There are many theorists on stresses which include pulleys.

The more modern 1930's-1940's classical theories are derived from Timeshenko:

1. Theory of Elasticity

2. Theory of Plates & Shells

3. Strength of Materials Timeshenko & Young

Full classical pulley analysis of 1960's-1990's are:



1. Helmut Lange 1963 Hannover University Ph.D. Thesis

First to formalize the Fourier series expansion for the triaxial state of stress for pulley shells and connected end disks.

2. Schmoltzi 1974 a disciple of Lange - help understand the locking device contact stress field and connection between end disk and shell. He published errors that have not been publicaly acknowledged.

The function and mechanism of conveyor pulley drums

SCHMOLTZI, W, "Designing Drums with transverse Shafts for Belt Conveyors". Thesis for Doctorate in Engineering, Hannover, 1974.

From:www.saimh.co.za/Beltcon/Beltcon3/paper313.html

3. Look to our website (below) for publications on pulley triaxial stress and fatigue analysis including: mean stress and alternating Principle Stresses (radial, axial, and tangential) & Von Mises Stress Limits :

23 Sethi, V. and L. K. Nordell " Modern Pulley Design Techniques and Failure Analysis Methods" AIME-SME Annual Convention, Reno, Nevada February 1993

24 Qiu, X. and V. Sethi "A New Pulley Stress Analysis Method Based on Modified Transfer Matrix" Bulk Solids Handling Trans Tech Publications, Vol. 13, No. 4 1993

4. You will need to incorporate British or American Welding Standards to correctly analysis the limiting fatigue stresses depending on type of weldments, weldment orientation, and metal surface finishes.

CDI has several programs that are used by major manufacturers, and consulting engineering companies, that treat the design of pulleys at several technical levels through Finite Element Analysis.

Our pulley design and stress analysis specifications are followed by many in this field.

There are many publications on the subject beyond the above.

Sitzwohl is not modern. There are many psuedo theorist that treat the subject in a superficial manner. Your use should depend on the risk and ecomomies that are at stake.

Feel free to contact me if you need further assistance.

Lawrence Nordell

Conveyor Dynamics, Inc.

www.conveyor-dynamics.com

nordell@conveyor-dynamics.com ■

Nicolas,

I am responding to your query on the forum, for other with simular interest.

In brief, Terry King's (Bosworth) derivations and conclusions are not ours. I have met and discussed the two methodologies with him many years ago ( about 10 or more) before he published the work you read. We differ in method and accuracy. I connected you to the ckit web site for your insight. His, like Sitzwohl's is not correct. Dr. Qiu's is the closest you will get to a correct solution bases on classical mechanics.

Terry, about 7 years ago, moved from South Africa to the U.K. I lost touch with him shortly there after. Maybe, if he is active on the forum, he will respond.

The shell stress, near the end disk, does under go large radial and hoop strain (not axial) due to the locking mechanism expansion. This magnitude varies with hub and end disk design. I have not analyzed the particular pulley configuration Terry published. His work and others fail to properly analyze the stress/strain field around this end connection. Large discrepancies can be present.

The strain and stress field change from hoop to shear at the transition from disk to shell. Here is the tricky part that Terry could not accurately analyze and why Dr. Qiu published his work on the Modified Transfer Matrix Method. No classical treatment, other than Dr. Qiu's, is close to the correct solution as shown by FEA. The other theorectical treatments cannot preserve the strain behavior, moments, and balance of forces around this connection. They omit treatment because of the complex nature of the differential equation solution. Dr. Qiu used a FEA element procedure to preserve the triaxial state equations.

Terry's photos show the attachment problem, when applying a single sided "J" weld. A full inner and outer weld is not applied between end disk and shell. Many pulleys have failed from this connection procedure. There is no proper analytic solution for this derelick design. Even by FEA, you have to assume a configuration of the weld tip which is not knowable and which is hopeless in 3-dimensions. It meanders around heaven and creates stress raiser beyond compreshension.

The reason more pulleys don't fail from this treatment is due to the large compression force applied by the locking device. If the compression stress does not allow the "mode one" tensile stress to exceed the metals surface energy capacity, the crack will not grow.

It is also the reason why designers opted for the turbine style end disk with large machined fillet transitions, at the shell attachment, and where no weld is allowed.

The shell butt weld between end disk and shell body must be ground flush and not have discontinuity between the machined end disk and rolled shell.

If a end disk to shell weld connection is to be used, it must have a full penetration weld from with the shell/disk and from the external side of the end disk. It then must be ground flush and free of weld surface anomolies.

I hope you keep up the interest in the field. It is not often explored with the advent of FEA tools.

Regards,

Lawrence Nordell

Conveyor Dynamics, Inc.

www.conveyor-dynamics.com ■

You have questioned the influence of wrap angle on shell stress.

Historically, pulley designers have used a stress limit fractional multiplier to correct against a 180 degree wrap angle. This is to correct for arch buckling. The following are examples of this correction:

wrap stress allow.

angle multiplier

20 0.60

30 0.55

40 0.50

50 0.45

60 0.45

70 0.45

80 0.50

90 0.55

....

180 1.00

190 0.95

200 0.90

.....

Good Luck,

Lawrence Nordell

Conveyor Dynamics, Inc. ■