混合润滑线接触热弹流数值分析及其在直齿轮传动中的应用
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摘要
众所周知，弹性流体动力润滑(EHL)分为边界润滑、混合润滑和全膜润滑。而油膜比厚Λ，即接触表面间的平均油膜厚度与综合均方根粗糙度的比值是区分润滑状态的一个重要参数。当0.5＜Λ＜3，一般认为是处于混合润滑状态；而Λ≤0.5和Λ≥3分别对应着边界润滑和全膜润滑。实践证明，在工业生产实际中，绝大多数渐开线齿轮传动都在混合润滑状态下工作。因此，选择齿轮混合润滑为题进行研究，既具有一定的理论意义，又有较强的实际价值。
本文首先综述了前人的研究工作，接着，分析了混合润滑线接触热弹流理论。在此基础上，采用顺解、逆解交叉使用的数值方法进行数值计算。计算中将待解区域分为三个子区域，在载荷较重的中间区采用改进后的逆解法，借助追赶法求解运动方程和连续方程；在载荷较轻的入口区和出口区则采用顺解迭代法，通过四阶龙格库塔法求解润滑方程组。
利用本文开发的计算机程序，选用渐开线直齿圆柱齿轮传动参数作为输入数据，共计进行了99组混合润滑线接触热弹流数值计算；从理论上分析了油膜比厚和齿面形貌参数对接触载荷比、压力分布、油膜厚度和温度分布的影响；探讨了不同油
太原理工大学硕士研究生学位论文
膜比厚条件下齿面摩擦系数沿齿轮传动啮合线的分布规律。总
结、分析理论计算结果后形成如下主要研究结论:
1在混合润滑状态下，总体载荷由齿面粗糙峰接触压力和
流体润滑油膜压力共同承担，二者之比称为接触载荷比。在此
状态下，该比值随着油膜比厚A的改变而发生显著变化，特别
是当八在0.5一1.5变动时，这种变化尤为明显;当3.0<八<6.0时，
接触载荷比随A的变化趋势较为平缓，粗糙峰承载比例微乎其
微;而当油膜比厚八之6时，几乎所有载荷全由流体压力承担。
2对于工业中常见的磨削加工齿面，其粗糙度纹理方向往
往垂直于齿面相对运动方向，此类条纹被称之为横向条纹。本
计一算结果昭示:横向条纹粗糙表面形成的油膜厚度大于相应光
滑表面的膜厚值。这乍看起来似乎有些荒诞，但己被理论计算
和实验结果所印证〔29]。究其原因，主要是此类条纹产生所谓的
“泵效应”，并且随着油膜比厚的逐渐降低，这种“泵效应”作
用日趋明显。但当油膜比厚A之6后，粗糙表面间的油膜厚度与
光滑表面间的膜厚值基本相同。
3粗糙齿面接触时的压力分布由流体压力和粗糙峰接触
压力两部分组成。当油膜比厚A引时，粗糙峰作用开始凸现。
当A二0.2口寸，压力分布变成单峰分布，粗糙峰所承担的载荷将
占到总体载荷的90%以上。就压力分布而言，随着油膜比厚的
降低，二次压力峰数值减小，且其位置逐渐向入口区移动。
4油膜比厚的变化对于温度分布具有重要影响。随着油膜
太原理工大学硕士研究生学位论文
比厚的减小，愈来愈多的粗糙峰参与接触，固体摩擦产生的大
量热造成了油膜温度的攀升。当轮齿在边界润滑状态下工作时一，
接触区的油膜温度几乎比全膜润滑时的温度值高出一倍。较高
的汕膜温度必然伴随着较大的齿面闪温，而后者与轮齿胶合失
效戚息相关。
5随着油膜比厚的增大，齿面摩擦系数先呈下降趋势，当
油膜比厚增大到一定值时，摩擦系数反而呈上升趋势，这主要
是山于油膜厚度增大到一定值时，润滑油粘度的增加，引起流
体粘性剪切增大的缘故。在边界润滑状态下，由于粗糙峰之间
的固体摩擦而导致较高的摩擦系数，且该系数大小沿轮齿传动
啮合线基本不变。到达混合润滑状态后直至全膜润滑，齿面摩
擦系数沿啮合线呈多峰值变化。在节点啮合时，摩擦系数达到
最低值;其最大值则出现在单、双齿啮合转折点。此结论与前
人的实验结果相当吻合〔‘”。这从一个侧面反映了本计算方法的
正确性和研究结果的可信性。
本文的不足之处在于:
1、木文未考虑齿轮传动中的非稳态性及润滑油的非牛顿性等
因素;
2、缺乏实验验证。
It is well knew that elasticity hydrodynamical lubrication(EHL) consists of the boundary lubrication, the mixed lubrication and the full lubrication, the ratio of the average film thickness and synthesis asperity of the average extract value( ) is an important parameter to tell the lubrication state. At the condition of 0. 5 This paper summarized former investigations firstly, then
analyzed the thermal EHL theory of mixed linear contact lubrication. Based on it, the paper adopted the numerical value method intersecting the gradation method and the reversion method. In the process of accounting, the calculational area was divided into three parts, using improved reversion method in the middle area where there were heavy loads, calculating the movement equation and the continuum equation by the pursue method. In the entrance area and the exit area where the loads were lighter, the paper used the gradation alternate method, computing the equation groups of lubrication by Runge-Kutta method of the forth order.
