Discussão sobre discos internos em tambores, Resumos de Engenharia Mecânica

Baixe Discussão sobre discos internos em tambores e outras Resumos em PDF para Engenharia Mecânica, somente na Docsity!

End disc and shell thickness

Dear sir pulley shell dia selection and shaft design are very easy and most of the conveyor designers design the same. However shell thickness and end disc thickness design is complex issue.Failure of very high tension pulleys are observed in case of end disc thickness design and its welding at hub is not properly done. Although softwres are available for pulley design including shell and end disc design. Can somebody explain how End Disc and shall thickness are designed.. Is there any hand book available indicating how these are designed. A R SINGH nordell WOW! Why ask questions of such complexity that cannot be answered in this forum? You can go to our website, listed below, to get references on the treatment of analyzing the stress limiting factors in designing pulley assemblies. A number of PhD papers have been published such as:

1. Helmut Lange 1963 - known by many to be the father of the modern triaxial stress analysis approach for hub, end disk and shell wrt turbine end disk shapes
2. Schmoltzi about 1974 on the stress mechanics of the Rf locking device with its

A.Banerjee Rim thickness Dear Mr.Singh, RIM THICKNESS Av. belt pull= (T1+T2)/2 in N Bending Moment= Fn x F/ Where Fn= 2T Sin A/ F= Pulley face in mm t= Rim thk. in mm A= Distorted angle=20 deg. Zb= Bending moment/fb fb= 100N/mm sq. t= Sq. root of (6Zb/F) T= Av. belt pull. in N Regards. A.Banerjee paul attiwell Dear Mr. Singh, Conveyor pulley shells have traditionally been designed using simple formulae, similar to as has been supplied to you in a previous reply. However, with the latest high-speed computers, the use of computational intensive formulae can easily and quickly be incorporated in a typical pulley design. As a world leader in the design and manufacture of conveyor pulleys Prok uses a technique where a force and moment equilibrium is analysed by considering the stress distribution over an infinitely small element of the pulley shell. Axial, radial and tangential external belt loads, shearing moments, bending moments, normal stress and shearing stress are considered in this equilibrium analysis. Biaxial stress and strain equations are applied to the small element to determine the deformation resulting from the stress levels induced. Calculus is used to replicate the solution for this infinitely small element over the entire conveyor pulley shell. Boundary conditions due to the restraint of the end discs are applied to this solution. The linear differential equations resulting from the aforementioned can be solved using Fourier series and matrix techniques. A minimum application requires the formulation of a 15 term Fourier series representing the axial, radial and tangential loads due to the belt, the generation and solution of the 30 3 x matrices describing the geometry of the pulley shell, and back substitution into equilibrium equations are used to determine the stress level at any particular point. This process must be repeated several times following the adjustment of the shell thickness before final arriving at the final solution. Using modern computing power this can all be achieved within a fraction of a second. The technique used, and described above, has been verified by us against modern finite element analysis techniques using Von Mises stress criterion. Paul Attiwell

Group Engineering Manager Sandvik Materials Handling arsingh pulley design dear Paul Attiwell Thankyou verymuch for information A R SINGH nordell Dear Mr. Singh, You can find the derivation in various publications of Timoshenko and others for treatment as noted by Mr. Banerjee. I have not validated his expression. This method is not used today because of the many simplifications and omissions such as: no influences of locking pressure, hub strain, end disk to shell connection elasticity and shear sensitivity. No treatment of weldments. No metal triaxial fatigue criteria. References on Timoshenko are:

Simplified Methods: do not define principal and combined (radial, tangential, bending and shear) stress components without fatigue and proper yield (von Mises) stresses

1. "Theory of Plates and Shells" Timoshenko & Woinowsky-Krieger Sect 63 pgs 288-289 1959 Original work 1929-1930 and citations back to 1911. Shell theory, Chapter 16, is also given but is very difficult reading. This work is expanded by H. Lange below.
2. "Formulas for Stress & Strain" Roark pgs 189-210 Second Edition 1943 with tables for ratio of inner to outer diameter and clamped or free outer edge -- this is based on Timoshenko and is the citation by Mr. Banerjee.

