Robot thermoplastic composite material winding path design method

Abstract

The invention belongs to the field of composite material manufacturing, and discloses a robot thermoplastic composite material winding path design method which comprises the steps that geometric model parameters of a rotary body are obtained, and a rotary body parameterized model is established; according to the rotary body parameterized model, a cylindrical section geodesic equation and a non-geodesic equation at an end socket are constructed; respectively solving non-geodesic line equations by setting different slip coefficients, and fitting an approximate polynomial relationship between the slip coefficient and a winding angle and an approximate polynomial relationship between the slip coefficient and a rotation center angle according to solving results; according to the algebraic mode theory of fiber winding, a series of linear parameters meeting uniform distribution are obtained; aiming at each group of linear parameters, a Newton iteration method is adopted to find a proper slip coefficient, so that a winding angle is continuous and fibers are uniformly distributed; and aiming at each group of linear parameters with the slippage coefficient, calculating a fiber winding path. According to the method, the linear design space of the pressure vessel with the unequal polar holes is expanded, and the winding path generation efficiency and precision can be improved.

Description

Technical Field

[0001] The invention relates to the field of composite material manufacturing, and in particular to a method for designing a robot thermoplastic composite material winding path. Background Art

[0002] Robotic thermoplastic composite winding technology is an advanced manufacturing technology that uses robots and prepreg impregnated with thermoplastic resin for winding. It is widely used in winding various rotating parts such as pressure vessels. Pressure vessels are usually composed of a left head, a barrel section, and a right head. In practice, due to constraints such as process and structure, the pole holes of the left and right heads of pressure vessels are usually inconsistent.

[0003] When designing the winding path of a pressure vessel, commonly used methods include the geodesic winding method and the non-geodesic winding method. The geodesic winding method can only be applied to the winding design of pressure vessels with equal polar holes. For the non-geodesic winding method, it is necessary to select a suitable slip coefficient to obtain the winding path. Without modifying the polar hole size, existing studies usually use intelligent algorithms or grid search methods to search for the slip coefficient. However, these methods are time-consuming and have no solutions. In addition, some studies use fitted polynomial functions instead of solving complex equations, but there is a problem of inaccurate path solution, which is not suitable for robotic thermoplastic composite winding molding. Some foreign commercial software (such as CADWIND and CADFIL) can generate winding paths for pressure vessels with unequal polar holes, but there will be deviations from the polar holes or asymmetry of the left and right heads, and there are large technical barriers. Therefore, it is very necessary to study fast and accurate winding path design methods for pressure vessels with unequal polar holes. Summary of the invention

[0004] In view of the above defects or improvement needs of the prior art, the present invention provides a robot thermoplastic composite winding path design method, which can quickly and accurately generate a feasible winding path, avoid a lot of calculations, and has practical engineering value.

[0005] To achieve the above object, according to one aspect of the present invention, a method for designing a robot thermoplastic composite winding path is provided, comprising the following steps:

[0006] S1: obtaining geometric model parameters of the rotating body, and establishing a parametric model of the rotating body according to the geometric model parameters of the rotating body, wherein the parametric model of the rotating body includes a mathematical model of the middle cylindrical section and a mathematical model of the end caps at both ends;

[0007] S2: According to the parameterized model of the rotating body obtained in step S1, the geodesic equation of the cylindrical segment and the non-geodesic equations at the left and right heads are constructed, and the non-geodesic equations are solved respectively by setting different slip coefficients to obtain the winding angle and the rotation center angle under different slip coefficients; according to the solution results, the approximate polynomial relationship between the slip coefficient and the winding angle, and the slip coefficient and the rotation center angle is fitted;

[0008] S3: According to the continued fraction theory of fiber winding, a series of linear parameters that satisfy uniform distribution are obtained. For each set of linear parameters, the Newton iteration method is used to find a suitable slip coefficient so that the winding angle is continuous and the fibers are evenly distributed. For each set of linear parameters with a slip coefficient, the geodesic equation of the cylindrical segment obtained in step S2, the non-geodesic equation at the head, and the approximate polynomial relationship are combined to calculate a single fiber winding path. After the single fiber winding path is rotated, a uniformly distributed winding path is obtained.

