3 Automatic Feeding and Orienting — Vibratory
3.18 ANALYSIS OF A TYPICAL ORIENTING SYSTEM
In general, an orienting system for a vibratory-bowl feeder consists of one or more orienting devices arranged in series along the bowl track. These devices FIGURE 3.51 Probabilities of natural resting aspects for cylinders dropped onto a soft surface. (From Boothroyd, G. and Ho, C., Natural Resting Aspects of Parts for Automatic Handling, Transactions of the ASME, Journal of Engineering for Industry, Vol. 99, pp.
314–317, May 1997. With permission.) 1.0
0.8
0.6
0.4
0.2
0
Prabability, P
0.1 0.2 0.3 0.4 0.6 0.8 1.0 1.5 2.0 3.0
L/D
Aspect b Aspect a
Theory [Eqs. (3.44) through (3.47)]
Experimental results (with 95% confidence limits)
are usually located near the outlet of the feeder along a horizontal portion of the track. Because the track section is level, the parts can travel at a conveying velocity that is greater than the velocity of the parts on the preceding incline, thus enabling parts to separate and eliminating interference between adjacent parts as they pass the various devices. Such a system is shown in Figure 3.54 for the feeding and orienting of right rectangular prisms. The six orientations for these prisms are also described in this figure.
The first device is a wiper blade, and it rejects orientations c, d, e, and f back into the bowl. It also serves to remove the secondary layers of parts, where one part rests on another instead of on the track. The output of this device is in either a or b orientation.
The narrow track is next, and it rejects orientation b back into the bowl, leaving only orientation a. The riser turns orientation a into orientation c, which is the output orientation of the system.
The matrices for these devices and systems are:
FIGURE 3.52 Probabilities of natural resting aspects for cylinders and various regular prisms dropped onto a soft surface. (From Boothroyd, G. and Ho, C., Natural Resting Aspects of Parts for Automatic Handling, Transactions of the ASME, Journal of Engineer-ing for Industry, Vol. 99, pp. 314–317, May 1997. With permission.)
1.0
0.8
0.6
0.4
0.2
00.1 0.2 0.3 0.4 0.6 0.8 1.0 1.5 2.0 3.0
L/D
Probability, P
Pa (on end)
Pb (on end)
L = length of prism
D = diameter of circumscribed cylinder Theory [Eqs. (3.44) through (3.49)]
Cylinders Hexagonal prisms Square prisms Triangular prisms
Experiment
FIGURE 3.53 Probabilities of natural resting aspects for prisms of regular cross section;
L is the length of prism and D the diameter of circumscribed cylinder. (From Boothroyd, G. and Ho, C., Natural Resting Aspects of Parts for Automatic Handling, Transactions of the ASME, Journal of Engineering for Industry, Vol. 99, pp. 314–317, May 1997. With permission.)
Rectangular prisms, when tossed onto a horizontal surface, can come to rest on one of three pairs of faces. These positions are the three natural resting aspects for these parts. The probabilities for a prism coming to rest in these three aspects are shown in Figure 3.55. The dimensions of the parts used in this particular system are 45mm × 30mm × 3 mm. The values c/s and c/b are 0.07 and 0.10, respectively. According to Figure 3.55, virtually all these parts will rest on their largest face when tossed onto a hard horizontal surface, such as the bottom of a bowl feeder. However, within this one natural resting aspect, there are two FIGURE 3.54 Orienting system for right rectangular prisms.
Wiper blade Narrow track Riser System
Side
a reorients to c
b cdef
FIGURE 3.55 Probabilities of natural resting aspects for right rectangular prisms. (From Boothroyd, G. and Ho, C., Natural Resting Aspects of Parts for Automatic Handling, Transactions of the ASME, Journal of Engineering for Industry, Vol. 99, pp. 314–317, May 1997. With permission.)
possible orientations (a and b). Parts in the bottom of the bowl tend to rotate into one of these orientations before they travel up the inclined track. For aluminum parts on a steel track, the coefficient of friction μ is 0.4. Thus, from Ho and Boothroyd [12], or Figure 3.56, it can be seen that, for these parts, the partition ratio R = Pa/(Pa + Pb) is 0.63 and, therefore, the probabilities are given by
Pa = R(Pa + Pb) = 0.63, Pb = 0.37
The initial distribution matrix (IDM) showing the probable distribution of the various orientations is, therefore,
Thus, the efficiency η of this system, which is given by the product of the IDM and the system matrix, is 63%.
