滚珠型弧面分度凸轮机构的啮合特性研究
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摘要
滚珠型弧面分度凸轮机构作为一种新型间隙传动机构,采用滚珠作为传动媒介,实现了“旋转——旋转”变换的滚动传动,因滚珠旋转轴线不受约束,具有适应性强、传动效率高、高速性能好、传动精度高、残余振动小等优点,能够在数控机床等大型设备及自动化生产线上实现高速、高精的分度运动,对于提高我国装备制造业发展水平有重要的现实意义。本文从工程实际出发,以提高机构的分度精度、运动平稳性和啮合效率为目的,研究了机构的啮合特性,分析其结构、受力、预紧、润滑、运动学、啮合效率和疲劳寿命等,研究完善了机构的啮合理论,为机构的实用化和进一步应用奠定了理论基础,也为机构的优化设计和制造提供理论指导,主要开展了如下研究工作：
对新型机构的具体结构型式进行了研究分析,机构的具体结构型式决定了其传动性能,是性能分析和优化的基础,结构的合理性决定着加工的难易程度和制造成本,结构设计主要包括凸轮工作滚道曲面形状及截形、分度盘和滚珠防脱结构。借鉴滚动轴承和滚珠丝杠的设计使用经验,采用双圆弧截形滚道可以抑制滚动螺旋传动中滚珠的侧向滑移,减少摩擦；应用表明滚道半径和滚珠直径比取值范围为0.51-0.56,此时机构的承载能力强,弹流润滑油膜较厚,摩擦较小；分度盘采用整体式结构,在径向圆柱面加工出球窝,为实现可控点接触,抑制滚珠的侧向滑移,球窝也采用双圆弧截形；滚珠防脱装置采用滚珠保持架,工作可靠。最后应用空间啮合理论和旋转变换张量法推导出双圆弧截形滚道的滚珠型弧面分度凸轮廓面方程和啮合方程,分析了机构的压力角和影响因素,得出了同时参与啮合的几个滚珠与相应凸轮滚道的压力角不同,且压力角随凸轮转角变化,采用不同的运动规律机构压力角不同。
滚珠与凸轮滚道为点接触,接触应力大,为防止凸轮滚道和滚珠的剧烈磨损与疲劳破坏,在设计时进行接触强度校核,因此对机构的受力展开了分析。安装时机构需要预紧,预紧力施加在滚珠上,传动时工作台和分度盘载荷也施加在滚珠上,滚珠承受两个力的合力。根据力的独立作用原则,首先研究了机构的载荷力分配,即计算每个滚珠承受的载荷力,然后分析了机构的预紧方法、预紧量和预紧力的关系,最后根据力的合成原则合成滚珠总的受力,进行了强度校核。
为保证传动的连续性和平稳性,机构有一定的重合度,在传动过程中,有多个滚珠同时参与啮合,参与啮合的滚珠数目和受力周期性变化,为精确计算每个滚珠的受力,研究了机构的载荷分配。根据机构的载荷特点,应用赫兹接触理论、机构变形协调条件和力矩平衡原理,推导出载荷在每个参与啮合的滚珠中的分配关系。分析结果表明惯性载荷是机构的主要载荷,受凸轮运动规律中加速度影响变化较大；由于凸轮滚道在不同接触点的法线、切线和主曲率不同,每个参与啮合的滚珠承受的载荷力不同；载荷的分配随凸轮转角变化,并受结构参数和运动规律的影响。
分析了机构的预紧,滚珠型弧面分度凸轮机构工作在预紧状态下,以提高机构的刚度和承载能力,消除制造和安装误差的影响,实现无间隙啮合传动。分析了机构的预紧方法,表明预紧改变了滚珠和凸轮滚道的接触点,影响机构的啮合特性和啮合效率,甚至让机构产生啮合干涉。应用赫兹接触理论、轴的弯曲变形理论和轴承弹性变形理论,分析了预紧调整量与机构的弹性变形和接触预紧力的关系。计算表明预紧力不仅和预紧量有关,还与机构的几何刚度有关,预紧力和预紧调整量成非线性关系,预紧时凸轮轴和分度盘轴产生的弯曲变形量很小,可以忽略,同时参与啮合的滚珠产生的接触预紧力不同,并随凸轮转角的变化而变化。比较了采用双圆弧截形滚道与单圆弧截形滚道的凸轮机构预紧时的预紧力和预紧后机构的压力角,表明采用双圆弧截形滚道的凸轮机构预紧力更连续,压力角变化更小,机构运动更平稳。
考虑到滚珠承受载荷力与预紧力的联合作用,进行了接触强度校核,分析了采用修正等速、修正梯形加速度和修正正弦加速度三种运动规律时滚珠和凸轮滚道之间的接触应力在分度期内的变化,结果表明珠与分度盘球窝之间的接触应力小于滚珠与凸轮滚道之间的接触应力,并且接触应力随凸轮转角的变化而变化,因此提出只校核滚珠与凸轮滚道之间的接触应力,并作为失效分析的依据。受惯性载荷的影响,采用不同的运动规律产生的接触应力不同；分度期滚珠和凸轮滚道间的接触应力较大,停歇期接触应力较小。最后采用ANSYS有限元软件分别分析了停歇期和分度期在载荷力、预紧及其联合作用下机构应力云分布,分析了接触应力和接触力随载荷和预紧量的变化规律,证实了载荷分配和预紧分析理论的正确性。
机构通过滚珠传递运动和动力,滚珠同时与凸轮滚道及分度盘啮合,其运动影响机构的润滑和啮合效率,因此研究了滚珠的运动规律。滚珠中心、滚珠与凸轮滚道的接触点及滚珠与分度盘球窝的接触点相对于凸轮轴线的运动轨迹为空间螺旋线,三螺旋线的螺旋升角和相互间的夹角不同,且随凸轮转角变化,利用滚动螺旋传动理论计算了滚珠的侧向滑移速度。分析结果表明在停歇期侧向滑移速度为0,滚珠不存在侧向滑移,在分度期侧向滑移速度随凸轮转角变化,滚珠球心两侧接触点的侧向滑移速度不同,推理出滚珠存在沿滚道截面的旋转运动。滚珠受凸轮滚道的拖动发生自转和锲紧,自转速度受滚珠与凸轮滚道间的摩擦力和滚珠与分度盘球窝之间的摩擦力相互关系的影响,具有较大的不确定性,假设滚珠发生纯滚动时,计算了滚珠的自转速度。
为研究机构的高速性能、分度精度和滚珠的运动规律,应用RecurDyn虚拟样机技术进行了机构的运动学仿真。基于Pro/E的滚珠型弧面分度凸轮的3D实体模型和RecurDyn虚拟样机工具,建立了虚拟样机模型,进行了运动学仿真。仿真结果表明受惯性载荷和滚珠与凸轮滚道及分度盘球窝接触碰撞关系的影响在停歇期分度盘的角加速度出现微小波动,即存在残余振动,影响停歇期的定位精度；在分度期分度盘输出的角加速度不连续,存在冲击。通过仿真还求得同时参与啮合的滚珠与凸轮滚道间的接触力,证实机构载荷分配计算理论的正确性,从仿真结果中得出的滚珠运动证实了滚珠侧向滑移和锲紧运动的存在。
