实时无隙钢球精密传动原理及热力耦合动力学性能研究

In order to realize the objective of constantly high precision transmission and high dynamics performance, take steel ball precise transmission mechanism as the research object. (1) Applied mechanism creative design method, the transmission structural principle of the poor stiffness no backlash steel ball engagement pair is put up. The wear clearance and the thermal expansion interference of the engagement pair can constantly be eliminated by the transmission structural principle. The precision transmission of constantly no backlash engagement is realized by the circumferential rigid rotation and the axial direction constantly micromotion of the engagement pair. (2) Applied multi-rigid-body nonlinear dynamics theory, the dynamics models of the thermo-dynamic coupleare are established. The dynamics models include the ones of the nonlinear vibration and the linear vibration of the parallel poor stiffness no backlash steel ball deceleration engagement pair and constant velocity engagement pair as well as the compound nonlinear vibration of the mechanism. (3) The dynamics performance and the influence factors of the mechanism and its parameter control method are studied with numerical simulation and decoupling method. (4) Based on thermal elastic and plastic theory and friction theory, the models of the friction analysis field, temperature field and thermo-dynamic coupl field in the steel ball engagement pair are established. The wearing clearance and the thermal expansion deformation of the steel ball engagement pair as well as their coupling relations are studied. (5) The influence parameters and control method of the engagement pair error effect on transmission ratio constantly stabilization and dynamics performance are studied by the error theory. This subject have important scientific significance and academic value for improveing level of the scientific research and the application technique of our country and for leading development of high precise transmission frontier discipline.

为实现实时高精密传动和高动态性能的目标，本项目以钢球精密传动为研究对象，（1）应用机构创新设计方法，提出能实时消除啮合副磨损间隙和热膨胀过盈的弱刚性无隙钢球啮合副的传动结构原理，以啮合副周向刚性转动、轴向实时微移动实现实时无隙啮合的精密传动。（2）应用多刚体非线性动力学理论，建立热力耦合的并联弱刚性无隙钢球减速啮合副非线性振动、等速啮合副线性振动和机构复合非线性振动的动力学模型。（3）利用数值模拟和解耦方法，研究机构动态性能及其影响因素关系和参数控制方法。（4）应用热弹塑性理论和摩擦学理论，建立钢球啮合副摩擦分析场、温度场和热力耦合场模型，研究磨损间隙、热膨胀变形及两者耦合关系的解析式。（5）应用误差理论，研究啮合副误差对定传动比实时稳定性和机构动态性能的影响参数和控制方法。本项目研究对提升我国高精密传动的科学研究和应用技术水平、引领高精密传动前沿学科的发展有重要的科学意义和学术价值。

本项目的研究内容和取得的研究成果主要体现在以下四个方面：. 提出并设计制造出弱刚性组合行星盘创新传动结构和实时无隙精密钢球传动微小型实验样机，该组合行星盘实现了实时消除摆线钢球减速啮合副和十字槽钢球等速啮合副的磨损间隙或热膨胀过盈，实现了两钢球啮合副的无隙啮合的精密传动。研制出弱刚性组合行星盘的销轴联接副和钢球联接副的轴向微位移两种结构型式，研究了两行星盘相对的周向不转动和轴向微移动的可靠性和精确性。. 基于外部激励、啮合状态和啮合刚度等非线性因素，建立了无隙精密钢球传动减速啮合副与等速啮合副并联系统的平移—扭转耦合、纯扭转强非线性耦合的动力学模型。研究了并联无隙多啮合副之间载荷分布规律及传动系统的全振动模态、输出轴静止和扭转振动模态等动态特性，分析了啮合刚度的时变性和系统振动的影响因素。利用谐波平衡法求解系统基频稳态响应，分析了系统非线性特性的影响规律及单双边冲击现象等。利用数值方法研究了系统分叉特性和系统稳定性的影响规律。研究了啮合副非赫兹接触及等效应力变化规律。. 建立了啮合副钢球滚-滑摩擦耦合模型。完成了有限元法和耦合模型法求解啮合力和对比分析，分析了钢球滚-滑运动产生的机理及其对啮合副的热变形影响，推导出滑动速度和滑动率公式并分析了变化规律和影响因素。建立了啮合副本体温度场和瞬时接触温升模型及各区域对流换热系数数学模型，推导出啮合副的最大接触应力和摩擦系数公式。分析了啮合副瞬时温升和瞬时生热率的变化和影响因素，研究了转速和外载荷对瞬时生热率和热特性的变化规和影响因素等。. 提出利用刚度系数精确求解啮合副法向力和弹性回差的方法，建立了啮合副弹性回差分析模型，推导出减速钢球啮合副和等速钢球啮合副的动态弹性转角和弹性回差公式，分析了齿形误差、弹性回差、动态转角和扭转刚度的变化规律及其对机构传动平稳性的影响。研究了影响啮合传动平稳性的外、内摆线槽实际齿廓的不顶切条件式和不顶切的刀具最大进给量并仿真验证。

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