Comprehensive Triaxial Stress & Fatigue Methods

3. "Investigations of Stresses in Belt Conveyor Pulleys" doctoral thesis by Helmut Lange 1963 based on Timoshenko Plates & Shells with the formulations noted by Paul Atttiwell
4. "The Design of Conveyor Belt Pulleys with Continuous Shafts" Doctoral Thesis by W. Schmoltzi 1974 -- expanded but erroneous treatment of locking

Methods" by V. Sethi and L Nordell. The big problem with all classical mechanics methods based on Lange, except Dr. Qiu and modern FEA codes, is that there is no solution for transmission and compatability of the strain and bending moment around the corner of the end disk to shell. This produced errors beyond 7%. The locking mechanism was not properly analyzed. This was due to the lack of sufficient computer capacity at the time. arsingh pulley design Dear Mr Nordell Thank you very much for your reply. Such a lengthy explanation shows your patience. I fully agree with your .earlier comment, this topic can not be discussed in forum. A R SINGH TMN Re: pulley design Quote: Originally posted by arsingh Dear Mr Nordell Thank you very much for your reply. Such a lengthy explanation shows your patience. I fully agree with your .earlier comment, this topic can not be discussed in forum. A R SINGH I also want to thank you for such an interesting reading. Best Regards, Mike Axel Witt Dear Sirs, with all my respect to the authors above, esp. Mr. Larry Nordell, I would like to draw your attention to the following: Calculating the occuring stresses in a pulley shell and the end discs, that are caused by the bending, the torque, the locking device, etc. is only 50% of the work. The other 50% are calculation the allowable stresses, esp. in the welds 1.hub to disc (if there are any;hopefully not) and 2. disc to shell. The allowable stresses are depending upon the static and the dynamic portion of the stress. Further the type of weld (notch factor), its quality, and last but not least the type and quality of the material have to be considered. The old German

DIN 15018 gives some of the basic facts and also a method how to calculate the allowable stresses in welds. In our computer programme we have combined the calculation of the stresses that are occuring and the calculation of the allowable stress, so that we are able to find the most reliable and economical design for a pulley. I think that this very important esp. for pulleys in the normal range with diameters upto 1000mm for belts with 1400mm width and pulley loads of approx. 500 kN. Above those values you will mostly end with the only possible and reliable solution: the T-shaped end disc. Further a lot of theoretical and practical experience is necessary to get the optimized pulley, even for the smallest and, of course in case of the very high loaded pulleys (Los Pelambres, Rheinbraun etc.). If anyone requires more detailed information, please contact me. GLÜCKAUF from Germany! nordell Dear Mr. Witt, I am not sure why you addressed me in particular since I agree with your thoughts and stated so in my thread second reply, points 5 and 5 regarding the treatment of weldment stress endurance limits and other factors which need consideration. CDI does have computer codes that provide the triaxial stresses in shaft, locking device, hub, end disk of many forms, and shell. The triaxial stresses are evaluated for Von Mises yield limiting criteria as well as Goodman (Schmitz) mean and alternating stress fatigue criteria for native metal and welded zones. The code does allow for optimization of the end disk, hub and locking deive optimization. In welded zones ,we apply the British and American weld standards for the various weld types (stress flow) and the altered weld limits by type (fillet; butt weld) and surface treatment (machined and non-machined to differing surface classes). I commend you on your vigor for also developing such code. Hopefully, it is also well verified when applying it to such pulleys are Los Pelambres. HAve you published your findings? CDI did also make the audit of Los Pelambres pulley designs in association with Krupp. THe thread starter was asking about a formulae for the calculations of the above. THis is too difficult to provide herein.  A.Banerjee Pulley design

guddu 1 Attachment(s) Quote: Originally Posted by nordell WOW! Why ask questions of such complexity that cannot be answered in this forum? You can go to our website, listed below, to get references on the treatment of analyzing the stress limiting factors in designing pulley assemblies. A number of PhD papers have been published such as:

_1. Helmut Lange 1963 - known by many to be the father of the modern triaxial stress analysis approach for hub, end disk and shell wrt turbine end disk shapes

2. Schmoltzi about 1974 on the stress mechanics of the Rf locking device with its methods and its advantages
3. Qiu, et al on the "Modified Transfer Matrix Method" in defining a classical approach to the stress/strain field transfer between end disk and shell connection published by Bulk Solids Handling for Conveyor Dynamics, Inc. as noted on our website. THis is not a PhD paper. However, it shows that a classical approach can come very close to FEM and is much easier to use. CDI has supplied this code PSTRESS V3.0 to a number of well respected North American pulley manufacturers.
4. Dr. Dietrich (from the old PWH firm) PhD on stub shaft designs
5. Many others - South Africa, England, Australia, Germany Go do your appropriate literature search!_ Dear sirs I have come across the intested topic in context of belt conveyor and is a challangeble issue. plea to respond me. Attached is the clarification  14th September 2010, 6: designer And what has this latest post got to do with the design of pulleys???  3rd August 2012, 22: edufonse could you please explain where i can find way to d

