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Shell and Tire Stress

Kindly explain the following Hertz Pressure and its significance. Tangential bending stress in live rings Tangential bending stress in kiln shell under live rings. Longitudinal bending stress in the clear span of the kiln shell

Hertz pressure is the contact pressure between the roller and the tire. It is a function of their diameters but mostly the face width of the tire. As the "line of contact" increases i.e. we make the tire and roller wider so the Hertz pressure decreases. High Hertz pressure can lead to surface spalling. High Hertz pressure can be caused by overloading the drum or limited face contact due to non cylindrical rolling surfaces or bad alignment. Suggested Allowable Hertz surface pressure < 58,000 - 62,000 psi = 400 - 428 MPa depending on application ( speed, etc. ) Tire bending stress (tangential bending stress) is calculated by taking the tire as a uniformly loaded and simply supported curved beam. The bending stress is a function of the tire face width, thickness, radius and the reactions at each roller. Suggested limits: Allowable Bending stress < 10,000 psi = 69 MPa ( forging ) Allowable Bending stress < 8,000 psi = 55 MPa ( cast steel ). The tangential bending stress of the shell under the tire is not calculated. It would be a very low number since it is almost continuously supported by the tire for most of the circumference around the lower 270 degrees. In that area the bending stress would only be induced by changes of curvature of the tire which are insignificant with respect to tangential shell stress. In the upper quadrant, where the shell is not in contact with the tire (applies to non fixed tire designs only) the critical shell parameter is deflection rather than stress. This is commonly referred to as shell ovality or shell flexing. As the tire itself continuously changes shape during rotation, its ovality must be calculated and limited. At the design stage the proportions of the tire may then be altered to satisfy maximum allowable ovality as calculated by Nies. Since the shell is not in contact with the tire in the upper quadrant its "ovality" will be approximately double that of the tire. Shell ovality is also not calculated but simply measured. Shell ovality increases as the tire bore and the shell chairs wear out over the years. High ovality is one common cause of premature refractory failures. For kilns up to 5 meters in diameter the shell ovality should not exceed 10% of the shell diameter in meters. E.g. a 5 meter kiln shell would have a maximum allowable ovality around 0.5%. Some would also say that 0.5% is the maximum allowable ovality for kilns larger than 5 meters. (0.5% of 5000mm = 25mm, which is the change in shell diameter during one complete rotation.) Suggested limits: Shell ovality (%) less than (kiln I.D. / 10) (m) with 2 mm gap Example: Kiln I.D. is 3.6 m => shell ovality < 0.36 % Tire ovality (Nies) is then about 0.12 … 0.20 % and should not exceed 0.35 % in any case If no refractories inside, shell ovality may be higher, but after 0.7 … 1.0 % we may see fatigue cracking in shell because of high deformations. Longitudinal shell bending stress usually peaks at the center of the tires and not at mid span as one might think. Between spans there are points where the longitudinal bending stress is typically zero (see attached shell stress diagram, which shows 4 such points between spans). The shell bending stress is calculated by using the shell as a simply supported beam with the cross section of a thin walled cylinder. When the shell has more than two supports it is statically indeterminate and the support reactions are iteratively calculated. Because the maximum stress is usually at the supports the shell plate thickness then also increases as we approach each tire and is maximum thickness directly under the tire. There are cases (somewhat unusual because they present other support related problems)where a long shell with a small diameter may have only two supports, each located at the extreme ends of the shell. In such cases the maximum longitudinal bending stress is at mid span and so we find the thickest shell plate extent in the center of the shell. It is also clear from the diagram that the circumferential welds joining the different plate thickness on each side of the tire are usually the highest stressed points on the shell. For that reason any circumferential cracks developing in or near these seams are potentially catastrophic. See Photo. Suggested allowable limits are: Heavy plate bending stress < 1,450 psi = 10 MPa Heavy plate shear stress < 400 psi = 2.76 MPa Flanking plate bending stress < 2,175 psi = 15 MPa Balance shell ( next to flanking plate ) bending stress < 2,900 psi = 20 MPa Balance shell ( at mid span ) bending stress < 2,175 psi = 15 MPa Shell max. deflection 0.25" = 6 mm Shell max. slope ( from deflection ) 0.004 "/ft = 0.0191 deg. = 0.0333 %

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