CN117669228A - Method for calculating winding speed of annular braiding arbitrary mandrel by considering yarn contact - Google Patents

Abstract

The invention relates to a method for calculating the coiling speed of an annular braiding arbitrary mandrel by considering yarn contact; according to the method, the mandrels are segmented and divided into a plurality of cake-shaped structures, and the winding speed required by weaving each segment of mandrel is solved. Comprising the following steps: firstly, solving an equivalent braiding angle under an ideal kinematic model according to an expected braiding angle through mechanical analysis of interaction among yarns in a convergence region; and then, through the kinematic analysis of the annular knitting process, the corresponding mandrel coiling speed is obtained according to the equivalent knitting angle. The invention can reversely solve the winding speed of the mandrel with any section in the annular knitting on the basis of considering yarn contact, so that the actual knitting angle of the annular knitting product is close to the expected target.

Description

Method for calculating winding speed of annular braiding arbitrary mandrel by considering yarn contact

Technical Field

The invention belongs to the technical field of textile weaving, and particularly relates to a method for calculating winding speed of an annular braiding arbitrary mandrel by considering yarn contact.

Background

Endless weaving is a process for forming seamless tubular fabrics in which the woven yarns are drawn from two sets of spools rotating clockwise and counterclockwise, respectively, and as the spools move, the yarns interweave with each other and gradually deposit on a moving mandrel to form the fabric. With the aid of resin injection technology, fabrics formed by chemical fiber yarns can be made into fiber reinforced composite components, and hollow components with different shapes can be obtained by changing the geometric shape of the mandrel. Due to the mechanical properties of the annular weaving integrally formed high-performance fabric, the composite material is widely applied to the fields of aviation, aerospace, automobiles, shipbuilding and the like.

The orientation of the yarns in the annular woven fiber reinforced composite component determines its geometry, which has an important influence on its mechanical properties, while the weave angle is a key parameter characterizing the orientation of the yarns. Therefore, before annular braiding, the coiling speed of the mandrel needs to be determined according to the expected braiding angle of the produced composite braided part so as to ensure that the braided part has expected mechanical properties. In the conventional production process, the process depends on long-term accumulated production experience and multiple trial and error before formal production, and considerable time and material are consumed. Meanwhile, in recent years, composite material knitted pieces show a trend of diversification and complexity in appearance form and performance indexes, and the traditional method cannot meet the requirements of actual production on efficiency and precision. The existing inverse solution method for the winding speed of the annular weaving mandrel is completely based on kinematic analysis, and the interaction among yarns in the weaving process is ignored, so that the weaving angle of the obtained fabric is greatly different from the expected angle.

Therefore, to improve the above-mentioned problems, it is necessary to provide an innovative inverse solution for winding speed of a mandrel with arbitrary cross section for annular knitting, which considers yarn contact, so as to overcome the defects existing in the prior art.

Disclosure of Invention

The invention aims to provide a method for calculating the winding speed of an annular braiding arbitrary mandrel by considering yarn contact aiming at the defects in the prior art.

In order to achieve the above purpose, the invention provides a method for calculating the winding speed of any mandrel in annular knitting in consideration of yarn contact, which comprises the following steps:

(1) Dividing a mandrel with any section in the axial direction into a plurality of cake-shaped mandrel units; dividing each cake-shaped mandrel unit into rectangular surfaces with the same number as the section vertexes according to the section vertexes in the rotation direction;

(2) One end of 2m yarns is arranged on the end face of the mandrel according to the production requirement, and each initial yarn drop point P is obtained ₁ And its contact point Q with the guide ring ₁ The method comprises the steps of carrying out a first treatment on the surface of the Wherein, the 2m yarns comprise m warp yarns and m weft yarns respectively;

(3) Drop point P for each yarn ₁ Contact point Q with guide ring ₁ Establishing a straight line equation P ₁ Q ₁ And determining the action points of warp yarns and weft yarns in the convergence zone;

(4) Calculating an equivalent knitting angle alpha' of each yarn under an ideal kinematic model;

(5) According to the equivalent braiding angle alpha', the drop point P of each yarn on the initial end face of the next mandrel unit is obtained ₂ And its contact point Q with the guide ring ₂ ；

(6) According to the equivalent braiding angle alpha' and P ₁ 、Q ₁ 、P ₂ 、Q ₂ Obtaining the coiling speed of the cake-shaped mandrel unit corresponding to the single yarn based on ideal kinematics analysis;

(7) Solving the coiling speed of the cake-shaped mandrel unit corresponding to each yarn for the residual yarns of the current cake-shaped mandrel unit, and taking the average value as the final coiling speed of the cake-shaped mandrel unit;

(8) And (3) repeating the steps (3) to (7), and obtaining the final coiling speed of each segment of cake-shaped mandrel unit until the end of the mandrel is reached, so as to obtain the complete mandrel coiling speed.