滚珠与凸轮滚道间的润滑属于弹性流体润滑,利用Hamrock-Dowson点接触最小油膜厚度公式和郑绪云点接触中心区油膜厚度公式,推导出滚珠和凸轮滚道之间接触油膜厚度的计算式,采用数值计算方法,分析了机构润滑油膜厚度,分析比较了采用修正等速、修正梯形加速度和修正正弦加速度运动规律时滚珠和凸轮滚道间的油膜厚度。分析结果表明润滑油膜厚度在整个分度期内是变化的,受惯性载荷的影响,前半程油膜较薄,后半程油膜较厚,文中还讨论了凸轮转速、分度盘负载力矩、滚珠直径、分度盘直径等结构参数对油膜厚度的影响,并采用膜厚比参数判断处于边界润滑状态,为分析机构的润滑状态和进行润滑设计提供了理论依据。
滚珠型弧面分度凸轮机构不仅要高速、精确地完成分度运动,同时还应具有较高的啮合效率,因此分析了机构的啮合效率及其影响因素。因滚珠的运动既有滚动又有滑动,滚动摩擦引起的功率损失占比例很小,在计算中被忽略。从滚珠运动分析出发,计算啮合过程中机构能量损失及分度盘的输出功率,推导出机构的啮合效率计算式。数值计算结果表明啮合效率随啮合点变化,摩擦系数和相对滑动速度是影响传动效率的主要因素,预紧力、滑滚比和不同的凸轮运动规律是次要影响因素。
采用Lundberg和Palmgren疲劳寿命理论,借鉴滚动轴承和滚珠丝杠副疲劳寿命研究方法及经验数据,进行了疲劳寿命分析,推导出滚珠型弧面分度凸轮机构的额定载荷和额度寿命计算公式,并采用国际标准寿命补偿方法对其疲劳寿命进行补偿。
As a new type of globoidal indexing cam, globoidal indexing cam mechanism with steel ball achieves "rotation to rotation" transmission through rolling steel ball, it can be used in CNC machine and automatic line to achieve high-speed and high-precision indexing motion, because it's spinning axis is not restrained and meshes at controlled point, it has advantages of high transmission efficiency, high speed, high precision and less residual vibration. It is meaningful for improving development level of equipment manufacturing industry of china. Under actual engineering conditions, for the purpose of improve indexing precision, moving stability and meshing efficiency, meshing characteristic of the mechanism is studied, and structure, force, preload, lubrication, kinetics and dynamics and fatigue life are analyzed, the study provides theoretical basis for optimization design, manufacture and application, the main research work done in the paper is as follows:
Struction of globoidal indexing cam mechanism with steel ball is designed firstly, it is foundation of analyzing feature and optimizing parameters, and affects cost of manufacture and function, it mainly includes the section of raceway, indexing plate and part preventing steel ball separating from indexing plate. Taking example by bearing and ball screw, double-circle arc raceway can prevent lateral slip existing in ball screw drive, the ratio between radius of cam raceway and steel ball diameter is between 0.51 and 0.56, the mechanism can improve bearing capacity, decrease friction and EHL oil film is thicker. Ball seat in indexing plate adopts double-circle arc raceway for meshing at controllable point, retainer is used to prevent steel ball separating from indexing plate. At last, profile equation and meshing equation are deduced by the space meshing theory and rotating matrix operators, and pressure angle and it's influence factor are analyzed, pressure angle changes with cam angle, and with different motion rules the mechanism has different pressure angle.
