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Load sharing between a primary and secondary or even a tertiary driven pulley system must solve for the equilibrium and compatability constraints.

Equalibrium:

Balance of power between drives must sum to the necessary power to move the conveyor at steady-state and with the motor electrical torque vs speed slip curve

Compatability:

Stretch or strain, of belt over each driven pulleyand belt stretch between pulleys, must yield the proper speed loss (reduction in belt length) and power reduction of the reference driven pulley.

The equations have been published in the 1970's, I believe by a Chech author studying fluid coupling drived. Dr. Alex Harrison also published a version in Trans Tech. I cant recall the Volume and year. If this is of special interest, request it and I will see if I can retrive it.

CDI developed our own pulley load sharing version, also in the 1970's, to demonstrate load sharing between fabric and steel cord belts of varying power distributions from 2.4:1 to 1:1, uphill and downhill, for the La Caridad copper mine in Mexico. Inverter drives accelerated each of 20 conveyors to speed and then transfered each conveyor to the grid line. This then allowed the next conveyor to be accelerated by the same inverter block. I published the concept and termed it"multiplexing" at the annual SME meeting in Atlanta Georgia in 1977. THe plant configuration of inverter started conveyors is: 2 driven pulleys each with 2x600 hp uphill (steel cord), 2 driven pulleys with 2x 600 & 1 x 600 hp downhill (steel cord), two driven pulleys @ 1x600 hp uphill (fabric), two driven pulleys with 1x600hp & 1x250 hp uphill (fabric), 150 hp single pulleys... The inverters are still running to my knowledge. All drives load share within 5%. However, I designed the drives to be balanced by introducing motor primary voltage tuning using a trim transformer, as the equations predicted.

High strength andhigh modulus belts may not need this tuning. La Caridad required it because the inverters were not dedicated and the low modulus belts ( more so with fabric).

The equations are two lengthy to publish and explain but are not difficult to derive. Motor electric slip and belt stretch must be simutaneously solved with total power demand. I model can be complicated when you include pulley lagging belt creep and belt cover deformation.

Lawrence Nordell

Conveyor Dynamics, Inc.

www.conveyor-dynamics.com ■

Continuing with the above description to answer the questions:

1. In dual drives there is always the problem of unequal load sharing between primary and secondary drives when motor ratings of primary and secondary are same.

Answer: There is a problem with the loss of belt length across the drive pulley due to loss of tension - ie low modulus belt. This causes the belt exiting the pulley to run slower than its entry speed to the same drive pulley. Then the belt will enter the secondary drive slower. The slower speed will cause the secondary drive to climb the motor speed curve and require more relative power. With a higher primary drive power, there will be more differential speed between primary and secondary drive and more difficulty in load sharing unless the design can accomodate the speed difference without the power difference such as with dedicated inverters. High modulus (stiff belts) have less sensitivity to load sharing. All such designs can be made to work.

2. What should be the ratio of motor ratings for primary and secondary drives of belt conveyors for dual drives?

Answer: Based on the description above - 1:1 primary: secondary power ratio is better than 2:1 or 3:1 due to the smaller difference in the primary to secondary drive pulley belt entry velocity. In the old days, designers made the secondary drive pulley larger in diameter than the primary. They then introduced electrical slip or fluid coupling slip so that, at full power of both pulleys, the powers matched as did the entry speed of the belt to each pulley. At low power, the drives do not match. The primary might become regenerative. Thus you comment about belt wrap angle and potential for drive pulley slip.

3. Can we have same motor rating?

Answer: Yes it is preferred. When I designed La Caridad, I made certain the rotor laminates came from the same metal fabrication lot. Differences in motor rotor material can cause some problems in matching the theory to the actual installations performance. The cited accuracy of slip and power between drives of the same size and design is about 7-10% variance. This is not good if both go out in opposite directions leaving a difference of up to 14%.

4 What is the role of wrap angle in determining motor ratings and how equal load sharing is achieved?

Answer: The wrap angle must be sufficient to transmit the required drop in belt tension across the drive without slip to the equation t1/t2 > ratio > (nat. log e raised to the friction coef. times the wrap in radians) of incoming(t1) to exiting tension (t2).

Load sharing is achieved in many ways depending on the nature of the specific design. Squirrel cage and the rotor designs, squirrel cage with inverters, wound rotor and the many types of resistor designs, fluid coupling and their many designs, DC drives, and others can and should be treated in different ways. Some have been noted herein.

Lawrence Nordell

Conveyor Dynamics, Inc.

www.conveyor-dynamics.com ■

Regarding dual drive power sharing, I would like to inform as below.

There is general misconception that wrap angle plays some role in power sharing between dual drive. Please note that belt slip on drive pulley is not permitted in any circumstances. If there is such slip, the belt and pulley will wear out in no time. Therefore, conveyor is designed such that belt tension T1 at entry and belt tension T2 at exit of each drive pulley is such that (T1/ T2) is less than or equel to e index (friction coefficient x wrap angle). If wrap angle is less at one pulley, its T2 will be relatively more but no slip is to occur. Therefore, for conveyor to be workable / operational, there is no slip between belt and drive pulley. Thus wrap angle can not affect power sharing in workable conveyor. It does affect relative value of belt tensions.

Widely used power division between dual drive are A) equal B) Two-third for primary and one-third for secondary. The equal division is beneficial for procurement, spares, and easy to match torque-speed characteristics. The power division as per (B) will result into least belt tension and consequent economy (but often it is marginal or not there due to minimum tension requirement)

Theoretically, one can select any kW rating for primary and secondary drive and still can have appropriate (in proportion to their rating) power sharing if following points are taken care.

1) Both the drives are operating as mechanically coupled drive. However, belt speed at secondary drive pulley will be slightly less (say app 0.25 % for EP belt). So if pulley diameter at secondary drive is less by that percentage, the rpm of both drive will be same (if first pulley is 630 mm, the other pulley will be 628.5 mm) If pulley sizes are not different as above, then if first motor rpm, is 1480 than other motor rpm will be say 1476.3

2) The power shared by each motor will be its kW output at above speed.

3) If there is fluid coupling with different value of slip, the effect is to be accounted

4) The power sharing is in accordance with each drive kW-rpm graph

5) Motor operational speed will depend upon mtph. So if load is very small the operation point may be say around 1490 rpm and so on, and then load sharing will be according to graph value at that point. Thus kW-rpm graph zone from full load rpm to synchronous is applicable for load sharing during steady speed operation. All the numerical figures indicated here are for explaining / under standing, and same do not make rule.

Regards,

I G Mulani,

Author of Book : Engineering Science and Application Design for Belt Conveyors.

Email : parimul@pn2.vsnl.net.in ■