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CONVEYOR SIMULATION

Velocities and belt tensions are simulated or starting, running and stopping in a single computer run. Inclusion

o static and inertial conditions or each mass o a distributed mass-elasticity mechanical model is used to assess

possible design problems. Eects o profle, rolling resistance, drive inertia, take-up riction and dispersive wave

action can be examined in advance o a fnal design.

Conveyor belts are conducive to

analysis using distributed mass-elas-ticity models. Numerous mechanically

equivalent methods have been described

in the literature over many years. In the

work described here, each mass of a

multi-element system is acted on by an

acceleration that includes inertia, forces

from adjacent spring-coupled masses

and body forces due to gravity inclines,

take-ups and rolling resistance. Once the

acceleration of each mass is def ined, ele-

ment velocities and displacements can be

accurately computed. The procedure uses

a modified Euler-simulation techniquecalled Euler-X developed to produce

very rapidly convergent solutions [1], giv-

ing a complete start and stop simulation

within a t ime of between 0.1 s and 1 s.

A computer simulation program simul-

taneously constructs transient forces in

the presence of body forces. Simulation

of the starting, runn ing and stopping

mechanics of a conveyor belt must inher-

ently include both the static (running)

and dynamic components of force, veloc-

ity and d isplacement. Alternatives such

as wave equation solutions require a su-

perposition of static and dynamic forcesas separate computational results. The

simulation method used in this paper

does not require use of any superposition

principles.

For general application, the simula-

tion method has been developed as a

normalized unit-standard. Each mass,

body force and damping component

have appropriate ratios relative to a unit

belt stiffness. In this way, the model is

infinitely scalable. Applications have

included an investigation of the inf luence

of rolling resistance on dynamic stresspropagation, the effect of sticky take-ups

and take-up payout on dynamic surges

in longwall conveyors, and the effect of

drive inert ia on wave amplitudes.

Single-run dynamic simulation

of conveyor belts

By Alex Harrison*, PhD, FIEAust, Conveyor Technologies Ltd., Denver

Figure 1.Simulation o starting, running and stopping in a single simulation. Belt speeds and tensions

are shown or 8 location (Traces : Black =T1, Red = T2, Blue = Tail, Green = Carry side near tail).

Figure 2. Inuence o rolling indentation loss on wave-ront amplitudes on breakaway starting.

Low Losses Medium Losses High Losses

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Typical simulationPredicted velocity and force histories for a 2 km long overland

belt are shown in Figure 1. The belt declines slightly then

rises with an overall li ft of 7 degrees for about half its length,

and conveys 2000 t/h at a speed of 3 m/s. The conveyor uses a

ST-2500 steel cord belt with a belt modulus E = 180,000 kN/m.

A damping-to-sti ffness rat io used for the model is c/k = 0.15 s

except at the tail where this value is increased for sag effects.

Applying this data to an 8 -mass model for the carry and re-

turn side, the auto-computed static tensions are taken directly

from the complete simulation graph of Figure 1 as follows :

T1 (running) = 570 kN; T1 (stopped) = 480 kN; Rolling Loss = 90 kN (Carry).

T2 (running) = 187 kN; T2 (stopped) = 237 kN; Rolling Loss = 40 kN (Return).

T1 accelerate = 650 kN; Start Time = 21.8 s; Stop Time = 6.6 s.

Wave action occurs on starting and stopping. The stopping

time is not an input to the model, since the model computes

the stopping impulse. On starting, the tail of the conveyor near

the load point reverses slightly due to dif ferences between

carry and return rolling losses for the initial belt tensions.

Elastic wave speed is determined from the tail start time-delay,

which is about 0.9 s, giving an average elastic wave-front speed

of 2,220 m/s. On the carry side near the tail, the belt tension

approaches zero on stopping. In this situation, the designwould require an increase in take-up pre-tension. A nominal

tail tension was set at 92 kN for the initial run.

Breakaway and rolling lossesAn important application of the mechanical simulation ap -

proach is an ability to show the influence of rolling resist-

ance on wave amplitude in the velocity domain. Low rolling

resistance belt covers result in a less severe dynamic impact

on breakaway. Several runs of the model for very low and

abnormally high indentation rolling resistance indicates that

the breakaway wave front amplitude increases as indentation

resistance rises, shown in Figure 2 for the example conveyor.

The model allows a breakaway value for idler seals as aseparate input to the static running idler drag which is a func-

tion of normal loading and speed, whereas the visco-elastic

indentation loss is considered to be constant for any given

rubber type, since the wave front speed considerably exceeds

the indentation rate at each idler. Low indentation loss would

be defined by a DIN friction factor of 0.007. A high indenta-

tion loss would equate to a DIN factor exceeding 0.03.

