# Friction Coefficients Definition in Compression-Fit Couplings Applying the Doe Method

## Abstract

The design of the fork-pin compression-fit couplings of front motorbike suspensions is uncertain mainly because of the poor knowledge of the mean coupling pressure *p*, due to the not symmetric geometry of the fork, and of the first friction coefficient μ_{11}. The axial releasing force *F*_{11}=μ_{11}*p.A*, which is the fundamental design parameter, indeed depends on the mentioned two factors, usually unknown. In this paper is presented a generalized methodology which is useful to calculate the μ_{11} parameter concerning the fork-pin couplings of the front motorbike suspensions. The present production is differentiated by the different material of the two elements in contact, the fork and the pin. The possible combinations are: the fork and the pin in steel, the fork in aluminium and the pin in steel and the fork and the pin in aluminium. In previous works two mathematical models have been defined: the first (Croccolo *et al* [1]) is useful to calculate the mean contact pressure p in every fork-pin coupling by introducing an overall mathematical function, which is able to correct the theoretical formulas valid only for axial-symmetric elements [2]; the second (Croccolo and Reggiani [3]) is useful to calculate the first friction coefficient μ_{11}, as a function of the production and assembly specifications, in couplings with both the fork and the pin in steel. The fundamental goal of this work is to define a mathematical model useful to calculate the first friction coefficients μ_{11} for the other two combinations of couplings, aluminium-steel and aluminium-aluminium. The second goal is to update an innovative software (Fork Design©), realized by the authors in Visual Basic® programming language, which is useful to perform the design and the verification of the all fork-pin couplings. The mathematical model for μ_{11} has been defined through FEM analyses, performed with Ansys 9.0® and applying the Design Of Experiment (DOE) method.

### References

- 1.Croccolo, D., Cuppini R., and Vincenzi N.,
*International Design Conference-*Design 2006 Dubrovnik-Croatia, May 15-18, 2006Google Scholar - 2.Niemann Winter, Elementi di macchine, Vol. I, EST-SPRINGER (1983)Google Scholar
- 3.Croccolo, D., Reggiani, S., Modello di calcolo del coefficiente di attrito in accoppiamenti stabili, Organi di trasmissione-Tecniche Nuove, Gennaio 2002-pp. 46–55.Google Scholar