Introduction A hydraulic power injection machine is designed to use a driving screw to inject melted plastic into a specified mold. This machine can be found at an automotive spare parts factory. The cantilever-style heavy-duty screw injector is supported by one roller and secured at the end. An obvious need for vibration analysis on the roller support is essential. A mass spring damper model is proposed for deeply investigating the friction induced vibration mechanism for this injection system to well understand and analyze its vibration behavior. Purpose A mechanical mode of two degrees-of-freedom (DOF) is designed to improve research on the dynamic features of the Plastic Hydraulic Injection System (PHIS) mechanism. Materials and methods Experimental investigation and analysis of this mechanism are explored to obtain the instability speed and critical stick slip (SS) speed. The numerical imitation results of this work will help with the design and development of the PHIS mechanism. Conclusion The stability of the system and SS behavior are next examined by determining the critical variability speediness and critical SS speed. A simulation study is carried out to evaluate the effect of various parameters of the system on its stability and on the behavior of the SS motion.

In this study, a model of two nonlinear spring masses subjected to a smooth friction-velocity curve is examined. The second order governing system of motion is obtained in view of the system friction forces. This system is transformed to another suitable one of first order to investigate the points of equilibrium using Hurwitz’s theory. The excitation and critical stick-slip (SS) speeds are determined in accordance with the characteristic equation for the Jacobian matrix of the system. The stability and behavior of the system motion, along with the behavior of the SS movement, are examined. The effect of various parameters, such as excitation speed, damping and fraction coefficients, linear and nonlinear stiffness of springs, and masses that affect the motion and stability of the system is analyzed and studied. This research has numerous practical applications in a variety of industries, including airports, modern car brakes, well drilling, explaining and understanding seismic events, mechanical transportation, friction in bridges, and civil systems, which all exhibit impacted friction in dynamics and stick-slip phenomena.