Based on the fractal theory,a normal contact stiffness model is established.In the model,the asperity is initially in elastic deformation under contact interference.As the interference is increased,a transition from e...Based on the fractal theory,a normal contact stiffness model is established.In the model,the asperity is initially in elastic deformation under contact interference.As the interference is increased,a transition from elastic to elastoplastic to full plastic deformation occurs in this order.The critical elastic interference,the first elastoplastic critical interference and the second elastoplastic critical interference are scale-dependent.According to the truncated asperity size distribution function,the relations between the total normal contact stiffness and the total contact load are obtained.The results show the total normal contact stiffness depends on the range of frequency indexes of asperities.The normal contact stiffness in elastic deformation is major contribution to the total normal contact stiffness.When the first six frequency indexes are less than the critical elastic frequency index,the dimensionless load-stiffness relation approximately isF^*r^(K^*r)^3.When the initial frequency index is greater than the critical elastic frequency index,the dimensionless load-stiffness relation approximately isF^*r^K^*r.The comparison between the theoretical results and the experimental results indicates that the theoretical results are consistent with the experimental data;therefore,the present fractal model of contact stiffness is reasonable.展开更多
<span style="font-family:Verdana;">This paper represents</span> <span style="font-family:Verdana;">a continuation of</span><span style="color:#C45911;"> <...<span style="font-family:Verdana;">This paper represents</span> <span style="font-family:Verdana;">a continuation of</span><span style="color:#C45911;"> </span><span><span style="white-space:nowrap;"><a href="#ref1" target="_blank">[1]</a></span><span style="font-family:Verdana;"> and</span> <span style="white-space:nowrap;"><a href="#ref2" target="_blank">[2]</a></span></span><span style="font-family:Verdana;">. </span><span style="font-family:Verdana;">Here, we consider the numerical analysis of a non-trivial frictional contact problem in a form of a system of evolution nonlinear partial differential equations. The model describes the equilibrium of a viscoelastic body in sliding contact with a moving foundation. The contact is modeled with a multivalued normal compliance condition with memory term restricted by a unilateral constraint and is associated with a sliding version of Coulomb’s law of dry friction. After a description of the model and some assumptions, we derive a variational formulation of the problem, which consists of a system coupling a variational inequality for the displacement field and a nonlinear equation for the stress field. Then, we introduce a fully discrete scheme for the numerical approximation of the sliding contact problem. Under certain solution regularity assumptions, we derive an optimal order error estimate and we provide numerical validation of this result by considering some numerical simulations in the study of a two-dimensional problem.</span>展开更多
Based on the space meshing theory, it is proven that non-involute beveloid gears meshing with crossed axes can achieve to line contact. The meshing equation and tooth profile equation are presented by using meshing th...Based on the space meshing theory, it is proven that non-involute beveloid gears meshing with crossed axes can achieve to line contact. The meshing equation and tooth profile equation are presented by using meshing theory. A theoretical way is put forward to calculate the induced normal curvature along the normal direction of the contact line.展开更多
A new type of worm gearing, rolling cone enveloping worm gearing possessing high virtues of transmission, is presented. With theoretical deduction, numerical calculations and parameter analyses, the effect of prime pa...A new type of worm gearing, rolling cone enveloping worm gearing possessing high virtues of transmission, is presented. With theoretical deduction, numerical calculations and parameter analyses, the effect of prime parameters to the character of instantaneous contact line are obtained. The ranges of the main parameters are selected reasonably. It provides the theoretical basis for the structure design and application of this new type of worm gearing.展开更多
典型的无网格方法采用移动最小二乘函数(moving least squares,MLS)作为近似函数,但由于MLS不具备Kronecker delta函数性质,本质边界施加困难。LRPIM是采用径向基点插值形函数的无网格方法,本质边界条件无需特殊处理,可以直接施加,在保...典型的无网格方法采用移动最小二乘函数(moving least squares,MLS)作为近似函数,但由于MLS不具备Kronecker delta函数性质,本质边界施加困难。LRPIM是采用径向基点插值形函数的无网格方法,本质边界条件无需特殊处理,可以直接施加,在保持高精度的前提下提高计算效率。将LRPIM应用于机械结合面接触问题的计算。根据位移连续条件推导了含接触特性的线性互补方程,建立了基于LRPIM的计算模型,采用线性互补算法利用数值积分计算了几种典型的接触问题,得到了接触面压力分布和接触变形,分析了插值函数形状参数和积分域尺寸对计算结果的影响。研究结果表明,插值函数形状参数α_(c)对接触力的影响较小,而形状参数q取-0.5~1.2时有较好的收敛效果;积分域无量纲尺寸a_(qx)、a_(qy)大于1.5时计算结果开始收敛,大于2.5时出现发散现象,取值2.1时收敛效果最佳。将计算结果与已有结果进行比较,表明本研究方法有较高的求解精度。展开更多
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.51105304,51475364)the China Postdoctoral Science Foundation funded project(Grant No.2014M552467).
