I think you first must ask: “what is the purpose of any criteria”? How many conditions are you interested in evaluating and how do you approach solving the risk such; what will your tools do to solve the conditions such as?

1. Limiting high belt stress so not to impact belt and splice life

2. Limiting low belt tension to control sag between idlers or limiting belt take-up travel to a reasonable level.

3. Control drive or brake forcing function to limit belt/pulley slip and belt festooing

4. Selection of convex, concave, and horizontal curve radii to control civil excavation, belt rating, idler roll damage, and belt festooning between idlers, and around pulleys

The above do not have any relationship to the aforementioned 3x or 5x wave periodicity criteria. After designing many of the world's longest, highest powered and highest strength belts, the noted criteria has never been invoked. It has no bearing on the above.

First, where in any of the four noted conditions does the wave periodicity have a direct effect? You get greatest response in the first wave front, unless one wave amplifies another due to a specific fundamental frequency, usually from short belts.

Second, show me an accurate prediction of the wave periodicity when there are evident low tension zones. Most dynamic codes cannot even follow low a tension wave front and its after effects such as a take-up hitting the upper or lower stops.

Third, about 20 years ago we made a brief attempt to understand the clamor and I had a discussion with Dr. Funke at Hannover. I demonstated a number of dynamic cases and asked how periodicity would solve the problem. He concurred it would not.

I demonstrated, to a RSA client, about a pending disaster from a notable conveyor engineer's design when applying a fixed take-up design. The purposed take-up would have been launched beyond sight along with many other dangerous side effects. The poor design was illustrated in very graphic terms. The client had the engineer redesign the TUP to a more conventional concept. This was after another RSA client had TWO similar bad experiences on the same conveyor, Chuquicamata $60 million take-up failure and Selby's 4 x overload of it tail pulley. The point is the fundamental periodicity had no meaning.

I can recite more than two dozen such design flaws that break or damage equipment, threaten personnel safety, cause downtime that would not have been solved using periodicity criteria. Look to: Henderson (tail pulley failure), Chuquicamata, Selby, Anglo Coal (Blue, crosses under freeway and is hor. curved -take-up and tail station failures), Anamax (take-up failure), US Steel Cumberland (tail and take-up failures), Mission (Head end bldg collapse), Quintette( both overlands and lawsuit), Spring Creek (bldg imminent failure), Morenci (rock catapulting), Nesher Cement (turnover collapse), Rockdale (turnover collapse) and many, many more. When I use the term failure - its is very graphic.

Stopping is far worse than starting. It’s usually the first impulse that is the strongest and causes the greatest destruction.

Both Dr./Prof Harrison and Dr./Prof Funke use a linear ordinary differential equation (ODE) solution. This method can turn low positive tension into a negative or compression wave, which cannot occur in life. There are many other such dynamic models which use ODE's. The system is very non-linear and must be solved using a numerical analysis integration approach. ■

Adi,

How do you add up the formulation with the following steel cord belts? All have noted theorectical shock wave speeds and on Selby we have published field measurements on wave speeds which agree with theory. We have many other field measurements which are in agreement with theory.

1. Morenci 1.5 km long with wave speed on return = 0.85 seconds or about 2km /second. Total wave cycle = 2.95 sec or 1.1 seconds for carry side. Morenci catapulted rock about the tail station.

2. Selby 12.2 km long with wave speed on return = 5 seconds or about 2 km/second. Had 4 x tail pulley tension increase from drive shutdown impulse, as did Chuquicamata. Chuquicamata's tail pulley steel foundation bolts were elongating and were about to fail due to stopping shock wave impulse. Both were redesigned. Both had fixed takeups during a stop. Selby went to a capstan controlled stop. Chuquicamata beefed up the structure.

3. Genmin (RSA) 6 km long with wave speed on return = 4 seconds or about 1.5 km/second. Had take-up changed from fixed to powered control simulating a gravity. ■

ADI,

Using Morenci as a bench mark we observe the following:

1. 1.5 seconds - 5000 hp (TE) is lost - 2500 ho primary & 2500 hp secondary

2. 4.0 seconds - Sag begins to be excessive at tail in 4 seconds from drive compression shock wave which is 1 mile from head

3. 8.26 seconds - Take-up hits maximum upward travel feeding slack belt into tail region

4. 10.0 seconds - Holdback begins to engage on primary drive

5. 16.5 seconds sag is completely removed from tail station causing 2.5 x multiple of tail tension which travels on return side from tail to take-up at head and carry side to head that will overload holdback

6. 17.6 seconds return side shock wave arrives at tail with 2.5x T.

