Warp tension during acceleration and deceleration of warp beam unwinding in sizing machines. Part I: dynamic model and experimental verification

Stable warp tension is crucial for sizing quality and production efficiency in sizing machines. However, during acceleration and deceleration unwinding, rapid speed changes make tension more prone to fluctuations. Traditional tension control methods struggle to maintain accuracy due to uncertainties like model errors and feedback delays. This series of studies aims to develop a novel warp tension control system specifically for these dynamic phases in sizing machines to enhance tension stability and precision. Two main parts are included: the first establishes and validates the dynamic model, while the second designs and applies the control methods. This paper first clarifies the mechanism of warp tension fluctuations during the acceleration and deceleration unwinding. The findings reveal that tension fluctuations are primarily caused by speed changes resulting from acceleration differences between the guide roller and the warp beam. Larger acceleration differences lead to greater tension fluctuations. Subsequently, a nonlinear dynamic model is developed and validated using the constructed devices to describe the relationship between warp tension, speed variation, air pressure, and initial offset torque. Experimental results demonstrate high model accuracy, with R2 values all exceeding 91.56% and 93.71% during the acceleration and deceleration phases for four measured warp beams, respectively. The standard errors and 95% confidence intervals of the model parameters are provided to evaluate parameter estimation uncertainty. In addition, the relatively low RMSE values and the absence of obvious systematic patterns in the residuals further support the model fitting performance. The proposed model provides a theoretical foundation for tension control in these phases. In the second part of this work, the model will be applied to explore control methods and construct a system for precise tension control during acceleration and deceleration unwinding in sizing machines.