[0009] Preferably, step S1 obtains the geometric model parameters of the rotating body including: the length of the cylindrical segment, the radius of the cylindrical segment, the elliptical parameters of the left elliptical head, the polar hole radius of the left elliptical head, the elliptical parameters of the right elliptical head and the polar hole radius of the right elliptical head, wherein the elliptical parameters of the left elliptical head include the major semi-axis of the left elliptical head and the minor semi-axis of the left elliptical head; the elliptical parameters of the right elliptical head include the major semi-axis of the right elliptical head and the minor semi-axis of the right elliptical head.

[0010] Preferably, step S1 specifically includes the following steps:

[0011] Step S11: obtaining geometric model parameters of the body of revolution, so that the radius of the cylindrical segment in the body of revolution is equal to the long semi-axis of the left elliptical head and the long semi-axis of the right elliptical head, one end of the barrel segment in the body of revolution is connected to the left elliptical head, and the intersection of the two is the left equatorial circle, and the other end of the barrel segment is provided with a right elliptical head, and the intersection is the right equatorial circle;

[0012] Step S12: According to the geometric model parameters of the rotating body in step S11, a Cartesian coordinate system is established, wherein the origin of the Cartesian coordinate system is the center of the right equatorial circle, the X coordinate axis of the Cartesian coordinate system is a vector starting from the center of the right equatorial circle and pointing to the right equatorial circle, the Z coordinate axis of the Cartesian coordinate system is the rotation axis of the rotating body, and the direction points to the left end cap, and the Y coordinate axis of the Cartesian coordinate system is defined by the Cartesian right-hand criterion;

[0013] In the Cartesian coordinate system, a parametric model of the body of revolution of the cylindrical segment, the left elliptical head and the right elliptical head rotational surfaces is established according to the geometric model parameters of the body of revolution.

[0014] Preferably, step S2 specifically includes the following steps:

[0015] Step S21: According to the general equation of non-geodesic of parametric surface and the parameterized model of the body of revolution obtained in step S1, the geodesic equation of the cylindrical segment and the non-geodesic equations at the left and right heads are derived. The general equation of non-geodesic of parametric surface is as follows:

[0016]

[0017] Where z is the coordinate in the Z direction in the Cartesian coordinate system, r is the radius of gyration, and is the first and second order derivatives of the radius of gyration with respect to z, λ is the slip coefficient, α is the winding angle, and θ is the central angle of rotation around;

[0018] When λ = 0, the equation is the geodesic equation of the parametric surface;

[0019] Step S22: by setting different slip coefficients, respectively solving the non-geodesic equations in step S21 to obtain the winding angle and the rotation center angle under different slip coefficients;

[0020] Step S23: According to the solution of the non-geodesic equation at the left head, the least square fitting method is used, and the approximate polynomial relationship between the slip coefficient and the winding angle, and the slip coefficient and the rotation center angle is expressed as:

[0021]

[0022] Where λ is the slip coefficient, f left (λ) is a polynomial with the slip coefficient as the independent variable, which represents the approximate relationship between the slip coefficient and the winding angle of the left elliptical head. is the winding angle at the approximate left equator, g left (λ) is a polynomial with the slip coefficient as the independent variable, which represents the approximate relationship between the slip coefficient of the left elliptical head and the rotation center angle. is the rotation center angle around the approximate left equator;

[0023] Step S24: According to the solution of the non-geodesic equation at the right end cap, the least squares fitting method is used, and the approximate polynomial relationship between the slip coefficient and the winding angle, and between the slip coefficient and the rotation center angle is expressed as:

[0024]

[0025] Where λ is the slip coefficient, f right (λ) is a polynomial with the slip coefficient as the independent variable, which represents the approximate relationship between the slip coefficient and the winding angle of the right elliptical head. is the winding angle at the approximate right equator, g right(λ) is a polynomial with the slip coefficient as the independent variable, which represents the approximate relationship between the slip coefficient of the right elliptical head and the rotation center angle. is the rotation center angle around the approximate right equator.