Further, in the step (3), for any warp yarn, P is applied to the warp yarn _k Q _k Equation is associated with P of m weft yarns _k Q _k The simultaneous combination of equations is formed into m equation sets, if one equation set has a solution in the range of convergence zone, the equation sets are stored as an action point X _i 。

Further, in the step (4), n action points are generated in the convergence zone by each warp yarn and m weft yarns, deflection angles generated at each action point by the warp yarn are respectively determined through mechanical analysis, deflection angles of the warp yarn in the convergence zone are obtained through accumulation, and then the end angles, namely equivalent weaving angles alpha', of the warp yarn are obtained; the equivalent braiding angle alpha' obtained by all yarns is averaged to be used as the equivalent braiding angle of the cake-shaped mandrel unit.

Further, point of action X _i The change formula of the deflection angle is as follows:

wherein F is _i For friction force, T _i =tcosθ is the yarn tension T before yarn deformation at friction force F _i The component in the plane, gamma _i Is the local braiding angle gamma before yarn deformation _i ' is the local braiding angle after yarn deformation.

Further, in the step (6), when the single yarn is taken as the study object, the winding speed v of the kth cake-shaped mandrel unit _k,k+1 The method comprises the following steps:

wherein dz _m For the displacement of the mandrel itself in the axial direction, dt is the time that the yarn has elapsed for deposition in the kth pie-shaped mandrel unit.

Compared with the prior art, the invention has the beneficial effects that: the method for calculating the winding speed of the annular braiding mandrel with any section considering yarn contact can calculate the winding speed of the mandrel required by producing the fabric with the designated braiding angle through annular braiding aiming at the mandrel with any section, obviously reduces the gap between the braiding angle of the fabric product and an expected target, avoids multiple trial and error and improves the production efficiency.

Drawings

FIG. 1 is a schematic diagram of a endless weave;

FIG. 2 is a diagram of an analytical model of a single yarn;

FIG. 3 is a graph of a single yarn equivalent braid angle development analysis;

FIG. 4 is a graph of the force analysis of a single yarn at the point of action Xi;

FIG. 5 is a schematic view of the spatial location of the action point Xi;

FIG. 6 is a schematic representation of yarn unit variation;

FIG. 7 is a graph of an analysis of the deposition process of a single yarn under an ideal kinematic model;

FIG. 8 is a flow chart of the loop braiding arbitrary section mandrel take-up speed inverse solution algorithm taking into account yarn contact in the present invention.

In the figure, 1, a winding mechanism; 2. a mandrel; 3. a yarn; 4. a spool; 5. a guide ring; 6. spool rail plate.

Detailed Description

In order to make the technical solution of the present invention more clear, the following further describes embodiments of the present invention with reference to the accompanying drawings and examples. The description of the specific embodiments can make the technical problems solved by the invention, the technical scheme adopted and the technical effect achieved clearer. It is to be understood that the specific embodiments described herein are merely illustrative of the invention and are not limiting thereof. It should be further noted that, for convenience of description, only some, but not all of the matters related to the present invention are shown in the accompanying drawings, and the protection scope of the present application is not limited in this way.

The present invention will be described in detail with reference to the accompanying drawings. The features of the examples and embodiments described below may be combined with each other without conflict.

As shown in fig. 1, the invention uses an annular braiding machine with a mandrel with any cross section (circular cross section is taken as an example in fig. 1), and mainly comprises a coiling mechanism 1, a mandrel 2, yarns 3, a spool 4, a guide ring 5 and a spool rail disc 6, wherein the coiling mechanism 1 pulls the mandrel 2 to move leftwards. The two groups of bobbins 4 respectively make clockwise and anticlockwise movements around the center of the bobbin track disc 6, the left end of the yarn 3 is fixed at the left end of the mandrel 2, and the right end of the yarn 3 is respectively wound on the two groups of bobbins 4, so that the yarn 3 also makes clockwise and anticlockwise movements along with the rotation of the bobbins.

