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Review and comparison of empirical friction coefficient formulation for multibody dynamics of lubricated slotted joints

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Abstract

In recent times, many industrial applications have demanded innovative energy-efficient solutions. One of the main causes of energy loss is due to friction between body surfaces in contact. A great amount of research has been aimed at understanding the friction mechanisms to allow for its reliable prediction during multibody simulation. In the 1950s and 1960s, many experimental studies were carried out, leading to the coefficient of friction formulas for lubricated surfaces under a combination of sliding and rolling relative motion. The formulas have been mainly derived by the mathematical fitting of results obtained from experimental measurements on rolling disks and different load, lubricating and kinematic conditions. The purpose of this paper is twofold: on the one hand, it reviews semi-empirical formulas for computing the friction coefficient in lubricated contact under various operating conditions; on the other hand, it implements and compares contact force models coupled with the metal-metal lubricated empirical friction formulas in a multibody dynamics simulation environment. Implementing empirical formulas is straightforward and computationally efficient, but one can evaluate the performance of these models in characterizing the dynamics of the lubricated joint. For this purpose, a multibody simulation of a Scotch yoke and a Whitworth quick return mechanisms with a nonideal prismatic joint are conducted. The existence of clearance causes the dynamic behavior of the system to be different from the ideal joint. The difference between each friction coefficient model is emphasized by simulation output and computation time.

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Data Availability

No datasets were generated or analysed during the current study.

Abbreviations

\(\alpha\) :

Piezo-viscosity coefficient of the lubricant

\(\delta\) :

Contact penetration

\(\dot{\delta}\) :

Contact penetration velocity

\(\dot{\delta}_{0}\) :

Impact velocity

\(\eta_{0}\) :

Dynamic viscosity of the lubricant

\(\lambda\) :

Specific film thickness

\(\mu\) :

Friction coefficient

\(\nu_{0}\) :

kinematic viscosity of the lubricant

\(\omega\) :

Rotational speed

\(\rho\) :

Density of the lubricant

\(\vartheta\) :

Rotational angle

\(c_{d}\) :

Dynamic correction factor

\(c_{r}\) :

Restitution coefficient

\(E\) :

Young’s modulus

\(f_{n}\) :

Normal contact force per unit length

\(F_{n}\) :

Normal contact force

\(F_{t}\) :

Friction Force

\(G\) :

Material parameter of the Hamrock and Dowson formulation

\(h_{c}\) :

Oil central film thickness

\(K\) :

Contact stiffness

\(L\) :

Contact width

\(n\) :

Stiffness exponent

\(R_{e}\) :

Equivalent radius of curvature

\(R_{i}\) :

Curvature radius of surface \(i\)

\(S\) :

Surface roughness

\(U\) :

Velocity parameter of the Hamrock and Dowson formulation

\(V_{0}\) :

Static threshold velocity

\(V_{1}\) :

Dynamic threshold velocity

\(V_{\Sigma}\) :

Sum of profiles velocities

\(V_{e}\) :

Lubricant entraining velocity

\(V_{r}\) :

Rolling velocity

\(V_{s}\) :

Sliding velocity

\(W\) :

Load parameter of the Hamrock and Dowson formulation

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Funding

This research was funded by Italian Ministry for University and Research, project PRIN 2020: “Innovative Contact Based multibody models for noise and vibration prediction in high-performance gears” grant number 202022Y4N5. CUP: E85F22000220006

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Authors and Affiliations

  1. Department of Enterprise Engineering, University of Rome Tor Vergata, via del Politecnico 1, 00133, Rome, Italy

    Marco Cirelli, Matteo Autiero, Giovanni Paoli, Ettore Pennestrì & Pier Paolo Valentini

  2. Dept. Industrial, Electrical and Mechanical Engineering, University “Roma Tre”, Via della Vasca Navale 79, 00146, Rome, Italy

    Nicola Pio Belfiore

Authors
  1. Marco Cirelli
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  2. Matteo Autiero
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  3. Nicola Pio Belfiore
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  4. Giovanni Paoli
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  6. Pier Paolo Valentini
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Contributions

Conceptualization, M.C., M.A., G.P., E.P., N.P.B. and P.P.V.; methodology, M.C., M.A., G.P., E.P., N.P.B. and P.P.V.; software, M.C., M.A., G.P., E.P.; validation, M.C., M.A., G.P.; formal analysis, M.C., M.A., G.P., E.P., N.P.B. and P.P.V.; investigation, M.C., M.A., G.P., E.P., N.P.B. and P.P.V.; resources, P.P.V.; data curation, M.A., G.P., E.P.; writing—original draft preparation, M.C., M.A., G.P.; writing—review and editing, E.P., N.P.B. and P.P.V.; visualization, M.C., M.A., G.P.; supervision, M.C., E.P. and P.P.V.; project administration, M.C.,and P.P.V.; funding acquisition, P.P.V. All authors have read and agreed to the published version of the manuscript.

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Correspondence to Marco Cirelli.

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Cirelli, M., Autiero, M., Belfiore, N.P. et al. Review and comparison of empirical friction coefficient formulation for multibody dynamics of lubricated slotted joints. Multibody Syst Dyn (2024). https://doi.org/10.1007/s11044-024-09988-y

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