Programming for Evaluating Strip Layout of Progressive Dies Alan C. Lin, Ho Minh Tuan and Dean K. Sheu Department of Mechanical Engineering National Taiwan University of Science and Technology Taipei, TAIWAN
[email protected] algorithms to screen the solution space and reused previously calculated results for speeding up the bending planning. This study may successfully reduce the number of possible alternatives; however, may also eliminate better solutions. Kannan and Shunmugam [5] used exhaustive searching to produce bending layout. Nevertheless, they assume that sheet metal parts mostly have no more than 8 bends. Unfortunately, there are, in general, more than 8 punches in practical cases. Lin and Dean [6] suggested a modified scheme of exhaustive search and punch grouping rules so as to find all the feasible layouts with eliminating unwanted searching paths. They also proposed an evaluation function for ranking feasible strip layouts in term of station number, moment balancing and strip stability. Their solution, nonetheless, only dues with shearing operations. The research presented in is paper is the succeeding project of [6] and it proposes a proper solution for automatically evaluating feasible strip layouts in progressive dies from their 3D models. The solution helps designers quickly fine tune and choose better results among many feasible layouts.
Abstract—A progressive die is an effective tool for efficient and economical production of sheet metal parts in large quantities. Nowadays, progressive die designers still spend much of their time on choosing better layouts among feasible ones. This study employs Pro/Web.Link, Hyper Text Markup Language (HTML) and JavaScript to develop an application which helps evaluate automatically strip layouts in Pro/Engineer software environment. This paper proposes solutions for calculating total evaluation score of the strip layout based on four factors: station number factor, moment balancing factor, strip stability factor and feed height factor. Keywords-CAD; Manufacturing; Programming
I.
INTRODUCTION
In today’s practical and cost-conscious marketplace, sheet metal parts have probably became the most versatile products of modern technology. There are a variety of sheet metal dies, but progressive die is a good choice for mass producing small and delicate parts where tolerances and specifications are relatively severe. A progressive die combines two or more stations to perform simultaneous operations as the sheet is transported incrementally through the die. The design of progressive die starts with the decision on which operations are to be performed at each station, which is called “strip layout.” In the design process, designers consider the sheet metal part (Fig. 1(a)) to understand its characteristics and specifications. The appropriate shearing and bending punches (Fig. 1(b)) are then determined depending on the internal holes, external outlines and bending features. Next, superimposing the designed punches on the strip (Fig. 2(a)) is a common method to achieve strip layout (Fig. 2(b)). It is quite simple because the designer merely tries to palace each designed punch on an appropriate station of the die [1]. In addition to simplicity, superimposition is also easy to spot any overlapping of the superimposed punches as well as easy to exchange idea between designers. However, superimposing of many punches results in a huge number of possible strip layouts because the number of possible solutions will grow exponentially with number of features [2]. Schaffer [3] were probably the explorer in researching strip layouts for progressive dies. Computer-aided design techniques are employed for the automation of die design. However, punch design and layout are still relied on designer’s wisdom. In order to shrink the enormous search space, artificial intelligent techniques and heuristic searching schemes are suggested for overcoming strip layout issue. Thanapandi et al. [4] had employed genetic
978-1-4577-1539-6/11/$26.00 ©2011 IEEE
II.
CRITERIA FOR STRIP LAYOUT EVALUATION
In order to choose better strip layouts from many feasible layouts, each feasible layout must be rank based on a total score relevant for that layout. Among many factors in planning strip layouts that affect the cost and quality of progressive die, four factors had proposed by Lin and Sheu [6] for layout evaluation function; they are: station number factor ܨ , moment balancing factor ܨ , strip stability factor ܨ௦ and feed height factor. The evaluation score is computed based on these four factors:
Fig. 1 Solid models: (a) sheet metal part, (b) shearing punches Pi and bending punches Bi
229
is known. Since the limitation of calculation in JavaScript, the Pro/Web.Link application can calculate exactly the centroid for line segment and arc of circle (as shown in Table 1). Other types of curve such as Spline, B-Spline, arc of ellipse, etc. are not considered in this research. (4) Finally, the acting point of shearing force is calculated as the centroid of its component edges by the following equations: ݔ௧̴௧ ൌ
σୀଵ ܮ ൈ ݔ σୀଵ ܮ
ݕ௧̴௧ ൌ
σୀଵ ܮ ൈ ݕ σୀଵ ܮ
(4) (5)
where ݔ௧̴௧ ǡ ݕ௧̴௧ : coordinate of acting point of shearing force, n: total number of sheared edges of that shearing punch, ݔ ǡ ݕ : coordinate of centroid of sheared edge i, ܮ : length of sheared edge i.
