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Fig. 3 Normal curvature and geodesic curvature. If the value of tan θ is zero, kn=0 can be de-duced. In this case, the winding trajectory is geo-desic, which means a stable winding. Based on the friction coefficient and the result achieved from Eq.(10), it is easy to judge whether Slip line condi-tion occurs as to make further decision on the winding angle and the winding path. 2.2 The judgment of Bridge condition A Bridge condition[9-10] happens when the fiber departs from the mould surface as shown in Fig.4. Fig.4 Bridge condition. The line AC is the wound fiber with Bridge condition. Points A, B and C are doffing points, and P is the point randomly chosen on the line AC. A Bridge condition will occur if there is a distance between the mould and the fiber at point B. During winding, the Bridge condition is the major factor affecting the capacity of weight toler-ance and usage life. Generally speaking, to elimi-nate Bridge condition, there are two common methods as follows: (1) To increase the winding angle. Usually, this γ is the most effective way to avoid Bridge condition. Therefore, it is the very method with which the pa-per will use to eliminate the Bridge condition. It should be noted that with a winding angle big enough, the resistance force of a product to axial intensity would be reduced. (2) To optimize the design. In avoidance of in-fluencing the performance of the product being wound, the sharp convexes or concaves on the mould surface should be obviated or lessened in the design. (3) To use the paving method[11-12]. By using the paving technology, the tape-shaped fiber can be paved onto the mould surface. The rolling motion of the paving tool would solve the Bridge condition effectively. In order to solve the problem of Bridge condi-tion, the location where the Bridge condition de-tected occurs should be at first. With an accurate data model established and the detailed mould sur-face information obtained, the potential Bridge con-dition could be detected and well controlled by software. An occurrence of a Bridge condition would suspend the wound fiber between A and C during winding. That is to say, the distance between B and the mould axis should be shorter than that from P to the mould axis. As a result, the fiber Bridge condition would not occur at the doffing point B only if Eq.(11) is met. 22 22BB PP y zyz +>+ (11) 3 Experiments 3.1 Program To verify the winding theory, the codes are programmed following the patch winding theory. Firstly, based on the design requirements, the data model is established by using CAD/CAM software; then the model is meshed by using ANASYS soft-ware. All the node coordinates are output and pro- cessed in an orderly way. Finally, following the patch winding theory, the nodes without the Slip line condition and the Bridge condition are chosen as the track doffing points by referring to the origi-nal doffing points and the winding angle. When seeking for the appropriate doffing points, the quadrant of the next doffing point should be determined according to the present doffing points and the winding angle. Then, the inquiry scope should be decided according to the set-up maximal step. All the nodes would be judged step-wise until the most stable doffing point is found. Taking the uncertain condition factors into account, the winding simulation is fulfilled. After having disposed the doffing points into NC code for a winding tool, the practical winding experiments on the winding tool are performed as shown in Fig.5. Fig.5 Program frame. The program includes following three main modules: (1) To calculate the stable trajectory. With the most appropriate doffing points found following the patch winding theory, all the doffing points on the same track are connected into one to-and-fro on the winding trajectory. The second original doffing point is found by choosing a point from the first original point by one tape width. By using the same winding angle, the process is repeated until the mould is covered with the fiber. (2) To simulate the winding trajectory. Ac-cording to the doffing point track, the winding process simulation is fulfilled to verify whether the trajectory is reasonable by means of three-dimen-sional animation or not. (3) To regulate and output the winding data. The mould reference frame should be translated into the machine tool reference frame, and, accordingly, the doffing points are translated into the spinning points. Then the codes could be programmed on the basis of the spinning point coordinates and the NC codes could be output in a certain form to control the tool. 3.2 Mould winding In order to verify the feasibility of patch wind-ing, two experiments are conducted. The two ex-perimental moulds are of the airplane inlet and the vane, which are of non-gyration and unable to be wound by using the traditional winding theory. Shaped as an “S”, the airplane inlet is extremely irregular and intricate to be described by an equa-tion. Although the vane body can be described with two different equations, it does not belong to gyra-tion mould and its tail part has an abnormal shape. Therefore, the two moulds cannot be wound with the traditional winding methods. (1) Airplane inlet winding This experiment requires that the tangent length from the spinning point to the doffing point should be constant.