Using the special computer program, the paper chose the transmission parameters of involute straight-teeth column gear, calculating 99 groups of data, been based on the thermal EHL of mixed linear contact lubrication. And it analyzed the ratio of the average film thickness and synthesis asperity of the average extract value(A) and gear surface parameters' s influences to the ratio of contact loads, the pressure distributions, the film thicknesses and the temperature distribution. At the same time, it discussed the distribution rule of gear surface friction coefficients along the mesh line at different A. Through summarizing and analyzing
the results of theory calculation, it got the conclusions as followings:
1. In the condition of mixed lubrication state, the total loads consists of the loads gear surface asperity contacting absolutely and the film pressure of hydro-lubrication. The ratio of the two kinds of loads is named as the ratio of contacting loads. The ratio changes greatly as the change of A, especially from 0. 5 to 1. 5. When 3.0 2. For the machining teeth surface of grinding in industry, the grain direction of asperity is often vertical to the opposite movement direction of teeth surface. The list is named as the list of landscape orientation. The results of calculation made clear to all that the film thickness formed by the asperity surface of landscape orientation was deeper than that of the smooth surface. Maybe some people amazed the result. But it has already been testified by the theory calculation and experimentation. The reason is mainly.about the so-called "pump domino affect" , and during the decrease of A , the domino affect occupied more and more
functions. WhenA 6, the film thickness between surfaces of asperity is almost equal to that between smooth surfaces.
3. When the teeth surfaces of asperity contacted, the pressure distribution consisted of hydro-pressure and contacted pressure of asperity. In the condition of A 1, the asperity action plays a role primitively. When A = 0.2 , the pressure distribution translated into the distribution of single asperity, and the loads beared by asperity occupied more than 90% of the total loads. For the pressure distribution, as the decreasing of film thickness, the value of the second top of pressure also decreased, and the place moved to the entrance area gradually.