In analysis, the present invention simplifies it to a model as shown in fig. 2. Setting the winding speed of the mandrel 2 to the left as v, the expected weaving angle of the target fabric as alpha, the rotation angular speed of the spool 4 as omega, and the radius of the guide ring 5 as R _g The radius of the mandrel 2 is r, the contact point of the yarn 3 and the guide ring 5 is Q, the contact point of the yarn 3 and the mandrel 2 is the drop point P, and the distance from the drop point of the yarn 3 to the guide ring 5, namely the length of the convergence zone, is H. The yarn is densely distributed in the convergence zone, the interaction such as friction between the yarns has a great influence on the knitting process, and the surface of the guide ring 5 is smooth, so that the interaction between the yarns 3 and the thickness of the yarns are taken into consideration, and the friction between the yarns 3 and the guide ring 5 is ignored, so that the movement of the spool 4 on the spool rail disc 6 and the movement of the yarns 3 on the contact point Q of the guide ring 5 can be considered to be synchronous, namely the spool rail disc 6 can be ignored in the model, and the angular speed of the contact point Q on the guide ring 5 is omega.

The invention provides a method for calculating the winding speed of an annular braiding arbitrary mandrel by considering yarn contact, which comprises the following steps of: yarn number 2m, angular velocity ω, target braiding angle α, guide ring radius R _g Yarn tension T. Referring to fig. 8, the method specifically includes the steps of:

(1) Dividing a mandrel with any section in the axial direction according to a certain step length (the step length is related to solving precision, and generally taking 1/100-1/50 of the length of the mandrel) into a plurality of cake-shaped mandrel units; and then each cake-shaped mandrel unit is divided into rectangular planes with the same number as the section vertexes according to the section vertexes (polygonal approximation is adopted if the cake-shaped mandrel units are curved surfaces) in the rotation direction.

(2) One end of 2m yarns (each of the warp yarn and the weft yarn) is arranged on the end face of the mandrel according to the production requirement, and an initial yarn falling point P is obtained ₁ And its contact point Q with the guide ring ₁ 。

(3) When the knitting process of the kth pie core shaft unit is started, set Q _k For the contact point of the yarn and the guide ring at the current moment, P _k Is the actual drop point of the yarn on the mandrel at the current moment. P respectively connecting each yarn _k 、Q _k 2m P's can be obtained _k Q _k A straight line equation; and determining the point of action of the warp and weft yarns in the convergence zone. For any warp yarn, P is applied to _k Q _k Equation is associated with P of m weft yarns _k Q _k The simultaneous combination of equations is formed into m equation sets, if one equation set has a solution in the range of convergence zone, the equation sets are stored as an action point X _i From the m sets of equations, n solutions are obtained, i.e. n points of action (n<m), and the rest (2 m-1) yarns are the same.

(4) The equivalent braiding angle of each of the 2m yarns under the ideal kinematic model is calculated. As shown in fig. 3, for each warp yarn, Q _k For its contact point with the guide ring, P _k For the actual drop point of the yarn on the mandrel at the current moment, X ₁ ，X ₂ ，…，X _n The point of action of the warp yarn with the n weft yarns coming into contact in the convergence zone is divided into n+1 analysis units according to the n points of action. When neglecting the effect of yarn interactions in the convergence zone, the warp yarn remains straight, e.g. P _k ’Q _k As shown, a braiding angle α' is formed; the interaction being such that the yarn, when actually woven, undergoes a certain deflection of curvature, e.g. P, in the convergence zone _k Q _k As shown, a braiding angle α is formed. With knowledge of the desired braiding angle, i.e. the actual braiding angle alpha, the braiding angle is defined by P _k To Q _k By mechanical analysis of each yarn unit, the deflection angle of the warp yarn in the convergence zone can be accumulated, and the end angle alpha' thereof can be obtained. That is, if yarns in the convergence zone are ignored from each otherThe effect of the effect will change from a to a ', so a' is defined as the equivalent braiding angle corresponding to the actual braiding angle a in a kinematic analysis ignoring yarn interactions.

The chemical fiber yarn used in annular knitting has the characteristics of high strength and high modulus, which means that the yarn hardly generates axial deformation when the yarn is interacted due to contact, but is mainly influenced by friction force among the yarns. For each yarn unit of the current warp yarn, an analysis is first performed in a plane perpendicular to the friction force F, as shown in fig. 4. In consideration of the yarn volume, the warp yarn is at the point of action X due to interweaving with the weft yarn _i An angle θ is created with respect to the mandrel surface such that the normal force W perpendicular to the mandrel surface includes the combined effect of the two-sided yarn tension T and the gravity G of the yarn unit itself:

W＝2Tsinθ+Gcosβ (1)

wherein beta is the action point X _i The corresponding corners in space are shown in fig. 5. Friction force F is determined by the development of normal force W through classical friction law:

F＝aW ^l (2)

wherein, the proportionality coefficient a and the index l are both constants of an empirical formula.