Fig. 2 An 8-station design: (a) superimposing punches, (b) resultant strip layout ܧ ൌ ݓ ൈ ܨ ݓ ൈ ܨ ݓ௦ ൈ ܨ௦ ݓ ൈ ܨ
(1) where ୬ ǡ ୠ ǡ ୱ ǡ ୪ are weighting factors for ୬ ǡ ୠ ǡ ୱ ǡ ୪ , correspondingly, Ͳ ୬ ǡ ୠ ǡ ୱ ǡ ୪ ͳ and ୬ ୠ ୱ ୪ ൌ ͳ. These four weighting factors are chosen by the designers who determine how much important each factor contributes to the strip layout evaluation. All these four evaluation factors are formulated to range from 10 to 100, which higher score indicates better efficiency in cost and production. The evaluation score itself has relative meaning within feasible layouts for one part; therefore, it can be used to rank these feasible layouts so as to find out better solutions for fabricate that product. In the other hand, the evaluation score cannot be used to compare layouts of different parts. III.
FORMULAE OF FORCE CALCULATION
A. Magnitude of shearing and bending forces If the friction between the punch and the sheet of metal is neglected, the shearing force ܨ௦ can be estimated form the following equation: ܨ௦ ൌ ܣൈ ߬௦ ൌ ܮ௦ ൈ ܶ ൈ ߬௦
Fig. 3 Calculating the acting point of shearing force for a sample punch Table 1 Centroid of various types of edge
(2)
Type of edge
where ܣ: sheared area, ܮ௦ : total length of sheared edges, ܶ: strip thickness, ߬௦ : shearing strength. Bending force ܨ can be determined by: ߬௦ ܨ ൌ ܮ ൈ ܶ ൈ (3)
Line segment
where ܮ : total length of bending edges B. Acting points of shearing and bending forces For shearing force, including punching and notching forces, the method of calculating the acting point is demonstrated on the sample shown in Fig. 3. (1) First, the sheared chain must be broken down into component sheared edges without considering the geometrical entities they form. (2) The length of each edge is then calculated and it should be called ܮ for sheared edge number i. (3) Next, the distance of edge’s center off the zero point in both x and y dimension is determined. The center, or centroid, of an arbitrary edge can be obtained exactly by integral operation if equation of this edge
Arc of circle
230
Image
Centroid
ݔ ݔ ʹ ݕ ݕ ݕ ൌ ʹ
ݔ ൌ
ሬሬሬሬሬԦ ൌ หܥܩ ሬሬሬሬሬԦ ห כሬሬሬሬሬሬԦ ݊ீ ܥܩ ݔ ൌ ݔሺͲǤͷሻ ݕ ൌ ݕሺͲǤͷሻ ሬሬሬሬሬԦ ܦܩ ݊ீ ൌ ሬሬሬሬሬሬԦ ݎ ሬሬሬሬሬԦ ห หܥܩ Ƚ െ Ƚ ݎൈ ݊݅ݏቀ ୗ ቁ ʹ ൌ Ƚୗ െ Ƚ ቀ ቁ ʹ
For bending force, the acting point is assumed as the centroid of moved region (Fig. 4). Consequently, calculating acting point of bending force is similar to calculating acting point of shearing force in punching case. However, outer contour of the moved surface is used instead of contour of the punch.
Fig. 4 Acting point of bending force
Fig. 5 An 8-station layout: (a) strip layout with superimposed punches, (b) acting points of component forces
C. Center of Equivalent Reaction Force The centre of equivalent reaction force ( ݔҧ ǡ ݕത ) can be calculated as the centroid of its components forces by the following equations: ݔҧ ൌ
IV.
