Analysis on Isothermal Elastohydrodynamic Lubrication of Orthogonal Face Gear

Face-gear drives have been applied in aviation transmissions, in particular, helicopter transmissions, and the lubrication characteristics are an important indicator for estimating the load-carrying capacity of face-gear teeth. In order to analyze the lubrication performance of the face gear under load, equations for the contact path of the face gear loaded tooth contact analysis (LTCA) were established on the basis of the load equivalent error of alignment (LEEA) and the load distribution among the teeth was calculated. Then a method for calculating the contact area and tooth surface velocity of face-gear drives was studied. Face-gear isothermal elastohydrodynamic lubrication (EHL) dimensionless equations are presented. A multigrid algorithm was used to complete the solution of the minimum film thickness and film pressure of face-gear drives. The lubricant film thickness and film pressure variation in the mesh cycle are expressed using example calculations that provide a theoretical basis for face-gear lubrication design.     

Analysis of rough line contacts operating under mixed elastohydrodynamic lubrication conditions

Heavily loaded machine elements, such as gears, usually operate in the mixed lubrication regime. Surface roughness has a significant effect on the pressure distribution, the subsurface stress field, and the friction coefficient. Based on the superposition of a dry rough and a fully flooded smooth contact, a mixed lubrication model has been developed. The roughness profile is assumed to be known. Surface deformation is calculated by taking into account the pressure distribution that is built up by asperity contacts, asperity interactions, and lubricant flow. Thermal and sliding effects are incorporated into the analysis. Non‐Newtonian lubricant behaviour is considered by using a power‐law rheological model. The pressure distribution, subsurface stress field, and friction coefficient were calculated from the model at several points along the contact path for an FZG type C gear pair. It was shown that a significant part of the load is carried by the contacting asperities. The position of the maximum shear stress is very close to the surface.     

Calculation of sliding power loss in spur gear contacts

An engineering-level calculation model for sliding power loss in spur gear contacts is presented. Teeth contact through the line of action is modelled as a constantly changing roller contact whose radius, speed, and load can be calculated from the gear geometry under the given operating conditions. The gear mesh cycle is approximated by a large number of elastohydrodynamic contacts. A constant film thickness and a Hertzian pressure distribution are assumed in each contact. The model includes non-Newtonian lubricant behaviour together with temperature and mixed lubrication effects in contact. The numerical solver is reasonably fast in evaluating effectively the sliding power loss dependence on the essential gear and lubricant parameters. The features and behaviour trends of the calculated sliding power losses have a close similarity with published results obtained from measurements and experiment-based power loss models with mineral oil. The limiting shear stress of the lubricant is observed to have an essential role in the power loss behaviour especially at high loads.     

Temperature—friction characteristics of cylinder lubrication in large,slow, cross‐head marine diesel engines under boundary lubrication conditions

In large, slow, cross‐head marine diesel engines research has increasingly shown that the lubrication regime between piston rings and cylinder liner at top dead centre is of the boundary lubrication type due to the high gas pressure, low sliding speed, and high temperature. This means that the tribological properties of piston ring, cylinder liner, and cylinder lubricant in these types of engine under boundary lubrication conditions should be considered simultaneously when friction and wear between the piston ring and cylinder liner are studied. Until now there has been no standard method to evaluate boundary lubrication performance. There are a few traditional methods used in lubricant research, but their results are not correlated with service conditions. It is important to find a suitable method to evaluate the boundary lubrication performance of lubricants at the laboratory testing stage or before the engine testing stage. The important parameters, such as sliding speed, normal load, materials of the contacting pairs, and lubricant, need all to be controlled. In this paper a systematic experimental procedure, the ‘five times heating and cooling test’, is introduced to assess lubricant properties under boundary lubrication conditions. Most of the parameters mentioned above are controlled. The model contact, of pin‐on‐plate form, is made from the actual piston and liner materials used in a large‐bore, slow, cross‐head marine diesel engine. The temperature characteristics of different blends of lubricants are investigated under boundary lubrication conditions using a pin‐on‐plate reciprocating test rig. These blends of lubricants have the same additives but different base fluids; they nevertheless fulfil the physical and chemical requirements of a real marine diesel engine. The test temperature range is from room temperature to the working temperature of the top piston ring. The experiments show that there are different temperature—friction characteristics for lubricants with different bases and the same additive package and there are also different temperature—friction characteristics during heating up and cooling down for each blend. Single‐base lubricants have more promising temperature—friction characteristics than those of a blend of a high‐viscosity base and a low‐viscosity base at high temperature.     

