STUDY ON THE LUBRICATION FACTOR OF INVOLUTE SPUR GEARS

Based on a lot of numerical solutions to the problems of the thermalnon-Newtonian elastohydrodynamic lubrication and some fatigue tests with rollers, the lubricationfactor of involute spur gears (called gear for short) is investigated. The results suggest that gearlubrication effects bear close relations to a dimensionless parameter D which is syntheticallydetermined by gearing rotational speed, load, material, dimension and lubricant viscosity. When D<=8, the gear fatigue life increases as the lubricant viscosity is increased; When D>8, however, thelife decreases with the viscosity addition, which is in marked contrast to the lubrication factorZ_L recommended by the International Standard for Computing Cylindrical Gear Strength. At the end, aset of formulae for calculating gear lubrication factors suitable for different working conditionsare advanced.

EFFECT OF INVOLUTE CONTACT RATIO ON THE DYNAMIC PERFORMANCE OF SPUR GEAR WITH NOTOOTH PROFILE MODIFICATION

The effect of involute contact ratio on the torsional vibration behavior ofspur gear-pair is studied analytically through a mass-spring model. The tooth stiffness in model notonly has a relation with time, as many prior studies presented, but, more important, with involutecontact ratio (ICR) as well. The ICR embodies its impact on the spur gear's dynamic performancethrough changing the proportion of tooth stiffness when there are n+1 teeth in contact to toothstiffness when there are n teeth in contact. A couple of curves about impact of ICR on the gear'sdynamic performance are presented, and they clearly demonstrate that the model can accuratelydescribe the effects of ICR on dynamic transmission error. Finally, some conclusions useful toreduce vibration and noise of gear-pair are proposed.

An intelligent method for contact fatigue reliability analysis of spur gear under EHL

To complete the contact fatigue reliability analysis of spur gear under elastohydrodynamic lubrication(EHL) efficiently and accurately, an intelligent method is proposed. Oil film pressure is approximated using quadratic polynomial with intercrossing term and then mapped into the Hertz contact zone. Considering the randomness of the EHL, material properties and fatigue strength correction factors, the probabilistic reliability analysis model is established using artificial neural network(ANN). Genetic algorithm(GA) is employed to search the minimum reliability index and the design point by introducing an adjusting factor in penalty function. Reliability sensitivity analysis is completed based on the advanced first order second moment(AFOSM). Numerical example shows that the established probabilistic reliability analysis model could correctly reflect the effect of EHL on contact fatigue of spur gear, and the proposed intelligent method has an excellent global search capability as well as a highly efficient computing performance compared with the traditional Monte Carlo method(MCM).

Effect of key factors on cold orbital forging of a spur bevel gear

Cold orbital forging is an advanced spur bevel gear forming technology. Generally, the spur bevel gear in the cold orbital forging process is formed by two steps: the preforming step and the final step. Due to the great importance of the final step to gear forming and its complication with interactive factors, this work aims at examining the influence of key factors on the final step in cold orbital forging of a spur bevel gear. Using the finite element(FE) method and control variate method, the influence rules of four key factors, rotation velocity of the upper tool, n, feeding velocity of the lower tool, v, tilted angle of the upper tool, γ, friction factor between the tools and the billet, m, on the geometry and the deformation inhomogeneity of the cold orbital forged gear are thoroughly clarified. The research results show that the flash becomes more homogeneous with increasing v, increasing m, decreasing n or decreasing γ. And the deformation of the gear becomes more homogeneous with increasing v, decreasing n or decreasing γ. Finally, a corresponding experiment is conducted, which verifies the accuracy of FE simulation conclusions.

Effect of integral squeeze film damper on vibration and noise of spur gear with center-distance error

When the actual installation center distance between a pair of spur gears is greater than the theoretical center distance,backlash increases,leading to increased vibration and noise.The structural parameters of an integral squeeze film damper(ISFD)were designed with the stiffness of rigid support as reference to investigate the effect of an ISFD on the dynamic characteristics of a spur gear transmission system with center-distance installation error.A spur gear test bench with center distance-error was built to investigate the vibration and noise reduction characteristics of ISFD.The experimental results indicate that,compared with a rigid support,the ISFD can reduce vibration by approximately 40%and noise by approximately 5 d B.ISFD can effectively absorb the impact energy caused by an increase of in backlash,which is conducive to the stable operation of the spur gear transmission system.

