3 Automatic Feeding and Orienting — Vibratory
3.15 ANALYSIS OF ORIENTING SYSTEMS
To determine the effect of certain aspects of part geometry on the efficiency with which the part can be fed and oriented, consider several parts having the same basic shape but different sizes [6]. Figure 3.28 shows a family of cup-shaped parts that take the form of plain cylinders, with a blind hole drilled axially from one end. These parts have the same diameter, 12.7 mm, with an 11.7-mm-diameter square bottom hole drilled from one end to a depth of 0.718 times the length of the part. It can be shown that, for all these parts, the center of mass is positioned at the bottom of the hole; the only geometric variable necessary to describe the part is its length-to-diameter ratio.
For a bowl feeder having a track that ensures single-file feeding of these parts, only four orientations of the part need to be considered. These orientations are shown in Figure 3.29 and are keyed a, b1, b2, and c. Orientation a shows the part fed standing on its base (that is, heavy end down). Orientations b1 and b2 show the part fed on its side, either heavy end first (b1) or light end first (b2).
Finally, orientation c shows the part fed heavy end up.
Before a study of the design of an orientation system for these parts can be made, it is necessary to know the probabilities with which these four orientations would initially occur. This information can then be used as the input to the orienting system analysis. Figure 3.30 presents the results of experimental and theoretical work. In the experiments, each part was repeatedly thrown onto a flat horizontal aluminum surface, and the resulting final resting aspect was noted for each trial. In this experiment, it is not possible to distinguish between orientations b1 and b2 because the direction of feeding is not defined. For this reason, the term natural resting aspect is employed, which is meant to describe the way in which a part can rest on a horizontal surface. Thus, natural resting aspect a designates
FIGURE 3.28 Parts used in the experiment. (From Murch, L.E. and Boothroyd, G., Design of Orienting Systems for Vibratory-Bowl Feeders, SME Technical Paper FC72–235, 1972.
With permission.)
l/d = 0.141
l/d = 0.566
0.2 0.283 0.4
No. 1
No. 5
2 3 4
6 7 8
0.8 1.132 1.6
parts resting on their bases, b designates parts resting on their sides, and c refers to parts resting with their heavy ends up. Those parts that come to rest on their sides will, when fed, separate about equally into the two orientations b1 and b2 described above. It can be seen from Figure 3.30 that, for example, the probability that a cup-shaped part having a length-to-diameter ratio of 0.8 will come to rest on its base (natural resting aspect a) is 0.4. Each experimental value in Figure 3.30 represents the results of at least 250 trials and has 95% confidence limits of less than ± 0.05.
FIGURE 3.29 Orientations of cup-shaped parts. (From Murch, L.E. and Boothroyd, G., Design of Orienting Systems for Vibratory-Bowl Feeders, SME Technical Paper FC72–235, 1972. With permission.)
FIGURE 3.30 Distribution of natural resting aspects. (From Murch, L.E. and Boothroyd, G., Design of Orienting Systems for Vibratory-Bowl Feeders, SME Technical Paper FC72–235, 1972. With permission.)
Direction of feeding
a b1
b2 c
1.0
0.8
0.6
0.4
0.2
00.1 0.15 0.2 0.3 0.5 0.8 1.0 1.5 2.0 3.0
/d
0.718
a b
c d
Probability
Aluminum surface
Aspect a Aspect c
Aspect b
•
The basis of a theoretical study of the distributions of natural resting aspects of parts is described later in this chapter. The solid lines shown in Figure 3.30 are based on theoretical values and can be seen to agree closely with the exper-imental results.
3.15.1 ORIENTING SYSTEM
A system for orienting cup-shaped parts is shown in Figure 3.31. It consists of one active device, a step; and two passive devices: a scallop and a sloped track with a ledge. The system is designed to deliver a part in orientation a (i.e., on its base).
In the orientation process, the parts first encounter the step device, whose purpose is to increase the proportion of parts in orientation a. This increase is achieved by arranging a step height that does not affect many of the parts in orientation a but reorients some of the parts in orientations b1 or c into orientation a as they pass over the step.
The remaining passive devices are simply designed to ensure that all parts in orientations b1, b2, and c are rejected back into the bowl. These rejected parts later make further attempts to filter through the orienting system.
The first of the passive devices, the scallop cutout, ensures rejection of a part in orientation c. Its design is based on data regarding the feeding motion of the part when the horizontal amplitude of vibration at the bowl wall was set at 1.0 mm with a vibration angle of 5°. The motion of the part under these conditions is shown in Figure 3.32 and was obtained using a computer program similar to that described by Redford and Boothroyd [1]. It can be seen from the figure that the part slides forward a distance of 0.86 mm after hopping and then slides 0.91
FIGURE 3.31 Experimental orienting system. (From Murch, L.E. and Boothroyd, G., Design of Orienting Systems for Vibratory-Bowl Feeders, SME Technical Paper FC72–235, 1972. With permission.)
Direction of feeding
Step
Scallop cutout
c a
c
b1 b2
Ledge
mm backward before hopping again. Although the distance the part hops is 2.72 mm, the maximum gap in the track that any point on the undersurface of the part can negotiate is 1.75 mm. With this information, it is possible to design the scallop device so that parts in orientation a are always supported, regardless of where they are situated on the device, whereas those parts in orientation c will, at some point, be situated in a position where they cannot be supported and will fall off the track into the bowl. Experiments [6] show that a small proportion of those parts in orientations b1 and b2 are also rejected by this device, but this does not affect the performance of the system because the next device will, in any case, reject parts in both these orientations.
The second passive device, the sloped track with a ledge, is designed to reject all those parts in orientations b1 and b2. The ledge retains parts in orientation a but does not prevent parts in orientations b1 and b2 from rolling off the track and back into the bowl.