The average length of a part entering this system is the product of the IDM and a matrix of the lengths of the part in the corresponding orientations in the conveying direction. For these parts, the average part length
-is
The feed rate F can be found from
(3.48)
where v is the conveying velocity of the parts on the inclined section of the track when adjacent parts are in contact. The feed rate of any system can be found in a similar manner, using the initial distribution matrix, system matrix, length matrix, and Equation 3.48. The feed rate can also be determined from
F = vE/A (3.49)
FIGURE 3.56 Probabilities of orientations of rectangular prisms on a bowl-feeder track.
Pa is the probability of orientation a; Pb is the probability of orientation b; partition ratio R = Pa/(Pa + Pb); μ is the coefficient of friction between parts and bowl track; and L1 and L2 are the length of long and short sides, respectively, for the part-track interface (L1 L2). (From Ho, C. and Boothroyd, G., Orientation of Parts on the Track of a Vibratory Feeder, Proceedings of the Fifth North American Metalworking Research Conference, SME, p. 363, Dearborn, Michigan, 1977. With permission.)
a b
a b
Side view Bowl wall
Bowl wall
Plan view L1
L2
1.0
0.9
0.8
0.7 0.6
0.5
Partition ratio, R
1.0 2.0 3.0 4.0 5.0
L1 L2
1μ
≥ 1.0
0.9
0.8
0.7
0.6
0.5
Partition ratio, R
1.0 2.0 3.0 4.0 5.0
L1 L2
1
< μ
L1/L2
where E is the modified efficiency of the orienting system and is given by
(3.50) 3.18.1 DESIGN OF ORIENTING DEVICES
To achieve the calculated 63% efficiency, the orienting devices that make up the system must be properly designed. Design data and performance curves for orienting devices used in vibratory-bowl feeders are provided in Appendix D, which is based on the Handbook of Feeding and Orienting Techniques for Small Parts [11].
For the wiper blade, which rejects orientations c, d, e, and f (Figure 3.54), the angle θ between the wiper blade and the bowl wall is set to avoid the jamming action produced by overlapping parts, as shown in Figure 3.57. The smallest jamming angle βw for these parts is arctan (3/45) or 3.8° (0.07 rad), and the maximum value of θw is 18° (0.31 rad). The height of the wiper blade should be 5 mm, which is sufficient to remove a secondary layer of parts.
The narrow-track device rejects orientation b but allows orientation a to pass.
From Figure 3.58 and a conveying velocity of 100 mm/sec, the corresponding
FIGURE 3.57 Wiper blade design.
E= η /A
βw
θw
Jamming occurs beneath wiper blade
Parts will not jam 80
60 40 20
00 5 10 15 20 25 30 35
Jamming angle, βw (degrees) Maximum blade angle, θwmax (degrees)
values for the dimensionless track width bt/w are 1.2 and 1.45, respectively. Thus, in millimeters,
(1.2) (22.5) > bt > (1.45) (15) or
27 > bt > 22
The narrow track should be 23 mm wide and 67 mm long.
The edge-riser orienting device turns orientation a into orientation c. The design information for this device is presented in Figure 3.59. For a 6° (0.10-rad) riser angle and parts measuring 45 mm × 30 mm × 3 mm, B/C equals 10, and the ramp length is 300 mm. Other riser angles and lengths will also produce satisfactory results.
FIGURE 3.58 Narrow-track design.
bt
~1.5 Part length
All parts rejected All parts accepted
Cylinders Rectangles 1.6
1.5 1.4 1.3 1.2 1.1 1.0 bt w
50 75 100 125
Conveying velocity, v (mm/s)
Bowl wall
w w
Center of
mass (r) (q)