Geometry traverse means passing from handling one geometry item (solid, surface, contour or edge) to handling another geometry item. Following methods are introduced by Pro/Web.Link in order to traverse the geometry of a solid block:
ቀσୀଵ ܨௌ ൈ ݔ σ ୀଵ ܨೕ ൈ ݔ ቁ
ቀσୀଵ ܨௌ σ ୀଵ ܨೕ ቁ σ ୀଵ ܮೕ ൈ ݔ ቇ ܶ ൈ ߬௦ ൈ ቆσୀଵ ܮௌ ൈ ݔ ൌ σ ୀଵ ܮೕ ቇ ܶ ൈ ߬௦ ൈ ቆσୀଵ ܮௌ σୀଵ ܮೕ ൈ ݔ ቆσୀଵ ܮௌ ൈ ݔ ቇ ൌ σ ୀଵ ܮೕ ቇ ቆσୀଵ ܮௌ
ݕത ൌ
σ ୀଵ ܮೕ ൈ ݕ ሻ σୀଵ ܮೕ ሻ ሺσୀଵ ܮௌ
ሺσୀଵ ܮௌ ൈ ݕ
PROGRAMMING FOR GEOMETRY TRAVERSAL
To traverse the geometry, follow the following steps: • Starting from the current working directory of Pro/Engineer, use pfcBaseSession.CurrentModel () to get handle to solid model. • From handle of a specific solid model, use pfcModelItemOwner.ListItems() with an argument of ModelItemType.ITEM_SURFACE to list all the surfaces contained in the current solid model. Then use pfcSurfaces.Item(i) to get handle to surface i. • From handle of a specific surface, use pfcSurface.ListContours() to list all the contours contained in that surface. Then use pfcContours.Item(j) to get handle to contour j. • From handle of a specific contour, use pfcContour.ListElements() to list all the edges contained in a specified contour. Then use pfcEdges.Item(k) to get handle to edge k. • From handle of a specific edge, use pfcEdge.Eval3DData() with an argument of parameter t in order to get handle to specific 3D point of that edge.
(6)
(7)
where ݔҧ ǡ ݕത: coordinate of center of the resultant reaction force, n, m: total number of shearing forces, bending forces, ܨௌ ǡ ܨೕ : shearing force i, bending force j, ୧ ǡ ୧ : coordinate of acting point of shearing force i, ݔ ǡ ݕ : coordinate of acting point of bending force j, ܮௌ ǡ ܮೕ : shearing length of shearing force i, bending length of bending force j. If bending is upward, the direction of bending force is bottom-up, opposite to the direction of shearing force (topdown); therefore, that bending length is assigned minus value, or ܮೕ ൌ െܮೕ
Once handle of a geometry item, an edge for instance, is get, we can extract geometry information of that item by using methods and properties introduced by Pro/Web.Link. V.
In Fig. 5, there is an example of eight-station layout, and the zero point O is at the middle of the left-hand side of station 1. The strip is punched simultaneously by the 8 shearing punches and 4 bending punches (Fig. 5(a)). Centre of equivalent reaction force is calculated based on the magnitudes and acting points (Fig. 5(b)) of these component forces by Eqs. (6) and (7). Actually, magnitudes of component forces are estimated by Eqs. (2) and (3), and acting points of component forces are estimated by Eqs. (4) and (5) at earlier stage.
PROGRAMMING FOR DETERMINING LIFT HEIGHTS
Lift height at each station ୧ need to be calculated in order to determine the lift height needed for the whole strip layout. This research concerns about wipe bending type. Wipe bending can be divided into two groups: upward bending and downward bending. For upward bending operation (Fig. 6), the lowest point of the blank need to be higher than the highest point of the die
231
with an amount of S (safety lift height) in order to avoid collision between the blank and the die. The reference plane of the die and the reference plane of the strip are chosen for calculating lift height (shown in Fig. 6(a)), so the lift height for upward bending (shown in Fig. 6(c)) is estimated by: ܪ ൌ ܵ ܤ ܦ
(8)
where ܪ : lift height need for station i, ܵ: safety lift height, usually choose S = 2mm, ܤ : height of the bending die (distance between the highest point of the die and the reference plane of the die) at station i, ܦ : height of downward portion of the blank (distance between the lowest point of the blank and the reference plane of the strip) at station i.