4. The variety of A played an important role to the temperature distribution. As the value of A is decreasing, more and more asperities take part in contacting each other. Th
本文首先综述了前人的研究工作，接着，分析了混合润滑线接触热弹流理论。在此基础上，采用顺解、逆解交叉使用的数值方法进行数值计算。计算中将待解区域分为三个子区域，在载荷较重的中间区采用改进后的逆解法，借助追赶法求解运动方程和连续方程；在载荷较轻的入口区和出口区则采用顺解迭代法，通过四阶龙格库塔法求解润滑方程组。
利用本文开发的计算机程序，选用渐开线直齿圆柱齿轮传动参数作为输入数据，共计进行了99组混合润滑线接触热弹流数值计算；从理论上分析了油膜比厚和齿面形貌参数对接触载荷比、压力分布、油膜厚度和温度分布的影响；探讨了不同油
太原理工大学硕士研究生学位论文
膜比厚条件下齿面摩擦系数沿齿轮传动啮合线的分布规律。总
结、分析理论计算结果后形成如下主要研究结论:
1在混合润滑状态下，总体载荷由齿面粗糙峰接触压力和
流体润滑油膜压力共同承担，二者之比称为接触载荷比。在此
状态下，该比值随着油膜比厚A的改变而发生显著变化，特别
是当八在0.5一1.5变动时，这种变化尤为明显;当3.0<八<6.0时，
接触载荷比随A的变化趋势较为平缓，粗糙峰承载比例微乎其
微;而当油膜比厚八之6时，几乎所有载荷全由流体压力承担。
2对于工业中常见的磨削加工齿面，其粗糙度纹理方向往
往垂直于齿面相对运动方向，此类条纹被称之为横向条纹。本
计一算结果昭示:横向条纹粗糙表面形成的油膜厚度大于相应光
滑表面的膜厚值。这乍看起来似乎有些荒诞，但己被理论计算
和实验结果所印证〔29]。究其原因，主要是此类条纹产生所谓的
“泵效应”，并且随着油膜比厚的逐渐降低，这种“泵效应”作
用日趋明显。但当油膜比厚A之6后，粗糙表面间的油膜厚度与
光滑表面间的膜厚值基本相同。
3粗糙齿面接触时的压力分布由流体压力和粗糙峰接触
压力两部分组成。当油膜比厚A引时，粗糙峰作用开始凸现。
当A二0.2口寸，压力分布变成单峰分布，粗糙峰所承担的载荷将
占到总体载荷的90%以上。就压力分布而言，随着油膜比厚的
降低，二次压力峰数值减小，且其位置逐渐向入口区移动。
4油膜比厚的变化对于温度分布具有重要影响。随着油膜
太原理工大学硕士研究生学位论文
比厚的减小，愈来愈多的粗糙峰参与接触，固体摩擦产生的大
量热造成了油膜温度的攀升。当轮齿在边界润滑状态下工作时一，
接触区的油膜温度几乎比全膜润滑时的温度值高出一倍。较高
的汕膜温度必然伴随着较大的齿面闪温，而后者与轮齿胶合失
效戚息相关。
5随着油膜比厚的增大，齿面摩擦系数先呈下降趋势，当
油膜比厚增大到一定值时，摩擦系数反而呈上升趋势，这主要
是山于油膜厚度增大到一定值时，润滑油粘度的增加，引起流
体粘性剪切增大的缘故。在边界润滑状态下，由于粗糙峰之间
的固体摩擦而导致较高的摩擦系数，且该系数大小沿轮齿传动
啮合线基本不变。到达混合润滑状态后直至全膜润滑，齿面摩
擦系数沿啮合线呈多峰值变化。在节点啮合时，摩擦系数达到
最低值;其最大值则出现在单、双齿啮合转折点。此结论与前
人的实验结果相当吻合〔‘”。这从一个侧面反映了本计算方法的
正确性和研究结果的可信性。
本文的不足之处在于:
1、木文未考虑齿轮传动中的非稳态性及润滑油的非牛顿性等
因素;
2、缺乏实验验证。
It is well knew that elasticity hydrodynamical lubrication(EHL) consists of the boundary lubrication, the mixed lubrication and the full lubrication, the ratio of the average film thickness and synthesis asperity of the average extract value( ) is an important parameter to tell the lubrication state. At the condition of 0. 5
analyzed the thermal EHL theory of mixed linear contact lubrication. Based on it, the paper adopted the numerical value method intersecting the gradation method and the reversion method. In the process of accounting, the calculational area was divided into three parts, using improved reversion method in the middle area where there were heavy loads, calculating the movement equation and the continuum equation by the pursue method. In the entrance area and the exit area where the loads were lighter, the paper used the gradation alternate method, computing the equation groups of lubrication by Runge-Kutta method of the forth order.