Application of response surface method for contact fatigue reliability analysis of spur gear with consideration of EHL

In order to consider the effects of elastohydrodynamic lubrication(EHL) on contact fatigue reliability of spur gear, an accurate and efficient method that combines with response surface method(RSM) and first order second moment method(FOSM) was developed for estimating the contact fatigue reliability of spur gear under EHL. The mechanical model of contact stress analysis of spur gear under EHL was established, in which the oil film pressure was mapped into hertz contact zone. Considering the randomness of EHL, material properties and fatigue strength correction factors, the proposed method was used to analyze the contact fatigue reliability of spur gear under EHL. Compared with the results of 1.5×105 by traditional Monte-Carlo, the difference between the two failure probability results calculated by the above mentioned methods is 2.2×10-4, the relative error of the failure probability results is 26.8%, and time-consuming only accounts for 0.14% of the traditional Monte-Carlo method(MCM). Sensitivity analysis results are in very good agreement with practical cognition. Analysis results show that the proposed method is precise and efficient, and could correctly reflect the influence of EHL on contact fatigue reliability of spur gear.

Effects of forging parameters on uniformity in deformation and microstructure of AZ31B straight spur gear

The effects of forging parameters on the deformation and microstructure distributions of as-forged straight spur gears wereinvestigated by finite element(FE)simulation and statistical analysis method.Spur gear forging using the movable cavity die designwas investigated by integrating the FE method with the microstructure evolution models for AZ31B magnesium alloys.The requiredinputs such as flow stress curves and microstructure evolution models,were obtained through the Gleeble thermal mechanical testingand quantitative metallography analysis method.Numerical simulation and experimental examination confirm that both thedeformation and microstructure are non-uniformly distributed in the as-forged gears.Decreasing deformation temperature orincreasing strain rate is beneficial to obtaining fine-grained microstructure but is harmful to the uniformity in deformation ormicrostructure.The level of the non-uniformity results from the complex shape of gear and the friction between the billet and dies,which is closely associated with the characteristics of flow stress curve.

Topological Modeling of a One Stage Spur Gear Transmission

Finding a basis of unification for the modeling of mechatronic systems is the search subject of several works.This paper is a part of a general research designed to the application of topology as a new approach for the modeling of mechatronic systems.Particularly,the modeling of a one stage spur gear transmission using a topological approach is tackled.This approach is based on the concepts of topological collections and transformations and implemented using the MGS（modeling of general systems）language.The topological collections are used to specify the interconnection laws of the one stage spur gear transmission and the transformations are used to specify the local behavior laws of its different components.In order to validate this approach,simulation results are presented and compared with those obtained with MODELICA language using Dymola solver.Since good results are achieved,this approach might be used as a basis of unification for the modeling of mechatronic systems.

Thermal elastohydrodynamic lubrication of modified gear system considering vibration

The thermal elastohydrodynamic lubrication characteristics of a modified gear system under a dynamic load were investigated,including the influence of the modification coefficient and vibrations.Based on the dynamic theory of gear systems,a six-degree-of-freedom tribo-dynamics model was established.Thermal elastohydrodynamic lubrication characteristics of a modified gear system under vibrations and a static load were analyzed.The results showed that the positive transmission gear system exhibited the better lubrication effect compared with other transmission types.A thick lubricating oil film could be formed,and the friction coefficient between the teeth and the oil film flash temperature were the smallest.As the modification coefficient increased,the lubrication condition was continuously improved,and the scuffing load capacity was enhanced.The increment of the modification coefficient increased the meshing stiffness of the gear system but reduced the stiffness of the oil film.

Effect of nonlinear impact damping with non-integer compliance exponent on gear dynamic characteristics

A nonlinear impact damping model of single-degree-of-freedom spur cylindrical gear with backlash and time-varying stiffness was established. Systematic analyses of the dynamic responses were performed. First, the nonlinear damping coefficient was considered as a constant parameter with two types of compliance exponent, meanwhile, dynamic factors were adopted to depict the dynamic characteristics. Second, the bifurcation graphs were plotted, where the damping coefficient was obtained along with the impact velocity and coefficient of restitution. The results show that light and heavy load conditions have an effect on the responses when the compliance exponent is integer. On the contrary, when the compliance exponent is non-integer, the dynamic responses are slightly affected, namely the system is more stable than the former situation.

