Elastohydrodynamic Lubrication of Involute Gears

1973 ◽  
Vol 95 (4) ◽  
pp. 1164-1170 ◽  
Author(s):  
A. Gu
Keyword(s):  
Steady State ◽  
Temperature Rise ◽  
Elastohydrodynamic Lubrication ◽  
Quasi Steady State ◽  
Line Contact ◽  
Viscosity Method ◽  
Temperature Calculation ◽  
Involute Gears ◽  
State Assumption ◽  
Zone Temperature

A criterion is suggested for the application of the steady state elastohydrodynamic theories to the analysis of involute gear contacts. The criterion is based on a comparison of two physical time scales characterizing the system. It is found that for heavily loaded gears the unsteadiness effect may be important. A mean-viscosity method using a composite pressure-viscosity model for the lubricant is introduced for contact zone temperature calculation. An example of involute gears is given for the computation of elastohydrodynamic contact variables based on quasi-steady state assumption. It is found that the surface temperature rise in the tooth tip contact is much higher than that in the pitch line contact.

Size effect on thermal elastohydrodynamic lubrication of industrial chain bush-pin hinge pair

2019 ◽  
Vol 71 (9) ◽  
pp. 1080-1085 ◽  
Author(s):  
Mingyu Zhang ◽  
Jing Wang ◽  
Yi Liu ◽  
Longjie Dai ◽  
Zhaohua Shang
Keyword(s):  
Friction Coefficient ◽  
Film Thickness ◽  
Temperature Rise ◽  
Elastohydrodynamic Lubrication ◽  
Curvature Radius ◽  
Line Contact ◽  
Content Type ◽  
Oil Film ◽  
Industrial Chain ◽  
Infinite Line

Purpose The purpose of this paper is to use elastohydrodynamic lubrication (EHL) theory to study the variation of the equivalent curvature radius “R” on the change of oil film thickness, pressure, temperature rise and friction coefficient in the contact zone between bush-pin in industrial chain drive. Design/methodology/approach In this paper, the contact between bush and pin is simplified as infinitely long line contact. The lubrication state is studied by numerical simulation using steady-state line contact thermal EHL. The two constitutive equations, namely, Newton fluid and Ree–Eyring fluid are used in the calculations. Findings It is found that with the increase of equivalent curvature radius, the thickness of oil film decreases and the temperature rise increases. Under the same condition, the friction coefficient of Newton fluid is higher than that of Ree–Eyring fluid. When the load increases, the oil film thickness decreases, the temperature rise increases and the friction coefficient decreases; and the film thickness increases with the increase of the entraining speed under the condition “R < 1,000 mm”. Research limitations/implications The infinite line contact assumption is only an approximation. For example, the distances between the two inner plates are 5.72 mm, by considering the two parts assembled into the inner plates, the total length of the bush is less than 6 mm. The diameter of the pin and the bore diameter of the bush are 3.28 and 3.33 mm. However, the infinite line contact is also helpful in understanding the general variation of oil film characteristics and provides a reference for the future study of finite line contact of chain problems. Originality/value The change of the equivalent radius R on the variation of the oil film in the contact of the bush and the pin in industrial chain drive was investigated. The size effect influences the lubrication characteristic greatly in the bush-pin pair.

scholarly journals A much better replacement of the Michaelis–Menten equation and its application

2019 ◽  
Vol 12 (01) ◽  
pp. 1950008
Author(s):  
Banghe Li ◽  
Bo Li ◽  
Yuefeng Shen
Keyword(s):  
Steady State ◽  
Enzyme Kinetics ◽  
Polynomial Equation ◽  
Mass Action ◽  
Reaction Process ◽  
Quasi Steady State ◽  
State Laws ◽  
New Equation ◽  
Reaction Processes ◽  
State Assumption