7. 19.2 seconds carry side shock wave arrives at primary drive holdback increasing its torque by about 3x nominal, with almost no torque carried by secondary drive. This would snap holdback shaft.

To correct these problems we installed a brake after head takeup, increased drive mass by 1.5 x primary and slightly different mass on secondary to obtain good load sharing. client went from 3000 tph with flying rock to 7200 tph design with not difficulty. THen they proceeded to 9000 tph to test system. No probelm.

Moral - what does shock wave timing do to give insight to the many problems? ■

I have come across this post by pure chance and would like to add my very late comments.

1. Dr. Funke's principle does not define starting and/or stopping time of a conveyor. Calculated value of 5 x T ( not 3 x T) defines time and by implication rate of torque change from minimum to maximum value (in the simplest terms).

2. It does not cover for deficient design and is not a substitute for proper design procedures.

3. It is completly of no consequence in cases where one has no control over torque change ie. for example during power cut off as shown by Mr. Nordell in the example.

Regards ■

Dear Marian,

I offer 20 km Channar overland as another comparison using the starting sequence, not stopping:

A. Starting time of conveyor is made of three parts:

1) Pre-starting dwell to build initial strain of ~10 seconds (0.5%/sec) to bring drive system to 5% speed.

2) Strain-equalizing period using 20 sec dwell operating at 5% speed before acceleration cycle. Why 20 seconds?

3) Non-linear polynomial start ramp to bring 10.5km overland to full speed from 5% speed in ~220 seconds.

B. Wave period from head drive to head take-up on return strand (360 degree loop) in about 20 seconds. This does not include at minimum the following 5 points:

1) Rate of rise of torque which is critical and any pre-strain cycle

2) Why we use a pre-strain cycle - allows proper control of PID loop

3) Does not acknowledge final belt speed

4) Drive distribution ( head, head and tail, head, tail; and mid-station, et al

5) Differing response of fixed and gravity TUP

We do know that the 5xT figure would yield 5 x 20 second ~ 100 seconds. So I ask, what does 100 seconds buy you?

Or, use 16 km ZISCO overland with 500 second start, as an example. You can see from field commissioning measurements and our publications of the same, that drive mfgr got big instabilities, with different starting regulation using 500 seconds. Final CDI design had no such problems.

My point top all this is - academics live in academia. They need real world feedback to verify these results and their importance.

I wonder if Alex would indorse his early publication on these points. I think he has a better perspective today. ■

Also, points:

6. Non-linear verses linear acceleration ramp - why linear is not so good, why 2nd order maybe better or worse than linear, why a higher order polynomial is best - something in between linear and 2nd order.

7. Horizontal and vertical curves will need other types of controls

8. Torque regulating latency between drives and the many necessary higher order control algorithms.

9. Why do we bring the conveyor to a low level speed to allow pre-strain?

These are learned details born from experience. We do not see publications on these points because? ■

Thanks for comments.

Starting sequence of a conveyor using Funke principle woul consist of two phases:

1. torque ramp over a period of time ( 100 s for Channar conveyor)

2. Phase of steady torque.

In the first phase one will see, in effect slow breakaway of conveyor sections without true acceleration. Full length of conveyor ( both strands would be in creap like motion by the end of the ramp). Acceleration proper will start from that point onwards. My estimation would be that itn total starting time would be around 230 s in Channar case.

From today's perspective the concept oversimplifies the issues and I am in agreement that on should develop control concepts on case by case basis. However, when the principle was proposed ( more than 30 years ago) it was, at the time, first step in the direction of proper conveyor start up or stopping control.

While it is frequently wrongly applied it is not my intention do defend it. Today, with a range of analitical tools and progress in reasearch we are obviously able to move froward and installations like Channar are good example of this progress.

Once again thank you for the exchange of thoughts.

