The normal contact force determines the behavior of a particle system.To investigate the normal contact force in a one‐dimensional sphere chain subjected to impact load,by comparing the simulation results of the exis...The normal contact force determines the behavior of a particle system.To investigate the normal contact force in a one‐dimensional sphere chain subjected to impact load,by comparing the simulation results of the existing typical normal contact force models embedded in the discrete element program,an improved normal contact force model was proposed in this paper.The improved model con-sists of two parts:the Cundall model for loading and the Daniel model for unloading.Moreover,a systematic test was designed to verify the accuracy and applicability of the improved model.The results showed that the calculated contact force curves agree well with the experimental results.Furthermore,the improved model is implemented in the solution algorithm without need for complex numerical methods and parameters fitting,leading to more efficient simulations.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
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
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
基金National Natural Science Foundation of China,Grant/Award Numbers:51874118,51778211supported by the National Natural Science Foundation of China(Nos.51874118,51778211).
文摘The normal contact force determines the behavior of a particle system.To investigate the normal contact force in a one‐dimensional sphere chain subjected to impact load,by comparing the simulation results of the existing typical normal contact force models embedded in the discrete element program,an improved normal contact force model was proposed in this paper.The improved model con-sists of two parts:the Cundall model for loading and the Daniel model for unloading.Moreover,a systematic test was designed to verify the accuracy and applicability of the improved model.The results showed that the calculated contact force curves agree well with the experimental results.Furthermore,the improved model is implemented in the solution algorithm without need for complex numerical methods and parameters fitting,leading to more efficient simulations.
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>
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。
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.