Using the special computer program, the paper chose the transmission parameters of involute straight-teeth column gear, calculating 99 groups of data, been based on the thermal EHL of mixed linear contact lubrication. And it analyzed the ratio of the average film thickness and synthesis asperity of the average extract value(A) and gear surface parameters' s influences to the ratio of contact loads, the pressure distributions, the film thicknesses and the temperature distribution. At the same time, it discussed the distribution rule of gear surface friction coefficients along the mesh line at different A. Through summarizing and analyzing
the results of theory calculation, it got the conclusions as followings:
1. In the condition of mixed lubrication state, the total loads consists of the loads gear surface asperity contacting absolutely and the film pressure of hydro-lubrication. The ratio of the two kinds of loads is named as the ratio of contacting loads. The ratio changes greatly as the change of A, especially from 0. 5 to 1. 5. When 3.0
functions. WhenA 6, the film thickness between surfaces of asperity is almost equal to that between smooth surfaces.
3. When the teeth surfaces of asperity contacted, the pressure distribution consisted of hydro-pressure and contacted pressure of asperity. In the condition of A 1, the asperity action plays a role primitively. When A = 0.2 , the pressure distribution translated into the distribution of single asperity, and the loads beared by asperity occupied more than 90% of the total loads. For the pressure distribution, as the decreasing of film thickness, the value of the second top of pressure also decreased, and the place moved to the entrance area gradually.
4. The variety of A played an important role to the temperature distribution. As the value of A is decreasing, more and more asperities take part in contacting each other. Th
引文
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[2] McEween E. The Effect of Variation of Viscosity with Pressure on the Load Carrying Capacity of Oil Film between Gear Teeth. Journal Institute of Petroleum. 1952, v. 38, 655-665.
[3] Adkins R W, Radzimovsky E I. Lubrication Phenomena in Spur Gears, Transaction ASME Journal Basic Eng. 1965, V. 87, 655-656.
[4] Dowson, Higginson, Theory of Involute Gear Lubrication, Inst. Pet. Gear lubrication Symposium.
[5] Gu A. Elastohydrodynamic Lubrication of Involute Gears. Transactions of the ASME Journal of Engineering for Industry. 1973, NOVEMBER, 1164-1170.
[6] Vichard J P. Transient Effects in the Lubrication of Hertzian Contacts. Journal of Mechanical Engineering Science. 1971, Vol. 13, 173-180.
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[39] Bo Jacobson. Thin film lubrication of real surfaces. Tribology. 2000.33, 205-210.
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[41] Hohn B-R, Michaelis K and Kopatsch K. Determination of film thickness, pressure and temperature in elastohydrodynamic lubrication in the past 20 years in Germany. Proc. Instn. Mech. Engrs.,2003,215(part J):235-242
[2] McEween E. The Effect of Variation of Viscosity with Pressure on the Load Carrying Capacity of Oil Film between Gear Teeth. Journal Institute of Petroleum. 1952, v. 38, 655-665.
[3] Adkins R W, Radzimovsky E I. Lubrication Phenomena in Spur Gears, Transaction ASME Journal Basic Eng. 1965, V. 87, 655-656.
[4] Dowson, Higginson, Theory of Involute Gear Lubrication, Inst. Pet. Gear lubrication Symposium.
[5] Gu A. Elastohydrodynamic Lubrication of Involute Gears. Transactions of the ASME Journal of Engineering for Industry. 1973, NOVEMBER, 1164-1170.
[6] Vichard J P. Transient Effects in the Lubrication of Hertzian Contacts. Journal of Mechanical Engineering Science. 1971, Vol. 13, 173-180.
[7] Cheng H S, Wang K L. A Numerical Solution to the Dynaamic Load, Film Thickness and Surface Temperature in Spur Gears. Transactions
of Journal of Mechanical Design, 1981, V. 103,177-195.
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