It is point contact between steel ball and cam raceway, so contact stress is large, contact strength should be checked in design for preventing intensive wear and fatigue failure, so force of the mechanism is analyzed firstly. Load is applied on steel ball in transmission, and pretightening force is applied on steel ball too because of pretightening, steel ball suffered resultant force. According to principle of independent role of force, force applied on steel ball by load and preload is analyzed firstly, then force of steel ball is composed, contact strength is checked.
For continuous transmission and stability of motion in the process of working, the mechanism has contact ratio factor, several steel balls participate in meshing together, and the number of meshing steel ball changes periodically. Load is not equally distributed on each steel ball because principal curvature, normal and helix angle of cam raceway are different at different contact point. Applying hertz contact theory, deformation compatibility condition and torque balance principle, relationship of load distribution applied on each steel ball is deduced. It can be acquired by example that load is not equally distributed on each steel ball, and it is affected by structural parameters and cam motion law.
In order to improve rigidity and bearing capacity of the mechanism, eliminate influence of manufacturing error, achieve transmission without clearance, globiodal indexing cam mechanism with steel ball works under preloading. Preload changes meshing point between steel ball and cam raceway, which changes the meshing character and meshing efficiency, even generates interference. Elastic deformation of the mechanism is generated by preload, and pretightening force has relationship not only with adjusting magnitude of preload, but also with rigidity of the mechanism. Theory of hertz contact, bending deformation of shaft and radial elastic deformation of bearing are used for analyzing the relationship between adjusting magnitude of preload and preload force. The calculation shows that relation between preload force and adjusting magnitude is non-linear, bending deformation of shaft is little enough to be ignored, in indexing period, pretightening force generated at each contact point is different and changes with cam angle. Actual pressure angle changes because preload changes engagement points of the mechanism. Compared with cam with single-circle arc raceway, pretightening force of cam with double-circle arc raceway is more continuous and pressure angle varies less, motion of the mechanism is more stable.
