Mathematical Modeling of a Small-Dimension Hydropulse Vibrator with a Valve-Driven Pressure Pulse Generator

Abstract

The article presents research on a new compact vibrator design based on a hydraulic pulse drive with a built-in valve-type pressure pulse generator. Based on scientific assumptions, an approximate cycle diagram of the working cycle, a structural diagram of the vibrator, and a representation of the hydraulic link of its hydraulic system as a Kelvin–Voigt model were developed. A dynamic model of the vibrator was designed, in which the hydraulic link interacts with the moving links via transmission ratios. Based on simplified dynamic models of the forward and reverse strokes of the executive element, a mathematical model of the vibrator was developed using the d"Alembert principle, resulting in a system of 2nd-order differential equations describing the motion of the executive element\"s mass during its forward and reverse strokes. Consumption for energy equations at time intervals was also considered according to the approximate cycle diagram of the vibrator"s working cycle and the conditions of uniqueness that limit the movement of the mass of the executive element and the deformation of the hydraulic link. To provide a detailed analysis of the developed mathematical model, Python program code was written. The workflow was visualized in Google Colab. It was confirmed that the operating frequency range of a hydraulic pulse vibrator of this design is not a single fixed number – it is parametric and depends on the settings of the hydraulic system. By adjusting the pumping station parameters and the stiffness of the vibrator"s elastic elements, it is possible to achieve an actuator frequency up to 150 Hz and an amplitude of up to 2 mm.