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CN-121983206-A - Non-geodesic track design method for iterative friction coefficient

CN121983206ACN 121983206 ACN121983206 ACN 121983206ACN-121983206-A

Abstract

The invention discloses a non-geodesic track design method of an iteration friction coefficient, which belongs to the technical field of material molding, wherein a winding track is obtained by solving a non-geodesic equation through the value of an initial condition, then whether the phase difference of the initial position of the winding track of one winding cycle meets a target phase difference is calculated, and then the phase difference is adjusted through the iteration friction coefficient so that the winding track performs certain offset in space on a closed basis to obtain a first basic cycle, and then the winding is expanded so as to form a continuous and complete winding effect. According to the method, the optimal friction coefficient is automatically determined through a numerical optimization technology, so that the winding track can be well closed and uniformly distributed while the friction coefficient is reasonable, and the product quality can be improved.

Inventors

  • SU XIE
  • FU JIE
  • FU PENG
  • PENG SHUANGYI
  • ZENG SHAN
  • ZHAO LONG

Assignees

  • 湖南江南四棱数控机械有限公司

Dates

Publication Date
20260505
Application Date
20260408

Claims (7)

  1. 1. The non-geodesic track design method for the iterative friction coefficient is characterized by comprising the following steps of: S1, constructing an error function according to the following formula: F (μ) =Φ n -φ target , n is a natural number; Where μ is the coefficient of friction, φ n is the actual drop point phase of the non-geodesic equation f (μ), φ target is the target phase; s2, setting two initial friction coefficients mu 0 、μ 1 ; s3, iterating the friction coefficient by adopting the following formula: μ n =μ n-1 -F（μ n-1 ）/k n-1 ,n≥2; Where k n-1 is the chordal slope of the error function F (μ) over the interval [ μ n-2 、μ n-1 ]; And S4, solving the actual falling point phase phi n of mu n in the non-geodesic equation f (mu), judging whether the error phi n -φ target meets the convergence condition, and if not, executing the step S3.
  2. 2. The method for designing a non-geodesic trajectory with iterative coefficients of friction according to claim 1, wherein in step S1, the target phase Φ target is obtained by: φ target =（360°+B degree P direction )/N Skip; Wherein B degree is the total phase angle of the yarn band, P direction is the direction coefficient, N is the tangential point number, skip is the tooth jump graduation.
  3. 3. The method for designing an iterative friction coefficient non-geodesic trace according to claim 2, wherein the total phase angle B degree of the ribbon is obtained by: B degree =（B effect /R) (180°/π)/Skip; B effect =B/cosα; Wherein B effect is the effective yarn width, B is the actual yarn width, alpha is the winding angle, R is the core mold radius, skip is the tooth jump graduation.
  4. 4. The method for designing a non-geodesic trajectory with iterative coefficients of friction according to claim 1, wherein in step S3, the chord slope is obtained according to the chord tangent method, specifically by the following formula: K n-1 =（F（μ n-1 ）-F（μ n-2 ））/（μ n-1 -μ n-2 ),n≥2。
  5. 5. The method for designing an iterative friction coefficient non-geodesic trace according to claim 1, wherein in step S3, a design friction coefficient μ design is empirically set, and the two initial friction coefficients μ 0 、μ 1 are selected based on the following formula: μ 0 =max（0.01,μ design -μ interval ); μ 1 =min（0.99,μ design +μ interval ); Wherein μ interval is a pitch gradient value, μ interval ranges from [0.01,0.50].
  6. 6. The method for designing a non-geodesic trajectory of an iterative coefficient of friction of claim 1, wherein the boundary protection is based on the following equation after the coefficient of friction is iterated: μ n =max（0.001,min（0.999,μ n )),n≥2。
  7. 7. The method of claim 6, wherein when the variable values output in the two previous and subsequent iteration steps are the same, terminating the iteration step and outputting the friction coefficient in the interval (0.001,0.999) last time as the final value.

Description

Non-geodesic track design method for iterative friction coefficient Technical Field The invention belongs to the technical field of material forming, and particularly relates to a non-geodesic track design method of an iterative friction coefficient. Background The fiber reinforced composite material is widely applied to the fields of aerospace, pressure vessels, hydrogen storage cylinders, pipelines, energy equipment and the like. The fiber winding forming technology is an important technology for manufacturing fiber reinforced composite materials, and a winding machine is generally used for driving a core mold and a fiber guiding mechanism to move relatively, so that continuous fibers are wound on the surface of the core mold according to a preset track in a resin impregnation state, and then a composite material product is obtained through curing forming. In the fiber winding technology, geodesic winding is the earliest winding method used. The geodesic winding means that the fiber is wound along the shortest path between two points of the curved surface of the core mold, the mode can avoid fiber sliding and overhead, the track calculation is relatively simple, and the process technology is mature. However, the fiber track of the geodesic winding is determined by the geometry of the mandrel and the initial winding conditions, and the wire type is difficult to optimally design, and the requirements of certain special structures are difficult to meet. In order to improve the designability of fiber placement, a non-geodesic winding technique is provided. The technology utilizes the friction force between the fiber and the core mold to lead the fiber to deviate from the geodesic path, thereby realizing the optimal design of the fiber track and improving the structural performance, but the phenomenon of sliding wire easily occurs in the actual winding process. In the winding design process of the non-geodesic wire, if the friction coefficient is selected unreasonably, the winding cycle line type is difficult to close, and the distribution uniformity of the fiber on the surface of the core mold is difficult to ensure, so that the overall quality and performance stability of the product are affected. At present, the method for obtaining the friction coefficient between the fiber and the core mold mainly comprises two types, namely, directly measuring through experiments and deriving the maximum sliding line coefficient by combining a stress balance relation and geometric conditions, and designing the core mold with a specific shape to gradually change the radius of the core mold along the axis direction, keeping the winding angle to be 90 degrees unchanged in the winding process, gradually increasing the sliding line coefficient along with the reduction of the radius of the core mold, and recording the instant position of the sliding line of the fiber through high-speed photographic equipment so as to determine the maximum sliding line coefficient. However, the above methods still have certain disadvantages. For example, the method of directly measuring the friction coefficient is often only suitable for theoretical verification or influence rule research due to the difference between the test condition and the actual winding condition, and it is difficult to accurately reflect the friction state in the actual winding process. The method for carrying out the sliding wire test by adopting the special core mould needs to design and process the core mould with high precision, the test preparation period is long, and the cost is high. Therefore, in the prior art, a large amount of test verification is usually needed when the friction coefficient in the filament winding process is determined, so that time and labor are consumed, the obtained friction coefficient is a fixed value, and the influence caused by the change of different fiber materials, core mold surface states and process parameters is difficult to adapt. Disclosure of Invention The invention aims to provide a non-geodesic track design method with an iterative friction coefficient, which aims to solve the problems in the prior art. The non-geodesic track design method for the iterative friction coefficient comprises the following steps: S1, constructing an error function according to the following formula: F (μ) =Φ n-φtarget, n is a natural number; Wherein phi n is the actual drop point phase of the non-geodesic equation f (mu), and phi target is the target phase; s2, setting two initial friction coefficients mu 0、μ1; s3, iterating the friction coefficient by adopting the following formula: μn=μn-1-F（μn-1）/kn-1,n≥2; Where k n-1 is the chordal slope of the error function F (μ) over the interval [ μ n-2、μn-1 ]; And S4, solving the actual falling point phase phi n of mu n in the non-geodesic equation f (mu), judging whether the error phi n-φtarget meets the convergence condition, and if not, executing the step S3. In step S1, the target phase phi target is