A comprehensive mathematical model for an accurate calculation of the oil film thickness of strip cold rolling

2019 ◽  
Vol 234 (3) ◽  
pp. 350-361
Author(s):  
Xinxiao Bian ◽  
Quan Wang
Keyword(s):  
Mathematical Model ◽  
Film Thickness ◽  
Hydrodynamic Lubrication ◽  
Rolling Force ◽  
Elastohydrodynamic Lubrication ◽  
Rolled Strip ◽  
Asperity Contact ◽  
Oil Film ◽  
Rolling Oil ◽  
Lubricant Viscosity

The surface quality of cold rolled strip is related to a greater extent on the rolling oil film thickness, and there are many factors that affect the oil film thickness. Considering the various factors comprehensively, an integrated mathematical model is established, such as roughness of rolls and strips, elastohydrodynamic lubrication, friction heat and plastic deformation heat in the rolling zone, viscosity varying with temperature and pressure, etc. A series of equations are developed, such as the Reynolds equation of partial membrane hydrodynamic lubrication based on average flow theory, equation of oil film thickness on rough elastic surface, the thermal interface equations between strip, oil film and roller surface, surface asperity contact pressure equation, lubricant viscosity and density equations, motion equation of the oil film, etc. This model is solved by finite difference method to get the film pressure, oil film thickness, and temperature distribution in the rolling zone. The average rolling pressure, the roll, and strip temperature calculated by the model are very close to the field test results. Comparing the minimum film thickness calculated by the model with the regression formula of other literature test, the error is less than 10%. The minimum oil film thickness is analyzed. It increases with the decrease of the rolling force and is approximately proportional to the rolling speed and lubricant viscosity.

scholarly journals Ultrasonic Measurement for Film Thickness and Solid Contact in Elastohydrodynamic Lubrication

2010 ◽  
Author(s):  
R. S. Dwyer-Joyce ◽  
J. Zhu ◽  
T. Reddyhoff
Keyword(s):  
Film Thickness ◽  
Elastohydrodynamic Lubrication ◽  
Theoretical Models ◽  
Asperity Contact ◽  
Oil Film ◽  
Real Area Of Contact ◽  
Nominal Thickness ◽  
Asperity Contacts ◽  
Mediated Contact ◽  
Ultrasonic Investigation

The reflection of ultrasound can be used to determine oil film thickness from the stiffness of the separating film. However, boundary or mixed film lubrication is a common occurrence in elastohydrodynamic lubricated (EHL) contacts, as the nominal thickness of the separating film approaches the surface asperity height. In this paper an ultrasonic investigation was carried out on the interface between a steel ball sliding on a flat disc as the speed was reduced into the boundary regime. The ultrasonic reflection then depends on the stiffness of the interface that now consists of an oil layer and asperity contacts. To distinguish the stiffness contribution from asperity contact and oil layer, a mixed lubrication model for circular contacts was established. This predicted the lubricant film thickness and proportions of solid and liquid mediated contact. The total stiffness predicted by theoretical models showed a good agreement with experimental measurement for kinematic cases. The model can then be used to extract the proportion of real area of contact, and the oil film thickness, from ultrasonic results.

Contact Damping and Stiffness Calculation Model for Rough Surface Considering Lubrication in Involute Spur Gear

2021 ◽  
Author(s):  
Gong Cheng ◽  
Ke Xiao ◽  
Jiaxu Wang
Keyword(s):  
Film Thickness ◽  
Contact Stiffness ◽  
Elastohydrodynamic Lubrication ◽  
Spur Gear ◽  
Calculation Model ◽  
Mixed Lubrication ◽  
Asperity Contact ◽  
Crucial Point ◽  
Normal Deformation ◽  
Oil Film

The contact properties of an interface are crucial to the performance of equipment, and it is necessary to study the contact damping and contact stiffness, especially in the case of mixed lubrication. A calculation model for contact damping and contact stiffness considering lubrication was proposed on the basis of the KE contact model and mixed elastohydrodynamic lubrication theory. Both the damping and the stiffness were composed of the oil film portion and the asperity contact portion. Since the damping and the stiffness of oil film mainly depended on the film thickness and the pressure, which can be obtained with the mixed lubrication model, another crucial point was to figure out the contribution of asperity contact. Ignoring the effect of the tangential deformation, the stiffness and the load determined with the normal deformation of the asperity were obtained. Then, the contact damping and the contact stiffness considering lubrication could be derived. Finally, the model was applied to the study of contact damping and stiffness of the involute spur gear.

