线接触高副机构摩擦学设计与分析
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摘要
控制摩擦、减少磨损、改善润滑性能以及合理发挥材料的潜能等摩擦学研究在工程中具有重要意义。线接触高副机构由于接触区小、接触应力大等原因,其摩擦、磨损和润滑等问题一直被广大科研工作者所重视,国内外在相关领域的研究取得不少成果。但线接触高副机构的摩擦学研究很不平衡,目前在工程应用方面的研究主要集中在轮轨接触、滚动轴承和齿轮接触,而凸轮等线接触高副机构的摩擦学研究相对较少,对于机构摩擦接触的安定分析研究则更少。
本文基于摩擦学基础理论的研究成果,结合常见的凸轮、齿轮等线接触高副机构的工作原理及其接触模型,利用接触疲劳、弹流润滑、磨损预测等摩擦学的基本原理和方法,对齿轮和凸轮等线接触高副机构的摩擦学设计和分析方法进行深入地探讨。同时基于弹塑性力学的安定极限分析模型,对齿轮接触的塑性变形失效准则进行探讨。取得的主要结果和结论如下：
1.齿轮啮合过程中,齿面间存在一定的相对滑动。齿面间的滑动摩擦力对齿面接触疲劳强度计算有影响,引入摩擦效应因数,得到考虑齿间滑动摩擦的齿面接触疲劳强度计算模型。计算结果表明,齿间滑动摩擦对齿面接触疲劳强度的影响随润滑状况发生变化,一般可达6%。设计过程中为保证可靠的齿面接触疲劳强度,可适当加大齿面接触疲劳的许用安全系数,或直接采用本文推导的校核模型计算。
2.直动滚子盘形凸轮机构容易出现疲劳点蚀和磨损失效,须校核凸轮的接触应力。凸轮的压力角和凸轮实际廓线曲率半径是凸轮转角的函数,且凸轮压力角和凸轮廓线曲率半径的计算需多次对运动规律方程求导。给出凸轮接触应力计算模型和基于MATLAB的相应计算程序,可满足工程实际对凸轮接触应力的计算要求。
3.基于凸轮的接触强度条件,结合凸轮的传动条件,讨论了接触应力、许用压力角、基圆半径以及偏心距等之间的关系,给出满足接触强度条件的直动滚子凸轮设计模型。
4.通过计算直动滚子盘形凸轮机构最小油膜厚度和膜厚比,可判别凸轮机构的润滑状态,从而可判断凸轮出现磨损的可能性。凸轮润滑涉及接触表面粗糙度、润滑油和凸轮材料性能、凸轮传动系统的运动规律和凸轮结构参数等诸多因素,且各因素在凸轮运转过程中不断变化,通过逐点分布计算的方法将凸轮廓线上的动态润滑转化成准稳态问题。给出MATLAB编制凸轮最小油膜的计算程序,可得凸轮最小油膜厚度随凸轮转角变化的情况,从而判断凸轮廓线各点的润滑状态。
5.基于平底盘形凸轮弹流润滑理论的最小油膜厚度计算模型,讨论了凸轮廓线最小曲率半径、基圆半径、从动件运动规律和最小油膜厚度之间的关系,给出基于弹流润滑理论的平底直动盘形凸轮机构的设计模型,该模型可按照给定的凸轮润滑状态确定最优的凸轮基圆半径。算例表明,可通过合理选择最佳的凸轮基圆半径和轮廓形状、或选用合理的润滑油和添加剂、或以最经济的加工方法改善凸轮和从动件的表面质量等措施改善凸轮润滑效果。
6.针对粘着磨损是平底直动盘形凸轮的主要失效形式之一,考虑润滑状况对凸轮磨损的影响,基于弹流润滑理论给出凸轮润滑的膜厚比,建立膜厚比与粘着磨损系数关系的简化模型,从而给出平底凸轮粘着磨损与弹流润滑的耦合计算模型。算例表明,该模型可近似求解平底凸轮各点的磨损状况。
7.在齿轮初始啮合阶段齿面将发生微小的塑性变形,在接触应力的作用下轮齿内部产生相应的残余应力,残余应力有利于提高齿轮抵抗接触应力的能力。考虑残余应力的影响,基于安定下限定理,导出齿轮材料的接触安定极限,讨论该值作为判断齿面塑性变形失效的许用值与相应的弹性极限作为许用值相比,可提高50%的材料利用率。
Tribology research involving friction control, wear reduction, improvement of lubrication property, reasonable play of materials potential and so on has important significance in engineering. Due to small contact area, big contact stress etc. in the line-contact higher pair mechanisms, the issues related to its friction, wear and lubrication have been always paid high attention by scientific researchers. Many research achievements have been reached in relative field nationally and internationally. However, the tribological research on line-contact higher pair mechanisms is very unbalanced. Currently, the studies on tribology engineering application mainly focus on the wheel-rail contact, rolling bearing and gear contact. However, the tribological researches on the line-contact higher pair mechanisms such as cam are relatively few. Moreover, the shakedown analysis on the mechanical frictional contact pair is much less.
