轮齿有倾角的短筒柔轮谐波传动优化设计及研究
发布时间：2018-12-21 13:07
【摘要】：谐波减速器由于安装空间有限,因此柔轮的筒长尺寸越短越好。但是短筒柔轮会造成轮齿的应力增大,传动刚度下降。将刚轮轮齿做成带有倾斜角度的形式可以显著地提高轮齿之间的接触面积,从而提高谐波传动的刚度。但是目前还没有一个完整的优化设计方法,也没有对短筒柔轮的几何变形特征进行分析对照。本文结合谐波传动中的运动学分析以及包络理论得到了刚轮齿廓。分析发现轮齿啮合对脱开位置处于尖点啮合状态,接触面积小,而波发生器长轴位置的啮合状况良好。通过三维空间内柔轮几何变形分析,发现短筒柔轮轮齿在波发生器长轴处以及夹角45°处会产生较大的张角。前者是由于柔轮轮齿的径向位移导致的,后者是由于周向位移导致的。结合轮齿接触状态分析,提出了一种评价轮齿之间接触面积的评价方法,通过有限元计算结果验证,评价指标与柔轮轮齿应力沿圆周方向的分布具有一致的变化规律。利用赫兹公式推导出不考虑轮齿倾斜时谐波传动啮合力分布状态,发现波发生器长轴处轮齿会承受更大负载。参考国标进行了谐波齿轮结构设计,并借助参数化建模方法建立了三维几何模型。针对对不同筒长以及径向变形系数的CSD14以及CSD20机型进行了有限元分析。对短筒柔轮与长筒柔轮做对比,发现长筒柔轮的应力主要集中区域位于波发生器长轴处柔轮轮齿根部,而短筒柔轮的应力还有一个集中区域在轮齿接近脱开处。对不同径向变形系数0*的谐波传动进行对比,发现0*增大会减小包络区间,增大轮齿的应力。分析柔轮的模态,发现其在实际工况下不会发生共振。针对短筒柔轮在轮齿接近脱开处轮齿应力值偏大的问题,提出了一种刚轮齿廓修正方法,使得柔轮的应力值下降。结合前文的分析,以轮齿接触面积评价指标为目标函数,建立了刚轮轮齿带有倾角的谐波传动的优化设计方法。针对CSD20机型的短筒柔轮谐波减速器,在刚轮轮齿倾斜角度取为0.25°并且进行了刚轮齿廓的修正时,接触面积相比于未加倾斜角度时增大了48.8%,显著地增大了传动刚度。
[Abstract]:Because of the limited installation space of harmonic reducer, the shorter the length of the flexible wheel is, the better. But the short flexible wheel will cause the stress of the gear tooth increase and the transmission stiffness decrease. The contact area between gear teeth can be significantly increased by making rigid gear teeth with inclined angle and thus the stiffness of harmonic transmission can be improved. However, there is not a complete optimal design method and no analysis and comparison of the geometric deformation characteristics of the short tube flexure wheel. Combined with kinematics analysis and envelope theory of harmonic transmission, the tooth profile of rigid wheel is obtained in this paper. It is found that the gear tooth meshing is in the cusp meshing state and the contact area is small, while the long axis position of the wave generator is in good meshing condition. By analyzing the geometric deformation of the flexible wheel in three dimensional space, it is found that the short tube flexible wheel teeth will produce a large angle at the long axis of the wave generator and at the angle of 45 掳. The former is caused by radial displacement of flexible gear teeth, and the latter is caused by circumferential displacement. Based on the analysis of gear tooth contact state, an evaluation method is proposed to evaluate the contact area between gear teeth. The results of finite element analysis show that the evaluation index is consistent with the stress distribution along the circumference direction of the flexible gear tooth. By using Hertz formula, the meshing force distribution state of harmonic drive without considering the inclination of the gear teeth is deduced, and it is found that the gear teeth on the long axis of the wave generator will bear more load. The harmonic gear structure is designed with reference to the national standard, and the 3D geometric model is established by means of parametric modeling method. Finite element analysis was carried out for CSD14 and CSD20 models with different tube length and radial deformation coefficient. By comparing the short tube flexible wheel with the long tube flexible wheel, it is found that the stress concentration area of the long tube flexible wheel is mainly located at the root of the flexible wheel tooth on the long axis of the wave generator, while the stress of the short tube flexible wheel has a concentrated area near the gear tooth unwinding. By comparing the harmonic transmission with different radial deformation coefficient 0 *, it is found that the increase of 0 * decreases the envelope interval and increases the stress of the gear teeth. By analyzing the mode of the flexible wheel, it is found that it will not resonate under the actual working conditions. In order to solve the problem that the stress value of short cylinder flexure wheel is larger than that of gear tooth when the gear tooth is near to detach, a method for correcting the tooth profile of rigid wheel is proposed, which can reduce the stress value of flexible wheel. Based on the analysis above, the optimal design method of harmonic transmission with inclination angle for rigid gear teeth is established by taking the evaluation index of gear tooth contact area as objective function. For the short cylinder flexible wheel harmonic reducer of CSD20 model, when the angle of tooth inclination of the rigid wheel is 0.25 掳and the tooth profile of the rigid wheel is corrected, the contact area is increased by 48.8% and the transmission stiffness is significantly increased compared with the one without the angle.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TH132.43
