Analytical model of the vibration protection system of the operator's seat under non-periodic external influence

BACKGROUND: Protecting ground-based transport and technological vehicle operators from dynamic impacts caused by chassis contact with uneven ground remains a pressing issue. The development of effective vibration-attenuating seat systems is inextricably linked to the use of mathematical models. Analytical models are the most accurate. AIM: Develop a mathematical model of the vertical displacements of an operator's seat on a vibration-attenuating suspension, based on analytical expressions describing the dynamic system's response to kinematic excitation, defined as vertical displacement of the seat base at a given velocity. METHODS: For the differential equation describing the vertical oscillations of a seat on a vibration-attenuating suspension under kinematic excitation, for the case of base lifting at a given velocity, analytical expressions were derived for calculating the time dependencies of the main system parameters, such as the vertical coordinate of the seat in a fixed coordinate system, its second derivative, and the local deformation coordinate of the seat's vibration-attenuating mechanism. Analytical expressions for the maximum deviation of the local deformation coordinate from zero and the maximum seat acceleration were also obtained. An algorithm using several analytical expressions was developed to calculate the maximum seat acceleration. This algorithm, based on these analytical expressions, allows one to calculate the maximum seat acceleration for any positive values of the system's stiffness and damping coefficients. RESULTS: As an example confirming the validity of the obtained analytical expressions and the algorithm for calculating the maximum seat acceleration, the functional dependencies of the maximum absolute value of the local coordinate and the maximum absolute seat acceleration on the stiffness and damping coefficients under a non-periodic external influence in the form of seat base displacement are presented. Lines corresponding to a constant value of the maximum deviation of the local coordinate from zero, obtained using spline interpolation, are also presented. This allowed us to determine the minimum values of the maximum seat acceleration for a number of specified base lifting speeds, at which the absolute local deformation coordinate of the vibration isolation system mechanism equals a constant limit value. CONCLUSION: The problem of developing a mathematical model of vertical oscillations of an operator's seat with a vibration-isolating suspension has been solved using analytical expressions. This model offers the advantage of higher accuracy compared to a numerical solution. The model describes the system's oscillations under a non-periodic external stimulus, in the form of movement of the seat base at a given velocity, beginning at time zero. Using this non-periodic external stimulus allows it to be characterized by a single parameter, which will potentially simplify solutions for optimizing vibration-isolating seat systems.