Based on the basic tribology theory, combining the operating principle and the contact model of common line-contact higher pair mechanisms such as cam, gear etc. and using the basic principles and methods for contact fatigue, elastohydrodynamic lubrication and wear prediction, the tribological design and analysis methods for gear and cam in line-contact higher pair mechanisms are deeply discussed in this paper. Meanwhile the plastic deformation failure criteria of gear are discussed based on the shakedown limit analysis model of plastoelasticity mechanics. The main results and conclusions obtained are as follows:
1. There is relative sliding between the tooth surfaces during the gear engagement. Sliding friction between the tooth surfaces has an affect on the calculation of tooth surface contact fatigue strength. The calculation model for the tooth surface contact fatigue strength, which considers the sliding friction, can be obtained by introducing the friction effect factor. The calculated results show that the influence of the sliding friction between gears on the tooth surface contact fatigue strength varies with the change of lubrication conditions and the average value is about 6%. To ensure reliable tooth surface contact fatigue strength in gear design, the allowable safety coefficient for the tooth surface contact fatigue can be appropriately increased or it can be directly calculated with the checking model by text derivation.
2. Straight moving roller disc cam is prone to fatigue pitting and wear failure, so the contact stress of the cam must be checked. The pressure angle and the actual contour curvature radius of the cam are the function of cam rotation angle. The calculation of pressure angle and contour curvature radius of the cam should be performed by deriving the equation of motion rule repeatedly. With the provision of the calculation model for cam contact stress and the corresponding calculation program based on MATLAB, the requirements for calculating the cam contact stress can be met in engineering practically.
3. According to the contact strength requirement of cam and in combination with the cam transmission condition, the relationship between contact stress, allowable pressure angle, base circle radius and eccentricity, etc. is discussed and the design model of straight moving roller cam meeting the contact strength requirement is provided.
4. Through calculating the minimal oil film thickness and the ratio of roughness depth to film thickness of the straight moving roller disc cam, the lubrication status of cam mechanism can be estimated, thus the possibility of cam wear can be judged. Cam lubrication relates to the roughness of contact surface, the properties of lubrication oil and cam materials, the movement rule of cam driving system, the cam parameters and so on. All factors aforementioned constantly change during the operation of cam. The problem of dynamic lubrication on the cam contour is converted into quasi-steady problem through the method of point-by-point distribution calculation. With the provision of calculation program for the minimal cam oil film thickness based on MATLAB, the variation of the minimal cam oil film thickness with the change of cam rotation angle can be known. Therefore, the lubrication status of various points on the cam contour can be learnt.
5. Based on the calculation model for the minimal oil film thickness of flat-bottomed disc cam, the relationship between the minimum cam contour curvature radius, the base circle radius, the motion rule of followers and the minimal oil film thickness is discussed. The design model of straight moving flat-bottomed disc cam is provided based on the theory of elasto-hydrodynamic lubrication, which can determine the optimal base circle radius of cam according to the given cam lubrication status. Calculation examples show that the lubrication effect of cam can be improved by reasonably selecting the best cam base circle radius and contour shape, or choosing reasonable lubrication oil and additives, or improving the surface quality of the cam and followers in most economical processing methods.
6. Since the adhesion wear is one of the major failure modes of the straight moving flat-bottomed follower disc cam, considering the affect of lubrication conditions on the cam wear, the simplified relationship model between the film thickness ratio and the adhesion wear coefficient is established based on the film thickness ratio of cam lubrication derived from the elasto-hydrodynamic lubrication theory. Thus the coupling calculation model for the adhesion wear of flat-bottomed follower disc cam and the elasto-hydrodynamic lubrication is provided. Calculation examples show that this model can approximately estimate the wear conditions of various contour points on the flat-bottomed follower disc cam.
