偏心圆柱凸轮与轴管液力连接应力和变形分析
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摘要
根据弹性力学中复势表示的应力和变形方程,选取适当复势,确定边界条件,得到了正交曲线坐标下偏心圆柱凸轮液力连接过程中的径向应力、环向应力和剪应力及径向、环向、x向和y向的变形公式。液力连接中轴管膨胀作用下,偏心圆柱凸轮壁厚最薄处外表面点环向应力系数最大为4.85。当极角大于152°时,外表面的环向应力系数大于内表面的。50 MPa液压压力作用下,内、外表面环向变形最大值分别为2.49μm和8.27μm,位于极角42°和62°处。径向和y向变形在壁厚最小处最大,分别为23.15μm和21.46μm。内、外表面x向变形最大值分别为16.59μm和12.15μm,位于极角114°和96°处。液力连接过程中偏心圆柱凸轮环向应力和变形随载荷线性增加。偏心圆柱凸轮环向应力的解析解和数值解相差较小。偏心圆柱凸轮液力连接过程中受内压作用,应力、变形计算公式为该类零件的失效分析提供理论基础。
According to the stress and deformation equations in terms of the complex potential and the boundary conditions, as for the eccentric cylindrical cam during the hydro-joining process, both the radical, hoop and shearing stresses and the radical, circular, x and y directional deformation formulas under the orthogonal curvilinear coordinates are obtained. The coefficient of hoop stress is 4.85 under the hydraulic pressure on the eccentric cylindrical cam's outer surface where the cam's wall is thickest. The hoop stress on the eccentric cylindrical cam's outer surface is larger than that on the inner surface, when the polar angle is larger than 152° under the same load. The greatest deformations on the inner and outer surfaces are 2.49 μm and 8.27 μm respectively, under the 50 MPa hydraulic pressure, at the polar angles of 42° and 62° respectively; the radial and y directional deformations are greatest at the minimμm wall thickness, with the values of 23.15 μm and 21.46 μm respectively,at the polar angles 114° and 96°. During the hydro-joining process, the hoop stress and deformation of eccentric cylindrical cam increase linearly with the load, the difference between the theoretical and numerical solutions is minor, and the eccentric cylindrical cam is subjected to the internal pressure. The derived formulas of stress and deformation provide theoretical basis for the failure analysis of such parts.
According to the stress and deformation equations in terms of the complex potential and the boundary conditions, as for the eccentric cylindrical cam during the hydro-joining process, both the radical, hoop and shearing stresses and the radical, circular, x and y directional deformation formulas under the orthogonal curvilinear coordinates are obtained. The coefficient of hoop stress is 4.85 under the hydraulic pressure on the eccentric cylindrical cam's outer surface where the cam's wall is thickest. The hoop stress on the eccentric cylindrical cam's outer surface is larger than that on the inner surface, when the polar angle is larger than 152° under the same load. The greatest deformations on the inner and outer surfaces are 2.49 μm and 8.27 μm respectively, under the 50 MPa hydraulic pressure, at the polar angles of 42° and 62° respectively; the radial and y directional deformations are greatest at the minimμm wall thickness, with the values of 23.15 μm and 21.46 μm respectively,at the polar angles 114° and 96°. During the hydro-joining process, the hoop stress and deformation of eccentric cylindrical cam increase linearly with the load, the difference between the theoretical and numerical solutions is minor, and the eccentric cylindrical cam is subjected to the internal pressure. The derived formulas of stress and deformation provide theoretical basis for the failure analysis of such parts.
引文
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[18]刘明涛,李根,李彦启,等.基于FEM的内平动分度凸轮机构中凸轮与针齿间接触分析[J].机械设计,2015,32(4):14-18.
[2] Liu G, Liu Q, Yuan S J,et al. Hydro-joining for assembledcamshaft s and its applications[C]//Verona:8th Interna-tional Conference on Technology of Plasticity, 2005:371-372.
[3] Wang C Y,Watson L T. Free rotation of a circular ring abouta diameter[J]. Journal of Applied Mathematics and Physics,1983,34(1):13-26.
[4] Ling C B. Stresses in a perforated circular ring[J]. AppliedScience Research,1974,4:99-119.
[5] Yeh Kaiyuan, Tang Renji, Zhen Jiqing. The bending of elas-tic circular ring of non-homogeneous and variable cross sec-tion under the action of arbitrary loads[J]. Applied Mathe-matic and Mechanics,1981,2(1):1-14.
[6] Chang Ming, Chang Lili. Anlysis of the eccentric cylindricalthin shell[J]. Applied Mathematic and Mechanics,1994, 15(9):887-895.
[7] Yiannopoulous A C. A general formulation of stress distribu-tion in cylinders subjected to non-uniform external pressure[J]. Jounal of Elasticity, 1999, 56:181-198.
[8]何福宝,侯宇.连续变截面弹性园环的弯曲问题[J].工程力学,1985,2(1):25-36.
[9]刘强,葛建国,刘钢,等.粉末冶金凸轮与轴管液力连接应力应变分析[J].材料科学与工艺,2007,15(5):614-618.
[10]刘强,刘钢,苑世剑,等.组合式空心凸轮轴液力连接及连接强度测试[J].内燃机工程,2007,28(5):68-70.
[11]周志方,王晓燕,顾剑锋.偏心圆柱凸轮淬火过程的数值模拟[J].机械工程学报,2011,47(12):62-67.
[12]汤任基,甄继庆.偏心圆柱凸轮多值位移问题的一般解[J].应用数学和力学,1983,4(4):671-677.
[13] Grigorenko Ya M,Vlaikov G G, Shevchenko S N. Stressesstate of hollow orthptropic noncircular cylinders under a lo-cal load[J]. International Applied Mechanics,1995,31(5):331-338.
[14] Zenkour A M. Stresses in rotating heterogeneous viscoelasticcomposite cylinders with variable thickness[J]. AppliedMathematics and Mechanics, 2011, 32(4):507-520.
[15] Ghosh B. Stresses in a long hollow cylindrically aeolotropiccircular cylinder with plane ends subjected to surface forces[J]. Applied Science Research,1971(11):113-125.
[16] Urban R L. Viscous flow between to rotating nonconcentriccylinders[J]. Applied Science Research,1971(6):105-126.
[17] Zhong RenBin, Zhou Jun, Liu WeiHao,et al. Theoreticalinvestigation of a terahertz transmission line in bipolar coor-dinate system[J]. Science China, 2012, 55(1):35-42.
[18]刘明涛,李根,李彦启,等.基于FEM的内平动分度凸轮机构中凸轮与针齿间接触分析[J].机械设计,2015,32(4):14-18.