Study on Residual Stress and Load Bearing Capacity of Induction Hardened Gears

采用有限元电磁场分析方法计算了圆棒感应加热产生的涡流分布和发热量，并将有限元计算结果与理论方程进行了比较，验证了该有限元程序的有效性。考虑磁导率、电阻率、热膨胀系数和屈服应力随温度的变化，采用有限元法对具有均匀截面和半圆形缺口的感应加热和水冷却轴进行了电磁分析、热传导分析和弹塑性应力分析。考察了电功率、频率、加热时间、直径和缺口对轴残余应力的影响。考虑了温度和含碳量分布对薄齿直齿齿轮表面硬化过程的影响，采用有限元法对其进行了热传导分析和弹塑性应力分析。研究了壳体深度、淬火零件（齿和孔）、轮辋厚度和标准压力角对齿轮残余应力的影响。本研究的主要结果总结如下：1。在轴的感应淬火过程中，随着电功率和频率的增加，表面温度达到淬火温度所需的时间t_h减小，表面与轴心温差T_s-T_c增大。随着轴径的增大，时间t_h增大，温差T_s-T_c减小。2. 对轴类淬火残余应力有一个最佳的感应淬火条件（功率、频率和加热时间）。3. 在加热时间较短的情况下，半圆形缺口轴的缺口底部附近因感应淬火产生的轴向残余应力sigma_z相对于直管件较小，但随着加热时间的增加，直管件的残余应力sigma_z逐渐接近于直管件。4. 直齿齿轮表面硬化在Hofer临界截面处的残余应力随轮辋厚度的增加而减小，随标准压力角的增加而增大(20 （]SY.ltoreq. [)alpha_0(] SY.ltoreq.[)27）。由于淬火，直齿齿轮的残余应力存在一个最佳壳体深度。少

Eddy current distribution and amount of heat originated from induction heating of a circular bar were caculated by means of FEM electromagnetic field analysis method, and the validity of this FEM program was confirmed by comparing the results by the FEM with those by the theoretical equatin. An electromagnetic fied analysis, a heat conduction analysis and an elastic-plastic stress analysis of the shafts during induction heating and water cooling processes with uniform cross-section and with semicircular notch were carried out by the FEM, considering changes of the magnetic ermeability, the resistivity, the thermal expansion coefficient and the yield stress with the temperature. The effects f the electric pwer, the frequency, the heating time, the diameter and the notch on the residual stress of the shaft were examined.A heat conduction analysis and an elastic-plastic stress analysis in case-hardening process of the thin-rimmed spur gear were carried out by the FEM, considering changes … More of the thermal expansion coefficient and the yield stress with the temperature and the carbon content distribution. The effects of the case depth, the parts (tooth and/or bore) of hardening, the rim thickness and the standard pressure angle on the residual stress of the gear were examined.The main results obtained from this investigation are summarized as follows.1. In the induction hardening process of the shaft, the time t_h taken for the surface temperature to reach the hardening teperature decreases with increasing electric power and frequency, and the temperature difference T_s-T_c between the surface and the center of the shaft increases. The time t_h increases with increasing diameter of shaft and the temperature difference T_s-T_c decreases. 2. There is an optimum induction hardening condition (electric power, frequency and heating time) for the residua stress of the ahaft due to induction hardening. 3. The axial residual stress sigma_z near the notch bottom of the shaft with semicircular notch due to induction hardening is fairly small compared with that of the straight part for short heating time, but approaches to sigma_z of the straight part with increasing heating time. 4. Residual stress at Hofer's critical section of the spur gear due to case-hardening decreases with rim thickness and increases with standard pressure angle (20ﾟ(〕SY.ltoreq.〔)alpha_0(〕SY.ltoreq.〔)27ﾟ). There is an optimum case depth for residual stress of the spur gear due t case-hardening. Less