Dear Dave,

I suggest you connect up with Prof. Craig Wheeler at Newcastle University in Australia. He is the most advanced person in Australia on the subject and will be glad to point to a number of his published works that you will find relevant.

You might find some of my publications of interest that you can find in Bulk Solids Handling. See our website for the references.

There is a lot to learn on testing machines (they differ), test methods and machine limits, rubber master curve formulation, and how they relate to E' and E" which are the viscoelasticity tensile and compression properties.

May I suggest you read Jonkers 1980 publication you will find referenced in most of our works as well as Gabriel's and Prof. Hager's publications during his leadership at Hanover.

Jonkers's professor was Spaan who has published a synopsis of his own rolling resistance research work at Delft in Bulk Solids Handling. You will find his work also relevant. I beleive Prof. Spaan was Prof. Lodewijks adviser and instructor.

I also believe Prof. Spaan retired after Gabriel left Delt to work here at CDI for 3 years.

"Fact or Fiction" was, I believe aimed at CDI, to reduce the influence of our claims. The industry needs further collaboration of research and validation by many others for it to become a standard and to drive the mining and manufacturing industries to invest in the benefits.

We claim to want to be good shepards and apply good environmental practices. However, there are those who will resist until many others, such as your future work is published, claiming that the benefits cannot be denied.

I look forward to your success. If you cannot find the details you need send me an email. We will see how to accomodate. ■

Dear Dave,

The answer to your first question on the second posting is yes. "Simple" I don't think so. I assume you know how the frequency is represented in the contact interface of the belt-to-idler and how it is represented in a viscoelastic measurement device.

Conveyor Dynamics, Inc. (CDI) has conducted research on belt conveyor rubber's rolling resistance since 1988. We still are advancing methods of analysis. To date CDI is the only firm that has published measurements between various mfgrs. and their field verifications.

Rubber properties, such as E', E", G' and G" , are measured in the lab, then applied to a set of constitutive equations. These constitutive methods solve contact deformation between conveyor belt and idlers. Rubber's relaxation cycle during contact with idler roll is the only to non-guess method which accurately predicts belt conveyor energy loss and power.

We have published the concepts in various forums. Your question on the relationships is answered by our publications as well as others I have noted. Since you have read Gabriel's discertation, I am trying to understand what is still a mystery? I will scan a copy of Jonkers and send it to you. For this and our assistance, I request you report on your progress. We might be of further help. I also strongly suggest you connect with Prof. Craig Wheeler. at Newcastle.

The task you have set for your self is daunting. Hanover (Germany), Delft(Holland) and Newcastle(Australia) have published a great deal of research on the subject but have yet to close the loop from measurements to predictions which are accurate. These universities are the leaders in this field. A case in point is to solve the contact pressure between idler and belt with various belt constructions, idler shapes and material loadings, while simutaneuosly and accurartely solving for the mineral trampling losses and belt flexure due to sag during movement from roll to roll.

Your question regarding the Maxwell model has no simple answer. We have modeled up to forty rheological elements of the Maxwell model to reasonably and accurately fit some Master Curve laboratory measured data. Note, data shifting is not trivial when you consider the range of the critical properties such as:

1. Strain

2. Frequency

3. Temperature

4. Prestrain corrections and offsets

5. E'; E"

6. G';G"

As a side note, CDI is developing an alternative to the Maxwell procedure.

There is no viscoelastic measurement machine on the planet that can record these properties directly in the range of typical conveyor applications. Some of the most expensive ($ million) machines fall down. We have invested >$0.5 million in machines and test procedures. More $$ have been devoted to the constitutive developement.

You must devise jigs that mimic real life and provide the necessary accurate measurements to allow extension of the results to build the rubber's Master Curve.

The Master Curve is a data set that utilizes the "activation molecular energy" equations of Arrhenius or WLF and/or other procedures to fit subsets of the total domain of a conveyor's rheology properties. This procedure allows computation of conveyor tension and power, based on rolling friction, over a wide range of field applications.

These comments barely scratch the surface of what you will need to know and use.

As I commented about the machine measurements, please make a serious effort to understand the viscoelastic measurement machines. Failure to know their limitations or inaccuracies will lead to frustation on closing the loop. Like in all things somethings are better than others. ■

Answering Point 1:

The range in the WLF domain is many times 1 Log scale.

Consider the properties, in use today, that govern the frequency:

1. belt speed ......................... 0.50 to 12.0 m/s

2. roll diameter ...................... 127 - 213 mm

3. temperature....................... -50 to +70 C

4. belt width ............... .......... 700 mm to 3200 mm

5. belt cover thickness .......... 3 mm to 25 mm

6. idler spacing ...................... 1.0 to 10.0 m

7. bulk loading ....................... 0 to 100%

8. bulk density ....................... 600 to 3000 kg/cm

9. idler trough angle ............. 0 to 60 degrees

10. carcass construction

11. belt tension

12. belt rubber properties

This names the obvious.

Do note that the new issue of CEMA does not address these points, is not based on any known rubber, has a very narrow field of reasonable application which is not defined.

We have a consultant, assisting with our development who is a "who’s who" and received his Ph.D. from one of the trio (WFL).

The 2% strain and 10Hz viscoelastic measurement domain is from my early work. It was the best available fit I could make in 1988 prior to developing our first generation Master Curve. We are now on the fourth generation and still learning.

We have run tests on very expensive machines to 1000 hz. As with all such tests machines, you must study the region where it is inaccurate, know why and what to do about it. As I said this is not trivial and is part of our expertise and significant investment.

So far the work has proven itself in the field and is ongoing.

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All Points -- past, present and future:

I wish you every success. Remember my bargain. We give one another quid quo pro. Sounds good to start - Jonkers for Povolo. ■