Page 757 - Mechatronics with Experiments

PROGRAMMABLE MOTION CONTROL SYSTEMS 743
Constant Gear Ratio Spacing Conveyors with a Queue (Smart)
Conveyor This design is appropriate when the parts can touch each other and the
speeds of two adjacent conveyors do not have to match during the transfer. In this case,
there will be three conveyors: 1. input conveyor, 2. queue conveyor (the smart conveyor),
3. output conveyor. Parts come to the input conveyor at a fixed average rate (N ), but with
1
non-uniform spacing. The queue (smart) conveyor runs slower than the input conveyor to
provide a constant supply of continuous parts (Figure 10.16). The output conveyor runs
faster to adjust the proper spacing. If the queue conveyor is always full and parts are touch-
ing, the spacing will be proportional to the speed ratio. Let us assume the part transfer
rate is N . In continuous operation, the part rate in the conveyors must be same. Length of
1
each part is L , and the average spacing is L . The speed of the queue conveyor will be
1
p
determined by the requirement that the average part rate must be same in both conveyors:
N = N 2 (10.14)
1
V 1 V 2
= (10.15)
(L + L ) L p
1
p
V = L ∗ N 1 (10.16)
2
p
L p
= ⋅ V 1 (10.17)
L + L 1
p
On the output conveyor, if the desired spacing between the parts is L , then the spacing
3
conveyor speed needs to satisfy the same average part rate requirement,
V V
2 3
= (10.18)
L p (L + L )
p
3
L + L 3
p
V = ⋅ V 2 (10.19)
3
L p
On the output conveyor, if the difference between V and V is so large that the acceleration
3
2
rate is too high for the part integrity (i.e., soft parts or fluid content), then more than one
spacing output conveyor would be used in order to reduce the maximum acceleration levels
experienced by the part. From the queue conveyor point of view, the cycle time per part is
L p
t = (10.20)
cycle
V 2
Let us assume that L is the portion of the part length L during which the part is in contact
pt p
with both conveyors and changes speed from V to V . The acceleration rate is then
2 3
L pt
t = ⋅ t (10.21)
transfer cycle
L p
(V − V )
3
2
A = (10.22)
t
transfer
The number of spacing output conveyors needed is determined by rounding the following
result to the next highest integer value
( )
A
N = Int (10.23)
spacing
A
max
where A max is the maximum allowed acceleration/deceleration. If the maximum allowed
acceleration or deceleration is a limiting factor, the conveyor design parameters can be
calculated to satisfy this constraint. Given A max , calculate either L 3,max in t cycle or the