Fig. 8 The Pro/Web.Link application for evaluating sheet metal strip layout Using the sheet metal part in Fig. 9(a) as an example, the 7 shearing punches and 2 bending punches employed to fabricate the part are shown in Fig. 9(b)
Fig. 6 Upward bending: (a) before bend, (b) bend finish, (c) lift after bend In this case, the bending die used to create the upward bending portion of the blank; therefore, the height of the bending die ܤ and the height of upward portion of the blank ܷ are proportional. If we assume that ܷ is equal to ܤ , the lift height for upward bending can be calculated as: ܪ ൌ ܵ ܷ ܦ ൌ ܵ ݄
(9)
where ݄ : total height of the blank at station i. For downward bending (Fig. 7), the lift height is estimated by: ܪ ൌ ܵ ܦ
(10)
Fig. 9 Solid models: (a) sheet metal part, (b) shearing punches Pi and bending punches Bi First, the feasible layouts, which are satisfied die design rules, for this part are determined manually based on the scheme suggested by [6]. Next, the Pro/Web.Link application is utilized as an automatic tool for evaluating 12 feasible layouts of the sample part. Their calculation time, which is needed for the application evaluating each layout, evaluation score (with wn/wb/ws/wl = 0.4/0.15/0.2/0.25) and four factors are shown in Table 2. Notice that Pi, Bj and i symbolize shearing punch number i, bending punch number j and idle station, correspondingly.
Fig. 7 Downward bending: (a) before bend, (b) bend finish, (c) lift after bend For shearing operations, the lift height is similar to downward bending. However, for the last stations, the blank is cut out of the scrap strip; so, the feed height is obviously as follow: ܪே ൌ Ͳ
(11)
where ܰ: the number of stations. VI.
It is easy to find that different layouts will have various punching areas, bending areas, connecting lengths, and center of equivalent reaction force and lift height needed; as a result, the evaluation scores will be changed accordingly.
RESULTS
A Pro/Web.Link application (Fig. 8) has been developed based on the proposed approach and calculation techniques in order to compute automatically the evaluation score for each given 3D model of strip layout. The application had been executed in Pro/Engineer Wildfire 5.0 environment on a PC.
In order to demonstrate the calculation process, layout #2 (Fig. 10(a)) is manually evaluated.
232
Table 2 Evaluation results of 12 feasible layouts for sample part
ܮమ ൈ ݔଶ ܮభ ൈ ݔଵ ܮௌళ ൈ ݔ൰ ܮమ ܮభ ܮௌళ ൰ ൬ܮௌభǡమ ܮௌయǡరǡఱ ܮௌల
൬ܮௌభǡమ ൈ ݔଵǡଶ ܮௌయǡరǡఱ ൈ ݔଷǡସǡହ ܮௌల ൈ ݔ
ൌ
#
Layout
Time (s)
Fn
Fb
Fs
Fl
EV
1 2 3 4 5 6 7 8 9 10 11 12
[P1,P2]+[P3,P4,P5]+P6+B1+B2+P7 [P1,P2]+[P3,P4,P5]+P6+B2+B1+P7 [P1,P2]+[P3,P4]+P5+P6+B1+B2+P7 [P1,P2]+[P3,P4]+P5+P6+B2+B1+P7 [P1,P2]+[P3,P4,P6]+P5+I+B1+B2+P7 [P1,P2]+[P3,P4,P6]+P5+I+B2+B1+P7 [P1,P2]+[P3,P5]+P6+B1+B2+P4+P7 [P1,P2]+[P3,P5]+P6+B2+B1+P4+P7 [P1,P2]+P3+P5+P6+B1+B2+P4+P7 [P1,P2]+P3+P5+P6+B2+B1+P4+P7 [P1,P2]+[P3,P6]+P5+I+B1+B2+P4+P7 [P1,P2]+[P3,P6]+P5+I+B2+B1+P4+P7
8.33 10.69 12.77 12.55 10.66 10.59 12.42 12.33 14.06 13.91 11.69 11.86
48.57 48.57 35.71 35.71 35.71 35.71 35.71 35.71 22.86 22.86 22.86 22.86
68.69 69.28 81.64 82.13 72.13 72.66 71.43 71.96 85.99 86.44 77.29 77.77
51.75 51.75 51.70 51.70 69.57 69.57 51.75 51.75 51.70 51.70 69.57 69.57
