Abstract: Displacement is a very important technological parameter in the tension straightening process. Building the mathematical model to illustrate the relationship between the displacement and tensile force is a basic research on determination of the technological parameter of tension straightening process. The tension straightening process consists mainly of the elastic loading I and unloading stage, the elastic loading II and unloading stage, the elastic-plastic loading stage on the basis of the change rule of tensile force. The circular bar of one-dimensional bending is selected for study and is assumed to be linear strain-hardening elastic-plastic material. Based on the elastic-plastic mechanics theory the mathematical displacement-force model of tension straightening process is established. The AZ31 magnesium alloy rod is taken as an example, the result of calculation by the displacement-force model is in good agreement with the experimental result. The research shows that the initial deflection has effect on the spring-back after unloading by influencing on the slope of elastic loading I. The displacement and tensile force needed for straightening increase with the increasing of initial deflection when other conditions remain unchanged.

Key words: AZ31 magnesium, Linear strain-hardening elastic-plastic material, Mathematic model, Tension straightening, displacement tracking, nonlinear disturbance observer, sliding mode control, four roller bending machine