The Effects of Small Sinusoidal Load Variations in Elastohydrodynamic Line Contacts

2015 ◽  
Vol 138 (3) ◽  
Author(s):  
C. J. Hooke ◽  
G. E. Morales-Espejel
Keyword(s):  
Pressure Distribution ◽  
Maxwell Model ◽  
Total System ◽  
Low Frequencies ◽  
Load Variations ◽  
Entrainment Velocity ◽  
Line Contacts ◽  
Sinusoidal Load ◽  
Voigt Model ◽  
Low Amplitude

A method of determining the response of elastohydrodynamic line contacts to low amplitude, sinusoidal variations in load is presented. It is shown that the load variations alter the Hertz width, cyclically increasing and reducing the effective entrainment velocity. This produces clearance variations in the inlet, which are transported through the conjunction altering the pressure distribution as they pass. The resulting pressure and clearance changes can be many times greater than when the load changes slowly. The results are used to determine the flexibility and damping of the conjunctions. These vary depending on the number of transported waves inside the contact. It is shown that a Maxwell model rather than the usual Voigt model is required to define the contact's behavior. While the Voigt model may be used at low frequencies, it has a damping coefficient that is not unique to the contact but depends on the total system stiffness.

The behaviour of low-amplitude surface roughness under line contacts: Non-Newtonian fluids

2000 ◽  
Vol 214 (3) ◽  
pp. 253-265 ◽  
Author(s):  
C. J. Hooke
Keyword(s):  
Surface Profile ◽  
Newtonian Fluids ◽  
Major Influence ◽  
Relative Slip ◽  
Long Wavelength ◽  
Entrainment Velocity ◽  
Pure Rolling ◽  
Rate Effects ◽  
Line Contacts ◽  
Low Amplitude

As a rough surface passes under an elastohydrodynamically lubricated (EHL) contact the surface profile is modified, with long-wavelength components being reduced in amplitude. The behaviour of the shorter wavelengths is complex. Where both surfaces have the same velocity-pure rolling-the roughness passes through the contact unaltered. Where there is relative slip and the fluid is assumed to be piezoviscous and Newtonian, analysis predicts that the roughness will be flattened. It is replaced by a surface profile with a different wavelength travelling through the contact at the entrainment velocity. The amplitude of this complementary wave may be smaller or larger than the roughness it replaces. This behaviour has not been found experimentally and does not occur in soft contacts where piezoviscous effects are absent. This paper extends a previous analysis for Newtonian fluids to include shear rate effects. It shows that while these effects are relatively unimportant for pure rolling they have a major influence where there is relative sliding of the surfaces. The formation of the complementary wave is largely eliminated and, at short wavelengths, instead of being modified the original roughness passes unchanged through the contact.

The behaviour of heavily loaded line contacts with transverse roughness

1999 ◽  
Vol 213 (4) ◽  
pp. 309-320 ◽  
Author(s):  
C. J. Hooke
Keyword(s):  
Surface Roughness ◽  
Full Range ◽  
Numerical Results ◽  
Operating Conditions ◽  
Entrainment Velocity ◽  
Original Surface ◽  
Line Contacts ◽  
Transverse Roughness ◽  
Inlet Length

In heavily loaded, piezoviscous contacts the surface roughness tends to be flattened inside the conjunction by any relative sliding of the surfaces. However, before it is flattened, the roughness affects the inlet to the contact, producing clearance variations there. These variations are then convected through the contact, at the entrainment velocity, producing a clearance distribution that differs from the original surface. The present paper explores this behaviour and establishes how the amplitude of the convected clearance varies with wavelength and operating conditions. It is shown that the primary influence is the ratio of the wavelength to the inlet length of the conjunction. Where this ratio is large, the roughness is smoothed and there is little variation in clearance under the conjunction. Where the ratio is small, significant variations in clearance may occur but the precise amplitude and phasing depend on the ratio of slide to roll velocities and on the value of a piezoviscous parameter, c. The numerical results agree closely with existing solutions but extend these to cover the full range of operating conditions.

Contact Mechanics of a Hard Cylinder on a Viscoelastic Layer

Tribology ◽  
2006 ◽  
Author(s):  
Steven R. H. Barrett ◽  
Alexander H. Slocum
Keyword(s):  
Pressure Distribution ◽  
Contact Mechanics ◽  
Normal Force ◽  
Maxwell Model ◽  
Sliding Contact ◽  
Viscoelastic Layer ◽  
Tractive Force ◽  
Rolling Velocity ◽  
One Dimensional ◽  
The One

The rolling/sliding contact of a hard cylinder on a viscoelastic layer is re-examined. The one-dimensional Maxwell model, with the addition of a parallel spring, is used to model the normal stiffness of the viscoelastic layer A solution for the pressure distribution is presented. It is shown that the maximum tractive force that the cylinder can sustain before complete sliding is a function of the sense and magnitude of the rolling velocity. Two regimes of loading are considered - constant cylinder normal force and constant cylinder indentation.

End Effect Attenuation in Tapered Roller Contacts

2009 ◽  
Author(s):  
Emanuel Diaconescu
Keyword(s):  
Pressure Distribution ◽  
Finite Length ◽  
Contact Length ◽  
Maximum Pressure ◽  
End Effect ◽  
End Effects ◽  
Maximum Value ◽  
Line Contacts ◽  
Tapered Roller

The end effect attenuation in finite length line contacts is mainly approached for cylindrical bodies. Multi-radius crowning may remove end effects in tapered roller contacts. Another method for leveling maximum pressure in these contacts is the use of polynomial generatrix. This paper investigates the effect of this generatrix in tapered roller contacts. An improved pressure distribution is obtained. This has a nearly flat maximum value along most of contact length.

