Fabrication of High-Quality Polymer Composite Frame by a New Method of Fiber Winding Process
Abstract
:1. Introduction
2. Manufacturing of Polymer Composite Frame
2.1. Fiber Winding Geometry
2.2. Mathematical Model of Winding Process
2.2.1. Fiber-Processing Head
2.2.2. Non-Bearing Core Frame
2.3. Robot Trajectory Optimization
2.3.1. Schematic Representation of the Procedure for Calculating the Optimal REE Trajectory
- Specification of the fiber-processing head in (including coordinates of centers and of outer rotating guide lines and of the head, vectors and , common radius of circles and ).
- Loading of the location of composite frame in (including coordinates of points , vectors , and values for , radius of frame ).
- Determination of more points on frame axis and corresponding vectors and .
- Calculation of the optimal REE trajectory to ensure the high-quality of fiber winding on the composite frame. A differential evolution algorithm (see Section 4) is used for the optimization procedure. Determining the optimal sequence () is the result of calculation.
- Storing the calculated sequence of () in the central robot unit. Determining the optimal trajectory by linking individual corresponding parameters of consecutive following (using programming instruction of robot—linear interpolations or cubic splines).
2.3.2. Use of Differential Evolution Algorithm to REE Trajectory Optimization
2.3.3. Pseudo-Code of MDEA
Algorithm 1. MDEA |
Input: The number of calculated generations , crossover probability , mutation factor , generation size , the dimension of individuals , lower limits and upper limits , . Internal computation:
collision:=true repeat (i) randomly select index (ii) randomly select indices where for ; ; (iii) for step to do if or ) then else end for (j) (iv) Testing of possible collisions of the frame location in defined by and the fiber-processing head. if does not include collisions then collision = false until collision = false end repeat (v) if then else end if end for (m) b) Store individuals and their evolutions of the new generation -st generation in the matrix , . c) Find index which satisfies the condition for , , where satisfies (13) end while (k). Output: The best found individual is represented by the row of matrix that contains the corresponding value . Comments. The repeat until condition cycle is always executed at least once, since the controlling condition is checked at the end of the cycle. Function randomly picks a number from the interval . The notation means the j-th component of an individual in the k-th generation. The individual in pseudo-code of MDEA is the final solution and corresponds to designation that includes optimized parameters , . However, it should be noted that in general parameters , calculated by MDEA can only be optimized (and not optimal) parameters in relation to equation (9). This is due to the calculation of the final number of generations of individuals using MDEA. Therefore we mark calculated parameters as optimal parameters . |
3. Mechanical Performance of Polymer Composite Frame
4. Practical Experimental Verification Tests of Optimization Procedure
4.1. Experimental Test 1—Composite Non-Bearing Core Frame Shaped in 2D
4.2. Experimental Test 2—3D Shape Non-Bearing Core Frame
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
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Mlýnek, J.; Petrů, M.; Martinec, T.; Rahimian Koloor, S.S. Fabrication of High-Quality Polymer Composite Frame by a New Method of Fiber Winding Process. Polymers 2020, 12, 1037. https://doi.org/10.3390/polym12051037
Mlýnek J, Petrů M, Martinec T, Rahimian Koloor SS. Fabrication of High-Quality Polymer Composite Frame by a New Method of Fiber Winding Process. Polymers. 2020; 12(5):1037. https://doi.org/10.3390/polym12051037
Chicago/Turabian StyleMlýnek, Jaroslav, Michal Petrů, Tomáš Martinec, and Seyed Saeid Rahimian Koloor. 2020. "Fabrication of High-Quality Polymer Composite Frame by a New Method of Fiber Winding Process" Polymers 12, no. 5: 1037. https://doi.org/10.3390/polym12051037