7. Tiny plastic deformation will occur on the tooth surface in initial gear engagement stage. The corresponding residual stress is produced inside the gear teeth under the action of the contact stress, which is helpful to improve the resistance of the gear to the contact stress. Considering the influence of the residual stress, the contact shakedown limit of gear material is derived based on lower bound shakedown theorems. It is indicated that the utilization ratio of gear material can be improved by about 50% in case this shakedown limit is used as the allowable value of tooth surface plastic deformation failure rather than elastic limit.
本文基于摩擦学基础理论的研究成果,结合常见的凸轮、齿轮等线接触高副机构的工作原理及其接触模型,利用接触疲劳、弹流润滑、磨损预测等摩擦学的基本原理和方法,对齿轮和凸轮等线接触高副机构的摩擦学设计和分析方法进行深入地探讨。同时基于弹塑性力学的安定极限分析模型,对齿轮接触的塑性变形失效准则进行探讨。取得的主要结果和结论如下：
1.齿轮啮合过程中,齿面间存在一定的相对滑动。齿面间的滑动摩擦力对齿面接触疲劳强度计算有影响,引入摩擦效应因数,得到考虑齿间滑动摩擦的齿面接触疲劳强度计算模型。计算结果表明,齿间滑动摩擦对齿面接触疲劳强度的影响随润滑状况发生变化,一般可达6%。设计过程中为保证可靠的齿面接触疲劳强度,可适当加大齿面接触疲劳的许用安全系数,或直接采用本文推导的校核模型计算。
2.直动滚子盘形凸轮机构容易出现疲劳点蚀和磨损失效,须校核凸轮的接触应力。凸轮的压力角和凸轮实际廓线曲率半径是凸轮转角的函数,且凸轮压力角和凸轮廓线曲率半径的计算需多次对运动规律方程求导。给出凸轮接触应力计算模型和基于MATLAB的相应计算程序,可满足工程实际对凸轮接触应力的计算要求。
3.基于凸轮的接触强度条件,结合凸轮的传动条件,讨论了接触应力、许用压力角、基圆半径以及偏心距等之间的关系,给出满足接触强度条件的直动滚子凸轮设计模型。
4.通过计算直动滚子盘形凸轮机构最小油膜厚度和膜厚比,可判别凸轮机构的润滑状态,从而可判断凸轮出现磨损的可能性。凸轮润滑涉及接触表面粗糙度、润滑油和凸轮材料性能、凸轮传动系统的运动规律和凸轮结构参数等诸多因素,且各因素在凸轮运转过程中不断变化,通过逐点分布计算的方法将凸轮廓线上的动态润滑转化成准稳态问题。给出MATLAB编制凸轮最小油膜的计算程序,可得凸轮最小油膜厚度随凸轮转角变化的情况,从而判断凸轮廓线各点的润滑状态。
5.基于平底盘形凸轮弹流润滑理论的最小油膜厚度计算模型,讨论了凸轮廓线最小曲率半径、基圆半径、从动件运动规律和最小油膜厚度之间的关系,给出基于弹流润滑理论的平底直动盘形凸轮机构的设计模型,该模型可按照给定的凸轮润滑状态确定最优的凸轮基圆半径。算例表明,可通过合理选择最佳的凸轮基圆半径和轮廓形状、或选用合理的润滑油和添加剂、或以最经济的加工方法改善凸轮和从动件的表面质量等措施改善凸轮润滑效果。
6.针对粘着磨损是平底直动盘形凸轮的主要失效形式之一,考虑润滑状况对凸轮磨损的影响,基于弹流润滑理论给出凸轮润滑的膜厚比,建立膜厚比与粘着磨损系数关系的简化模型,从而给出平底凸轮粘着磨损与弹流润滑的耦合计算模型。算例表明,该模型可近似求解平底凸轮各点的磨损状况。
7.在齿轮初始啮合阶段齿面将发生微小的塑性变形,在接触应力的作用下轮齿内部产生相应的残余应力,残余应力有利于提高齿轮抵抗接触应力的能力。考虑残余应力的影响,基于安定下限定理,导出齿轮材料的接触安定极限,讨论该值作为判断齿面塑性变形失效的许用值与相应的弹性极限作为许用值相比,可提高50%的材料利用率。
Tribology research involving friction control, wear reduction, improvement of lubrication property, reasonable play of materials potential and so on has important significance in engineering. Due to small contact area, big contact stress etc. in the line-contact higher pair mechanisms, the issues related to its friction, wear and lubrication have been always paid high attention by scientific researchers. Many research achievements have been reached in relative field nationally and internationally. However, the tribological research on line-contact higher pair mechanisms is very unbalanced. Currently, the studies on tribology engineering application mainly focus on the wheel-rail contact, rolling bearing and gear contact. However, the tribological researches on the line-contact higher pair mechanisms such as cam are relatively few. Moreover, the shakedown analysis on the mechanical frictional contact pair is much less.