[0026] Preferably, the line type parameters satisfying uniform distribution in step S3 are obtained as follows:

[0027] According to the continued fraction theory of fiber winding, the set winding angle α0 is substituted into the approximate polynomial obtained in step S23 and step S24, and the initial slip coefficient λ of the left and right elliptical heads is obtained by using the root-finding formula. l0 , r0 ;

[0028] Substitute the winding angle and the initial slip coefficients of the left and right elliptical heads into the geodesic equation of the cylindrical segment and the non-geodesic equations of the left and right heads, and use the Runge-Kutta method to solve them. The rotation center angles θ of the cylindrical segment, the left elliptical head, and the right elliptical head are obtained respectively. c ,θ l and θ r ;

[0029] Set the central angle deviation and the range of the number of divisions. Within the set deviation range, use the continued fraction theory to obtain a series of linear parameters {k i ,N i}, where k i Indicates the number of jumps, N i Indicates the number of cycles.

[0030] Preferably, in step S3, for each set of line type parameters {k i ,N i}, the Newton iteration method is used to find the appropriate slip coefficient, and the single fiber winding path is obtained by combining the geodesic equation of the cylindrical segment, the non-geodesic equations at the left and right heads, and the parameterized model of the rotating body.

[0031] The specific method of the Newton iteration method is as follows:

[0032] (1) Select λ l0 , r0 as the initial slip coefficient;

[0033] (2) Substitute the winding angle and the initial slip coefficients of the left and right elliptical heads into the geodesic equation of the cylindrical segment and the non-geodesic equations of the left and right heads, and solve them using the Runge-Kutta method to obtain the winding angle α at the left and right equator lines. l , α r , the rotation center angle θ at the left and right equator lines l ,θ r , and the rotation center angle θ of the cylindrical segment c ;

[0034] (3) Calculate the objective function:

[0035]

[0036] Among them, α l With α r are the winding angles at the left and right equator respectively, F1 is the objective function related to the winding angle, θ1=2(θ l +θ r +θ c ), θ2 is the rotation center angle determined by the linear parameters and has nothing to do with the slip coefficient, and F2 is the objective function related to the rotation center angle;

[0037] (4) If |F1|≤10 -4 and |F2|≤10 -4 , terminate the iteration and output the current slip coefficient; if the iteration termination number is reached, terminate the iteration and record the group of linear parameters as having no solution; otherwise, perform the following steps;

[0038] (5) Using the approximate polynomial relationship obtained in step S2, the gradient matrix of the slip coefficient is constructed as follows:

[0039]

[0040] Among them, Δλ is the set tolerance, R is the radius of the cylindrical segment, and L is the length of the cylindrical segment;

[0041] (6) Update the slip coefficient. The update formula is as follows:

[0042]

[0043]

[0044] Among them, λ l and λ r is the updated slip coefficient of the left and right elliptical heads;

[0045] (7) Repeat steps (2)-(6) so that the winding angle is continuous and the rotation center angle satisfies the uniform coverage condition.

[0046] Preferably, a single fiber winding path is obtained to obtain a uniformly filled winding path after rotation.

[0047] Preferably, the number of rotations of a single fiber winding path in step S3 is N. i times, and the angle of each rotation is

[0048] In general, the above technical solution conceived by the present invention has the following beneficial effects compared with the prior art:

[0049] (1) The robot thermoplastic composite winding path design method of the present invention can generate an accurate winding path.

[0050] (2) The present invention expands the winding path design space of pressure vessels with unequal polar holes.