Load and preload force are composed into resultant force applied on steel ball, then contact strength is checked. Calculation shows that contact stress changes with cam angle, contact stress between steel ball and cam raceway is larger than that between steel ball and ball seat, so it is proposed that contact between steel ball and cam raceway is checked only. Contact stress is analyzed when three kinds of motion law is adopted respectively, affected by inertial load contact stress in indexing period is large, and in dwelling period it is little.
Globoidal indexing cam mechanism with steel ball transfers movement and power through steel ball, and steel ball meshes with cam and ball seat at the same time, motion of steel ball affects the failure mode, lubrication and meshing efficiency.
Motion trajectories of steel ball center, contact point between steel ball and cam raceway and contact point between steel ball and ball seat are space spiral curve relative to cam axis, helical angle and intersection angle of the three helical curves are different and change with cam angle. lateral slip speed is calculated based on ball helical transmission theory, it changes with cam angle, and lateral slip speed of two contact point on steel ball is different, which deduces that steel ball rotates along section of cam raceway too. Steel ball dragged by cam raceway self-rotates and is wedged, self-rotation speed is undecided affected by relationship of frictional force between steel ball and cam raceway and that between steel ball and ball seat, self rotation speed is calculated supposing that steel ball rotates purely.
For the research of high speed capacity, output property of the mechanism and motion of steel ball, kinematics simulation is studied applying virtual prototype technology. Profile surface of globoidal indexing cam with steel ball is undevelopable space surface, process of build of 3D models is complicated, point coordinate data of profile curve is generated by VC++ firstly,3D models is built using Pro/E, model data is imported into RecurDyn through format of Parasolid, and 3D models of other work parts are established in RecurDyn, the mechanism is assembled according to the position relationship, restrictions and loads are applied basing on motion relationship, and virtual prototype model is established, then kinetics simulation is carried out. In dwelling indexing period, angle acceleration of indexing plate waves slightly, which is residual oscillation of indexing plate, which affects indexing precision, in indexing period, the angle acceleration of indexing plate is not continuous, impact exists. Contact forces between steel ball and cam raceway are acquired by simulation, which proves that theory of load distribution is right, simulation also proves that lateral slid and wedge exist in the motion of steel ball.
Though rolling transmission is achieved through rolling steel ball, friction property also is an important factor affected by lateral slid and wedge existing in ball helix transmission. Friction will leads to attrition and fatigue failure of steel ball and cam raceway, in high speed occasion, temperature raise caused by friction affects indexing precision and friction character, even makes the mechanism stuck. Lubrication between steel ball and cam raceway belongs to EHD, based on Hamrock-Dowson and Zheng Xuyun film thickness calculation formulae, the EHD film thickness formulae of globoidal indexing cam mechanism with steel ball between steel ball and cam raceway is deduced. Applying numerical calculation method, film thickness is analyzed and calculated when the modified constant velocity motion curve, modified trapezoidal acceleration motion curve and modified sine acceleration motion curve are adopted respectively. Analysis shows that oil film thickness varies in indexing period, affected by inertia load oil thickness is thick in former half of indexing period and is thin in latter half of indexing period. The influence of cam speed, load torque, ball diameter, indexing plate diameter and curvature ratio, on film thickness are also discussed, lubrication between steel ball and cam raceway is in boundary lubrication state judging by film thickness ratio, which provides theoretical basis for the lubrication design of globoidal indexing cam mechanism with steel ball.
Globoidal indexing cam mechanism with steel ball should not only achieves indexing motion precisely and high speed, but also has high meshing efficiency. Based on the motion of steel balls, theoretical calculation equation of meshing efficiency of the mechanism is derived by analyzing power loss of the mechanism and the output power of indexing plate. Based on the features of loads, meshing efficiency and its influencing factors are analyzed, results show that meshing efficiency varies with the positions of contact points, friction coefficient and sliding velocity are primary influencing factors, and pretightening force, slide-roll ratio and cam motion rule are secondary factors. This research has guiding significance for design and manufacture of the mechanism.
