210 FILAMENT WINDING AND FIBER PLACEMENT fiber feed corresponding to one rotational revolution.The relation be- tween the rotational distance and axial distance can be written as: 元D L=- (5.1) tano If h represents the length of the straight part of the cylinder to be built, the number of revolutions required for the fiber feed to travel this dis- tance is given as: h htano. n三 (5.2) LπD Equation(5.2)gives the number of revolutions.This can be a whole number or a decimal number.One needs to convert this into the number of degrees(by multiplying n by 360)in order to determine the number of degrees of revolution. Since filament winding is a continuous process,the fiber feed has to re- verse its motion to go back to the other end.Also it is essential that ten- sion be maintained in the fibers to ensure good properties of the final product.One also needs to identify the location of the fiber feed(point A in Figure 5.6)and the point of separation between the fiber band and the surface of the mandrel (point B). When the point B reaches the end of the straight part of the cylinder, this point will move over the surface of the head of the component to be built (i.e.a vessel).The fiber feed (point A)starts to go into reverse.It takes some time before point B touches the end of the straight part of the cylinder again(point B).The number of degrees of rotation of the man- Traverse B Mandrel FIGURE 5.6 Relative position of the fiber feed (point A)and point of separation (point B)between fiber band and mandrel surface
fiber feed corresponding to one rotational revolution. The relation between the rotational distance and axial distance can be written as: L D = π tanα (5.1) If h represents the length of the straight part of the cylinder to be built, the number of revolutions required for the fiber feed to travel this distance is given as: n h L h D = = tanα π (5.2) Equation (5.2) gives the number of revolutions. This can be a whole number or a decimal number. One needs to convert this into the number of degrees (by multiplying n by 360) in order to determine the number of degrees of revolution. Since filament winding is a continuous process, the fiber feed has to reverse its motion to go back to the other end. Also it is essential that tension be maintained in the fibers to ensure good properties of the final product. One also needs to identify the location of the fiber feed (point A in Figure 5.6) and the point of separation between the fiber band and the surface of the mandrel (point B). When the point B reaches the end of the straight part of the cylinder, this point will move over the surface of the head of the component to be built (i.e. a vessel). The fiber feed (point A) starts to go into reverse. It takes some time before point B touches the end of the straight part of the cylinder again (point B′). The number of degrees of rotation of the man- 210 FILAMENT WINDING AND FIBER PLACEMENT FIGURE 5.6 Relative position of the fiber feed (point A) and point of separation (point B) between fiber band and mandrel surface
Filament Winding 211 angular Br advance B1 FIGURE 5.7 Relative angular position of the point of separation at the end and at the be- ginning of a circuit. drel during this time is termed the dwell angle.A dwell angle exists at both ends of the cylinder. 1.2.3.Circuit and Pattern When the point B has gone one complete cycle and returns to the same axial position along the length of the cylinder and goes in the same direc- tion,a circuit has been completed.Due to the complexity of the motion, there is no guarantee that after one circuit,the point B at the end of one circuit will have the same angular position as its position at the beginning of the circuit(B )Figure 5.7 illustrates this point. It takes a number of circuits before the point B can return to its position at the beginning.When this happens,one has a pattern.This can be illus- trated in the following example. Example 5.1 It is desirable to wind a 30 cm diameter by 100 cm long cylinder at a 30 wind angle. The fiber band width is assumed to be 0.6 cm and the dwell angle is 180.Determine the number of circuits required to make a pattern. Solution First,define the reference circle as the circle of the cross-sectional area of the cylinder at one end,say,the left end.Assume that winding starts from a point B on that circle. In one circuit,the feed moves twice the length of the mandrel.This means forward once and backward once along the length of the mandrel.When a pattern is complete, a set of circuits has been made and the fiber path returns to the initial position