Surface roughness modification in elastohydrodynamic line contacts operating in the elastic piezoviscous regime

1998 ◽  
Vol 212 (2) ◽  
pp. 145-162 ◽  
Author(s):  
C. J. Hooke
Keyword(s):  
Surface Roughness ◽  
Spatial Distribution ◽  
Analytical Solution ◽  
Film Thickness ◽  
Numerical Solutions ◽  
Entrainment Velocity ◽  
Original Surface ◽  
Ehd Lubrication ◽  
Line Contacts

In heavily loaded elastohydrodynamic (EHD) lubrication contacts operating in the piezoviscous regime, the original surface roughness is largely flattened as it enters the conjunction and is replaced by an inlet generated clearance variation. This clearance variation is convected through the contact at the entrainment velocity. It has a spatial distribution that differs (except for rolling without slip) from the original surface and a different amplitude. This amplitude may be smaller or greater than that of the original profile. An analytical solution of this behaviour is presented for contacts operating well inside the elastic piezoviscous regime for the situation where the roughness is relatively small compared with the film thickness. This solution allows the main features of surface roughness modification to be understood and produces results that compare well with the few numerical solutions available.

Robot compliant catching by Maxwell model based Cartesian admittance control

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Le Fu ◽  
Jie Zhao
Keyword(s):  
Control Method ◽  
Maxwell Model ◽  
Admittance Control ◽  
End Effector ◽  
Content Type ◽  
Model Based ◽  
Time Optimal ◽  
Voigt Model ◽  
Optimal Movement ◽  
The Impact

Purpose Admittance control is a typical complaint control methodology. Traditionally, admittance control systems are based on a dynamical relationship described by Voigt model. By contrast, after changing connection of spring and damper, Maxwell model produces different dynamics and has shown better impact absorption performance. This paper aims to design a novel compliant control method based on Maxwell model and implement it in a robot catching scenario. Design/methodology/approach To achieve this goal, this paper proposed a Maxwell model based admittance control scheme. Considering several motion stages involved in one catching attempt, the following approaches are adopted. First, Kalman filter is used to process the position data stream acquired from motion capture system and predict the subsequent object flying trajectory. Then, a linear segments with parabolic blends reaching motion is generated to achieve time-optimal movement under kinematic and joint inherent constraints. After robot reached the desired catching point, the proposed Maxwell model based admittance controller performs such as a cushion to moderate the impact between robot end-effector and flying object. Findings This paper has experimentally demonstrated the feasibility and effectiveness of the proposed method. Compared with typical Voigt model based compliant catching, less object bounding away from end-effector happens and the success rate of catching has been improved. Originality/value The authors proposed a novel Maxwell model based admittance control method and demonstrated its effectiveness in a robot catching scenario. The author’s approach may inspire other related researchers and has great potential of practical usage in a widespread of robot applications.

scholarly journals Elastic and viscous bond components in the adhesion of colloidal particles and fibrillated streptococci to QCM-D crystal surfaces with different hydrophobicities using Kelvin–Voigt and Maxwell models

2017 ◽  
Vol 19 (37) ◽  
pp. 25391-25400 ◽  
Author(s):  
Rebecca van der Westen ◽  
Prashant K. Sharma ◽  
Hans De Raedt ◽  
Ijsbrand Vermue ◽  
Henny C. van der Mei ◽  
...  
Keyword(s):  
Phenomenological Models ◽  
Bacterial Adhesion ◽  
Colloidal Particles ◽  
Maxwell Model ◽  
Crystal Surfaces ◽  
Maxwell Models ◽  
Voigt Model

Analysis of initial bacterial adhesion using phenomenological models such as the Kelvin–Voigt model and the Maxwell model.

scholarly journals Identification of the Process of Dynamic Stretching of Threads in Warp-Knitting Technology

2017 ◽  
Vol 17 (4) ◽  
pp. 334-343 ◽  
Author(s):  
Aleksandra Prążyńska ◽  
Zbigniew Mikołajczyk
Keyword(s):  
Standard Model ◽  
Dynamic Stiffness ◽  
Maxwell Model ◽  
Viscosity Coefficient ◽  
Rheological Models ◽  
Zener Model ◽  
Dynamic Stretching ◽  
Input Parameters ◽  
Voigt Model ◽  
Stretching Process

Abstract The publication presents a theoretical study of the susceptibility of rheological models of threads to dynamic stretching in the context of modern, highly efficient textile technologies. Input parameters of the four analyzed models, the Kelvin-Voigt model, the Maxwell model, Standard model 2, and the Zener model, corresponded to the actual values of the coefficients of viscosity, elasticity, kinematic and dynamic loading, and stretching speed for the analyzed polyester silk threads produced in a knitting process, with knitting speeds from 700 to 1,600 courses/min. The research proves that the tested thread models behave differently in the stretching process-the Kelvin-Voigt model is sensitive to both the increases in kinematic loading and viscosity coefficient, Standard model 2 is only susceptible to dynamic stiffness, and the Zener model is significantly sensitive to kinematic loading. All responses of the models increase with the increase in stretching speeds. The obtained results indicate substantial “accuracy tolerance” in setting input parameters while identifying dynamics of the knitting process on warp-knitting machines.

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