Dynamic Analysis of Belt Conveyors
Dynamic analysis is the new buzz-word in the design of belt conveyors. What are the uses - and the abuses - of this science of analysing belt conveyors correctly. By removing the mystery surrounding this comparatively new technique, we hope to encourage its use in major belt conveying projects in the future.
WHAT IS DYNAMIC ANALYSIS
For simple conventional belt conveying systems there are many well documented procedures to calculate required powers, tensions and other factors. With the assistance of computers, this rigid body analysis has been successfully streamlined, allowing the designer to concentrate on the problems of chute design, drive house layouts and components of manufacture.
However, with the growing need for larger, longer conveying systems, there is a need to refine the analysis procedures. Generally, when conveying systems are analysed as rigid bodies in a stationary state, the effects of boundary conditions - starting and stopping are ignored.
Dynamic Analysis is a computer simulation of the properties and performance of the system in motion - an analysis of the starting and stopping characteristics of a belt conveyor.
EXPLAINING DYNAMIC ANALYSIS
During steady state running ... Figure 1 shows a simple conveyor system during steady state running, modelled a a series of masses and springs. In a steady state condition, the spring extension before the drive (L1) and after the drive (L2) remain constant. In the steady state condition, the torque due to the effective belt tension on the pulley is matched by the torque produced by the drive.
The tension in the springs between the masses is determined by their stiffness and extension. Since during steady-state running, the distance between the masses (and the spring extension) remains constant, the tension in the springs also remains constant.
FIG. 1: Mass-spring representation of stead state running
After a coasting stop
Figure 2 shows the same system, after the drive has been turned off.
FIG 2.: Mass-spring representation of coasting stop
1. The removal of the drive torque from the pulley leaves the torque unbalanced. This results in a rapid deceleration of the drive pulley from v to (v._v), so that the rim of the pulley moves a shorter distance than to the masses adjacent to it.
2. This results in the shortening of the spring upstream of the pulley (with a resulting decrease in tension) and a lengthening of the spring downstream and an increase in tension.
3. The change in tension on only one side of the masses adjacent to the pulley, subsequently produces a force imbalance on these masses which causes them to decelerate.
4. The deceleration causes changes in the extensions and hence tension on the springs on the other side of the masses. The resulting force imbalance causes the disturbance to propagate further along the conveyor.
The resulting wave of decreased tension propagates down the carry side of the conveyor and a wave of increased tensions propagates down the return side. For simplicity , the variations in tension will be referred to as "compression" and "tension" waves. These labels are not entirely accurate, since it is not possible to get true compression on a conveyor belt, but the terms are widely accepted.
If the magnitude of the "compression" wave is greater than the actual steady-state tension of a region of the conveyor through which the wave passes, highly non-linear behaviour will result. The belt tension in the region will not become negative but extremely low tensions and large belt sag between idlers will occur. Destructive dynamic effects frequently result from this type of occurrence.
Coasting stop with gravity take-up
FIG 3.: Mass-spring representation of coasting stop with gravity take-up
Figure 3 is the same as Figure 2, except that a take-up is located immediately downstream of the drive. The increase in tension downstream of the pulley, instead of inducing a tension wave, produces a force imbalance on the take-up, causing it to accelerate upwards. This upward movement of the take-up, absorbs the "tension" wave. As a result, the return side of the belt is unaffected by the drive stopping until the "compression" wave from the carry side has travelled completely around the conveyor.
The speed with which the initial wave propagates is a function of the system mass and belt axial stiffness. The loaded side of the belt will be heavier and consequently waves on the carry side will propagate more slowly than waves on the return side. Other important factors are the drive inertia and the belt stiffness. The steady state velocity of the belt does not influence the magnitude of the stress wave.
WHEN DO WE USE DYNAMIC ANALYSIS
There are no cut off points to dynamically analysing a conveying system. At present it is usual to analyse large systems with complex profiles. Dynamic analysis tends to be introduced for conveyors in excess of 1000m with capacities about 100tph. This may be the norm, however any conveying system experiencing large take-up movements or adverse shock wave propagation resulting in premature pulley or drive failure, should fall into the spectrum.
It is often possible to identify dynamic problems in a conveyor when large movements of the take-up occur. These movements are related either to elastic stretch in the belt, thus certain sections of the belt moving at different speeds to other sections, or large quantities of belt being dumped between the idlers causing a loss of tension, or a combination of these symptoms.
It has unfortunately become common practice to eliminate the symptom of take-up movement by "fixing it" with a winch. This has the effect of making the design perform as a rigid body, and it must therefore be over designed to cater for the effects of wave propagation. Failure to over design, results in the shock wave destroying pulley or drive components. Since this normally occurs in a progressive way (fatigue), it does not always show itself as a dynamic problem.
BENEFITING FROM DYNAMIC ANALYSIS
The advantages are generally seen in reduced costs and downtime. A dynamic analysis can give the designer the confidence to reduce safety factors, thereby lower the specifications for belting and allowing an increase in idlers spacing, thus reducing power use and component spares holding. It should be noted that conveyors set up with dynamic analysis techniques are operating with a safety factor for the belt of less than five.
FIG 4.: A typical example of theoretical and actual readings. The take-up movement is an ideal test for model accuracy as it can be measured in the field, giving substantial justification for confidence in the modeling
Setting up a basic model, although very time consuming and highly complex, allows the designer greater freedom in designing the system . A full analysis needs upward of 100 runs to satisfy all the possible combinations of events. Today's computers require two hours to complete a single analysis, and a full analysis would therefore take in the region of 200 working hours.
When the basic analysis has been concluded, and problems like shock wave propagation, excessive take-up or negative belt tensions have been identified, it is then possible to test various solutions. What if a brake were installed ? Where is the best position for a brake ? Should we increase system inertia ? All of these questions can be investigated.
Once this exercise has been completed, it is then possible to show the results of the full analysis using computer simulated models which, through a time base, can display the operating parameters allowing for the correct formulation of the control philosophy.
By using the simulation approach right from the design stage, the designer can advance the roll of the conveyor to greater heights and lengths. Eliminating transfer points and pushing the conveyor to higher speeds, knowing that he is not sacrificing safety, will ensure that the final system will provide cost effective bulk transportation for many years to come.