10.00 40.35 10.00 40.35 10.00 40.35 10.00 40.35 10.00 40.35 10.00 40.35
42.58 50.26 39.37 47.03 41.52 49.19 37.85 45.52 34.88 42.54 37.15 44.81
ൌ
ൌ ͵ͶǤʹͻͷ
ݕത ൌ
σ ୀଵ ܮೕ ൈ ݕ ሻ σ ܮ ୀଵ ೕ ሺσୀଵ ܮௌ ሻ
ሺσୀଵ ܮௌ ൈ ݕ
ܮమ ൈ ݕଶ ܮభ ൈ ݕଵ ܮௌళ ൈ ݕ൰ ܮమ ܮభ ൬ܮௌభǡమ ܮௌయǡరǡఱ ܮௌల ܮௌళ ൰
൬ܮௌభǡమ ൈ ݕଵǡଶ ܮௌయǡరǡఱ ൈ ݕଷǡସǡହ ܮௌల ൈ ݕ
ൌ
ൌ
ሺെͷሻ ൈ Ͷͻ ͷ ൈ ͵ ʹͶǤ ൈ Ǥ൰ ሺെͷሻ ͷ ʹͶǤ൰ ൬ͻǤͶʹ ͳͲʹǤͷʹ ͳͲǤͲͺ
൬ͻǤͶʹ ൈ ͳʹǤͷ ͳͲʹǤͷʹ ൈ ʹͷǤʹ͵ ͳͲǤͲͺ ൈ ͶͳǤ͵
ሺെͷሻ ൈ ሺെͳʹǤͶሻ ͷ ൈ ሺെǤͲሻ ʹͶǤ ൈ ͳͶǤͳ൰ ሺെͷሻ ͷ ʹͶǤ൰ ൬ͻǤͶʹ ͳͲʹǤͷʹ ͳͲǤͲͺ
൬ͻǤͶʹ ൈ Ͳ ͳͲʹǤͷʹ ൈ ሺെͳǤʹʹሻ ͳͲǤͲͺ ൈ ሺെͳͶǤͶሻ
ൌ ͲǤͷʹ
One thing should be notice from the previous equation is that we group punches which perform at the same station. For example, shearing punch P1 and P2 perform at station number 1, so ܮௌభǡమ and ሺݔଵǡଶ Ǣ ݕଵǡଶ ሻ are the shearing length and acting point of grouped punch (1, 2). Next, the centre of the die for a six-station design is 42 ௧ൈே௨ைௌ௧௧௦ ଵସൈ ൌ ൌ Ͷʹ) units away from the ( ൌ ଶ ଶ ଶ zero point on the left-hand side (Fig. 11(b)).
After obtaining center of the equivalent reaction force (ݔҧ ǡ ݕത) and center of the die ( ǡ Ͳ); the following equations [6] are ଶ employed to calculate maximum deviation ܦ௫ and the real deviation ݀ of the center of equivalent reaction force with respect to the center of the die (as shown in Fig. 11(b)):
Fig. 10 Feasible layout #2: [P1,P2]+[P3,P4,P5]+P6+B2+B1+P7 of the sample part: (a) strip layout, (b) punch superimposing
ͳͶ ൈ ଶ ͵Ͷ ଶ ܦ௫ ൌ ඥሺܮȀͶሻଶ ሺܹȀͶሻଶ ൌ ඨ൬ ൰ ൬ ൰ ൌ ʹʹǤͷͷ Ͷ Ͷ
(1) Stage number factor Fn
݀ ൌ ඥሺݔҧ െ ܮȀʹሻଶ ݕത ଶ ൌ ඥሺ͵ͶǤʹͻͷ െ Ͷʹሻଶ ሺͲǤͷʹሻଶ ൌ Ǥʹͷ
The value of nine punches for a six-station layout (Fig. 10(b)) is calculated by the following equation: ܨ ൌ ͳͲͲ െ ͻͲ ൈ
ܰ െ ܰ െʹ ൌ ͳͲͲ െ ͻͲ ൈ ൌ ͶͺǤͷͳ ܰ௫ െ ܰ ͻെʹ
(2) Moment balancing factor Fb First, the shearing length ܮௌ and acting point (ݔ ǡ ݕ ) of each shearing punch as well as the bending length ܮೕ and acting point (ݔ ǡ ݕ ) of each bending punch (illustrated in Fig. 11(a)) are investigated from the solid model in Pro/ENGINEER. So we obtain the magnitude and acting point of all component forces (shearing and bending forces) Then, Eqs. (6) and (7) are employed to find the center of the equivalent reaction force (ݔҧ ǡ ݕത) for these component forces: ቆσୀଵ ܮௌ ൈ ݔ ݔҧ ൌ
σ ୀଵ ܮೕ ൈ ݔ ቇ
ቆσୀଵ ܮௌ
σ ୀଵ ܤ ቇ
Fig. 11 Moment balancing calculation: (a) acting points of component forces, (b) deviation of center of equivalent reaction force
233
Finally, the following equation [6] is used to determine moment balancing factor Fb : ܨ ൌ ͳͲͲ െ ͻͲ ൈ
݀ ܦ௫
ܨ ൌ ͳͲͲ െ ͻͲ ൈ
In summary of these four factors, the evaluation score Ev is obtained by Eq. (1):
Ǥʹͷ ൌ ͳͲͲ െ ͻͲ ൈ ൌ ͻǤ͵ͳͳ ʹʹǤͷͷ
ܧ ൌ ݓ ൈ ܨ ݓ ൈ ܨ ݓ௦ ൈ ܨ௦ ݓ ൈ ܨ ൌ ͲǤͶ ൈ ͶͺǤͷͳ ͲǤͳͷ ൈ ͻǤ͵ͳͳ ͲǤʹ ൈ ͷͳǤͳ ͲǤʹͷ ൈ ͶͲǤ͵ͷʹ ൌ ͷͲǤʹͷ
(3) Strip stability factor Fs The total connecting length of the sheet metal part in Fig. 12 is 81.490, and it will be reduced gradually by punching operations performed at every station (illustrated in Fig. 12). The detail information of connecting length Lk at each station for layout 2 is investigated from the solid model in Pro/ENGINEER (shown in Table 3). There is no reduction of connecting length at stations 1 and 5; so, connecting length for the strip stability factor would consider only stations 2, 3 and 4.