In globoidal indexing cam mechanism with steel ball, it is point contact between steel ball and cam raceway, between steel ball and ball seat in the indexing plate, so contact stress is large, sliding friction and rolling friction exist in working process, steel ball and cam raceway contact periodically, so fatigue life is an important factor in design. Referencing the calculation methods and empirical data of fatigue life of bearing and ball screw, the fatigue life formula of globoidal indexing cam with steel ball was calculated by using the life theory of Lundberg and Palmgren, the rated load and rated fatigue life formula was deduced. Fatigue life of globoidal indexing cam mechanism with steel ball is compensated using the international standards of bearing life on life.
对新型机构的具体结构型式进行了研究分析,机构的具体结构型式决定了其传动性能,是性能分析和优化的基础,结构的合理性决定着加工的难易程度和制造成本,结构设计主要包括凸轮工作滚道曲面形状及截形、分度盘和滚珠防脱结构。借鉴滚动轴承和滚珠丝杠的设计使用经验,采用双圆弧截形滚道可以抑制滚动螺旋传动中滚珠的侧向滑移,减少摩擦；应用表明滚道半径和滚珠直径比取值范围为0.51-0.56,此时机构的承载能力强,弹流润滑油膜较厚,摩擦较小；分度盘采用整体式结构,在径向圆柱面加工出球窝,为实现可控点接触,抑制滚珠的侧向滑移,球窝也采用双圆弧截形；滚珠防脱装置采用滚珠保持架,工作可靠。最后应用空间啮合理论和旋转变换张量法推导出双圆弧截形滚道的滚珠型弧面分度凸轮廓面方程和啮合方程,分析了机构的压力角和影响因素,得出了同时参与啮合的几个滚珠与相应凸轮滚道的压力角不同,且压力角随凸轮转角变化,采用不同的运动规律机构压力角不同。
滚珠与凸轮滚道为点接触,接触应力大,为防止凸轮滚道和滚珠的剧烈磨损与疲劳破坏,在设计时进行接触强度校核,因此对机构的受力展开了分析。安装时机构需要预紧,预紧力施加在滚珠上,传动时工作台和分度盘载荷也施加在滚珠上,滚珠承受两个力的合力。根据力的独立作用原则,首先研究了机构的载荷力分配,即计算每个滚珠承受的载荷力,然后分析了机构的预紧方法、预紧量和预紧力的关系,最后根据力的合成原则合成滚珠总的受力,进行了强度校核。
为保证传动的连续性和平稳性,机构有一定的重合度,在传动过程中,有多个滚珠同时参与啮合,参与啮合的滚珠数目和受力周期性变化,为精确计算每个滚珠的受力,研究了机构的载荷分配。根据机构的载荷特点,应用赫兹接触理论、机构变形协调条件和力矩平衡原理,推导出载荷在每个参与啮合的滚珠中的分配关系。分析结果表明惯性载荷是机构的主要载荷,受凸轮运动规律中加速度影响变化较大；由于凸轮滚道在不同接触点的法线、切线和主曲率不同,每个参与啮合的滚珠承受的载荷力不同；载荷的分配随凸轮转角变化,并受结构参数和运动规律的影响。
分析了机构的预紧,滚珠型弧面分度凸轮机构工作在预紧状态下,以提高机构的刚度和承载能力,消除制造和安装误差的影响,实现无间隙啮合传动。分析了机构的预紧方法,表明预紧改变了滚珠和凸轮滚道的接触点,影响机构的啮合特性和啮合效率,甚至让机构产生啮合干涉。应用赫兹接触理论、轴的弯曲变形理论和轴承弹性变形理论,分析了预紧调整量与机构的弹性变形和接触预紧力的关系。计算表明预紧力不仅和预紧量有关,还与机构的几何刚度有关,预紧力和预紧调整量成非线性关系,预紧时凸轮轴和分度盘轴产生的弯曲变形量很小,可以忽略,同时参与啮合的滚珠产生的接触预紧力不同,并随凸轮转角的变化而变化。比较了采用双圆弧截形滚道与单圆弧截形滚道的凸轮机构预紧时的预紧力和预紧后机构的压力角,表明采用双圆弧截形滚道的凸轮机构预紧力更连续,压力角变化更小,机构运动更平稳。
考虑到滚珠承受载荷力与预紧力的联合作用,进行了接触强度校核,分析了采用修正等速、修正梯形加速度和修正正弦加速度三种运动规律时滚珠和凸轮滚道之间的接触应力在分度期内的变化,结果表明珠与分度盘球窝之间的接触应力小于滚珠与凸轮滚道之间的接触应力,并且接触应力随凸轮转角的变化而变化,因此提出只校核滚珠与凸轮滚道之间的接触应力,并作为失效分析的依据。受惯性载荷的影响,采用不同的运动规律产生的接触应力不同；分度期滚珠和凸轮滚道间的接触应力较大,停歇期接触应力较小。最后采用ANSYS有限元软件分别分析了停歇期和分度期在载荷力、预紧及其联合作用下机构应力云分布,分析了接触应力和接触力随载荷和预紧量的变化规律,证实了载荷分配和预紧分析理论的正确性。
机构通过滚珠传递运动和动力,滚珠同时与凸轮滚道及分度盘啮合,其运动影响机构的润滑和啮合效率,因此研究了滚珠的运动规律。滚珠中心、滚珠与凸轮滚道的接触点及滚珠与分度盘球窝的接触点相对于凸轮轴线的运动轨迹为空间螺旋线,三螺旋线的螺旋升角和相互间的夹角不同,且随凸轮转角变化,利用滚动螺旋传动理论计算了滚珠的侧向滑移速度。分析结果表明在停歇期侧向滑移速度为0,滚珠不存在侧向滑移,在分度期侧向滑移速度随凸轮转角变化,滚珠球心两侧接触点的侧向滑移速度不同,推理出滚珠存在沿滚道截面的旋转运动。滚珠受凸轮滚道的拖动发生自转和锲紧,自转速度受滚珠与凸轮滚道间的摩擦力和滚珠与分度盘球窝之间的摩擦力相互关系的影响,具有较大的不确定性,假设滚珠发生纯滚动时,计算了滚珠的自转速度。
为研究机构的高速性能、分度精度和滚珠的运动规律,应用RecurDyn虚拟样机技术进行了机构的运动学仿真。基于Pro/E的滚珠型弧面分度凸轮的3D实体模型和RecurDyn虚拟样机工具,建立了虚拟样机模型,进行了运动学仿真。仿真结果表明受惯性载荷和滚珠与凸轮滚道及分度盘球窝接触碰撞关系的影响在停歇期分度盘的角加速度出现微小波动,即存在残余振动,影响停歇期的定位精度；在分度期分度盘输出的角加速度不连续,存在冲击。通过仿真还求得同时参与啮合的滚珠与凸轮滚道间的接触力,证实机构载荷分配计算理论的正确性,从仿真结果中得出的滚珠运动证实了滚珠侧向滑移和锲紧运动的存在。
