Mathematical Model of the Energy Discharge Process of the Vibrating Bucket of the Hydraulic Excavator

Abstract

The paper considers a nonlinear model of the polytropic process of energy discharge of the pneumatic accumulator of the vibration-impact bucket of a hydraulic excavator associated with the acceleration of the striker of the impactor. A nonlinear differential equation of the second order and two integration methods are used for the analysis: lowering the order of the differential equation with the transition to phase coordinates and using the Taylor series (in the form of the McLaurin series). Studies have shown that the coefficients of the McLaurin series have varying degrees of influence on the calculation result. Only the coefficients with even numbers were found to be influential in calculating the process of discharging a pneumatic accumulator. Moreover, as the number of the coefficient increases, its influence on the calculation results decreases. Application of the developed methodology and calculation model in the Mathcad system made it possible to study the process of striker acceleration and determine the rational energy parameters of the impact device — a hydraulic hammer of a hydraulic excavator’s vibration-impact bucket. This is important to ensure the maximum impact of the hydraulic hammer on the destruction of solid soil or rock. Implementation of the proposed methodology for solving nonlinear differential equations using phase coordinates and Taylor series is recommended. The developed methodology can be helpful to for achieving maximum impact energy transfer to the working environment, which is critical for improving the performance and reliability of hydraulic equipment. The results obtained are essential for improving technological solutions in hydraulic equipment and their further implementation in industrial production. The study opens up the possibility for the adaptive operation of hydraulic hammers, considering the technological environment’s parameters and substantiating the rational parameters of the impactor of the vibration-impact bucket of a hydraulic excavator. These results significantly contribute to developing modern hydraulic systems and their application in industry.