Abstract — This paper presents a mathematical model of the weft yarn filling insertion process in rapier looms. A finite length segment of yarn is spatially discretized. Each element can interact only with the nearest neighbors by a viscoelastic interaction. The elastic and damping constants have been estimated by using experimental data obtained with different yarns. The resulting model has lumped parameters and it is completely described by a set of ordinary differential equations. The model provides the time and spatial profile of the tension in the considered yarn segment as a response to external forces applied to the weft yarn by the rapiers and the weft brake. Also, interactions with guide-eyes and piezoelectric feelers have been considered in the model. The simulation results confirm that the proposed model can be a useful tool in predicting weft yarn breakage and in design of tension control systems by weft braking action. I. INTRODUCTION roduction of woven textile using rapier or projectile looms is performed by alternate introduction of weft yarns between the shed in the warp yarns. Weft yarn insertion is made by two rapiers each inserted approximately halfway through the shed. The yarn is picked up at the left side of the loom by the left-hand rapier (the “giver”) and strongly accelerated (up to 3000 m/s 2 ) during the first half of his trajectory. Then, the yarn is transferred to the right-hand rapier (the “taker”), whose aim is to bring the yarn at the right side of the loom at a full stop. Finally, the weft yarn is cut at the fabric left edge and the cycle is repeated (up to 600 times per second in medium speed commercial looms). Weft brakes are placed at the left side of the loom to keep the yarn stretched during the filling insertion process. The joint action of the high intensity insertion forces, applied by the rapiers, and the braking force, applied by the weft brake, Manuscript received March 7, 2005. This work was supported by Promatech s.p.a., Italy. F. Previdi is with the Department of Management and Information Technology, University of Bergamo, via Marconi 5, I-24044 Dalmine (BG), Italy (corresponding author phone: +39.035.2052357; fax: +39.035.2052377; e-mail: previdi@unibg.it). S.M. Savaresi is with the Department of Electronics and Computer Science, Politecnico di Milano, p.zza Leonardo da Vinci 32, I-20133 Milano, Italy (e-mail: savaresi@elet.polimi.it). C. Volpi is with Promatech s.p.a, via Divisione Tridentina 19/21, I- 24020, Villa di Serio (BG), Italy (e-mail: Corrado.Volpi@promatech.it). could often result in high tension peak values with a high risk of yarn breakage. This is a particularly noxious event, because yarn breakages need direct human intervention and a complete stop of the loom operations. In order to avoid breaking events, active weft braking is currently under development: by knowing the time and space profile of the tension into the yarn, it is possible to electronically regulate the brake force to control the tension in the weft yarn avoiding or at least reducing breaking events. So, it is strongly advisable to have a mathematical model which is able to give at any time the tension value in each point of the weft yarn. Unfortunately, to the best of the authors’ knowledge, software tools for simulation of the complete filling insertion process in rapier or projectile looms are not available. In literature there is a fundamental lack of a mathematical model of the filling insertion process. However, some works about this subject, providing partial interesting results, are noteworthy. For instance, in [1] the tip transfer process is analyzed and a prediction of the velocity changes, which result in local high tension values, is provided. In [2] a dynamical model of yarn in constrained conditions using linear differential algebraic equations is presented. In [3] a model of warp yarn tension is presented. In [4] and [5] the tension variations determined by high speed yarn unwinding from package are modeled. In [6] it is provided a numerical model, validated by experimental results, of the interaction of the lower warp sheet with objects moving in the loom. Although none of this works is directly related to the subject of the present paper, they put in evidence the high interest around the problem of mathematical modeling of the operations of a rapier loom. In this paper, starting from the results described in [2] and [7], a mathematical model of the filling insertion process in rapier weaving looms is presented. The model provides the time and space profiles of the tension in the weft yarn moving through the warp shed during the filling insertion process. In order to develop such a model, different tools seemed to be feasible. First, partial differential equations could have been used. Unfortunately, they require a high numerical effort. Moreover, it could be difficult to introduce in the equations the interactions between the loom elements and the yarn. As an alternative, also multibody simulation tools could have been used. These require specific skill and A Numerical Model of the Weft Yarn Filling Insertion Process in Rapier Looms Fabio Previdi, Sergio M. Savaresi, Member, IEEE, and Corrado Volpi P Proceedings of the 2006 American Control Conference Minneapolis, Minnesota, USA, June 14-16, 2006 WeA11.4 1-4244-0210-7/06/$20.00 ©2006 IEEE 376