Starting and stopping: the belt as a spring

Everything in lesson 1 was steady state, and a conveyor is most at risk when it is not in steady state. A belt is not a rigid coupling between drive and load. It is a long elastic member, and on a conveyor several hundred metres long an elastic wave travels along it at a finite speed, typically 1 000 to 2 000 m/s in a fabric belt. When the head drive applies torque, the tail of the belt does not know about it for a noticeable time: the material at the far end is still at rest while the head is already moving, and the difference is taken up as belt stretch. This lesson is course section 5.1.4.

Two consequences

A tension wave. An abrupt start sends a tension wave down the belt. It reflects off the tail pulley and comes back, adding to the applied tension. The transient peak can be well above the steady running tension, and it is this peak, not the running value, that sets splice life. Splices are the weakest part of any belt, and repeated transient overload is the usual reason they fail.

A huge inertia. Beyond the motor, gearbox and pulleys, the drive must accelerate the whole mass of belt and material on both strands. On a loaded overland conveyor this travelling mass outweighs the rotating inertia by an order of magnitude, so acceleration times of tens of seconds are normal, and a direct-on-line start is out of the question.

A ramp longer than the belt

Controlled starting therefore uses a ramp long enough for the belt to behave almost statically: an acceleration time several times the belt's natural travelling-wave period $T_n$ (about $4L/c$ for a belt of length $L$ and wave speed $c$).

• The classic solution was the fluid coupling, which passes torque through a fluid and fills gradually: an inherently soft start with no electrical control at all. It is still common on older installations because it is robust and needs no electronics.
• The wound-rotor motor with rotor-resistance starting was the traditional controlled alternative: high starting torque at reduced current.
• Both have largely given way to the VFD, which delivers any programmed acceleration profile, and in particular a jerk-limited S-curve, which limits the rate of change of acceleration and so suppresses the tension wave at its source instead of only spreading it out in time.

The widget models the Tutorial 5.1 belt (56 t moving on both strands, 9.9 kN running resistance, 2.5 m/s) as a chain of masses and springs whose first mode has period $T_n$, and plots the belt force at the drive pulley during the start.

Ramp time t_a

8.0 s

Belt natural period T_n

2.0 s

About 4 L / c: a 400 m fabric belt with a 1 000 m/s wave is near 2 s; an overland belt can reach 10 s.

• Linear ramp
• S-curve

t_a / T_n

4.0

Peak, linear ramp

4.43 ×

Peak, S-curve

4.11 ×

The ramp outlasts the belt: the S-curve gives the lower peak.

The design rule (fig. 5.3b): peak force against ramp time, for this belt. The cursor marks your ramp.

T_n ≈ 4 L / c ; S-curve: a_peak = 1.5 v / t_a

Predict first

With T_n = 2 s, shorten the ramp from 8 s to 3 s (t_a / T_n = 1.5). Which profile now gives the lower peak force?

The S-curve, as alwaysThe linear rampThey are the same

Stopping

Stopping raises a different problem on an incline. A loaded incline that loses power runs backwards under gravity, so a backstop (a mechanical one-way clutch on the drive shaft) is fitted as a fail-safe device independent of the control system.

A loaded decline is the opposite: an overhauling load. The drive must brake all the time to hold the belt at speed, which makes it a regenerative machine for its whole running life. It needs either a braking resistor rated for continuous duty or, more economically, an active front end returning the energy to the supply, the same choice as the crane hoist in Chapter 4 but with a 100 % duty cycle.

FoundationStart here if this is new to you

Stretch a long spring along a table with a book tied to its far end, and pull the near end sharply: the spring stretches, the book stays put, then it jumps and the spring bounces. Pull slowly and steadily and the book simply follows. A long belt is that spring, and the drive must pull slowly compared with how long the stretch takes to travel to the far end and back.

ExplorerGo deeper: derivations and open questions

An overland belt. A 1.5 km belt has a wave speed of 1 500 m/s. Estimate $T_n$, then the shortest ramp for which an S-curve is worth having. Check your estimate with the widget.

Loaded restart. After an emergency stop the belt is fully loaded. Using lesson 1, why is its breakaway torque higher than its running torque, and what does that mean for the drive's current limit?