[0051] (3) The present invention is based on the Newton iteration method and utilizes a fitting relationship to improve the parameter search speed, and can ensure the continuity of the winding angle and ensure that the fibers are evenly distributed. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 The present invention is a flow chart of a method for designing a robot thermoplastic composite winding path.

[0053] Figure 2 It is a schematic diagram of fitting the slip coefficient and the winding angle, and the slip coefficient and the rotation center angle according to an embodiment of the present invention.

[0054] Figure 3 for Figure 1 Flowchart for searching the slip coefficient using the Newton iteration method.

[0055] Figure 4 This is the simulation result of a single winding path of an embodiment of the present invention.

[0056] Figure 5 The simulation result of a winding path that is evenly distributed is achieved according to an embodiment of the present invention. DETAILED DESCRIPTION

[0057] The technical solution of the present invention will be clearly and completely described below through specific implementation methods. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0058] This embodiment describes the present invention in detail with reference to the accompanying drawings:

[0059] like Figure 1 As shown, a method for designing a robot thermoplastic composite winding path is provided, comprising the following steps:

[0060] S1: Acquire the geometric model parameters of the rotating body, and establish a parametric model of the rotating body according to the geometric model parameters of the rotating body, wherein the parametric model of the rotating body includes a mathematical model of the middle cylindrical section and a mathematical model of the end caps at both ends; specifically, the steps include:

[0061] Step S11: obtaining the geometric model parameters of the rotating body including: the length of the cylindrical segment, the radius of the cylindrical segment, the elliptical parameters of the left elliptical head (major semi-axis, minor semi-axis), the polar hole radius of the left elliptical head, the elliptical parameters of the right elliptical head (major semi-axis, minor semi-axis) and the polar hole radius of the right elliptical head;

[0062] The radius of the cylindrical section in the rotating body is equal to the long semi-axis of the left elliptical head and the right elliptical head. One end of the barrel section in the rotating body is connected to the left elliptical head, and the intersection of the two is the left equatorial circle. The other end of the barrel section is provided with a right elliptical head, and the intersection is the right equatorial circle.

[0063] Step S12: According to the geometric model parameters of the body of revolution, the implementation method of establishing the parametric model of the body of revolution is as follows:

[0064] Establish a Cartesian coordinate system, wherein the origin of the Cartesian coordinate system is the center of the right equatorial circle, the X coordinate axis of the Cartesian coordinate system is a vector starting from the center of the right equatorial circle and pointing to the right equatorial circle, the Z coordinate axis of the Cartesian coordinate system is the rotation axis of the rotating body, and the direction points to the left head, and the Y coordinate axis of the Cartesian coordinate system is defined by the Cartesian right-hand rule;

[0065] In the Cartesian coordinate system, a parametric model of the rotational surfaces of the cylindrical segment, the left elliptical head and the right elliptical head is established according to the geometric parameters of the revolution body.

[0066] S2: According to the parameterized model of the rotating body obtained in step S1, the geodesic equation of the cylindrical segment and the non-geodesic equations at the left and right heads are constructed. By setting different slip coefficients, the non-geodesic equations are solved respectively to obtain the winding angle and the rotation center angle under different slip coefficients; according to the solution results, the approximate polynomial relationship between the slip coefficient and the winding angle, and the slip coefficient and the rotation center angle is fitted; the specific operation steps are as follows:

[0067] Step S21: According to the general equation of non-geodesic of parametric surface and the parameterized model of the body of revolution obtained in step S1, the geodesic equation of the cylindrical segment and the non-geodesic equations at the left and right heads are derived. The general equation of non-geodesic of parametric surface is as follows:

[0068]

[0069] Where z is the coordinate in the Z direction in the Cartesian coordinate system, r is the radius of gyration, and is the first and second order derivatives of the radius of gyration with respect to z, λ is the slip coefficient, α is the winding angle, and θ is the central angle of rotation around;