Lubrication Phenomena in Spur Gears: Capacity, Film Thickness Variation, and Efficiency

1965 ◽  
Vol 87 (3) ◽  
pp. 655-663 ◽  
Author(s):  
R. Wayne Adkins ◽  
E. I. Radzimovsky
Keyword(s):  
Shear Stress ◽  
Film Thickness ◽  
Pressure Distribution ◽  
Power Loss ◽  
Hydrodynamic Lubrication ◽  
Thickness Variation ◽  
Spur Gears ◽  
Oil Film ◽  
Lubrication Conditions ◽  
Lubricant Viscosity

In this paper the oil film separating the mating surfaces of involute spur gears operating under hydrodynamic lubrication conditions is analyzed. This analysis surpasses previous analyses in as much as the actual motion of the involute profiles (rolling, sliding, and squeezing motion) and the total number of teeth engaged at any one time are considered. Expressions are derived for the pressure distribution, shear stress, and power loss in the oil film at any phase of tooth engagement. A method is developed by which these expressions can be applied to determine the film thickness at any instant and the power loss for a given load, speed, and lubricant viscosity.

Elastohydrodynamic Lubrication Design of Planetary Gear Transmission

2011 ◽  
Vol 228-229 ◽  
pp. 681-685
Author(s):  
Pei De Bao ◽  
Jun Xie ◽  
Xiao Qin Yin ◽  
Qi Zhi Yang ◽  
Lu Zhong Ma
Keyword(s):  
Film Thickness ◽  
Hydrodynamic Lubrication ◽  
Elastohydrodynamic Lubrication ◽  
Planetary Gear ◽  
Gear Transmission ◽  
The Sun ◽  
Oil Film ◽  
Lubrication Film ◽  
Planet Gear ◽  
The Many

Based on elastic hydrodynamic lubrication (EHL) theory, an EHL model of the meshing between the sun gear and planet gear in planetary gear transmission was established. The EHL oil film thicknesses at meshing areas and those distributions for two operation cases were calculated: one case with the sun gear as the driving gear and another case with the ring gear as the driving gear. The Lubrication with second case was worse. Through the many comparing calculations the lubrication film thickness can be significantly increased by right parameter design. Reasonable raise of lubricant viscosity can get better gear lubrication. Increased gear pressure angle can greatly increase the oil film thickness. The increase of oil film thickness can improve the lubrication of gears and prevent wearing and reduce the production cost of gears, which have great practical value.

Effect of Nanotexturing on Increase in Elastohydrodynamic Lubrication Oil Film Thickness

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Tomoko Hirayama ◽  
Mitsutaka Ikeda ◽  
Toshiteru Suzuki ◽  
Takashi Matsuoka ◽  
Hiroshi Sawada ◽  
...  
Keyword(s):  
Femtosecond Laser ◽  
Film Thickness ◽  
Hydrodynamic Lubrication ◽  
Contact Point ◽  
Elastohydrodynamic Lubrication ◽  
Groove Depth ◽  
Optical Interferometer ◽  
Oil Film ◽  
Friction Tester ◽  
Steel Balls

The effects of nanotexturing on oil film thickness and shape under pointcontact elasto-hydrodynamic lubrication (EHL) conditions were experimentally investigated. A disk-onball friction tester with an optical interferometer was used to measure oil film thickness and to observe the oil film shape. Periodic groove structures with a spiral, perpendicular, or parallel shape and with various groove depths and distances were formed by irradiation of a femtosecond laser onto the surface of steel balls. These nanotextured balls were tested under a load of 20 N and at rotational speeds from 1.0 to 3.0 m/s. Most of the balls with nanotexturing had a thicker oil film than those without texturing. The groove depth and angle were the key parameters determining the thickness of the oil film as they controlled the amount of side leakage of oil from the contact point. Optimization of these parameters resulted in an oil film that was almost twice as thick as that on the ball without texturing.

scholarly journals Remarks on Modeling the Oil Film Generation of Rod Seals

Lubricants ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 95
Author(s):  
Oliver Feuchtmüller ◽  
Nino Dakov ◽  
Lothar Hörl ◽  
Frank Bauer
Keyword(s):  
Film Thickness ◽  
Hydrodynamic Lubrication ◽  
Elastohydrodynamic Lubrication ◽  
Numerical Results ◽  
Physical Parameters ◽  
Oil Film ◽  
Polished Rod ◽  
Rod Seals ◽  
Potential Remedy ◽  
Theory And Experiments

The oil film generation of a U-cup rod seal and the oil film thickness on the rod after outstroke were analyzed analytically, numerically, and experimentally. The analyzed sealing system consists of an unmodified, commercially available U-cup, a polished rod, and mineral oil. The inverse theory of hydrodynamic lubrication (IHL) and an elastohydrodynamic lubrication (EHL) model—both based on the Reynolds equation for thin lubricating films—were utilized to simulate the oil film generation. In the EHL analysis, physical parameters and numerical EHL parameters were varied. Both the analytical and numerical results for the varied parameters show that the film thickness follows a square-root function (i.e., with a function exponent of 0.5) with respect to the product of dynamic viscosity and rod speed, also referred to as the duty parameter. In comparison to the analytical and numerical results, the film thickness obtained via ellipsometry measurements is a function of the duty parameter with an exponent of approximately 0.85. Possible causes for the discrepancy between theory and experiments are discussed. A potential remedy for the modeling gap is proposed.

