Solution of Load Distribution on the Contact Line of Helical Gears With EHL Theory

1994 ◽  
Author(s):  
Yu Tonghui ◽  
Chen Chenwen ◽  
Wang Liqin
Keyword(s):  
Contact Line ◽  
Load Distribution ◽  
Multigrid Method ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Elastohydrodynamic Lubrication ◽  
Helical Gear ◽  
Contact Lines ◽  
Helical Gears ◽  
Special Boundary Condition

Abstract On the base of analysis of the effects of each term in Renolds equaiton on the lubrication state of helical gears, the three dimensional elastohydrodynamic lubrication (EHL) problem is discomposed into two dimensional problems to deal with. A special boundary condition for helical gear EHL problem is led in and applying multigrid method (MGM), numerical solutions for the helical gear EHL problem are accomplished along the contact line. Film shapes and pressure ditributions with typical EHL features are obtained at discreted points on the contact line. The procedure presented here to calculate the load distribution on the contact line can also be used to calculate the load shares among different contact lines.

Meshing Efficiency of Involute Helical Gears Based on Elastohydrodynamic Lubrication

2014 ◽  
Vol 597 ◽  
pp. 450-453
Author(s):  
Bin Wang ◽  
Xin Bo Chen
Keyword(s):  
Load Distribution ◽  
Integration Method ◽  
Elastohydrodynamic Lubrication ◽  
Helical Gear ◽  
Dynamic Efficiency ◽  
Unit Load ◽  
Helical Gears ◽  
Double Integration ◽  
Simulation Results ◽  
Meshing Process

To analyze the dynamic efficiency of helical gear during meshing process, a meshing efficiency model based on elastohydrodynamic lubrication (EHL) was established. The meshing plane between the pinion and gear was divided into seven parts in accordance to the regularity of unit load distribution. The total meshing power lose and average meshing power lose were calculated through a double integration method. The simulation results show that the method is feasible to calculate the meshing efficiency of gear pairs.

The dynamics of three-dimensional liquid bridges with pinned and moving contact lines

2012 ◽  
Vol 707 ◽  
pp. 521-540 ◽  
Author(s):  
Shawn Dodds ◽  
Marcio S. Carvalho ◽  
Satish Kumar
Keyword(s):  
Contact Line ◽  
Liquid Bridge ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Liquid Bridges ◽  
Contact Lines ◽  
Flat Surfaces ◽  
Moving Contact ◽  
Moving Contact Lines ◽  
Contact Line Friction

AbstractLiquid bridges with moving contact lines are relevant in a variety of natural and industrial settings, ranging from printing processes to the feeding of birds. While it is often assumed that the liquid bridge is two-dimensional in nature, there are many applications where either the stretching motion or the presence of a feature on a bounding surface lead to three-dimensional effects. To investigate this we solve Stokes equations using the finite-element method for the stretching of a three-dimensional liquid bridge between two flat surfaces, one stationary and one moving. We first consider an initially cylindrical liquid bridge that is stretched using either a combination of extension and shear or extension and rotation, while keeping the contact lines pinned in place. We find that whereas a shearing motion does not alter the distribution of liquid between the two plates, rotation leads to an increase in the amount of liquid resting on the stationary plate as breakup is approached. This suggests that a relative rotation of one surface can be used to improve liquid transfer to the other surface. We then consider the extension of non-cylindrical bridges with moving contact lines. We find that dynamic wetting, characterized through a contact line friction parameter, plays a key role in preventing the contact line from deviating significantly from its original shape as breakup is approached. By adjusting the friction on both plates it is possible to drastically improve the amount of liquid transferred to one surface while maintaining the fidelity of the liquid pattern.