[0070] When λ = 0, the equation is the geodesic equation of the parametric surface;

[0071] Step S22: by setting different slip coefficients, respectively solving the non-geodesic equations in step S21 to obtain the winding angle and the rotation center angle under different slip coefficients;

[0072] Step S23: In a given slip coefficient interval (λ min ,λ max ), from λ min Start taking values ​​at equal intervals until λ is obtained max , and obtain a series of slip coefficients (λ1,λ2,...,λ n );

[0073] The slip coefficients (λ1,λ2,...,λ n ) is substituted into the non-geodesic equation of the left elliptical head, and the winding angle at the polar hole is set to 90° as the initial condition. The fourth-order Runge-Kutta method is used to solve the winding angle (α at the left equator under different slip coefficients. 1l ,α 2l ,...,α nl ) and the rotation center angle (θ 1l ,θ 2l ,...,θ nl ),like Figure 2 As shown;

[0074] According to the solution of the non-geodesic equation at the left head, the least square fitting method is used, and the approximate polynomial relationship between the slip coefficient and the winding angle, and the slip coefficient and the rotation center angle is expressed as follows:

[0075]

[0076] Where λ is the slip coefficient, f left (λ) is a polynomial with the slip coefficient as the independent variable, which represents the approximate relationship between the slip coefficient and the winding angle of the left elliptical head. l is the winding angle at the approximate left equator, g left (λ) is a polynomial with the slip coefficient as the independent variable, which represents the approximate relationship between the slip coefficient of the left elliptical head and the rotation center angle. is the rotation center angle around the approximate left equator;

[0077] Step S24: Slip coefficients (λ1, λ2, ..., λ n ) is substituted into the non-geodesic equation of the right elliptical head, and the winding angle at the polar hole is set to 90° as the initial condition. The winding angle (α) at ​​the right equator line can be obtained under different slip coefficients by using the fourth-order Runge-Kutta method. 1r ,α 2r ,...,α nr ) and the rotation center angle (θ 1r ,θ2r ,...,θ nr ),like Figure 2 As shown;

[0078] According to the solution of the non-geodesic equation at the right head, using the least squares fitting method, the approximate polynomial relationship between the slip coefficient and the winding angle, and the slip coefficient and the rotation center angle can be expressed as:

[0079]

[0080] Where λ is the slip coefficient, f right (λ) is a polynomial with the slip coefficient as the independent variable, which represents the approximate relationship between the slip coefficient and the winding angle of the right elliptical head. is the winding angle at the approximate right equator, g right (λ) is a polynomial with the slip coefficient as the independent variable, which represents the approximate relationship between the slip coefficient of the right elliptical head and the rotation center angle. is the rotation center angle around the approximate right equator.

[0081] S3: A series of linear parameters that satisfy uniform distribution are obtained according to the continued fraction theory of fiber winding. For each set of linear parameters, a suitable slip coefficient is found by using the Newton iteration method so that the winding angle is continuous and the fibers are evenly distributed. For each set of linear parameters with a slip coefficient, a single fiber winding path is calculated by combining the geodesic equation of the cylindrical segment obtained in step S2, the non-geodesic equation at the head, and the approximate polynomial relationship. The single fiber winding path is rotated to obtain a uniformly distributed winding path. The specific operation steps are as follows:

[0082] Step S31: The line type parameters satisfying uniform distribution are obtained as follows:

[0083] According to the continued fraction theory of fiber winding, the set winding angle α0 is substituted into the approximate polynomial obtained in step S23 and step S24, and the initial slip coefficient λ of the left and right elliptical heads is obtained by using the root-finding formula. l0 , r0 ;

[0084] Substitute the winding angle and the initial slip coefficients of the left and right elliptical heads into the geodesic equation of the cylindrical segment and the non-geodesic equations of the left and right heads, and use the Runge-Kutta method to solve them. The rotation center angles θ of the cylindrical segment, the left elliptical head, and the right elliptical head are obtained respectively. c ,θ l and θ r ;

