A method for designing robot-assisted thermoplastic composite winding paths

Abstract

The present invention belongs to the field of composite material manufacturing and discloses a method for designing a robotic thermoplastic composite winding path. The method includes obtaining geometric model parameters of a body of revolution and establishing a parametric model of the body of revolution; constructing a geodesic equation for a cylindrical segment and a non-geodesic equation for a head portion based on the parametric model of the body of revolution; solving the non-geodesic equations separately by setting different slip coefficients, and fitting approximate polynomial relationships between the slip coefficient and the winding angle, and between the slip coefficient and the rotation center angle based on the solution results; obtaining a series of linear parameters that satisfy uniform distribution based on the algebraic pattern theory of fiber winding; using the Newton iteration method to find a suitable slip coefficient for each set of linear parameters so that the winding angle is continuous and the fibers are evenly distributed; and calculating a fiber winding path for each set of linear parameters with a slip coefficient. The present invention expands the linear design space for pressure vessels with unequal polarity holes and can improve the efficiency and accuracy of winding path generation.

Description

Technical Field

[0001] The present 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 technique that uses a robot to wind prepreg impregnated with thermoplastic resin. It is widely used to wind various rotating components such as pressure vessels. Pressure vessels typically consist of a left end cap, a barrel, and a right end cap. In practice, due to process and structural constraints, the pole holes on the left and right end caps of pressure vessels are often inconsistent.

[0003] When designing the winding path of a pressure vessel, commonly used methods include geodesic winding and non-geodesic winding. The geodesic winding method can only be applied to the winding design of pressure vessels with unequal polar holes. For the non-geodesic winding method, it is necessary to select an appropriate 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 computationally time-consuming and have no solutions. In addition, some studies use fitted polynomial functions instead of solving complex equations, but there is the 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 hole or asymmetry of the left and right heads, and there are large technical barriers. Therefore, it is very necessary to develop a fast and accurate winding path design method for pressure vessels with unequal polar holes. Summary of the Invention

[0004] In response to the above-mentioned defects or improvement needs of the existing technology, the present invention provides a robotic thermoplastic composite winding path design method, which can quickly and accurately generate a feasible winding path, avoid a large amount of calculation, and has practical engineering value.

[0005] To achieve the above objectives, 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: Acquire 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. The parametric model of the rotating body includes a mathematical model of the middle cylindrical segment and mathematical models of the ends;

[0007] S2: Based on the parametric 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 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; based on 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: Based on 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 extreme hole radius of the left elliptical head, the elliptical parameters of the right elliptical head and the extreme hole radius of the right elliptical head, 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, such that the radius of the cylindrical segment in the body of revolution is equal to the semi-major axis of the left elliptical head and the semi-major 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 the right elliptical head, and the intersection is the right equatorial circle;

[0012] Step S12: Based on 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-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-axis of the Cartesian coordinate system is the rotation axis of the rotating body, and its direction points to the left head, and the Y-axis of the Cartesian coordinate system is defined by the Cartesian right-hand rule;

[0013] In the Cartesian coordinate system, a parameterized 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: Based on the general non-geodesic equation of the parametric surface and the parametric 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 non-geodesic equation of the 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 are the first and second derivatives of the radius of gyration with respect to z, λ is the slip coefficient, α is the winding angle, and θ is the rotation center angle around;

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

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

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

[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: Based on the solution of the non-geodesic equation at the right head, the least squares fitting method is used to express the approximate polynomial relationship between the slip coefficient and the winding angle, and between the slip coefficient and the rotation center angle as follows:

[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 expresses 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 that satisfy 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 using the root-finding formula. l0 ,λ 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 solve them using the Runge-Kutta method to obtain the rotation center angles θ of the cylindrical segment, the left elliptical head, and the right elliptical head, respectively. c ,θ l and θ r ;

[0029] Set the center 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] As a preference, in step S3, for each set of line type parameters {k i ,N i}, the Newton iteration method is applied 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 of 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 ,λ 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, respectively. 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 target 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 set 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] Where 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) to (6) until 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 distributed winding path after rotation.

[0047] As an example, 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 solutions conceived by the present invention have 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 polarity holes.

[0051] (3) The present invention is based on the Newton iteration method and utilizes the 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 flowchart of a method for designing a robot thermoplastic composite winding path.

[0053] Figure 2 Schematic diagram of the fitting of 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 This is the simulation result of achieving a uniformly distributed winding path according to the embodiment of the present invention. DETAILED DESCRIPTION

[0057] The technical solutions of the present invention will be clearly and completely described below through specific implementation methods. Obviously, the described embodiments are only some of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts 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 based on the geometric model parameters of the rotating body. The parametric model of the rotating body includes a mathematical model of the middle cylindrical segment and a mathematical model of the end caps at both ends. The specific steps include:

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

[0062] The radius of the cylindrical section in the rotating body is equal to the major 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 right elliptical head is provided at the other end of the barrel section, and the intersection is the right equatorial circle.

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

[0064] Establish a Cartesian coordinate system, where the origin of the Cartesian coordinate system is the center of the right equatorial circle, the X-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-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-axis of the Cartesian coordinate system is defined by the Cartesian right-hand rule;

[0065] In the Cartesian coordinate system, parameterized models of the rotational surfaces of the cylindrical segment, the left elliptical head, and the right elliptical head are established according to the geometric parameters of the rotation body.