And then to the plane in which the friction force F lies for analysis, as shown in fig. 6. The yarn unit, to which the warp yarn is attached, moves under the traction of a spool moving at an angular velocity of-omega and in a converging zone with a weft yarn moving in the opposite direction at an application point X _i Where contact is made. Is subjected to friction force F _i The effect of the warp yarn at X _i The position generates flexible deformation, and under the balance action of force, the deflection angle is changed from gamma to gamma'. The corresponding relation is:

wherein F is _{Omega of the combination} F for resultant force in rotation direction _{Z is the same as} T is the axial resultant force of the mandrel _i =tcosθ is the yarn tension T before yarn deformation at friction force F _i The component in the plane in which it lies,T′ _i for yarn tension T after yarn deformation at friction force F _i Component in plane F _i For friction, gamma _i Is the local braiding angle gamma before yarn deformation _i ' is the local braiding angle after yarn deformation.

Further from (3) can be deduced to be gamma _i And gamma is equal to _i The relationship of' is:

for n points of action per yarn, at the current point of action X _i The obtained gamma' is the next action point X _i+1 Gamma at, i.e.:

γ _i+1 ＝γ _i ' (5)

the friction force action of each action point is accumulated to obtain an equivalent knitting angle alpha'. The above calculation was performed on all 2m yarns, and the average value of the equivalent knitting angle α' was obtained as the equivalent knitting angle of the segment of the pie core shaft unit. This process allows for consideration of interactions between yarns in the convergence zone.

(5) For each yarn, when solving at the kth pie core unit, it is necessary to determine its point of fall P at the (k+1) th pie core unit _k+1 And contact point Q with guide ring _k+1 . As shown in fig. 7, the yarn is at time t _k And time t _k+1 Deposition begins at the kth pie-shaped mandrel unit and the kth+1th pie-shaped mandrel unit, respectively. Since the cross section of the mandrel is polygonal (or polygonal for approaching the curved mandrel), the yarn falling point after the beginning of knitting is necessarily located on the mandrel edge line, namely the cross section vertex, and the axial included angle of the yarn and the mandrel is the equivalent knitting angle alpha', thereby being formed by P _k Determining P _k+1 。

(6) According to the equivalent braiding angle and P _k 、Q _k 、P _k+1 、Q _k+1 And (5) solving the coiling speed of the cake-shaped mandrel unit based on an ideal kinematic model.

To determine Q _k Extension of P _k P _k+1 P to the starting end face of the next spindle unit _k+1 ”，P _k+1 "is the drop point of yarn at the beginning end of the kth +1 pie-shaped mandrel unit after complete deposition of the face of the mandrel. When the yarn is just deposited on one surface of the mandrel, the yarn is tangent to the surface, so that the angle range of the corresponding spool of the yarn in the deposition process of the surface can be determined, and P can be obtained by equal proportion _k+1 Corresponding spool angleI.e. the spool angle at which the yarn starts to deposit at the k+1-th pie core unit. And spool angle->The time dt that it takes for the yarn to deposit on the kth pie core unit is known as:

and can determine Q _k+1 Coordinates ofThe method comprises the following steps:

on the other hand, during the time dt, the yarn starts at the drop point P _k And the drop point P at the end time _k+1 The spatial distance in the axial direction (z direction) of the spindle is known and is set as dz _t Which is in fact the displacement dz of the spindle itself in the axial direction (z-direction) _m And a change dz in the length of the convergence zone of the two drop points _pq The composition, i.e. the following relationship exists:

dz _t ＝dz _m -dz _pq (8)

wherein the change dz of the length of the convergence zone of two drop points _pq The method comprises the following steps:

and->Respectively P _k And Q is equal to _k 、P _k+1 And Q is equal to _k+1 Distance in the radial direction (z direction) of the spindle. In general, for arbitrary +.>And->Can be calculated from formula (10):

thereby obtaining the winding speed v of the kth pie core shaft unit when the single yarn is taken as the research object _k,k+1 The method comprises the following steps:

(7) All 2m yarns were subjected to the above calculation to find v _k,k+1 And (5) averaging, so that the solution of the winding speed of the kth pie core shaft unit is completed.