[0085] Set the central angle deviation and the range of the number of divisions. Within the set deviation range, use the continued fraction theory to obtain a series of linear parameters {k i ,Ni}, where k i Indicates the number of jumps, N i Indicates the number of cycles;

[0086] Step S32: For each set of line type parameters {k i ,N i}, the Newton iteration method is used to find the appropriate slip coefficient, and the geodesic equation of the cylindrical segment, the non-geodesic equations at the left and right heads, and the parameterized model of the rotating body are combined to make the winding angle continuous and the rotation center angle meet the uniform coverage condition, and obtain a single fiber winding path. The specific algorithm is as follows:

[0087] (1) Select λ l0 , r0 as the initial slip coefficient.

[0088] (2) Substitute the winding angle and the initial slip coefficients of the left and right elliptical heads into the geodesic equation of the cylindrical segment and the non-geodesic equations of the left and right heads, and solve them using the Runge-Kutta method to obtain the winding angle α at the left and right equator lines. l , α r , the rotation center angle θ at the left and right equator lines l ,θ r , and the rotation center angle θ of the cylindrical segment c .

[0089] (3) Calculate the objective function:

[0090]

[0091] Among them, α l With α r are the winding angles at the left and right equator respectively, F1 is the objective function related to the winding angle, θ1=2(θ l +θ r +θ c ), θ2 is the rotation center angle determined by the linear parameters and has nothing to do with the slip coefficient, and F2 is the objective function related to the rotation center angle.

[0092] (4) If |F1|≤10 -4 and |F2|≤10 -4 , terminate the iteration and output the current slip coefficient. If the iteration termination number is reached, terminate the iteration and record the group of linear parameters as having no solution. Otherwise, proceed to the following steps.

[0093] (5) Using the approximate polynomial relationship obtained in step 2, the gradient matrix of the slip coefficient is constructed as follows:

[0094]

[0095] Among them, Δλ is the set tolerance, R is the radius of the cylindrical segment, and L is the length of the cylindrical segment.

[0096] (6) Update the slip coefficient. The update formula is as follows:

[0097]

[0098]

[0099] Among them, λ l and λ r is the updated slip coefficient of the left and right elliptical heads.

[0100] (7) Repeat (2)-(6);

[0101] Step S33: For each set of linear parameters {k i ,N i}, according to the searched slip coefficient, combined with the geodesic equation of the cylindrical segment, the non-geodesic equation at the head and the parameterized model of the rotating body, a single fiber winding path can be obtained. Based on the single fiber winding path, N i The angle of each rotation is A uniformly distributed winding path can be obtained.

[0102] The embodiments described above are merely descriptions of preferred implementation modes of the present invention, and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the scope of protection determined by the claims of the device of the present invention.

Claims

1. A method for designing a robot thermoplastic composite winding path, characterized in that: The following steps are involved: S1: obtaining geometric model parameters of the rotating body, and establishing a parametric model of the rotating body according to the geometric model parameters of the rotating body, wherein the parametric model of the rotating body includes a mathematical model of the middle cylindrical section and a mathematical model of the end caps at both ends; S2: According to the parameterized model of the rotating body obtained in step S1, the geodesic equation of the cylindrical segment and the non-geodesic equations at the left and right heads are constructed, and the non-geodesic equations are solved respectively by setting different slip coefficients to obtain the winding angle and the rotation center angle under different slip coefficients; according to the solution results, the approximate polynomial relationship between the slip coefficient and the winding angle, and the slip coefficient and the rotation center angle is fitted; S3: According to the continued fraction theory of fiber winding, a series of linear parameters that satisfy uniform distribution are obtained. For each set of linear parameters, the Newton iteration method is used to find a suitable slip coefficient so that the winding angle is continuous and the fibers are evenly distributed. For each set of linear parameters with a slip coefficient, the geodesic equation of the cylindrical segment obtained in step S2, the non-geodesic equation at the head, and the approximate polynomial relationship are combined to calculate a single fiber winding path. After the single fiber winding path is rotated, a uniformly distributed winding path is obtained.