An Experimental and Theoretical Study of Quasi-Static Behavior of Double-Helical Gear Sets

2020 ◽  
Vol 143 (4) ◽  
Author(s):  
M.R. Kang ◽  
A. Kahraman
Keyword(s):  
Load Distribution ◽  
Theoretical Study ◽  
Power Transmission ◽  
Transmission Error ◽  
Helical Gear ◽  
Static Behavior ◽  
World Congress ◽  
Helical Gears ◽  
Support Conditions ◽  
Stagger Angle

Abstract The quasi-static behaviors of a double-helical gear pair is investigated both experimentally and theoretically with the main focus on the influence of the key design and manufacturing parameters associated with double-helical gears, including nominal right-to-left stagger angle, the stagger angle deviation (error) from the nominal stagger angle, and axial gear supporting conditions. On the experimental side, a double-helical gear test setup proposed earlier (Kang, M. R., and Kahraman, A., 2015, “An Experimental and Theoretical Study of Dynamic Behavior of Double-Helical Gear Sets,” J. Sound Vib., 350, pp. 11–29). for studying dynamics of the same system is employed that allows adjustable right-to-left stagger angles, intentional stagger errors, and axial support conditions. Specific measurement systems are developed and implemented simultaneously to measure the static motion transmission error and axial motions of the gears under low-speed conditions, as well as gear root strains to determine right-to-left load-sharing factors. A test matrix that covers wide ranges of stagger angles, intentional stagger error, and axial support conditions is executed within a range of torque transmitted to establish an extensive database. On the modeling side, the measured quasi-static behavior of double-helical gear pairs is simulated by using an existing quasi-static double-helical load distribution model (Thomas, J., and Houser, D. R., 1992, “A Procedure for Predicting the Load Distribution and Transmission Error Characteristics of Double Helical Gears,” World Congress-Gear and Power Transmission, The 3rd World Congress—Gear and Power Transmission, Paris.). Direct comparison of the measurements and predictions of loaded static transmission error, axial play, root stresses, and right-to-left load-sharing factors are used to validate the quasi-static model as well as describing the measured behavior.

scholarly journals An Improved Algorithm for Calculating Friction Force and Torque in Involute Helical Gears

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Lin Han ◽  
Wentie Niu ◽  
Dawei Zhang ◽  
Fujun Wang
Keyword(s):  
Friction Coefficient ◽  
Friction Force ◽  
Load Distribution ◽  
Distribution Model ◽  
Contact Lines ◽  
Helical Gears ◽  
Constant Friction ◽  
Single Tooth ◽  
The Difference ◽  
Typical Design

Time varying frictional force and torque are one of the main exciting sources of vibration in helical gears. This paper presents an approach to determine the friction force and torque in involute helical gears considering nonuniform load distribution along contact lines. An analytical load distribution model is employed and extended to obtain the load per unit of length along contact lines. Friction force and torque models under nonuniform assumption are derived. Comparisons of the determined friction force and torque with the results from uniform assumption are made. In addition, the differences between constant friction coefficient and varying coefficient are revealed. Moreover, two typical design cases of helical gears are studied. Results show that the fluctuations of friction force and torque under uniform assumption are more significant than those under nonuniform assumption in sample I for a single tooth, but less significant for the sum of those of the three teeth, while in sample II, the fluctuations under uniform assumption are less significant than those under nonuniform assumption. The friction coefficient induced difference is negligible compared with the difference induced by load distribution assumptions.

scholarly journals Effect of load and speed on warship power rear drive system helical gear anti-scuffing properties in thermal elasto-hydrodynamic lubrication

2017 ◽  
Vol 9 (1) ◽  
pp. 168781401668470
Author(s):  
Yongmei Wang ◽  
Junpeng Shao ◽  
Xigui Wang ◽  
Xuezeng Zhao ◽  
Shubao Li ◽  
...  
Keyword(s):  
Hydrodynamic Lubrication ◽  
Contact Region ◽  
Three Dimensional ◽  
Experimental Tests ◽  
Helical Gear ◽  
Film Pressure ◽  
Helical Gears ◽  
Operating Load ◽  
Gear Surface Temperature ◽  
Oil Film Pressure

