Balancing and mathematical model of the knife roller of leather-processing machines

This paper investigates the balancing of an opening roller and evaluates the condition of the opening roller blade with constant and variable pitch during the opening process of semi-finished leather products. A constructive method was implemented to determine the reaction forces of servo constraints that account for misalignments while facilitating the restoration of broken constraints. Extended equations for a mechanical system that includes servo constraints, using the principles of parametric release, were developed. A generalized mathematical model was created for machines equipped with squeezing and spreading tables that have knife rollers rotating at constant angular velocities. The extended equations of motion for the knife roller were derived and analyzed, taking into consideration its parametric release from holonomic servo constraints. The findings indicate that these extended equations of motion enable the simultaneous calculation of both the system's equations of motion and the reaction forces of the servo constraints, thereby ensuring the stabilization of motion relative to the manifold defined by the holonomic servo constraints.