渐开线直齿圆柱齿轮非稳态热弹流润滑分析

应用多重网格技术,不考虑轮齿表面粗糙度的影响,假设润滑剂为牛顿流体,考虑齿轮重合度对轮齿载荷的影响,根据实际轮齿载荷谱简化的轮齿载荷函数,求得了渐开线直齿圆柱齿轮非稳态热弹流润滑问题的完全数值解。结果表明,考虑油膜温升后,温度对轮齿啮入和啮出点的油膜厚度有显著影响。齿轮啮合过程中的最大油膜压力、最高油膜温升和轮齿间摩擦因数最大值都发生在啮合节点附近。在传动比大于1时,齿轮啮合过程中的最小油膜厚度通常在轮齿的初始啮入点。两轮齿间的油膜温升和摩擦因数受滑滚比、卷吸速度和载荷的影响。     

Global and local analysis of gear scuffing tests using a mixed film lubrication model

Gear tests were performed in a FZG test rig in order to evaluate the influence of the operating conditions (torque, speed and oil bath temperature), gear geometry and base oil viscosity on gear scuffing.A mixed film lubrication model was used to evaluate the normal pressures and shear stresses in several points along the gear meshing line, for each load stage and for all the gear scuffing tests performed.The gear scuffing results were analyzed using two different approaches: one considering global gear parameters defined at the meshing line scale and another based on local parameters at the roughness asperity scale, determined using the mixed film lubrication model.The analysis at the roughness asperity level was used to complete the scuffing study performed with global gear contact parameters, explaining the occurrence of scuffing during ‘running-in’, justifying the zones in teeth flanks where the first scuffing marks appear and supplying indicators for low scuffing resistance at high oil bath temperatures.     

Thermo-elastohydrodynamic lubrication of an involute gear

This paper analyses the thermo-elastohydrodynamic lubrication on an involute spur gear tooth surface and the influence of the inlet temperature of the lubricant. The oil film temperature distribution shows a minimum near the point where the pressure distribution is a maximum and the energy loss a minimum. Then the temperature increases slightly in the outlet region. Calculated results show a decrease of a few percent in the maximum pressure distribution compared with an oil film on a rigid surface. Based on oil film thickness and gear tooth deflection, the load sharing coefficient and the relative transmitting errors are calculated. The behaviour of the oil film due to the variation of the normal tooth load at the transition point of the meshing is investigated also     

Geometric effects in high‐temperature vapour‐phase lubrication using hydrocarbon feed gases

The effectiveness of ‘far‐field’ vapour‐phase lubrication, in which areas of a bearing surface that are cycled through the contact are exposed to vapour while outside the contact, has been demonstrated in both sliding and combined roll slide tests using acetylene vapours to deposit pyrolytic graphite. Friction coefficients as low as μ = 0.008 have been measured for steel at 540°C with far‐field acetylene concentrations as low as 5%. Effective vapour‐phase lubrication depends on solid lubricant deposition that exceeds the contact's capacity to remove solid lubricant through wear. While the rate of removal is increased by increasing the sliding velocity, in far‐field vapour‐phase lubrication the rate of lubricant deposition, and therefore the lubrication effectiveness, is augmented by increased areas available for far‐field deposition, such as those provided by performing wear tests with increased wear‐track diameters. These geometric concepts may be considered in rolling‐element bearing and gear set applications where vapour‐phase lubrication is to be employed.     

A Theoretical Analysis of Mixed Lubrication by Macro Micro Approach: Part I—Results in a Gear Surface Contact

Mixed lubrication is a key to bring the performance analysis to the failure analysis in most tribological components. A macro-micro approach to mixed lubrication has been developed in the present model. The relation between the average contact pressure and the average gap for a typical rough contact patch is first determined numerically in micro scale. Using this relation, the average gap, average oil-film pressure, and average contact pressure in a mixed-lubricated elastohydrodynamic contact can be solved simultaneously in macro scale by treating the contact to be smooth. The total pressure is assumed a superposition of average asperity contact pressure and lubricant pressure. The new approach is simple, efficient and robust, and covers entire range of the load ratio, from unity (dry contact) to zero (full-film EHL). In addition, it can be used for a wide range of operating conditions and on a much larger contact area with a much less computing time than deterministic simulation of mixed lubrication. Implementation of the Fast Fourier Transform (FFT) allows for a rapid calculation of the elastic deformation and asperity con/act pressure. As a demonstration to this new approach, a parametric study of dimensionless speed, load and contact shape on the load ratio and gap ratio was conducted for a gear rough surface of the load ratio, from unity (dry contact) to zero (full-film EHL). In addition, it can be used for a wide range of operating conditions and on a much larger contact area with a much less computing time than deterministic simulation of mixed lubrication. Impletmentation of the Fast Fourier Transform (FFT) allows for a rapid calculation of the elastic deformation and asperity contact pressure. As a demonstration to this new approach, a parametric study of dimensionless speed, load and contact shape on the load ratio and gap ratio was conducted for a gear rough surface     