VII. CONCLUSIONS Process planning, which is the core issue in progressive dies, is a challenging and time-consuming task which requires experienced designers and their great deal of trial and error. After utilizing designers’ expertise and design rules, there are still so many feasible layouts for designers to select from. The subjects for this research are feasible layouts, which are manually determined using the scheme proposed by Lin and Dean [6]. In this study, we have suggested an approach for recognizing punching, notching and bending operations from given 3D model of strip layout. In addition, we have also proposed a method for automating layout evaluation and developed a Pro/Web.Link application which helps designers quickly determine the most appropriate layouts among many feasible ones. The followings are the main features of this application: • 3D models of strip layouts are used as input data for the process of operation recognitions and calculations. • The sheet metalworking range varies from punching, notching and bending operations. • The four factors, or criteria, used for layout evaluation are combined with their weighting factors. Hence, the evaluation function can be flexibly adjusted to satisfy various designers’ preferences. • The evaluation score can be obtained very quickly; for example, approximately sixteen seconds for an eightstation layout in comparison with one hour of manual extraction and calculation.
Fig. 12 Connecting length Lk at each station of layout #2 of the sample part Using the following equation [6] to compute strip stability factor Fs for layout 2 as follow: ܨ௦ ൌ Ͳ ൈ
ܮ ʹͳǤ͵ʹ ͳǤͶ ͷͲǤʹ ͵ൈ Ͷൈ ʹൈ ܮ ͶͲǤͶ ʹͲǤ͵ ͳǤͳʹ ൌ Ͳ ൈ σேିଵ ʹ͵Ͷ ୀଵ ݇
σேିଵ ୀଵ ݇ ൈ
ൌ ͷͳǤͳ
Table 3 Strip stability factor for layout #2 of the sample part Reduced connecting length
Connecting length (Lk)
---
---
81.490
NA
[P1,P2]
0
81.490
87.40
[P3,P4,P5]
30.87
50.62
Station number
LLk
1.43LLk
0
81.490
---
1
NA
2
61.12
Punches
ܪെ ܪ ͳͲ െ ʹ ൌ ͳͲͲ െ ͻͲ ൈ ൌ ͶͲǤ͵ͷʹ ܪ௫ െ ܪ ͳͶǤͲͲͺ െ ʹ
ACKNOWLEDGMENTS This project was supported in part by the National Science Council, Taiwan, under project number 97-2628-E-011-002MY3. REFERENCES
3
40.74
58.26
P6
29.21
21.32
[1]
4
20.37
29.13
B2
3.86
17.46
[2]
5
NA
NA
B1
0
17.46
6
0
0
P7
17.46
0
[3] [4]
(4) Feed height factor Fl
[5]
The feed height for the whole strip of that six-station layout is determined by Eqs. (9) and (10): H = max (H1, H2, H3, H4, H5, H6) = max (2, 2, 2, 10, 8, 0) = 10 ܪ ൌ ܵ ൌ ʹ (safe lift height) ܪ௫ ൌ ܵ ͳʹǤͲͲͺ ൌ ͳͶǤͲͲͺ
[6]
234
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