Note from Figure 2 that a belt with high rolling losses

(which includes indentation, belt and material f lexure and

idler seal drag) is more prone to some initial runback on

breakaway at low-tension areas. Here, the initia l velocity wave

amplitude increases in intensity, as does the starting tension.

In effect, the belt is resisting displacement in the presence of

a tension change. An overall low combined rolling resistance

will result is a smoother, less dynamic start of the belt.

Winches with frictionOther dynamic effects can occur in conveyors that have active

tensioning. For example, winches located behind the drive

at T2 often show unpredictable slewing which results from

payout of belt into the system as material load-on occurs. If

the winch carr iage or rope sheaves contain suf ficient friction,

a winch may not pay out or pull i n immediately in response to

belt tension changes at T2. The delay in winch response can

cause drive slip or momentary belt speed changes on take-up

pay-out when friction resists take-up carr iage motion [2].

Underground long-wall belts that are similar to the exam-

ple belt often exhibit erratic take-up position changes. Figure

3 shows a simulation of a winch paying out just a fter the ex-

ample belt has reached full speed. In th is situation, a dynamicincrease in belt speed will be observed unti l tensions are

recovered in the T2 area.

The simulation shows the effect on T1 and T2 tension

for the example in which the tail area winch activates just

after ful l speed. If a winch were located at T2, any slack belt

resulting from take-up pay-out will launch a wave front and

may cause a low tension pulse to be propagated to the tail of

the belt. Such a condition can also occur when winches and

capstan combinations are used to maintain a nominal take-up

mass position between limits, particularly if the limit control

is affected by friction in the mechanical structure. The take-

up motion is not shown on the figure, but is easily displayed

from take-up mass displacement arrays when required.

Drive inertia effectsAnother factor that influences the dynamic forces and mass

displacements, particularly on stopping, is the rotating drive

mass inertia translated to the belt line. To study this effect,

CONVEYOR SIMULATION

Figure 3. Take-up pay-outand adjustment simulation,

activated about 4 seconds

ater the belt reaches ull speed.

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the stopping dynamics of the example belt is shown in Figure

4 for 3 equivalent drive masses. New theories have been

developed to allow modelling of the effects shown by both

Figures 2 and 4, however it is suf ficient here to present typi-

cal simulation findings.

In Figure 4, the drive mass input is a model variable. Forstopping simulation, the model derives a forcing function (the

impulse) which includes the drive mass. Stopping dynamics at 8

locations along the carry and return belt runs are computed from

the model and used to display the different effects of drive inertia.

For the case of a low drive inertia, the initial stopping ve-

locities are rapid and the introduction of third-order vibration

modes is evident. These effects will place greater demand on,

say, a winch take-up to respond or slew on stopping if the winch

is active. For the case of high drive inertia, tensions near the

tail become more positive and a winch take-up would need to

slew less rapidly. Sometimes, a longer stopping time caused by

increased drive inertia may exceed the stop time of out-by belts,

or local safety laws. In each case, the analysis process works toallow design parameters to be established.

ConclusionsDynamic simulation of conveyor belts requires mechanical

analysis of the belt to derive the equations that govern ele-

ment accelerations. Once developed, the model has broad

applications for the simulation of many conditions of real

conveyor operating and control conditions. The unit-standard

model used in this paper is scalable to any input variable

range. The simulations discussed in the paper shed new lighton the way wave fronts propagate in the presence of rolling

resistance. Much of the research into the dynamic behaviour

of belts over many years can be explained using modelling

techniques shown in the paper, such as the effects of drive

inertia on wave severity during stopping.

Stopping dynamics has a substantial impact on winch

slew rate and control design. Modelling dynamic behaviour

of belts is a challenge that required a model that is based on

sound mechanical principals, is guided by field test results

wherever possible, and result s in a mathematically stable

simulation program. The use of simulation to derive control

dynamics and to investigate non-linear and friction related

effects in real systems has been d iscussed and is an ongoing

area of application.

Other references by the author[1] (2008). Non-Linear Belt Transient Analysis. Bulk Solids

Handling. Vol. 23, No.4, pp 240 245 (in press)

[2] (1992), Modern Belt Take-ups and Thei r Dynamic Motion.

Bulk Solids Handling, Vol. 12., No.4, pp 581-584 (1992)

* Alex Harrison. PhD, FIEAust, Formerly Professor in Me-

chanical Engineering Dept., MERZ/TUNRA Chair of Bulk

Handling and Conveying, University of Newcastle, NSW and

currently Manager of Conveyor Technologies Ltd. LLC in the

USA.

CONVEYOR SIMULATION

Figure 4. Efect o drive inertia on dynamic wave action.

M drive = 40000 kg M drive = 80000 M drive = 180000 kg

Contact: aharrison@conveyorscience.com or conveyorscience@aol.com