18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS THE EFFECT OF PROCESSING PARAMETERS ON STRUCTURAL PROPERTY FOR FILAMENT-WOUND COMPOSITE PRESSURE VESSELS T.Lili 1* , Z.Limin 2 , W. Zhenqing 1 1College of Aerospace and Civil Engineering Material , Harbin Engineering University , Harbin , China 2 Department of Mechanical Engineering, Hongkong Polytechnic University, Hongkong, China * Corresponding author( tonglili@hrbeu.edu.cn ) Keywords : Filament winding; composite pressure vessel; Fiber path, CAM 1 Introduction two methods for calculating mandrel rotated Filament winding is a popular production technique angle are discussed. for composite structures. Cylinder pressure vessel 2 Theory for filament winding trajectories with elliptical dome is an efficient product which can make full use of tensile strength of fiber. To 2.1 Plane-hypothesis theory achieve the most efficient use of the reinforcement This is a simplified method that supposes the material the fiber should be placed in the maximum fiber path at dome lies in a plane. It is easy to load directions or in geodesic path. This is not calculate the mandrel rotating angle at dome as always achievable as the fibers must not slip during following: the winding process due to windability. Windability htg α − ⎛ ⎞ means fiber bands should cover uniformly on the 2 d − θ = + ⎜ ⎟ 1 2 90 sin mandrel without voids or significant overlap toward 1 ⎝ ⎠ D radial and circumferential directions. Realistic A series of two consecutive fiber paths is called pattern information is very important for an optimal a winding circuit. The first fiber path crosses the design because it is directly related with the mandrel from one end to the other end, and the accuracy if finite element analyses. second fiber path returns to the first end. The F.H.Abdalla9[1] design a lathe-type machine for mandrel rotating angle during a winding circuit low cost filament winding process. Haisheng Li[2] presents a new class of trajectories with followed: ⋅ α α − ⎛ ⎞ more freedom by generalizing spline and give L tg 2 htg d − θ = ⋅ + + ⎜ 1 ⎟ 360 2 90 sin the conditions to make these splines on π n ⎝ ⎠ D D cylinders and cones stable. Cheol[4] use semi- where L is length of cylinder, α is winding geodesic path algorithm to calculate possible angle, D is diameter of cylinder, d is diameter of winding patterns taking into account the polar opening. H is the height of the dome. windability and slippage between the fiber and the mandrel surface. D.T.Jones[5] describes delta-axisymmetric methods that result in a constant thickness lay-up of composite over the end closures of a dome-end cylindrical vessel. Tae-kyung[6] verified the size effect on the fiber strength of a composite pressure vessel but Fig.1 fiber path for plane-hypothesis didn’t mention the winding pattern. 2.2 Geodesic theory In this paper, the practical process parameters which areis important for design are studied and According to differential geometry of generalized
relationship of K and N should be relative prime in order to satisfy the windability. Practical mandrel rotating angle is equal to: K b （ 3 ） θ = ⋅ + ⋅ 360 360 π α n N N D cos Where b is width of fiber band. Data for relationship between mandrel rotating angle and number of fiber bands showed in table-1. Fig.2. parameter figure for ellipse equation Table-1 relationship between mandrel rotating angle spaces, a regular three-dimensional surface can be and number of fiber bands described as a vector function of two independent parameters: Patten Angle Patten Angle Patten Angle bands ° ° ° K/N K/N K/N ( ) { ( ) ( ) ( ) } θ , φ ∈ ℜ θ φ = θ φ θ φ θ φ S , x , , y , , z , with 1 1/1 360 2/1 720 3/1 1080 2 1/2 180 3/2 540 5/2 900 For ellipsoid shape of mandrel dome, its surface can 1/3 120 4/3 480 7/3 840 3 be described as following: 2/3 240 5/3 600 8/3 960 { } = 1/4 90 5/4 450 9/4 810 r b cos u cos v , b cos u sin v , a sin u 4 3/4 270 7/4 630 11/4 990 Coefficients of the first fundamental form are equal 1/5 72 6/5 432 11/5 792 to: 2/5 144 7/5 504 12/5 864 5 ⎛ ∂ ⎞ 2 ⎛ ∂ ⎞ 2 ⎛ ∂ ⎞ 2 3/5 216 8/5 576 13/5 936 x y z = + + = + ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ 2 2 2 2 E b sin u a cos u 4/5 288 9/5 648 14/5 1008 ∂ ∂ ∂ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ v v v 1/6 60 7/6 420 13/6 780 6 ∂ ∂ ∂ ∂ ∂ ∂ 5/6 300 11/6 660 17/6 1020 x x y y z z = ⋅ + ⋅ + ⋅ = F 0 ∂ ∂ ∂ ∂ ∂ ∂ Winding pattern for different number of fiber u v u v u v bands is showed in fig.