| Warp-knitted run-in value is a critical process parameter for warp knitting production,whose prediction is a challenge in warp knitting industry.Currently warp-knitted run-in values are mainly confirmed by manual debugging repeatedly based on technologists’ experience.It is significant for warp knitting production to predict run-in values accurately before knitting on machine.With the precise prediction of run-in values,fabric weight and production cost can be calculated without making samples.Materials will be saved,and product quality will be improved with higher production continuity.It is quite urgent to accurately predict warp-knitted run-in values during fabric design.This research aims to develop a predictive model of warp-knitted run-in based on three-dimensional geometric parametric modeling of warp-knitted fabrics.Based on the model,run-in values can be precisely estimated without knitting on machine according to process parameters obtained when designing.Prediction of warp-knitted run-in is to solve a multivariate nonlinear function.Firstly,the influence on warp-knitted run-in value from factors of fabric structure,fabric density on machine,yarn specification and threading was analyzed.With univariate analyzing,response surface methodology and multilayer perceptron artificial neural network,relationships between six quantized factors and warp-knitted run-in were analyzed.Moreover,regression models and response surfaces were fitted in the condition of other process parameters unchanged.Furthermore,the influence weight of process parameters on the warp-knitted were analyzed,which indicates fabric structure and density on machine were main influencing factors,and the impact weights of quantitative influence factors of warp-knitted run-in were sequenced as follows: underlap,overlap,take-up desity,machine gauge,yarn fineness and total threading rate.The development of parametric 3-D geometric model is an essential part of the predictive model of warp-knitted run-in value.In order to improve the prediction accuracy of warp-knitted run-in value,this paper developed a parametric 3-D geometric model of warp-knitted fabrics.Fabric on machine was selected as modeling state,which is closely related to warp-knitted run-in prediction,and geometric models of units such as stitch structure,inlay structure and koper structure were proposed.By combining feature sizes measurement on fabric and unary regression,correlations between process parameters and feature sizes of warp-knitted structures were analyzed,and predictive algorithms of feature sizes based on impact factors of warp-knitted run-in were suggested.By using mass-spring model,internal stress of warp-knitted structures on machine was analyzed to calculate deformation of loop arc,and predictive equations for coordinates of mass point were obtained by using impact factors of warp-knitted run-in as input variable.Then,parametric 3-D geometric model of warp-knitted units was developed combining feature size,coordinates of mass points and hierarchical relationship of data points.Moreover,based on cubic Hermite polynomial interpolation,the 3-D geometric model was optimized by auxiliary control points interpolation and space curve fitting.Moreover,3-D coordinates of closely-spaced points in yarn space path were calculated,and the parametric 3-D model ofwarp-knitted fabrics on machine was developed,which is suitable for warp-knitted run-in prediction.The geometric model of warp-knitted fabrics was simulated with Matlab software.The suggested 3-D geometric warp-knitted model was validated by analyzing the errors between the measured values of feature sizes and the predicted ones,as well as the comparison between the simulation results and the fabric micrographs.Experiment results showed that the errors between the predicted value of feature sizes and the measured value are relative small.Moreover,with variation of process parameters,spatial trajectories of the model simulation results keep highly consistent with the micrographs of actual fabrics.It is indicated that the proposed loop model can well simulate spatial trajectories and feature sizes with different values of impact factors of warp-knitted run-in.The predictive model of warp-knitted run-in was developed based on the proposed parametric 3-D geometric model.Firstly,an algorithm for space curve length in the 3-D geometric model was suggested by the method of dense straight-line segments approximation.The difference between the warp-knitted run-in value and the path length of the geometrical model was analyzed.Combining influence of warp extension in let-off process and threading,the algorithm for space curve length was optimized,and predictive model of warp-knitted run-in under moderate warp yarn tension was developed.With experimental results of dynamic tension of warp yarn,negative linear correlation between mean warp yarn tension and run-in value was obtained,which was used to reduce the forecast error caused by fabric style adjustment.Then,predictive model of warp-knitted run-in by using process parameters and subjective index of warp tension as input variable was developed.Predictive accuracy of the proposed model was validated by comparing the predicted run-in values and the measured ones with linear regression and error analysis.The experimental results showed significant correlation between the predicted run-in values calculated from the proposed model and the measured ones.The slope of regression equation for the predicted and measured values was0.994 with very small intercept,which indicated that the predicted run-in values keep almost the same trend with the measured values and have no significant difference with the variation of impact factors of run-in.For the 22 sample with different parameters,the maximum relative error and average relative error of the predicted run-in values with different process parameters was respectively 7.73% and 2.49%.Consequently,it is concluded that the proposed predictive model has high precision for warp-knitted run-in values. |