Michaelis–Menten equation is a basic equation of enzyme kinetics and gives acceptable approximations of real chemical reaction processes. Analyzing the derivation of this equation yields the fact that its good performance of approximating real reaction processes is due to Michaelis–Menten curve (8). This curve is derived from Quasi-Steady-State Assumption (QSSA), which has been proved always true and called Quasi-Steady-State Law by Banghe Li et al. [Quasi-steady state laws in enzyme kinetics, J. Phys. Chem. A 112(11) (2008) 2311–2321]. Here, we found a polynomial equation with total degree of four [Formula: see text] (14), which gives more accurate approximation of the reaction process in two aspects: during the quasi-steady-state of the reaction, Michaelis–Menten curve approximates the reaction well, while our equation [Formula: see text] gives better approximation; near the end of the reaction, our equation approaches the end of the reaction with a tangent line the same to that of the reaction process trajectory simulated by mass action, while Michaelis–Menten curve does not. In addition, our equation [Formula: see text] differs to Michaelis–Menten curve less than the order of [Formula: see text] as [Formula: see text] approaches [Formula: see text]. By considering the above merits of [Formula: see text], we suggest it as a replacement of Michaelis–Menten curve. Intuitively, this new equation is more complex and harder to understand. But, just because of its complexity, it provides more information about the rate constants than Michaelis–Menten curve does. Finally, we get a better replacement of the Michaelis–Menten equation by combing [Formula: see text] and the equation [Formula: see text].

A thermal EHL investigation on plate-pin hinge pairs in silent chains using a narrow finite line contact

2020 ◽  
Vol 72 (10) ◽  
pp. 1139-1145
Author(s):  
Mingyu Zhang ◽  
Jing Wang ◽  
Jinlei Cui ◽  
Peiran Yang
Keyword(s):  
Film Thickness ◽  
Temperature Rise ◽  
Elastohydrodynamic Lubrication ◽  
Radius Of Curvature ◽  
Line Contact ◽  
Equivalent Radius ◽  
Content Type ◽  
Finite Line Contact ◽  
Pressure Peak ◽  
Finite Line

Purpose The purpose of this paper is to numerically study the variations of oil film pressure, thickness and temperature rise in the contact zone of plate-pin pair in silent chains. Design/methodology/approach A steady-state thermal elastohydrodynamic lubrication (EHL) model is built using a Ree–Eyring fluid. The contact between the plate and the pin is simplified as a narrow finite line contact, and the lubrication state is examined by varying the geometry and the plate speed. Findings With increase in the equivalent radius of curvature, the pressure peak and the central film thickness increase. Because the plate is very thin, the temperature rise can be neglected. Even when the influence of the rounded corner region is less, a proper design can beneficially increase the minimum film thickness at both edges of the plate. Under a low entraining speed, strong stress concentration results in close-zero film thickness at both edges of the plate. Originality/value This study reveals the EHL feature of the narrow finite line contact in plate-pin pairs for silent chains and will support the future works considering transient effect, surface features and wear.

scholarly journals On the quasi-steady-state assumption applied to Michaelis-Menten and suicide substrate reactions with diffusion

1991 ◽  
Vol 337 (1646) ◽  
pp. 299-306 ◽  
Keyword(s):  
Steady State ◽  
Substrate Concentration ◽  
Quasi Steady State ◽  
Enzyme Substrate ◽  
Steady State Assumption ◽  
Suicide Substrate ◽  
Substrate Ratio ◽  
State Assumption ◽  
Recent Extension

We consider a recent extension to the validity of the quasi-steady-state assumption ( QSSA ) which includes the case where the ratio of the initial enzyme to substrate concentration is not necessarily small. We extend the analysis to include diffusion of substrate, in which case the initial enzyme to substrate ratio is spatially dependent and no longer constant. We show that the region in which the QSSA holds depends on the nature of the enzyme-substrate reaction: if the enzyme is inactivated by the substrate then the QSSA holds in a growing disc; if the enzyme is unchanged after reaction then the QSSA holds in a ring travelling through space.

scholarly journals The Quasi-Steady-State Assumption: A Case Study in Perturbation

SIAM Review ◽  
1989 ◽  
Vol 31 (3) ◽  
pp. 446-477 ◽  
Author(s):  
Lee A. Segel ◽  
Marshall Slemrod
Keyword(s):  
Steady State ◽  
Quasi Steady State ◽  
Steady State Assumption ◽  
State Assumption
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