[Abstract]:Because of the limited installation space of harmonic reducer, the shorter the length of the flexible wheel is, the better. But the short flexible wheel will cause the stress of the gear tooth increase and the transmission stiffness decrease. The contact area between gear teeth can be significantly increased by making rigid gear teeth with inclined angle and thus the stiffness of harmonic transmission can be improved. However, there is not a complete optimal design method and no analysis and comparison of the geometric deformation characteristics of the short tube flexure wheel. Combined with kinematics analysis and envelope theory of harmonic transmission, the tooth profile of rigid wheel is obtained in this paper. It is found that the gear tooth meshing is in the cusp meshing state and the contact area is small, while the long axis position of the wave generator is in good meshing condition. By analyzing the geometric deformation of the flexible wheel in three dimensional space, it is found that the short tube flexible wheel teeth will produce a large angle at the long axis of the wave generator and at the angle of 45 掳. The former is caused by radial displacement of flexible gear teeth, and the latter is caused by circumferential displacement. Based on the analysis of gear tooth contact state, an evaluation method is proposed to evaluate the contact area between gear teeth. The results of finite element analysis show that the evaluation index is consistent with the stress distribution along the circumference direction of the flexible gear tooth. By using Hertz formula, the meshing force distribution state of harmonic drive without considering the inclination of the gear teeth is deduced, and it is found that the gear teeth on the long axis of the wave generator will bear more load. The harmonic gear structure is designed with reference to the national standard, and the 3D geometric model is established by means of parametric modeling method. Finite element analysis was carried out for CSD14 and CSD20 models with different tube length and radial deformation coefficient. By comparing the short tube flexible wheel with the long tube flexible wheel, it is found that the stress concentration area of the long tube flexible wheel is mainly located at the root of the flexible wheel tooth on the long axis of the wave generator, while the stress of the short tube flexible wheel has a concentrated area near the gear tooth unwinding. By comparing the harmonic transmission with different radial deformation coefficient 0 *, it is found that the increase of 0 * decreases the envelope interval and increases the stress of the gear teeth. By analyzing the mode of the flexible wheel, it is found that it will not resonate under the actual working conditions. In order to solve the problem that the stress value of short cylinder flexure wheel is larger than that of gear tooth when the gear tooth is near to detach, a method for correcting the tooth profile of rigid wheel is proposed, which can reduce the stress value of flexible wheel. Based on the analysis above, the optimal design method of harmonic transmission with inclination angle for rigid gear teeth is established by taking the evaluation index of gear tooth contact area as objective function. For the short cylinder flexible wheel harmonic reducer of CSD20 model, when the angle of tooth inclination of the rigid wheel is 0.25 掳and the tooth profile of the rigid wheel is corrected, the contact area is increased by 48.8% and the transmission stiffness is significantly increased compared with the one without the angle.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TH132.43
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