Influence of Surface Waviness on the Thermal Elastohydrodynamic Lubrication of an Eccentric-Tappet Pair

2013 ◽  
Vol 135 (2) ◽  
Author(s):  
J. Wang ◽  
C. H. Venner ◽  
A. A. Lubrecht
Keyword(s):  
Film Thickness ◽  
Elastohydrodynamic Lubrication ◽  
Surface Waviness ◽  
Film Pressure ◽  
Oil Film ◽  
Working Cycle ◽  
Temperature Oscillations ◽  
Minimum Film Thickness ◽  
Traction Coefficient ◽  
Oil Film Pressure

The effect of single-sided and double-sided harmonic surface waviness on the film thickness, pressure, and temperature oscillations in an elastohydrodynamically lubricated eccentric-tappet pair has been investigated in relation to the eccentricity and the waviness wavelength. The results show that, during one working cycle, the waviness causes significant fluctuations of the oil film, pressure, and temperature, as well as a reduction in minimum film thickness. Smaller wavelength causes more dramatic variations in oil film. The fluctuations of the pressure, film thickness, temperature, and traction coefficient caused by double-sided waviness are nearly the same compared with the single-sided waviness, but the variations are less intense.

Theoretical and experimental studies of the oil film in lubricated point contact

1966 ◽  
Vol 291 (1427) ◽  
pp. 520-536 ◽  
Keyword(s):  
Surface Layer ◽  
Film Thickness ◽  
Strong Evidence ◽  
Experimental Studies ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Experimental Results ◽  
Point Contacts ◽  
Previous Theory ◽  
Oil Film

A technique using Newton’s rings for mapping the oil film of lubricated point contacts is described. A theoretical value for the film thickness of such contacts in elastohydrodynamic lubrication is derived. The experimental results give the exit constriction predicted by previous theory but never shown in detail. The comparison of theoretical and experimental oil film thicknesses, which is satisfactorily accurate, gives strong evidence for a viscous surface layer some 1000Å thick. This film agrees with the known ‘lubricating power’ of the various oils tested.

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.

Use of a Micro-Contact Model to Optimize SI Engine’s 3-Piece Oil Ring Profiles Regarding Wear and Lubrication

2002 ◽  
Author(s):  
Eduardo Tomanik ◽  
Andre´ Ferrarese
Keyword(s):  
Film Thickness ◽  
Contact Pressure ◽  
Wear Behavior ◽  
Bench Test ◽  
Asperity Contact ◽  
Oil Consumption ◽  
Tangential Load ◽  
Oil Film ◽  
Operation Temperature ◽  
Contact Pressures

A computer model that addresses the wear behavior by calculating hydrodynamic and asperity contact pressures was used to optimize the running face of three-piece oil control rings. The model incorporates Reynolds equation to calculate the oil film thickness for two sliding surfaces under a given condition (profile and topography of the surfaces, load, speed, lubricant viscosity grade and operation temperature). Prediction of the resultant asperity contact pressures is made by Greenwood-Williamson model. More scraping ring rail profiles are better for oil control, but present more wear due to higher asperity contact pressures. This higher wear can lead to less scraping profile, increasing ring end gap and lower ring tangential load, which deteriorates long term oil consumption control, hence engine durability. In the present work, a relatively simple computer program was used to predict lube oil film thickness and wear for different rail running profiles. Ring wear was assumed to be proportional to the calculated asperity contact pressure. Different rail profiles where the running profiles had a flat portion varying from less than 0.10 mm to higher than 0.20 mm were simulated and then tested in a bench test consisting in an electrical motored engine. Except for the combustion absence, all other engine characteristics were preserved (e.g., stroke, piston-ring pack, lubrication system) in the bench test. The measured oil control ring wear correlated very well with the predicted one. The model allowed the numerical optimization of the running profile of ring rail, which has lower asperity contact pressure, hence wear, but still has a good scraping capability. Two actual ICE tests were also realized. The predicted lower wear of the optimized profile was experimentally confirmed and no differences on LOC were found.

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