Alex,

Dynamic analysis is indeed very important for proper conveyor design especially when the conveyor has a large installed drive power or if it is a long conveyor. The fact that the conveyor belt is flexible means that it stretches when tensions are applied to it by the drive during starting or when the power is cut for stopping the conveyor. These changes in drive tension can cause large changes in belt tensions back down the conveyor and if you do not know the magnitude of these tensions and the response time of the conveyor as a system, your design will not work as you think it will if you have only made the normal "rigid body" or static analysis calculations shown in handbooks such as CEMA and ISO 5048 etc. On large conveyors the worst case is often encountered when the conveyor has an emergency stop such as if a power failure occurs or if a pull wire stop switch is activated. In this case it is often low tensions which cause the biggest problems and these can result in equipmant and or structural failures. If you perform a dynamic analysis you can adjust factors such as the take-up tension, the brake torque and drive inertia or add flywheels in order to control the tensions during starting and stopping and this will ensure that the conveyor will work properly.

Dynamic analysis calculations are complex and not something which can be done by hand calculation, they involve solving differential equations using numerical methods. Also there are many inputs required to model a conveyor accurately, however we do have a conveyor Dynamic analysis software called the Helix delta-T software which is used by many engineering design companies. Please feel free to visit our website at www.helixtech.com.au where you will get a lot more details about the software and its capabilities. ■

Dynamic analysis is the study of:

a) momentary belt tension fluctuations induced by a forcing function (motor, brake, take-up regulator, et al), at fixed locations around the belt, that results in

b) shockwave propagation emanating from the drive (sharp fluctuation in tractive tensions at a drive or brake),

c) where the shockwave moves at the speed of sound in the belt's tension member

d) where we wish to control of the shockwaves to limit undesirable belt tensions, belt sag between idlers, and

e) excessive belt displacement (strain) induced along the conveyor path that may result in significant take-up travel, which impacts belt sag and

f) undesirable forces on pulleys and structures.

Historically, the solution was to solve the "closed form" of the ordinary differential equations as often is published for a series of lumped-mass spring damped models to mimic the belt loop. Because the belt sags between idlers, the apparent elastic modulus is not linear, and the rolling resistance varies with tension, the solution cannot be solved "close form". We must resort to non-linear numerical analysis solver techniques. One such non-linear differential equation solver is the forward predictor algorithm of Runge-Kutta. We use a modified 4th order R-K solver in BELTFLEX. See: http://en.wikipedia.org/wiki/Runge%E...3Kuttamethods.

Many have published some details on the approach. The method goes back to the old analog computer days where the mechanical equivalent can be constructed from a electrical circuit. The method was abandoned in the 1960's. You can obtain an idea from Dr. Alex Harrison's doctoral work. He then used a "closed form" solution, but in later years has seen the light and necessity of the non-linear. ■

I agree entirely with the comments made by Mr Nordell and emphasise that in order to get a proper solution and accurate dynamic analysis results the methods used must:

1. Determine the conveyor friction factors based on the belt tensions at the particular time step in the analysis. The conveyor frictions / resistances change depending on the belt tensions and belt sag in the system at each time step (and at each idler) during starting or stopping and if your algorithm does not take this into account the results will not be accurate. Assumptions based on merely using a "High" or "Low" global friction factor will not give accurate results.

2. It is necessary to use the forward predictor Runge-Kutta algorithms in order to obtain accurate solutions. If the fixed step Runge Kutta methods are used the solution can be found for very flexible belts such as fabric belts, however large conveyors use steel reinforced belts and the high forces required to induce relatively small strains in the belt require a very accurate solution and the adaptive Runge-Kutta methods which estimate the truncation errors and adjust the step size accordingly are essential for a good solution. The Dormand-Prince method is one such method and is utilised in the Helix delta-T software. ■