-3. ∂ 2 ∂ 2 ∂ 2 ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ x y z = + + = ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ 2 2 G b cos u ∂ ∂ ∂ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ u u u Differential equation of geodesic line at revolutionary curved surface is: ∂ τ ∂ ∂ (1) N=3 (2) N=4 (3) N=5 (4)N=6 1 E nE nG = − τ = ⋅ τ tg tgu tg ∂ ∂ ∂ u 2 G v u Fig.-3 Winding pattern for different number of fiber bands According to equation (1) or (2), mandrel ∂ + 2 2 v E sin u k cos u = τ = τ (2) tg tg rotating angle can be calculated. The nearest ∂ u G cos u winding pattern can be found in table-1. spatial Where τ is winding angle and v is mandrel trajectories was adjusted slightly to be identical rotating angle. with the practical winding pattern. The following winding angle at dome of arbitrary 3. Windability and practical wind pattern position can be obtained: As mentioned above, windability is very Δ θ ⋅ π D important because some of the patterns 360 α = (4) arcsin calculated by Eq.(1) and Eq.(2) may be useless ( ) ( ) ( ) − 2 + − 2 + − 2 x x y y z z for the manufacture of filament wound 2 1 2 1 2 1 structures unless uniform coverage is considered. Thickness at dome is equal to: If the number of fiber bands in a layer is N and the circumferential shifted integer is K, the
PAPER TITLE α D cos 90 = 0 t t (5) α α winding angle at dome quati-geodesic method-450 f f d cos 75 geodesic line-443 Where d is diameter at dome of arbitrary plane-hypothesis method-504 60 position, t is thickness of cylinder. α f 45 4. Result and discussion 30 The performance of composite structures 15 completely depends on the distribution of the 0 fiber, which is determined by the filament 15 25 35 45 55 65 75 winding pattern. r(mm) 3-D spatial data of the winding trajectories were Fig.-5 Winding angle for different methods simulated by using C++ programming language. The thickness was related with the friction The parameters were showed in fig.4. coefficient between fiber band and mandrel. Therefore, the fiber path should be close to the geodesic line to avoid fiber stack and sliding. The result for different parameters showed in Fig.-7. 3000 method1-ro/R=0.1 mandrel rotating angle method2-ro/R=0.1 2400 method1-ro/R=0.5 method2-ro/R=0.5 1800 method1-ro/R=0.9 method2-ro/R=0.9 1200 Fig.-4 Winding trajectories simulation For example, L=410mm, D=146mm, h=40mm, 600 d=31.5mm, p=0.55. mandrel winding angle 0 according to equation(1) is 502°,504°should be 0 0.2 0.4 0.6 0.8 1 chosen according to table-1. It is 442.7° R/L according to equation(2) and 450°is the nearest Fig.-7 mandrel rotating angle at different parameters angle for windability. For L=500mm,p=0.5,radius of cylinder R and 442.7°is the most stable pattern at dome due to radius of polar opening r 0 is variable. The result it is geodesic line and 450°is the nearest angle to showed that the mandrel winding angle geodesic trajectories meanwhile it keeps to decreased as radius of cylinder increase and windability. Comparatively, the winding pattern radius of polar opening decrease. The difference according to plane-hypothesis is farther to the between result of two methods increases as r 0 geodesic line and unstable though it is applied increase, but it is nearly constant when R widely because it is simple and easy to be used. increased. The thickness was calculated according to equation (5). The results showed that nearly no 5. Conclusion difference between the result of two method. In this research, winding patterns considering However, this was not the real truth because the windability were presented. Two methods for fiber would slide toward stable trajectories calculating mandrel rotating angle were when it was far from the geodesic line. The discussed. Plane-hypothesis method gave the result was that the thickness near polar hole was unstable winding trajectories far from the bigger than anticipated due to the bigger geodesic line and result in fiber stack especially mandrel rotating angle. 3
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