drel during this time is termed the dwell angle. A dwell angle exists at both ends of the cylinder. 1.2.3. Circuit and Pattern When the point B has gone one complete cycle and returns to the same axial position along the length of the cylinder and goes in the same direction, a circuit has been completed. Due to the complexity of the motion, there is no guarantee that after one circuit, the point B1′ at the end of one circuit will have the same angular position as its position at the beginning of the circuit (B1). Figure 5.7 illustrates this point. It takes a number of circuits before the point B can return to its position at the beginning. When this happens, one has a pattern. This can be illustrated in the following example. Filament Winding 211 FIGURE 5.7 Relative angular position of the point of separation at the end and at the beginning of a circuit. Example 5.1 It is desirable to wind a 30 cm diameter by 100 cm long cylinder at a 30° wind angle. The fiber band width is assumed to be 0.6 cm and the dwell angle is 180°. Determine the number of circuits required to make a pattern. Solution First, define the reference circle as the circle of the cross-sectional area of the cylinder at one end, say, the left end. Assume that winding starts from a point B on that circle. In one circuit, the feed moves twice the length of the mandrel. This means forward once and backward once along the length of the mandrel. When a pattern is complete, a set of circuits has been made and the fiber path returns to the initial position
212 FILAMENT WINDING AND FIBER PLACEMENT Equation(5.2)gives the number of revolutions required for the fiber feed to move a distance h which is equal to the length of the cylinder.For a circuit,two cylinder lengths need to be traveled.The corresponding number of revolutions will therefore be: 2n=2htand=(2)(100 cm)tan 30=1.23 (a) πD π(30cm) The corresponding number of degrees is: (1.23)(360)=441° (b) In addition to the number of degrees in Equation (b),one has to add two times the dwell angle in order to obtain the total number of degrees required to make a circuit. This gives: 0=441+2(180)=801° (c) If one subtracts the above number by a whole multiple of 360,one would obtain the angular advance of the starting point(new point B)as compared to starting point B on the reference circle.This angular advance is 801-(360)(2)=81.This is shown in Figure 5.7. In order to make a pattern,one needs to have a multiple of the advance angles such that this multiple will be equal to a multiple of 360.This can be expressed as: (m)(81)=(n)(360) (d) where m and n are integers and should be as small as possible. Equation (d)shows that m and n can be quite large before the equation is satisfied. This may not be practical.In order to reduce the numbers m and n,one needs to adjust the operation to make the advance angle a good whole number.One good whole num- ber close to 81 is 90.This can be done by adjusting the dwell angle to be 180+9/2= 184.5° (This can be done by adjusting the machine setting.)If this is done,Equation (d)be- comes: (m)(90)=(n)(360)or m=4 (e) One can select m=4 and n=1.What this means is that it takes 4 times the advance an- gle (or 4 circuits)to make a pattern. Note:In the pattern calculated above,the fiber band will go back exactly to the same position on the reference circle as at the beginning of the winding process.This may not be desirable because if one continues this process,the fiber will follow the same path as before and one may not be able to cover the whole surface of the mandrel.It is desirable to advance the position B one bandwidth distance along the circumfer- ential direction after one pattern.This distance in angular value can be calculated to be (note that the circumferential coverage of a bandwidth b is b/cos a):