文摘Based on the fractal theory,a normal contact stiffness model is established.In the model,the asperity is initially in elastic deformation under contact interference.As the interference is increased,a transition from elastic to elastoplastic to full plastic deformation occurs in this order.The critical elastic interference,the first elastoplastic critical interference and the second elastoplastic critical interference are scale-dependent.According to the truncated asperity size distribution function,the relations between the total normal contact stiffness and the total contact load are obtained.The results show the total normal contact stiffness depends on the range of frequency indexes of asperities.The normal contact stiffness in elastic deformation is major contribution to the total normal contact stiffness.When the first six frequency indexes are less than the critical elastic frequency index,the dimensionless load-stiffness relation approximately isF^*r^(K^*r)^3.When the initial frequency index is greater than the critical elastic frequency index,the dimensionless load-stiffness relation approximately isF^*r^K^*r.The comparison between the theoretical results and the experimental results indicates that the theoretical results are consistent with the experimental data;therefore,the present fractal model of contact stiffness is reasonable.
文摘<span style="font-family:Verdana;">This paper represents</span> <span style="font-family:Verdana;">a continuation of</span><span style="color:#C45911;"> </span><span><span style="white-space:nowrap;"><a href="#ref1" target="_blank">[1]</a></span><span style="font-family:Verdana;"> and</span> <span style="white-space:nowrap;"><a href="#ref2" target="_blank">[2]</a></span></span><span style="font-family:Verdana;">. </span><span style="font-family:Verdana;">Here, we consider the numerical analysis of a non-trivial frictional contact problem in a form of a system of evolution nonlinear partial differential equations. The model describes the equilibrium of a viscoelastic body in sliding contact with a moving foundation. The contact is modeled with a multivalued normal compliance condition with memory term restricted by a unilateral constraint and is associated with a sliding version of Coulomb’s law of dry friction. After a description of the model and some assumptions, we derive a variational formulation of the problem, which consists of a system coupling a variational inequality for the displacement field and a nonlinear equation for the stress field. Then, we introduce a fully discrete scheme for the numerical approximation of the sliding contact problem. Under certain solution regularity assumptions, we derive an optimal order error estimate and we provide numerical validation of this result by considering some numerical simulations in the study of a two-dimensional problem.</span>
基金the work is supported by Natural Science Fund of Heilongjiang Province (E0 1 - 1 8) and Doctor Fund(Z0 0 1 0 2 1 30 2 2 )
文摘Based on the space meshing theory, it is proven that non-involute beveloid gears meshing with crossed axes can achieve to line contact. The meshing equation and tooth profile equation are presented by using meshing theory. A theoretical way is put forward to calculate the induced normal curvature along the normal direction of the contact line.
文摘A new type of worm gearing, rolling cone enveloping worm gearing possessing high virtues of transmission, is presented. With theoretical deduction, numerical calculations and parameter analyses, the effect of prime parameters to the character of instantaneous contact line are obtained. The ranges of the main parameters are selected reasonably. It provides the theoretical basis for the structure design and application of this new type of worm gearing.
文摘典型的无网格方法采用移动最小二乘函数(moving least squares,MLS)作为近似函数,但由于MLS不具备Kronecker delta函数性质,本质边界施加困难。LRPIM是采用径向基点插值形函数的无网格方法,本质边界条件无需特殊处理,可以直接施加,在保持高精度的前提下提高计算效率。将LRPIM应用于机械结合面接触问题的计算。根据位移连续条件推导了含接触特性的线性互补方程,建立了基于LRPIM的计算模型,采用线性互补算法利用数值积分计算了几种典型的接触问题,得到了接触面压力分布和接触变形,分析了插值函数形状参数和积分域尺寸对计算结果的影响。研究结果表明,插值函数形状参数α_(c)对接触力的影响较小,而形状参数q取-0.5~1.2时有较好的收敛效果;积分域无量纲尺寸a_(qx)、a_(qy)大于1.5时计算结果开始收敛,大于2.5时出现发散现象,取值2.1时收敛效果最佳。将计算结果与已有结果进行比较,表明本研究方法有较高的求解精度。