The key parameters which caused the scoring failure of helical gears are operating load and speed. In this study, the simulations using geometric meshing theory were carried out to investigate the effect of load and speed of warship transmission helical gear system on thermal elasto-hydrodynamic lubrication. The numerical algorithm for the analysis of three-dimensional thermal elasto-hydrodynamic lubrication used in this work has advantage that the film pressure and distributions can be calculated from Reynolds equation for all mixed lubrication regions without any specific boundary condition for the edge of solid contact region. Oil film pressure, film thickness as well as film temperature under different load and speed conditions were obtained and compared. In addition, experimental tests were conducted to determine gear surface temperature under different load and speed conditions. This work provided a guidance to understand the load- and speed-dependent thermal elasto-hydrodynamic lubrication.

scholarly journals A Special Multigrid Strategy on Non-Uniform Grids for Solving 3D Convection–Diffusion Problems with Boundary/Interior Layers

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1123
Author(s):  
Tianlong Ma ◽  
Lin Zhang ◽  
Fujun Cao ◽  
Yongbin Ge
Keyword(s):  
Present Method ◽  
Multigrid Method ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Finite Difference Schemes ◽  
Interior Layer ◽  
Convection Diffusion ◽  
Uniform Grids ◽  
Interior Layers ◽  
Diffusion Problems

Boundary or interior layer problems of high-dimensional convection–diffusion equations have distinct asymmetry. Consequently, computational grid distributions and linear algebraic systems arising from finite difference schemes for them are also asymmetric. Numerical solutions for these kinds of problems are more complicated than those symmetric problems. In this paper, we extended our previous work on the partial semi-coarsening multigrid method combined with the high-order compact (HOC) difference scheme for solving the two-dimensional (2D) convection–diffusion problems on non-uniform grids to the three-dimensional (3D) cases. The main merit of the present method is that the multigrid method on non-uniform grids can be performed with a different number of grids in different coordinate axes, which is more efficient than the multigrid method on non-uniform grids with the same number of grids in different coordinate axes. Numerical experiments are carried out to validate the accuracy and efficiency of the present method. It is shown that, without losing the high precision, the present method is very effective to reduce computing cost by cutting down the number of grids in the direction(s) which does/do not contain boundary or interior layer(s).

Analysis of isothermal elastohydrodynamic point contacts lubricated by Newtonian fluids using multigrid methods

1997 ◽  
Vol 211 (7) ◽  
pp. 493-508 ◽  
Author(s):  
P Ehret ◽  
D Dowson ◽  
C M Taylor ◽  
D Wang
Keyword(s):  
Smooth Surface ◽  
Multigrid Method ◽  
Integration Method ◽  
Large Range ◽  
Three Dimensional ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Point Contacts ◽  
Dimensional Surface ◽  
Good Agreement

A multigrid multi-integration method has been used to solve the elastohydrodynamic lubrication (EHL) point contact problem over a large range of loads. Solutions obtained with the multigrid method are compared with those computed with an effective influence Newton method. Good agreement has been obtained, which validates the results obtained by both of these independent methods. Smooth surface problems have been used to test the multigrid method, but an example that takes into account a wavy surface has demonstrated the robustness and the large potential of the multigrid method to analyse EHL problems with three-dimensional surface roughness.

Analytical Method on Contact Stress of Helical Gear with Asymmetric Involutes

2011 ◽  
Vol 321 ◽  
pp. 157-160 ◽  
Author(s):  
Ning Li ◽  
Wei Li ◽  
Ning Liu ◽  
Hua Gang Liu
Keyword(s):  
Contact Stress ◽  
Contact Line ◽  
Side Surface ◽  
Helical Gear ◽  
Gear Pair ◽  
Line Contact ◽  
Contact Lines ◽  
Large Pressure ◽  
Helical Gear Pair ◽  
Meshing Process

Helical gear with asymmetric involutes is a new kind gear which driving side surface is large pressure angle profile. The numbers of meshing tooth are discussed during helical gear pair meshing process, thus the length of total contact lines is determined easily. It is difficult to calculate contact stress by existing formula because this kind gear is non-standard. A calculating formula is derived which can calculate contact stress of helical gear with asymmetric involutes in this paper. A computer’s software is written in order to calculate instantaneous contact stress of contact line. Contact stress is compared between symmetric helical gear and asymmetric helical gear.

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