滚珠与凸轮滚道间的润滑属于弹性流体润滑,利用Hamrock-Dowson点接触最小油膜厚度公式和郑绪云点接触中心区油膜厚度公式,推导出滚珠和凸轮滚道之间接触油膜厚度的计算式,采用数值计算方法,分析了机构润滑油膜厚度,分析比较了采用修正等速、修正梯形加速度和修正正弦加速度运动规律时滚珠和凸轮滚道间的油膜厚度。分析结果表明润滑油膜厚度在整个分度期内是变化的,受惯性载荷的影响,前半程油膜较薄,后半程油膜较厚,文中还讨论了凸轮转速、分度盘负载力矩、滚珠直径、分度盘直径等结构参数对油膜厚度的影响,并采用膜厚比参数判断处于边界润滑状态,为分析机构的润滑状态和进行润滑设计提供了理论依据。
滚珠型弧面分度凸轮机构不仅要高速、精确地完成分度运动,同时还应具有较高的啮合效率,因此分析了机构的啮合效率及其影响因素。因滚珠的运动既有滚动又有滑动,滚动摩擦引起的功率损失占比例很小,在计算中被忽略。从滚珠运动分析出发,计算啮合过程中机构能量损失及分度盘的输出功率,推导出机构的啮合效率计算式。数值计算结果表明啮合效率随啮合点变化,摩擦系数和相对滑动速度是影响传动效率的主要因素,预紧力、滑滚比和不同的凸轮运动规律是次要影响因素。
采用Lundberg和Palmgren疲劳寿命理论,借鉴滚动轴承和滚珠丝杠副疲劳寿命研究方法及经验数据,进行了疲劳寿命分析,推导出滚珠型弧面分度凸轮机构的额定载荷和额度寿命计算公式,并采用国际标准寿命补偿方法对其疲劳寿命进行补偿。
As a new type of globoidal indexing cam, globoidal indexing cam mechanism with steel ball achieves "rotation to rotation" transmission through rolling steel ball, it can be used in CNC machine and automatic line to achieve high-speed and high-precision indexing motion, because it's spinning axis is not restrained and meshes at controlled point, it has advantages of high transmission efficiency, high speed, high precision and less residual vibration. It is meaningful for improving development level of equipment manufacturing industry of china. Under actual engineering conditions, for the purpose of improve indexing precision, moving stability and meshing efficiency, meshing characteristic of the mechanism is studied, and structure, force, preload, lubrication, kinetics and dynamics and fatigue life are analyzed, the study provides theoretical basis for optimization design, manufacture and application, the main research work done in the paper is as follows:
Struction of globoidal indexing cam mechanism with steel ball is designed firstly, it is foundation of analyzing feature and optimizing parameters, and affects cost of manufacture and function, it mainly includes the section of raceway, indexing plate and part preventing steel ball separating from indexing plate. Taking example by bearing and ball screw, double-circle arc raceway can prevent lateral slip existing in ball screw drive, the ratio between radius of cam raceway and steel ball diameter is between 0.51 and 0.56, the mechanism can improve bearing capacity, decrease friction and EHL oil film is thicker. Ball seat in indexing plate adopts double-circle arc raceway for meshing at controllable point, retainer is used to prevent steel ball separating from indexing plate. At last, profile equation and meshing equation are deduced by the space meshing theory and rotating matrix operators, and pressure angle and it's influence factor are analyzed, pressure angle changes with cam angle, and with different motion rules the mechanism has different pressure angle.