2. A method for designing a robot thermoplastic composite winding path as claimed in claim 1, characterized in that: Step S1 obtains the geometric model parameters of the rotating body including: the length of the cylindrical segment, the radius of the cylindrical segment, the elliptical parameters of the left elliptical head, the polar hole radius of the left elliptical head, the elliptical parameters of the right elliptical head and the polar hole radius of the right elliptical head.

3. A method for designing a robot thermoplastic composite winding path as claimed in claim 2, characterized in that: The elliptical parameters of the left elliptical head include the major semi-axis of the left elliptical head and the minor semi-axis of the left elliptical head; the elliptical parameters of the right elliptical head include the major semi-axis of the right elliptical head and the minor semi-axis of the right elliptical head.

4. A method for designing a robot thermoplastic composite winding path as claimed in claim 3, characterized in that: Step S1 specifically includes the following steps: Step S11: obtaining geometric model parameters of the body of revolution, so that the radius of the cylindrical segment in the body of revolution is equal to the long semi-axis of the left elliptical head and the long semi-axis of the right elliptical head, one end of the barrel segment in the body of revolution is connected to the left elliptical head, and the intersection of the two is the left equatorial circle, and the other end of the barrel segment is provided with a right elliptical head, and the intersection is the right equatorial circle; Step S12: According to the geometric model parameters of the rotating body in step S11, a Cartesian coordinate system is established, wherein the origin of the Cartesian coordinate system is the center of the right equatorial circle, the X coordinate axis of the Cartesian coordinate system is a vector starting from the center of the right equatorial circle and pointing to the right equatorial circle, the Z coordinate axis of the Cartesian coordinate system is the rotation axis of the rotating body, and the direction points to the left end cap, and the Y coordinate axis of the Cartesian coordinate system is defined by the Cartesian right-hand criterion; In the Cartesian coordinate system, a parametric model of the body of revolution of the cylindrical segment, the left elliptical head and the right elliptical head rotational surfaces is established according to the geometric model parameters of the body of revolution.

5. The method for designing a robot thermoplastic composite winding path according to claim 1, characterized in that: Step S2 specifically includes the following steps: Step S21: According to the general equation of non-geodesic of parametric surface and the parameterized model of the body of revolution obtained in step S1, the geodesic equation of the cylindrical segment and the non-geodesic equations at the left and right heads are derived. The general equation of non-geodesic of parametric surface is as follows: Where z is the coordinate in the Z direction in the Cartesian coordinate system, r is the radius of gyration, and is the first and second order derivatives of the radius of gyration with respect to z, λ is the slip coefficient, α is the winding angle, and θ is the central angle of rotation around; When λ = 0, the equation is the geodesic equation of the parametric surface; Step S22: by setting different slip coefficients, respectively solving the non-geodesic equations in step S21 to obtain the winding angle and the rotation center angle under different slip coefficients; Step S23: According to the solution of the non-geodesic equation at the left head, the least square fitting method is used, and the approximate polynomial relationship between the slip coefficient and the winding angle, and the slip coefficient and the rotation center angle is expressed as: Where λ is the slip coefficient, f left (λ) is a polynomial with the slip coefficient as the independent variable, which represents the approximate relationship between the slip coefficient and the winding angle of the left elliptical head. is the winding angle at the approximate left equator, g left (λ) is a polynomial with the slip coefficient as the independent variable, which represents the approximate relationship between the slip coefficient of the left elliptical head and the rotation center angle. is the rotation center angle around the approximate left equator; Step S24: According to the solution of the non-geodesic equation at the right end cap, the least square fitting method is used, and the approximate polynomial relationship between the slip coefficient and the winding angle, and the slip coefficient and the rotation center angle is expressed as: Where λ is the slip coefficient, f right (λ) is a polynomial with the slip coefficient as the independent variable, which represents the approximate relationship between the slip coefficient and the winding angle of the right elliptical head. is the winding angle at the approximate right equator, g right (λ) is a polynomial with the slip coefficient as the independent variable, which represents the approximate relationship between the slip coefficient of the right elliptical head and the rotation center angle. is the rotation center angle around the approximate right equator.