Integrated wear prediction model for cylindrical gear with variable hyperbolic circular arc tooth trace under mixed elastohydrodynamic lubrication

Cylindrical gear with variable hyperbolic circular arc tooth trace (VH-CATT) is a new type of gear. Sliding wear is the main mode of the surface failure of multiple mechanical parts. Both the lubrication state and contact temperature considerably influence wear characteristics, which may aggravate the transmission performance of gear pairs. Wear, contact temperature, as well as lubrication states are jointly explored. Therefore, an integrated wear prediction model was proposed through taking into account flash contact temperature and surface roughness of VH-CATT cylindrical gears in mixed elastohydrodynamic lubrication. According to the equivalent ellipse contact model of VH-CATT cylindrical gears and tooth surface equation, normal curvature and velocity relations for VH-CATT cylindrical gears were observed, and the normal meshing force was obtained through the consideration of load sharing coefficients and quality grades. Flash contact temperature was estimated by using the literature. This study proposes analytical solutions for investigating how various surface roughness, operation, and geometric parameters affect asperity contact ratio (ACR), asperity contact pressure (ACP), flash contact temperature (FCT), as well as wear depth (WD) related to driving gears. ACR, ACP, FCT, as well as WD initially decrease and then increase from engaging-in to engaging-out processes. The minimum occurs at the pitch point. The WD declines as module, cutter radius, and rotational velocity increase while augmenting when surface roughness and torques increase. The maximum and minimum wear depths in driving gears occur at the dedendum and pitch point, respectively. Its overall wear is reduced by 23.16 % compared to the wear of spur gears. The results are valuable for the studies of tooth pitting, wear resistance, and fatigue life improvement for VH-CATT cylindrical gear. These studies can provide verification data and references required for engineering designs and VH-CATT cylindrical gear operations.

     

On the theory of time-dependent micro-TEHL for a non-Newtonian lubricant in line contacts

This paper presents a relatively complete numerical solution to time-dependent micro-thermoelastohydrodynamic lubrication in line contacts subjected to constant load and entraining velocity. Sinusoidal functions are employed to model the traverse roughness on contact surfaces. The Eyring model is used to describe the non-Newtonian flow of the lubricant. With respect to time, the problem is treated as a periodic one so that most variables, such as pressure, film thickness and temperature, can be considered as periodic functions. An efficient algorithm is developed, and a number of cases are solved. The results indicate that the lubricant squeeze induced by the motion and interaction of rough surfaces significantly affects the solution of micro-thermoelastohydrodynamic lubrication.     

渐开线直齿轮瞬态微观热弹流润滑分析

考虑了瞬态效应、轮齿表面油膜温度场和轮齿表面纵向粗糙度等因素,对渐开线直齿圆柱齿轮的弹流润滑问题进行研究。载荷由双齿或单齿承担,根据实际载荷谱简化的轮齿载荷曲线,利用压力求解的多重网格法和弹性变形求解的多重网格积分法以及温度求解的逐列扫描技术,得到渐开线直齿轮瞬态微观热弹流润滑问题的完全数值解,讨论了轮齿间油膜的厚度、压力、温度沿啮合线的变化规律。数值计算结果表明,齿轮表面纵向粗糙度对轮齿间油膜的压力、膜厚、温升都有较大影响。考虑轮齿表面粗糙度后,油膜压力和温升明显增大,并随压力的增加而影响越来越显著,粗糙峰使油膜压力分布和温度分布产生振荡,轮齿表面的粗糙峰对摩擦因数影响较小,摩擦因数和最高温升在节点两侧最大。     

A method for testing lubricants under conditions of scuffing. Part I. Presentation of the method

A method for the tribological assessment of lubricants under conditions of scuffing is presented. The method uses a four‐ball tester, and allows one to assess the effect of lubricant on scuffing intensity through an analysis of changes in the friction torque and wear of the stationary balls, at continuously increasing load. The behaviour of a lubricant under scuffing conditions can be characterised using the so‐called limiting pressure of seizure p_oz, which depends on the load at which the balls seize and the average value of the wear area calculated from the wear‐scar diameters measured on the stationary balls. A comparison is made ‐ from the point of view of the resolution, time consumption, and cost ‐ of the new method with the existing, standard tests, using a four‐ball tester and a gear test rig (FZG). It is concluded that the proposed method, unlike standard FZG and certain four‐ball tests, enables one to differentiate between gear oils, in agreement with their API GL performance level. The very short run‐time of the new method enables one to perform more tests and obtain a low standard deviation. The new method is much cheaper than the standard four‐ball and FZG methods.     

