Numerical Simulation Study Of The Tire Calendering Process Based On Viscoelastic-Plastic Constitutive Model

Calendering is one of the most basic molding processes in which many semi-finished parts in the tire industry are formed into a specific thickness and shape by calendering equipment.During the tire calendering process,due to the elastic recovery of the polymer chain after separation between the rubber and the calenders,the free swelling behavior of unvulcanized rubber will affect the size and quality of the calendered product and increase the production cost.Therefore,the analysis of the calendering process is a long-term and challenging basic application issue that scholars have paid wide attention and conducted research for decades,but they have not been able to satisfactorily solve swelling problem in the tire calendering process.This paper has carried out a series of research work,mainly established a set of numerical simulation solution strategies based on viscoelastic-plastic solid constitutive model for the tire calendering process.The relevant results will be helpful to the optimization and improvement of the tire calendering process.The unvulcanized rubber was subjected to quasi-static cyclic loading-unloading tests at different strain rates(0.001/s,0.005/s,0.01/s and 0.05/s)and 100? by the chuck displacement strain test technology.The experimental results show that unvulcanized rubber has complex viscoelastic-plastic mechanical behaviors at the test temperature,including rate-dependent hyperelasticity,stress softening,hysteresis,and plastic flow.Based on the results of the tensile test,the viscoelastic-plastic solid constitutive model(parallel network model)consisting of a rate-independent hyperelastic network and two rate-dependent elastic-viscoplastic networks is used to characterize the mechanical behaviors of unvulcanized rubber.Finally,the PNM constitutive model has achieved a good fitting effect,and obtained the material parameters of unvulcanized rubber required in the numerical simulation of the calendering process.Based on the Lagrangian method,a steady-state solution strategy is proposed for numerical simulation of the two-dimensional(2D)and three-dimensional(3D)tire calendering process by the software Abaqus:firstly two calendars move towards the middle and the unvulcanized rubber between two calendars is precompressed before calendaring.Secondly,the calendars scroll at a specific angular velocity.The numerical results show that:(1)when the speed of calenders remains constant,the thickness/width ratios increase/decrease sharply,and then flatten until stabilizing with the distance from the roll-gap to downstream;(2)the thickness/width ratios increase/decrease rapidly with speeds from 1m/min to 6m/min,and tends to be stable at the speed of more than 6m/min,which is same as actual measurement results on site.The divergence of thickness ratio between the experimental and the 2D simulation results at the speed 6m/min is 7.63%,and the 3D divergence is 3.54%,which fully proves the validity of the numerical model.In addition,the width of the unvulcanized rubber has a very limited influence on the swelling ratio.Finally,the 3D stress distribution is much smaller on both sides and larger in the middle of the cross-section,which is consistent with actual production and is also the root cause of production quality problems in the tire calendering process.