It is point contact between steel ball and cam raceway, so contact stress is large, contact strength should be checked in design for preventing intensive wear and fatigue failure, so force of the mechanism is analyzed firstly. Load is applied on steel ball in transmission, and pretightening force is applied on steel ball too because of pretightening, steel ball suffered resultant force. According to principle of independent role of force, force applied on steel ball by load and preload is analyzed firstly, then force of steel ball is composed, contact strength is checked.
For continuous transmission and stability of motion in the process of working, the mechanism has contact ratio factor, several steel balls participate in meshing together, and the number of meshing steel ball changes periodically. Load is not equally distributed on each steel ball because principal curvature, normal and helix angle of cam raceway are different at different contact point. Applying hertz contact theory, deformation compatibility condition and torque balance principle, relationship of load distribution applied on each steel ball is deduced. It can be acquired by example that load is not equally distributed on each steel ball, and it is affected by structural parameters and cam motion law.
In order to improve rigidity and bearing capacity of the mechanism, eliminate influence of manufacturing error, achieve transmission without clearance, globiodal indexing cam mechanism with steel ball works under preloading. Preload changes meshing point between steel ball and cam raceway, which changes the meshing character and meshing efficiency, even generates interference. Elastic deformation of the mechanism is generated by preload, and pretightening force has relationship not only with adjusting magnitude of preload, but also with rigidity of the mechanism. Theory of hertz contact, bending deformation of shaft and radial elastic deformation of bearing are used for analyzing the relationship between adjusting magnitude of preload and preload force. The calculation shows that relation between preload force and adjusting magnitude is non-linear, bending deformation of shaft is little enough to be ignored, in indexing period, pretightening force generated at each contact point is different and changes with cam angle. Actual pressure angle changes because preload changes engagement points of the mechanism. Compared with cam with single-circle arc raceway, pretightening force of cam with double-circle arc raceway is more continuous and pressure angle varies less, motion of the mechanism is more stable.
Load and preload force are composed into resultant force applied on steel ball, then contact strength is checked. Calculation shows that contact stress changes with cam angle, contact stress between steel ball and cam raceway is larger than that between steel ball and ball seat, so it is proposed that contact between steel ball and cam raceway is checked only. Contact stress is analyzed when three kinds of motion law is adopted respectively, affected by inertial load contact stress in indexing period is large, and in dwelling period it is little.
