热量。3.在高频情况下，轴大直径有肩圆角部分表面的轴向和周向因感应淬火而产生的残余应力sigma_z^&lt；**&gt；和sigma_z^&lt；**&lt；**&gt；；在低频情况下，两部分的Rheta&gt；^&lt；**&gt；均为压应力。4.厚壁圆筒感应加热过程中内表面温度高于外表面温度。两面温差随功率和频率的增大而增大。5.厚壁圆筒内表面感应淬火后，内表面轴向和周向的残余应力sigma_z^&lt；**&gt；和sigma_&lt；Rheta&gt；^&lt；**&gt；随功率的增大而减小。6.蜗轮感应加热过程中齿顶齿底温差随电功率和频率的增大而增大。7.在齿轮的强度设计中，应考虑在高频、大功率加热条件下，正齿轮内外齿轮感应淬火所产生的齿面残余应力在某些情况下变为齿底拉应力。8.采用双频感应淬火方法对带肩圆角的直齿圆柱齿轮进行感应淬火是有效的。较少

Temperatures during induction heating process of a shaft with uniform cross-section were calculated by FEM electromagnetic field analysis and heat conduction analysis method, considering changes of the magnetic permeability and the resistivity with the temperature, and measured. The validity of this FEM calculation program was confirmed by comparing the calculated temperatures with the measured ones. An electromagnetic field analysis, a heat conduction analysis, and an elastic-plastic stress analysis during induction heating and water cooling processes of shafts with uniform cross-section and with shoulder fillet, of the inner surface of thick-walled cylinder, of the worm gear, and of the spur external and the internal gear were carried out by the FEM,considering changes of the magnetic permeability, the resistivity, the thermal expansion coefficient, and the yield stress with the temperature. The effects of the electric power and the frequency on the temperature and the stress during … More the induction hardening process and the residual stress due to the hardening were examined.The main results obtained from this investigation are summarized as follows.1. The calculated temperatures during induction heating process of a shaft with uniform cross-section by the FEM program developed in this investigation agree well with the measured temperatures. 2. Amount of heat of surface of the part of major diameter of the shaft with soulder fillet due to induction heating is greater in the case of high frequency but smaller in the case of low frequency than that of the part of minor diameter. 3. Residual stresses sigma_Z^<**> and sigma_<rheta>^<**> in the axial and the circumferential direction of the surface of the part of major diameter of the shaft with shoulder fillet due to the induction hardening become large compressive stresses and sigma_z^<**> and sigma_<rheta>^<**> of the part of minor diameter small tensile stress in the case of high frequency, while sigma_z^<**> and sigma_<rheta>^<**> of both parts become compressive stresses in the case of low frequency. 4. The temperatures of the inner surface during induction heating process of the inner surface of a thick-walled cylinder are higher than those of the outer surface. The difference between temperatures of both surfaces increase with electric power and frequency. 5. Residual stresses sigma_z^<**> and sigma_<rheta>^<**> in the axial and the circumferential direction of the inner surface due to induction hardening of the inner surface of a thick-walled cylinder decrease with increasing electric power. 6. The difference between temperatures at the tooth tip and the tooth bottom during induction heating process of worm gear increases with electric power and frequency. 7. It should be taken into consideration in the strength design of gear tooth that the residual stress along the tooth surface due to the induction hardening of spur external and internal gear becomes tensile stress in some cases at the tooth bottom under the heating condition of high frequency and large electric power. 8. Induction hardening by dual frequency method is considered to be valid for a shaft with shoulder fillet and a spur gear. Less