212 FILAMENT WINDING AND FIBER PLACEMENT Equation (5.2) gives the number of revolutions required for the fiber feed to move a distance h which is equal to the length of the cylinder. For a circuit, two cylinder lengths need to be traveled. The corresponding number of revolutions will therefore be: 2 2 2 100 30 30 n 1 23 h D == = tan ( )( tan ( . α π π cm) cm) (a) The corresponding number of degrees is: (1.23)(360) = 441° (b) In addition to the number of degrees in Equation (b), one has to add two times the dwell angle in order to obtain the total number of degrees required to make a circuit. This gives: θ = 441 + 2(180) = 801° (c) If one subtracts the above number by a whole multiple of 360°, one would obtain the angular advance of the starting point (new point B1′ ) as compared to starting point B1 on the reference circle. This angular advance is 801 − (360)(2) = 81°. This is shown in Figure 5.7. In order to make a pattern, one needs to have a multiple of the advance angles such that this multiple will be equal to a multiple of 360°. This can be expressed as: (m)(81) = (n)(360) (d) where m and n are integers and should be as small as possible. Equation (d) shows that m and n can be quite large before the equation is satisfied. This may not be practical. In order to reduce the numbers m and n, one needs to adjust the operation to make the advance angle a good whole number. One good whole number close to 81 is 90. This can be done by adjusting the dwell angle to be 180 + 9/2 = 184.5°. (This can be done by adjusting the machine setting.) If this is done, Equation (d) becomes: ( )( ) ( )( ) m n m n 90 360 = = or 4 (e) One can select m = 4 and n = 1. What this means is that it takes 4 times the advance angle (or 4 circuits) to make a pattern. Note: In the pattern calculated above, the fiber band will go back exactly to the same position on the reference circle as at the beginning of the winding process. This may not be desirable because if one continues this process, the fiber will follow the same path as before and one may not be able to cover the whole surface of the mandrel. It is desirable to advance the position B1′ one bandwidth distance along the circumferential direction after one pattern. This distance in angular value can be calculated to be (note that the circumferential coverage of a bandwidth b is b/cos α):
Filament Winding 213 △0= b (360)= 0.6 -(360)=2.65 (⑤ πDcosa π(30)cos(30 This advanced angular value is accumulated over 4 circuits.The value for each circuit is 2.65/4 =0.66.This angle is then divided by two dwell angles.The dwell angle is then adjusted to be:184.5+0.66/2 184.8. 1.2.4.Layer A pattern may consist of fiber intersections (fiber crossovers-see Figure 5.4)at certain sections.Crossovers may occur at more than one section,depending on the wind angle.A layer is defined as a set of pat- terns that completely cover the surface of the mandrel with fibers. From Figure 5.5,it can be seen that the relation between the circumfer- ential coverage S and the bandwidth b can be written as: b S=- (5.3) cosO In order to make a layer,the whole circumferential distance nD has to be covered.The number of circuits per layer C can be calculated as: πDπDCOs C= (5.4) S b Example 5.2 Continue with Example 5.1 and determine the number of circuits required to make a layer. Solution Fora=30°，one has(from Equation5.4): c=m30)cos30=136 0.60 There are 136 circuits to make up a layer.Recall from Example 5.1 that it takes 4 cir- cuits to make a pattern.The number of patterns per layer is then 136/4=34. 1.2.5.Hoop Winding Hoop or circumferential layers are wound close to 90.The feed ad- vances one bandwidth per revolution.The layer is considered a single
1.2.4. Layer A pattern may consist of fiber intersections (fiber crossovers—see Figure 5.4) at certain sections. Crossovers may occur at more than one section, depending on the wind angle. A layer is defined as a set of patterns that completely cover the surface of the mandrel with fibers. From Figure 5.5, it can be seen that the relation between the circumferential coverage S and the bandwidth b can be written as: S b = cosα (5.3) In order to make a layer, the whole circumferential distance πD has to be covered. The number of circuits per layer C can be calculated as: C D S D b = = ππ α cos (5.4) 1.2.5. Hoop Winding Hoop or circumferential layers are wound close to 90°. The feed advances one bandwidth per revolution. The layer is considered a single Filament Winding 213 ∆θ πα π == = b Dcos ( ) . ( )cos( ) 360 (). 0 6 30 30 360 2 65 (f) This advanced angular value is accumulated over 4 circuits. The value for each circuit is 2.65/4 = 0.66°. This angle is then divided by two dwell angles. The dwell angle is then adjusted to be: 184.5 + 0.66/2 = 184.8°. Example 5.2 Continue with Example 5.1 and determine the number of circuits required to make a layer. Solution For α = 30°, one has (from Equation 5.4): C = = π( )cos . 30 30 0 60 136 There are 136 circuits to make up a layer. Recall from Example 5.1 that it takes 4 circuits to make a pattern. The number of patterns per layer is then 136/4 = 34.