Marian ■

Marian,

I read again your latest point on the rate of rise of torque from minimum to maximum as the 5 x T value. I do not believe this value will illustrate good design when applied to any overland of reasonable length.

When we analyze conveyors with rigid body techniques, the process requires we assume the acceleration torque is delivered to full throttle in zero seconds. For many years ( early 1980's), this was the process. Funke published his theory in 1974, by memory. Dr. Harrison published his theory on this subject in the early 1980's. We published our understanding of dynamic shock wave tuning at a SME Hawaii convention around 1981, again, by my memory. We further published the defining condition of 2-dimensional wave analysis influence in 1984.

Neither of the other noted parties acknowledged the need for 2-D fundementals. The first dimension is belt axial. The second dimension is vertical or gravity induced (sag). This is a must. It is the rational for the dwell cycle before full blown acceleration.

Anyone with knowledge and experience with axial instability, during starting using a proportional control algorithm (PID), will know the reason for this special control of strain-energy propogation.

Today, all respected dynamicists practice the 2-D elastic wave displacement theory process. They have employed different ways to solve the problem. Unfortunately, some still do not understand why it is needed and therefore advocate a flawed solution.

The point of all this hyperbola is in order to define the peak tension and the application on the rate of rise of torque do not employ the 3xT or 5xT process.

Ideally, we wish to minimize the starting cycle and minimize capital cost. Two concepts at odds with each other. However, there is a common ground. How can we get to maximum acceleration tension without causing a heavy reflected reaction shock wave?

Part of this solution deals with placing the belt in the "acceleration strained mode" as we begin to accelerate in the minimum time, and in the near steady-state running strain mode, as we approach full speed. Everything in between should strive for constant acceptable peak belt acceleration tensions for the duration of the acceleration cycle (ie minimize reflected waves that cause local peaks and valleys over the acceleration time). In this way, we accelerate in the minimum amout of time, while minimizing the peak belt tension. ■

Marian,

Channar can reach peak torque in far less that 100 seconds. I published this point on the BSH book in around 1991. Its total acceleration cycle is 220 seconds including a 30 second dwell.

This can be viewed on the CKIT website:

http://www.c-kit.com/secure/conveyor.../channar20.htm

"The Channar 20 Km Overland

The Flagship of Modern Belt Conveyor Technology"

Although the peak acceleration tension is shown around 130 seconds, this was done with deference for a 2nd order symmetrical polynomial algorithm. to allow variable final speed selection which had to be programmed into an ancient PLC Modicon system circa 1989. We could have easliy moved the peak torque to about 70 seconds, if we did not care about the need for special speed ranges in old form PLC programming.

I do take your point that 1974 and 1980 technology should not govern today's designs. ■

Thanks for your comments.

The way how Channar conveyor is controlled it is correct that max. torque is reached at a different point that in the case of a control using dr. Funke's principle. However if that concept were to be applied and for the argument sake torque ramp were to be of 100 s magnitude max. torque would be reached ( under max. load) at 100 th second.

There is an interesting point here. Channar consists of two conveyors: 10,4 and 10,1 km long. At the first stage proposed torque ramp would be: around 29 sec. This is close to the value of the dwell period which is used in the control. If my understanding is correct in both concepts by that time all sections of belt are moving before conveyor is properly accelerated.

Regards and thanks

Marian ■

At the time of the design, in 1987, we had not optimized the feedback accelration ramp. Close, but not optimum. So, we separated the dwell from the acceleration ramp. In particular, all of the belt was near its ultimate steady-state tension. All low tension zones were eliminated.

We did understand that the 2nd order polynomial was not ideal from a belt tension control, but also knew that its was easy to add time to reduced any ill effects.

Channar was designed with a belt safety factor of 5:1 during full load steady-state. The actual safety factor was closer to 8:1 due to the client's in-house consultant and outside design auditors not accepting the rheology model and the superior low-rolling resistance rubber selected.

All planning with special care for belt tension control was not required. Both of the design auditors made the situation worse by arguing that the conveyor was underpowered and belt strength was insufficient. After installation, Hamersley removed one of the three 700 kW motors from each conveyor due to their error.

Bottom line, design optimization and their economic benefits are still not practiced in most design houses. Design standards has yet to accept the significant differences between best practice and old wives tails. ■