6. A method for designing a robot thermoplastic composite winding path as claimed in claim 5, characterized in that: In step S3, the line type parameters that satisfy uniform distribution are obtained as follows: According to the continued fraction theory of fiber winding, the set winding angle α0 is substituted into the approximate polynomial obtained in step S23 and step S24, and the initial slip coefficient λ of the left and right elliptical heads is obtained by using the root-finding formula. l0 , r0 ; Substitute the winding angle and the initial slip coefficients of the left and right elliptical heads into the geodesic equation of the cylindrical segment and the non-geodesic equations of the left and right heads, and use the Runge-Kutta method to solve them. The rotation center angles θ of the cylindrical segment, the left elliptical head, and the right elliptical head are obtained respectively. c ,θ l and θ r ; Set the central angle deviation and the range of the number of divisions. Within the set deviation range, use the continued fraction theory to obtain a series of linear parameters {k i ,N i }, where k i Indicates the number of jumps, N i Indicates the number of cycles.

7. A method for designing a robot thermoplastic composite winding path as claimed in claim 6, characterized in that: In step S3, for each set of line type parameters {k i ,N i }, the Newton iteration method is used to find the appropriate slip coefficient, and the single fiber winding path is obtained by combining the geodesic equation of the cylindrical segment, the non-geodesic equations at the left and right heads, and the parameterized model of the rotating body.

8. A method for designing a robot thermoplastic composite winding path as claimed in claim 7, characterized in that: The specific method of the Newton iteration method is as follows: (1) Select λ l0 , r0 as the initial slip coefficient; (2) Substitute the winding angle and the initial slip coefficients of the left and right elliptical heads into the geodesic equation of the cylindrical segment and the non-geodesic equations of the left and right heads, and solve them using the Runge-Kutta method to obtain the winding angle α at the left and right equator lines. l , α r , the rotation center angle θ at the left and right equator lines l ,θ r , and the rotation center angle θ of the cylindrical segment c ; (3) Calculate the objective function: Among them, α l With α r are the winding angles at the left and right equator respectively, F1 is the objective function related to the winding angle, θ1=2(θ l +θ r +θ c ), θ2 is the rotation center angle determined by the linear parameters and has nothing to do with the slip coefficient, and F2 is the objective function related to the rotation center angle; (4) If |F1|≤10 -4 and |F2|≤10 -4 , terminate the iteration and output the current slip coefficient; if the iteration termination number is reached, terminate the iteration and record the group of linear parameters as having no solution; otherwise, perform the following steps; (5) Using the approximate polynomial relationship obtained in step S2, the gradient matrix of the slip coefficient is constructed as follows: Among them, Δλ is the set tolerance, R is the radius of the cylindrical segment, and L is the length of the cylindrical segment; (6) Update the slip coefficient. The update formula is as follows: Among them, λ l and λ r is the updated slip coefficient of the left and right elliptical heads; (7) Repeat steps (2)-(6) so that the winding angle is continuous and the rotation center angle satisfies the uniform coverage condition.

9. A method for designing a robot thermoplastic composite winding path as claimed in claim 8, characterized in that: The single fiber winding path is obtained by rotating to obtain a uniformly distributed winding path.

10. The method for designing a robot thermoplastic composite winding path according to claim 9, characterized in that: The number of rotations of a single fiber winding path in step S3 is N. i times, and the angle of each rotation is

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