EFFECT OF FRICTIONAL FORCE ON GEARING CONTACT FATIGUE STRENGTH

The model for computing frictional coefficient between two teeth faces at the state of mixed elastohydrodynamic lubrication is established. And then more than 80 sets of numerical calculations and six sets of disc fatigue tests are completed. The results show that when the film thickness ratio λ 〈1.6, frictional coefficient μ is drastically decreased as λ. rises; Thereafter it decreases smoothly until λ=4.5. When λ〉4.5, however, it goes up again with λ, which indicates that the excessive film thickness ratio will deteriorate gearing contact fatigue strength. At the end, the formulae for determining the frictional coefficients are formed.

The Design of Gear Parameters Visual System based on LISP

Article use Visual LISP development tools and DCL dialog technology, which implements the standard straight teeth, a two- dimensional cylindrical gear paranaetric drawing on AutoCAD platform, with easy to operate and improve design efficiency. We achieved that using the dialog box design input parameters, and gear parts of the design calculations, parameters proofreading and all kinds of gear design drawing different structures by programming. The output is fully automated computer-aided design system. The results show that the design of the system significantly improves the efficiency of the part design.

Controlling Flow Instability in Straight Spur Gear Forging Using Numerical Simulation and Response Surface Method

Workability domain without the onset of flow instability was developed by numerical simulation and response surface method （RSM） for complex-shaped straight spur gear forging. The processing map of AZ31B alloys was calculated from flow stress curves and then integrated with the finite element model to simulate the distribution of flow instability in the straight spur gear undergoing isothermal forging process. Occurrence of flow instability depends on forging temperature, punch velocity and billet reduction. Taking forging temperature and punch velocity as design variables, while billet reduction as response variable, RSM of workability domain was established. Analysis of variance indicates that forging temperature is the most significant factor determining the appearance of flow instability in the forged gear. Flow instability is easier to take place at lower temperatures of 250 and 300 ℃ in the early stage of forging but at higher temperatures of 350 and 400 ℃ in the later stage of forging, which is attributed to different deformation mechanisms and dynamic recrystallization behaviors at different temperatures or deformation levels. Meanwhile, increasing punch velocity further reduces the workability of the forged gear. Four different processing paths were chosen to carry out the gear forging trials. Visual observations and metallographic examinations demonstrate that the developed workability domain contributes to optimization of forging parameters.

Two Step Forging Process of Spur Gear Based on Rigid Parallel Motion

To improve the forging process of spur gear,the metal flow rule is investigated in detail,and a hypothesis of radial rigid-parallel-motive (RPM) flow mode is given. Based on the RPM mode a novel specific gear forging technology is put forward by introduced upend forging process and constrained divided-flow technique. Firstly,finite element method is used to simulate the upend forging pre-forming and RPM finish forging,and equivalent stress field and load-stroke curve are investigated. Secondly,a corresponding experiment is carried out with pure lead to validate the numerical simulation. Thirdly,the peak value of conventional forging process is also simulated and is used to compare with the novel forging process,and the result shows that the forming force decreases significantly,about 35%. Finally,the effect on forming load of two key process parameters (the height of gear tooth after pre-forming and friction factor) is analyzed,and the superiority of the novel forging process is further proved.

Experimental-based study of gear vibration characteristics incorporating the fractal topography of tooth surface

Microscopic roughness is inevitable on the gear meshing surface,which is also a key parameter affecting the dynamic response.The surface roughness exhibits self‐affine characteristics across multiscales.To explore the influence of surface fractal topography on the vibration amplitude of the gear system under different rotational speeds and loads,an experimental setup of spur gear transmission is devised.The fractal dimension and fractal roughness of the meshing surface are calculated by the power spectral density method.The relationships between gear response and fractal parameters are revealed experimentally.Results indicate that a rougher tooth surface,that is,a smaller fractal dimension or larger fractal roughness,corresponds to an intense vibration amplitude.The sensitivity of dynamic response to the tooth surface topography varies at different rotational speeds and loads.Under low speed and light load conditions,the fractal dimension and fractal roughness have a more obvious influence on the dynamic response of the gear transmission system.With the increase of speed and load,the macroworking conditions gradually become the main factor attributed to vibration amplitude.