Based on the basic tribology theory, combining the operating principle and the contact model of common line-contact higher pair mechanisms such as cam, gear etc. and using the basic principles and methods for contact fatigue, elastohydrodynamic lubrication and wear prediction, the tribological design and analysis methods for gear and cam in line-contact higher pair mechanisms are deeply discussed in this paper. Meanwhile the plastic deformation failure criteria of gear are discussed based on the shakedown limit analysis model of plastoelasticity mechanics. The main results and conclusions obtained are as follows:
1. There is relative sliding between the tooth surfaces during the gear engagement. Sliding friction between the tooth surfaces has an affect on the calculation of tooth surface contact fatigue strength. The calculation model for the tooth surface contact fatigue strength, which considers the sliding friction, can be obtained by introducing the friction effect factor. The calculated results show that the influence of the sliding friction between gears on the tooth surface contact fatigue strength varies with the change of lubrication conditions and the average value is about 6%. To ensure reliable tooth surface contact fatigue strength in gear design, the allowable safety coefficient for the tooth surface contact fatigue can be appropriately increased or it can be directly calculated with the checking model by text derivation.
2. Straight moving roller disc cam is prone to fatigue pitting and wear failure, so the contact stress of the cam must be checked. The pressure angle and the actual contour curvature radius of the cam are the function of cam rotation angle. The calculation of pressure angle and contour curvature radius of the cam should be performed by deriving the equation of motion rule repeatedly. With the provision of the calculation model for cam contact stress and the corresponding calculation program based on MATLAB, the requirements for calculating the cam contact stress can be met in engineering practically.
3. According to the contact strength requirement of cam and in combination with the cam transmission condition, the relationship between contact stress, allowable pressure angle, base circle radius and eccentricity, etc. is discussed and the design model of straight moving roller cam meeting the contact strength requirement is provided.
4. Through calculating the minimal oil film thickness and the ratio of roughness depth to film thickness of the straight moving roller disc cam, the lubrication status of cam mechanism can be estimated, thus the possibility of cam wear can be judged. Cam lubrication relates to the roughness of contact surface, the properties of lubrication oil and cam materials, the movement rule of cam driving system, the cam parameters and so on. All factors aforementioned constantly change during the operation of cam. The problem of dynamic lubrication on the cam contour is converted into quasi-steady problem through the method of point-by-point distribution calculation. With the provision of calculation program for the minimal cam oil film thickness based on MATLAB, the variation of the minimal cam oil film thickness with the change of cam rotation angle can be known. Therefore, the lubrication status of various points on the cam contour can be learnt.
5. Based on the calculation model for the minimal oil film thickness of flat-bottomed disc cam, the relationship between the minimum cam contour curvature radius, the base circle radius, the motion rule of followers and the minimal oil film thickness is discussed. The design model of straight moving flat-bottomed disc cam is provided based on the theory of elasto-hydrodynamic lubrication, which can determine the optimal base circle radius of cam according to the given cam lubrication status. Calculation examples show that the lubrication effect of cam can be improved by reasonably selecting the best cam base circle radius and contour shape, or choosing reasonable lubrication oil and additives, or improving the surface quality of the cam and followers in most economical processing methods.
6. Since the adhesion wear is one of the major failure modes of the straight moving flat-bottomed follower disc cam, considering the affect of lubrication conditions on the cam wear, the simplified relationship model between the film thickness ratio and the adhesion wear coefficient is established based on the film thickness ratio of cam lubrication derived from the elasto-hydrodynamic lubrication theory. Thus the coupling calculation model for the adhesion wear of flat-bottomed follower disc cam and the elasto-hydrodynamic lubrication is provided. Calculation examples show that this model can approximately estimate the wear conditions of various contour points on the flat-bottomed follower disc cam.
7. Tiny plastic deformation will occur on the tooth surface in initial gear engagement stage. The corresponding residual stress is produced inside the gear teeth under the action of the contact stress, which is helpful to improve the resistance of the gear to the contact stress. Considering the influence of the residual stress, the contact shakedown limit of gear material is derived based on lower bound shakedown theorems. It is indicated that the utilization ratio of gear material can be improved by about 50% in case this shakedown limit is used as the allowable value of tooth surface plastic deformation failure rather than elastic limit.
引文
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