Could you please tell me where i can get way to determinate a and b values named disc constant Quote: Originally Posted by A Banerjee Dear Mr. Singh, Disc thickness can be found out by Roark's formulae for stress & as given: dr= pxb(L-X )x X / 40000xDx txtx I(1/at+X/20000xI) Where dr= radial stress in N/mm Sq. p= total resultant belt pull on pulley in N D=disc dia. in mm a= disc constant b=disc constant L=bearing centre in mm X =disc centre in mm t= disc thickness in mm I=moment of inertia of shaft in cm to the power 4 We have develop one programe for it. Mr. Singh it is very difficult for me to type the relation properly & to furnish table also.I think Mr. Nordell is very correct in this regard.Have a nice day Regards. A.Banerjee  4th August 2012, 15: Author Address correction requested Dear designer, Our emails to you come back. Please go to your registration page and make necessary corrections. Please also notify me about any address change, wohlbier@bulk-online.com. For all Forum Members: Please check if your registration form is up-to-date. We have deleted hundreds of names during the past weeks, because emails came back. We are bound to delete also still existing persons if the information in the registration page is not correct. I thank you all sincerely for your cooperation.

the circumferential direction d) fb= 100N/mm sq. : The maximum allowed stress. (MHEA suggest 93 N/mm^2) e) stress = Mc / I, with c = t/2 , fb = BM * 6 / (F t^2) f) solving for t: t = sqrt( BM * 6 / (fb * F) ) = sqrt ( 6 * Zb / F ) where Zb = BM/ fb which is in agreement with your equation above. The 2 things that I am unclear on if the above math is correct:

1. The maximum bending moment is calculated in the longitudinal direction but used to calculate the bending stresses in the circumferential direction.
2. The maximum bending moment, as calculated above, only occurs at the center of the beam, but is assumed to be at this same level across the entire face width when calculating the bending stresses. Curious if there is more to this old equation than what I have shown above? Best regards, Andrew  20th October 2015, 8: johngateley Tim O'Shenko Lives On. Hi Andrew, The old equation mentioned in the MHEA Blue Book. MHEA publications bear a strong resemblance to CEMA and were long considered as a conveniently metricated and simplified version. Perhaps more light could be gained from examining early CEMA. In the earlier MHEA Grey Book, which I mislaid, there was a shorter equation which was considered safe to use in those days. When improved performance was demanded at eg Selby coalfield, the early work was found wanting. I was instructed to replace 147 pulleys due to cracking issues. The new pulleys also cracked up and were eventually replaced by equipment designed using pioneering FEA techniques. The first and second vendors had probably decided that FEA was a NASA thing and anyway they had been paid, up to retention, by a very generous Owner. MHEA published their 1986 revision just after the 1984 experience described.  20th October 2015, 14: ahustrulid Quote:

Originally Posted by johngateley Hi Andrew, The old equation mentioned in the MHEA Blue Book. MHEA publications bear a strong resemblance to CEMA and were long considered as a conveniently metricated and simplified version. Perhaps more light could be gained from examining early CEMA. In the earlier MHEA Grey Book, which I mislaid, there was a shorter equation which was considered safe to use in those days. When improved performance was demanded at eg Selby coalfield, the early work was found wanting. I was instructed to replace 147 pulleys due to cracking issues. The new pulleys also cracked up and were eventually replaced by equipment designed using pioneering FEA techniques. The first and second vendors had probably decided that FEA was a NASA thing and anyway they had been paid, up to retention, by a very generous Owner. MHEA published their 1986 revision just after the 1984 experience described. Hi John, Appreciate your insight. I don't have a copy of the earlier MHEA book. Is this the one published in 1977 or ???. If you do find your copy I'd be interested in the section on pulleys. I've looked at the early CEMA books. They don't address the shell thickness in any way. This was left up to the manufacturers. Best regards, Andrew  30th October 2015, 23: johngateley Oops! Hi Andrew, I'm quite thoroughly gobsmacked that MHEA had deviated from CEMA and done something off their own bat regarding shell thickness. I never paid much attention because once the metric version is there the old avoirdupois version never gets a second glance. I had just taken CEMA's original work to have covered the issue. Your 1977 copy is the earlier 'Grey Book'. The "Blue Book" came out in 1986.  2nd November 2015, 7: Roland Heilmann mechanical point of view