Analytical expression for approximation of the friction force of the vibration protection mechanism of the operator’s seat

In mathematical modeling of dynamic and vibration protection systems of operators of construction and road machines, it is necessary to take into account the damping properties of the mechanisms. Accounting for the friction force in mathematical models is often performed using a coefficient, according to the viscous friction model. In more complex models, it is common to use a well-known expression in which the functions of the exponent and hyperbolic tangent are present, and the independent parameters are the Coulomb and separation friction forces, the separation friction rate, and the coefficient of viscous friction. This expression is used in a well-known mathematical package. However, the well-known expression does not accurately approximate the experimental friction curves. In the present work, an alternative expression for the total friction force has been supplemented. The refinement made it possible to apply a new formula for the entire range of change in the velocity argument and more accurately reproduce the characteristic shape of the experimental friction characteristics. For the new expression, complementary formulas were obtained that establish the relationship between the input parameters and a number of others that have a clear and simple physical meaning of the parameters. A comparison was made of the generally accepted and proposed expressions according to experimental data, graphs of the relative error were constructed. Also, a comparison of two expressions of the total friction force was made, as an example, on a dynamic model of forced oscillations of a concentrated mass on a moving base. The comparison results showed a significant discrepancy between the generally accepted expression in comparison with the proposed one, in terms of the total friction force, as well as a discrepancy in the amplitudes of relative displacements and absolute mass accelerations obtained on the dynamic model. The proposed expression can be used to approximate the total friction force in mathematical models of dynamic vibration protection systems for operator seats.