The only orienting system variable considered here is the height of the active step orienting device and, in order to perform an optimal design analysis, it is necessary to carry out an experimental program to measure the effect of various step heights on different orientations of each of the eight specimens. Typical results of such experiments are presented in Figure 3.33, which shows the effects of feeding a part in each of its four initial orientations, over the step, with step heights varying from zero to a maximum of 7 mm. It was found that, for step heights greater than 7 mm, the parts would bounce erratically upon landing on the track below the step, an effect that would be unacceptable in practice.
3.15.2 METHOD OF SYSTEM ANALYSIS
The object of an analysis of a bowl-feeder orienting system is to design each device so that the highest value for the efficiency of the complete system is obtained. The efficiency of the system is defined as the number of properly oriented parts delivered by the system, divided by the number of parts entering the system.
FIGURE 3.32 Motion of part relative to track during experiments. (From Murch, L.E. and Boothroyd, G., Design of Orienting Systems for Vibratory-Bowl Feeders, SME Technical Paper FC72–235, 1972. With permission.)
Part hops Part slides forward
Part slides backward
2.72 mm 0.86 1.75 mm 0.91 mm
Effective hop
To calculate this efficiency for a system of orienting devices, a matrix tech-nique has been developed [7]. Each device is represented by a matrix whose number of rows and columns depends on the number of orientations in the devices’ respective input and output. If these matrices are multiplied in the order in which the parts encounter the devices, the resulting single-column matrix represents the performance of the system. If this matrix is then premultiplied by a single-row matrix representing the initial distribution of orientations of the part, the efficiency of the system is obtained.
Figure 3.34 shows a schematic diagram for the present system, together with the appropriate matrices. The terms in the matrix that represent the step device are only symbolic. The term AA indicates the proportion of those parts in orien-tation a that will remain in orienorien-tation a, AB1 represents those parts in orientation a that are reoriented into b1, and so on. In the matrix for the scallop device, q1
and q2 represent the proportion of parts that enter the device in orientations b1
and b2, respectively, and exit in the same orientation. For part 7 and a step height of 7 mm, the step orienting device matrix becomes
FIGURE 3.33 Effect of step on part 7. (From Murch, L.E. and Boothroyd, G., Design of Orienting Systems for Vibratory-Bowl Feeders, SME Technical Paper FC72–235, 1972.
With permission.)
(3.18)
and the resulting system matrix is
(3.19)
This result means that 50% of those parts that enter the system in orientation a exit in orientation a, 100% of those parts that enter in orientation b1 exit in orientation a, and so on.
From Figure 3.30, the initial distribution matrix for part 7 is
(3.20) Thus, premultiplying the system matrix, Equation 3.19, by the input distri-bution matrix, Equation 3.20, gives
FIGURE 3.34 Orienting system analysis. (From Murch, L.E. and Boothroyd, G., Design of Orienting Systems for Vibratory-Bowl Feeders, SME Technical Paper FC72–235, 1972.
With permission.)
which means that, under these conditions, the efficiency of the system is 61%.
Hence, if the bowl was set to feed parts at a rate of 10 parts/min, the mean delivery rate of parts in orientation a would be 6.1 parts/min.
3.15.3 OPTIMIZATION
To optimize the design of this system, it is necessary to determine the step height that gives the maximum efficiency for each of the eight parts. The simplest method is to calculate the system efficiency for increments of step height within the practical range. The results of this procedure are shown in Figure 3.35 and Figure 3.36, where it can be seen that the maximum efficiency for five of the parts occurs at the maximum allowable step height of 7 mm. These maxima are plotted in Figure 3.37 (curve B) and compared with the initial distribution of parts in orientation a (curve A). This initial distribution is the same as the system efficiency that would be obtained if the step device had not been included in the system, and the figures show clearly the advantages of including the step device. In many cases, the efficiency of the system is almost doubled; in other words, the output rate of oriented parts would be almost doubled. Because such significant advan-tages of including the step device in the system can be demonstrated, it is of interest to consider the effect of including a further step device. In this case, a further variable is introduced, and the upper curve shown in Figure 3.37 is obtained. In all cases, it can be seen that the overall maximum efficiency is achieved with parts having a length-to-diameter ratio l/d of 0.4.
FIGURE 3.35 Effect of step height on efficiency (parts 1, 2, 3, and 4). (From Murch, L.E.
and Boothroyd, G., Design of Orienting Systems for Vibratory-Bowl Feeders, SME Tech-nical Paper FC72–235, 1972. With permission.)
100
80
60
40
20
00 1 2 3 4 5 6 7
Step height (mm)
Efficiency (percent)
Part number 4
3 2
1
FIGURE 3.36 Effect of step height on efficiency (parts 5, 6, 7, and 8). (From Murch, L.E.
and Boothroyd, G., Design of Orienting Systems for Vibratory-Bowl Feeders, SME Tech-nical Paper FC72–235, 1972. With permission.)
FIGURE 3.37 Effect of part shape on efficiency of orienting system. (From Murch, L.E.
and Boothroyd, G., Design of Orienting Systems for Vibratory-Bowl Feeders, SME Tech-nical Paper FC72–235, 1972. With permission.)
100
80
60
40
20
00 1 2 3 4 5 6 7
Step height (mm)
Efficiency (percent)
Part number 5
6
7
8
d
2
3 4
5 6
7
8 Part number 1
One step (B)
No step (A)
Two steps (C) 100
80
60
40
20
0
Efficiency (percent)
0.1 0.15 0.2 0.3 0.5 0.8 1.0 1.5 2.0 3.0
/d