(8) And (3) repeating the steps (3) to (7), and sequentially solving each pie-shaped mandrel unit according to the general method until the last pie-shaped mandrel unit at the tail end of the mandrel is reached, so that the complete mandrel coiling speed can be obtained.

The foregoing is merely illustrative of the present invention and is not to be construed as limiting the scope of the invention. Various changes, combinations, simplifications, modifications, substitutions and rearrangements of the parts will now become apparent to those skilled in the art without departing from the scope of the invention. Therefore, while the present invention has been described in considerable detail with reference to the foregoing illustrative embodiments, it is not intended to restrict the invention to the foregoing illustrative embodiments, but is to be construed as including other equivalent embodiments within the scope of the present invention.

Claims (5)

1. The method for calculating the winding speed of the annular braiding arbitrary mandrel by considering the yarn contact is characterized by comprising the following steps:

(1) Dividing a mandrel with any section in the axial direction into a plurality of cake-shaped mandrel units; dividing each cake-shaped mandrel unit into rectangular surfaces with the same number as the section vertexes according to the section vertexes in the rotation direction;

(2) One end of 2m yarns is arranged on the end face of the mandrel according to the production requirement, and each initial yarn drop point P is obtained ₁ And its contact point Q with the guide ring ₁ The method comprises the steps of carrying out a first treatment on the surface of the Wherein, the 2m yarns comprise m warp yarns and m weft yarns respectively;

(3) Drop point P for each yarn ₁ Contact point Q with guide ring ₁ Establishing a straight line equation P ₁ Q ₁ And determining the action points of warp yarns and weft yarns in the convergence zone;

(4) Calculating an equivalent knitting angle alpha' of each yarn under an ideal kinematic model;

(5) According to the equivalent braiding angle alpha', the drop point P of each yarn on the initial end face of the next mandrel unit is obtained ₂ And its contact point Q with the guide ring ₂ ；

(6) According to the equivalent braiding angle alpha' and P ₁ 、Q ₁ 、P ₂ 、Q ₂ Obtaining the coiling speed of the cake-shaped mandrel unit corresponding to the single yarn based on ideal kinematics analysis;

(7) Solving the coiling speed of the cake-shaped mandrel unit corresponding to each yarn for the residual yarns of the current cake-shaped mandrel unit, and taking the average value as the final coiling speed of the cake-shaped mandrel unit;

(8) And (3) repeating the steps (3) to (7), and obtaining the final coiling speed of each segment of cake-shaped mandrel unit until the end of the mandrel is reached, so as to obtain the complete mandrel coiling speed.

2. The method for calculating the take-up speed of any mandrel in endless weaving in consideration of yarn contact according to claim 1, wherein in the step (3), P is applied to any warp yarn _k Q _k Equation is associated with P of m weft yarns _k Q _k The simultaneous combination of equations is formed into m equation sets, if one equation set has a solution in the range of convergence zone, the equation sets are stored as an action point X _i 。

3. The method according to claim 1, wherein in the step (4), n action points are generated in the convergence zone between each warp yarn and m weft yarns, and the deflection angle of each warp yarn at each action point is determined by mechanical analysis, and the deflection angle of the warp yarn in the convergence zone is obtained by accumulation, so that the end angle, namely the equivalent weaving angle alpha', of the warp yarn is obtained; the equivalent braiding angle alpha' obtained by all yarns is averaged to be used as the equivalent braiding angle of the cake-shaped mandrel unit.

4. A method of calculating the take-up speed of an endless weaving arbitrary mandrel taking into account yarn contact as claimed in claim 3, characterized in that the point of action X _i The change formula of the deflection angle is as follows:

wherein F is _i For friction force, T _i =tcosθ is the yarn tension T before yarn deformation at friction force F _i The component in the plane, gamma _i Is the local braiding angle gamma before yarn deformation _i ' is the local braiding angle after yarn deformation.

5. As claimed in claim 1The method for calculating the winding speed of the annular knitting arbitrary mandrel taking the yarn contact into consideration is characterized in that in the step (6), when a single yarn is taken as a research object, the winding speed v of a kth cake-shaped mandrel unit _k,k+1 The method comprises the following steps:

wherein dz _m For the displacement of the mandrel itself in the axial direction, dt is the time that the yarn has elapsed for deposition in the kth pie-shaped mandrel unit.