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The operator in Figure 1 operates a conveyor belt that holds granule material ready to be despatched.
Figure 1 – Manually controlled conveyor
The concepts of operation can be described in 3 steps:
- Start the conveyor to reach preferred speed
- Release granule material from hopper when conveyor reaches speed
- Stop granule material from hopper when material reaches end of conveyor (full conveyor)
The state of the conveyor will finish as shown in Figure 2.
Figure 2 – Conveyor loaded with granule material stopped
$F=\frac{2Tl}{D}$ $u=w1\frac{D}{2}$
Note that in Figure 2, the parameters are:
- D = diameter of conveyor roller
- u = linear velocity of conveyor in m/s
- ${\omega}_{l}$ = rotational speed of conveyor roller in rad/s
- ${\tau}_{l}$ = rotational torque delivered by the motor through the gearbox in Nm
- F = force delivered by the motor through the gearbox pushing the conveyor forward
The motor is a DC voltage control motor with the following characteristics:
- Stalled torque at 24V input voltage = 3.4286 Nm
- No load RPM at 24V input voltage = 515.66 RPM
The voltage control box is operated by a handle.
Figure 3 – Voltage control box and control handle
The right hand side diagram in Figure 3 illustrates the operator’s handle pulling the handle to change the angle $\alpha $. The left hand side diagram in Figure 3 illustrates the potentiometer circuit that can be used to produce the variable output voltage v:
$v={K}_{p}\alpha $
where:
K_{p} = Voltage regulator constant
The user specified the following performance parameters:
- The length of granule dump on the conveyor L = 1 m.
- Operating cycle time should be as fast as possible but the conveyor must move smoothly, i.e. no vibration.
Assuming a smooth conveyor (frictionless), which set of system design would you recommend.
Formulae applicable to this question:
Motor characteristics is given by:
${K}_{m}{\tau}_{m}+{K}_{o}{\omega}_{m}=v$
where:
- K_{m} = free running constant
- K_{o} = stall constant
The speedometer indicates speed in a scale of 0 to 100 by the following characteristics:
$s={K}_{s}u$
where:
- K_{s} = speedometer constant
- u = linear velocity of conveyor in m/s
- s = speedometer reading (integers between 0 to 100)
Equation of motion for the conveyor before material dumping is started:
${M}_{c}\frac{du}{dt}=F$
where:
- M_{c} = mass of empty conveyor
- u = linear velocity of conveyor in m/s
- F = force delivered by the motor through the gearbox pushing the conveyor forward
Equation of motion for the conveyor after granule material dumping has started:
$({M}_{c}+mt)\frac{du}{dt}=F$
where:
M_{c} = mass of empty conveyor
m = rate of granule material dumping on the conveyor (kg/s)
t = time in seconds since dumping starts
u = linear velocity of conveyor in m/s
F = force delivered by the motor through the gearbox pushing the conveyor forward