Thin film lubrication of sliding point contacts of AISI 52100 steel

The mechanism of thin film lubrication of sliding point contacts of AISI 52100 steel has been studied as a function of load, sliding speed, composition and temperature of the lubricant.Below certain critical combinations of Hertzian pressure, speed and temperature the surfaces are kept apart by an elastohydrodynamic lubricant film. The load carrying capacity of this film depends primarily on the effective viscosity of the lubricant in the contact region which decreases with bulk oil temperature and with increasing sliding speed, because of friction induced thermal effects. After breakdown of the EHD film, boundary lubrication may still prevent severe adhesive wear. The transition from the boundary lubricated regime towards the regime of severe adhesive wear is a function of load (normal force), speed and bulk oil temperature and possibly depends on the conjunction temperature. Irrespective of the initial lubrication condition, oxidation of the steel surfaces leads to the (re)establishment of low friction, mild wear conditions.     

The Effect of Lubricants on Gear Tooth Scuffing

This paper discusses the effect of some lubricant variables and other relevant factors on gear tooth scuffing. Scuffing is defined as any form of scoring or abrasion of the tooth surface due to metal-to-metal contact. The scuff-limited load is defined as the tooth load at which an arbitrary amount of the working tooth area is scuffed. The factors considered include lubricant bulk viscosity, lubricant type and deterioration, test gear and test machine variables, gear speed, the location and rate of lubricant supply, lubricant supply temperature, and the presence of inert gas atmospheres. The results are compared with, and examined in the light of, other published data.     

FHERMAL ANALYSIS OF FRICTIONAL DISK IN SPEEDING WET CLUTCH

Multi-frictional disks are employed to transmit the torque in speeding wet clutch,and the oil thickness within frictional disks could be adjusted for practical output speeding.As oil combined with u-hydrocarbon or polyester is getting widely used as lubricant and the speeding wet clutch works within hydrodynamic lubrication,mixture lubrication,boundary lubrication and contact situation,established the thermal analysis model for investigating the behavior of frictional disks in speeding wet clutch,which covers the power-law fluid model,Patir-Cheng average flow model,GT asperity contact model,oil film inertia and heat effects,mean energy equation,and heat conduction equation.The for-mulas in the model are deduced.The numeral calculation and analysis for hydrodynamic lubricationand mixture lubrication are executed.Relationships and variations among transmitting torque,mean push pressure,output speed,and load are presented.Thermal effect should be considered during the hydrodynamic lubrication and larger transmitting torque makes earlier entrance to mixture lubrication.     

渐开线直齿圆柱齿轮非牛顿瞬态弹流润滑分析

齿轮的润滑设计都是应用理想牛顿流体的结果,但实际上,在中、轻载荷下Ree Eyring流体更符合实际。因 此研究齿轮在非牛顿润滑下的瞬态弹流机理,对于指导齿轮润滑问题的设计更具有工程实际价值。本文应用数值 稳定性好、收敛速度快和计算精度高的多重网格算法,得到了用Ree Eyring流体润滑的齿轮瞬态弹流问题的完全数 值解。     

WN齿轮传动弹流润滑及接触摩擦效率研究

应用WN齿轮接触摩擦与弹流润滑机制结合的方法进行效率分析.依据WN齿轮副啮合原理,创建该齿轮动力润滑与混合摩擦分析模型,分析了啮合中载荷与弹性接触对油膜厚度的影响,探讨油膜形成机制和承载特性;通过啮合过程中的接触摩擦分析,推导出WN齿轮啮合时动力传动效率计算新方程;分析齿轮运转速度、负载及润滑等对传动效率的影响.结果表明:在高速下WN齿轮的传动效率高于渐开线齿轮而在低速下却相反;旋转速度对传动效率的影响要比载荷的影响更大.通过实例计算和试验分析验证了本方法的有效性.