[0066] S2: Based on 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; based on 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: Based on the general non-geodesic equation of the parametric surface and the parametric 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 non-geodesic equation of the 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 are the first and second derivatives of the radius of gyration with respect to z, λ is the slip coefficient, α is the winding angle, and θ is the rotation center angle around;

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

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

[0072] Step S23: In a given slip coefficient range (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 winding angle at the left equator (α) can be obtained under different slip coefficients by using the 4th-order Runge-Kutta method. 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 squares 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 at the right equator (α) can be obtained under different slip coefficients by using the 4th-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, the approximate polynomial relationship between the slip coefficient and the winding angle, and between the slip coefficient and the rotation center angle can be expressed as follows using the least squares fitting method:

[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 expresses 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: Based on 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, 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 using the root-finding formula. l0 ,λ 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 solve them using the Runge-Kutta method to obtain the rotation center angles θ of the cylindrical segment, the left elliptical head, and the right elliptical head, respectively. c ,θ l and θ r ;

[0085] Set the center 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. The geodesic equation of the cylindrical segment, the non-geodesic equations of the left and right heads, and the parameterized model of the body of revolution are combined to ensure that the winding angle is continuous and the rotation center angle satisfies the uniform coverage condition. The single fiber winding path is obtained. The specific algorithm is as follows:

[0087] (1) Select λ l0 ,λ 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, respectively. 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 target 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 number of iterations reaches the end, terminate the iteration and record the set of linear parameters as unsolvable. 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] Where 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 of 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 rotations, each rotation angle is A uniformly distributed winding path can be obtained.

[0102] The embodiments described above are merely descriptions of preferred implementations of the present invention and are not intended to limit the scope of the present invention. Without departing from the 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 fall within the scope of protection determined by the claims 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: Acquire 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. The parametric model of the rotating body includes a mathematical model of the middle cylindrical segment and mathematical models of the ends; S2: Based on the parametric 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 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; based on 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: Based on 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. The method for designing a thermoplastic composite winding path of a robot according to claim 1, wherein: Step S1 obtains the geometric model parameters of the rotating body including: cylindrical segment length, cylindrical segment radius, elliptical parameters of the left elliptical head, left elliptical head extreme hole radius, elliptical parameters of the right elliptical head and right elliptical head extreme hole radius.

3. The method for designing a thermoplastic composite winding path of a robot according to claim 2, wherein: The elliptical parameters of the left elliptical head include the major semi-axis and the minor semi-axis of the left elliptical head; the elliptical parameters of the right elliptical head include the major semi-axis and the minor semi-axis of the right elliptical head.

4. The method for designing a thermoplastic composite winding path of a robot according to claim 3, wherein: Step S1 specifically includes the following steps: Step S11: obtaining geometric model parameters of the body of revolution, such that the radius of the cylindrical segment in the body of revolution is equal to the semi-major axis of the left elliptical head and the semi-major 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 the right elliptical head, and the intersection is the right equatorial circle; Step S12: Based on 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-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-axis of the Cartesian coordinate system is the rotation axis of the rotating body, and its direction points to the left head, and the Y-axis of the Cartesian coordinate system is defined by the Cartesian right-hand rule; In the Cartesian coordinate system, a parameterized 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, wherein: Step S2 specifically includes the following steps: Step S21: Based on the general non-geodesic equation of the parametric surface and the parametric 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 non-geodesic equation of the 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 are the first and second derivatives of the radius of gyration with respect to z, λ is the slip coefficient, α is the winding angle, and θ is the rotation center angle around; When λ = 0, the equation is the geodesic equation of the parametric surface; Step S22: by setting different slip coefficients, solving the non-geodesic equations in step S21 respectively to obtain the winding angle and the rotation center angle under different slip coefficients; Step S23: Based on the solution of the non-geodesic equation at the left head, the least squares fitting method is used to express the approximate polynomial relationship between the slip coefficient and the winding angle, and between the slip coefficient and the rotation center angle as follows: 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: Based on the solution of the non-geodesic equation at the right head, the least squares fitting method is used to express the approximate polynomial relationship between the slip coefficient and the winding angle, and between the slip coefficient and the rotation center angle as follows: 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 expresses 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. The method for designing a thermoplastic composite winding path of a robot according to claim 5, wherein: The line type parameters that satisfy uniform distribution in step S3 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 using the root-finding formula. l0 ,λ 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 solve them using the Runge-Kutta method to obtain the rotation center angles θ of the cylindrical segment, the left elliptical head, and the right elliptical head, respectively. c ,θ l and θ r ; Set the center 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. The method for designing a thermoplastic composite winding path of a robot according to claim 6, wherein: In step S3, for each set of line type parameters {k i ,N i }, the Newton iteration method is applied 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 of the left and right heads, and the parameterized model of the rotating body.

8. The method for designing a thermoplastic composite winding path of a robot according to claim 7, wherein: The specific method of the Newton iteration method is as follows: (1) Select λ l0 ,λ 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, respectively. 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 target 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 set 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: Where 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) to (6) until the winding angle is continuous and the rotation center angle satisfies the uniform coverage condition.

9. The method for designing a thermoplastic composite winding path of a robot according to claim 8, wherein: The single fiber winding path is obtained by rotating to obtain a uniformly distributed winding path.

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

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