First, let us look at the mill itself. Fig. 1 shows that there are four basic components – The shell, the heads, the ring gear and the trunnions. The heads are usually bolted to the shell. The trunnions are secured to the heads by bolts or made integrally with the head. The ring gear is usually bolted to one head section.
The forces acting on the mill are both static and dynamic. Static forces consist primarily of the weights of the various mill components and the material being ground. Dynamic forces include ring gear teeth forces and grinding process forces. When the mill is in operation, the material to be ground and the grinding elements are lifted by lifters on the mill lining and by frictional forces until they fall back, of their own weight. The centre of gravity of the material in the mill is thus displaced laterally. This is indicated in Fig. 1 which also shows forces applied by the ring gear and the bearings. The combined forces applied by the bearings are considerable and can give rise to dangerous stresses and deformations in the mill itself.
Since the bearing forces act on the trunnion at a certain distance from the head, a bending moment is produced which gives rise, principally, to radial stresses in the head. The magnitude of these stresses is somewhat dependent on the magnitude of the bearing forces, but depends primarily on the distance along the trunnion at which these forces act. If this point of action can be moved towards the head, the bending moment is reduced, thus providing a considerable reduction in stress. Fig. 2 shows one example of the way in which radial stresses can be distributed over the outside surface of the head in a vertical plane. It can be seen that the stress is zero at a certain distance from the axis of rotation. If the trunnion is bolted to the head, the bolts should be sited where the radial stress is small.
The moment load applied by the trunnion causes elastic deformation of the head. A typical example of how this deformation occurs is shown in Fig. 3. Here, it can be seen that the head is no longer flat at the periphery but bulges axially; this has a considerable effect on the strength of the shell. The shell bolts force it to follow the movements caused by deformation. This deformation is concentrated in the vicinity of the attachment points and diminishes rapidly as one approaches the middle section of the shell, where pure bending stresses are completely dominant.
Morgardshammar AB has developed a computer program that can be used to calculate stresses and deformation in a mill of random size. The theory on which the program is based appears in references. Using this program, calculations have been made to investigate how stress is influenced by varying the distance of the point of action of the bearing forces from the end face of the shell (this is referred to as the moment are in the following). The result, which is shown in Fig. 4, indicates clearly that the magnitude and distribution of stress is influenced significantly by the length of the moment arm.
This fact can be exploited to make the head slimmer and to dispense with ribs, so that a further reduction in the moment arm is possible. The shell is not subjected to any greater stress if the trunnion is short. However, there is a marked increase in stress towards the end face of the shell for the longest trunnion with a moment arm of 1115 mm. What is particularly dangerous in this case is that the greatest stress lies at the points of attachment and that it has different directions in the upper and lower parts with an attendant risk of fatigue.
Since the head is usually much stiffer than the shell, the end face of the shell will follow the deformation of the head. The magnitude of this deformation will not be influenced by small variations in shell stiffness. An increase of the shell thickness at the end face will rather give rise to higher stresses, as the deformation remains unchanged.
Plain Bearings & Rolling Bearings
The use of a long trunnion cannot be avoided if hydrodynamic plain bearings are to be used, since such mill bearings are usually designed with a width/diameter ratio of approximately 0.4. This is because the oil film thickness is heavily influenced by this ratio. If the bearings are too narrow, the side leakage flow will be high and the film thickness small. This can be seen in Fig. 5, where relative bearing load is shown as a function of the relative trunnion displacement for different width/diameter ratios. It can be seen that for a given relative load the relative trunnion displacement decreases as the width/diameter ratio increases.
Fig. 6 presents the two different trunnion bearing arrangements on which the calculation example given earlier was based. The plain bearing to the left is of conventional design. The trunnion diameter is 1180 mm, the width/diameter ratio is 0.40 and the moment arm is 1115 mm. A spherical roller bearing, 239/1180 CAK/W33, on a tapered seating is shown at right. The trunnion diameter is the same. To better exploit the narrowness of the spherical roller bearing, the bearing housing is offset relative to its base plate. This reduces the moment arm to 800 mm. This design is now used by Morgardshammar AB and a number of mills that incorporate this design have been supplied in recent years. The illustration also shows that the right-hand head is thinner as a result of the lower moment load applied by the roller bearing. It is assumed here that the two heads have the same maximum stress. The maximum thicknesses of the heads are 150 mm and 230 mm respectively.
There is another point in favor of short trunnions, namely simplified feed. Fig. 7 compares a mill having roller bearings and short trunnions with a mill having plain bearings and long trunnions. With the roller bearing design, the feed chute extends throughout practically the entire trunnion. The trunnion lining can thus be very simple, and is not subjected to heavy wear. However, the plain bearing design requires a special lining for the trunnion, since the length of the chute is limited to prevent it from becoming blocked. Here, the lining is subjected to heavy . wear and must be replaced at regular intervals.
The design is described in detail in reference and shoe bearings are presently operating fully satisfactorily on three Morgardshammar mills. Fig. 15 shows the first bearing arrangement. The advantage of the hydrostatic shoe bearing arrangement, apart from its narrowness, is that there are no limits with regard to runner diameter or load and that the requirements with regard to runner or girth ring accuracy are reasonable. The shoes adapt themselves completely to the ring and are insensitive to misalignment. For large sizes, this bearing arrangement is economically very favorable. For smaller sizes, the fixed costs for the pump system etc. are more dominant, but down to 1800 mm this arrangement is competitive with hydrodynamic plain bearings and roller bearings.