Globoidal indexing cam mechanism with steel ball transfers movement and power through steel ball, and steel ball meshes with cam and ball seat at the same time, motion of steel ball affects the failure mode, lubrication and meshing efficiency.
Motion trajectories of steel ball center, contact point between steel ball and cam raceway and contact point between steel ball and ball seat are space spiral curve relative to cam axis, helical angle and intersection angle of the three helical curves are different and change with cam angle. lateral slip speed is calculated based on ball helical transmission theory, it changes with cam angle, and lateral slip speed of two contact point on steel ball is different, which deduces that steel ball rotates along section of cam raceway too. Steel ball dragged by cam raceway self-rotates and is wedged, self-rotation speed is undecided affected by relationship of frictional force between steel ball and cam raceway and that between steel ball and ball seat, self rotation speed is calculated supposing that steel ball rotates purely.
For the research of high speed capacity, output property of the mechanism and motion of steel ball, kinematics simulation is studied applying virtual prototype technology. Profile surface of globoidal indexing cam with steel ball is undevelopable space surface, process of build of 3D models is complicated, point coordinate data of profile curve is generated by VC++ firstly,3D models is built using Pro/E, model data is imported into RecurDyn through format of Parasolid, and 3D models of other work parts are established in RecurDyn, the mechanism is assembled according to the position relationship, restrictions and loads are applied basing on motion relationship, and virtual prototype model is established, then kinetics simulation is carried out. In dwelling indexing period, angle acceleration of indexing plate waves slightly, which is residual oscillation of indexing plate, which affects indexing precision, in indexing period, the angle acceleration of indexing plate is not continuous, impact exists. Contact forces between steel ball and cam raceway are acquired by simulation, which proves that theory of load distribution is right, simulation also proves that lateral slid and wedge exist in the motion of steel ball.
Though rolling transmission is achieved through rolling steel ball, friction property also is an important factor affected by lateral slid and wedge existing in ball helix transmission. Friction will leads to attrition and fatigue failure of steel ball and cam raceway, in high speed occasion, temperature raise caused by friction affects indexing precision and friction character, even makes the mechanism stuck. Lubrication between steel ball and cam raceway belongs to EHD, based on Hamrock-Dowson and Zheng Xuyun film thickness calculation formulae, the EHD film thickness formulae of globoidal indexing cam mechanism with steel ball between steel ball and cam raceway is deduced. Applying numerical calculation method, film thickness is analyzed and calculated when the modified constant velocity motion curve, modified trapezoidal acceleration motion curve and modified sine acceleration motion curve are adopted respectively. Analysis shows that oil film thickness varies in indexing period, affected by inertia load oil thickness is thick in former half of indexing period and is thin in latter half of indexing period. The influence of cam speed, load torque, ball diameter, indexing plate diameter and curvature ratio, on film thickness are also discussed, lubrication between steel ball and cam raceway is in boundary lubrication state judging by film thickness ratio, which provides theoretical basis for the lubrication design of globoidal indexing cam mechanism with steel ball.
Globoidal indexing cam mechanism with steel ball should not only achieves indexing motion precisely and high speed, but also has high meshing efficiency. Based on the motion of steel balls, theoretical calculation equation of meshing efficiency of the mechanism is derived by analyzing power loss of the mechanism and the output power of indexing plate. Based on the features of loads, meshing efficiency and its influencing factors are analyzed, results show that meshing efficiency varies with the positions of contact points, friction coefficient and sliding velocity are primary influencing factors, and pretightening force, slide-roll ratio and cam motion rule are secondary factors. This research has guiding significance for design and manufacture of the mechanism.
In globoidal indexing cam mechanism with steel ball, it is point contact between steel ball and cam raceway, between steel ball and ball seat in the indexing plate, so contact stress is large, sliding friction and rolling friction exist in working process, steel ball and cam raceway contact periodically, so fatigue life is an important factor in design. Referencing the calculation methods and empirical data of fatigue life of bearing and ball screw, the fatigue life formula of globoidal indexing cam with steel ball was calculated by using the life theory of Lundberg and Palmgren, the rated load and rated fatigue life formula was deduced. Fatigue life of globoidal indexing cam mechanism with steel ball is compensated using the international standards of bearing life on life.
引文
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