Table of Contents

Hydrostatic trunnion bearings were recently provided on large Semi-Autogenous Grinding (SAG) mills driven by wraparound motors assembled on the head to shell flanges. A conventional SAG mill would have a ring gear driven through one or two pinions. The effects of the magnetic air gap forces from this new SAG mill drive arrangement on the performance of the bearing are discussed. A step-by-step systematic analytical design of the hydrostatic trunnion bearing is presented, followed by a discussion of grinding mill erection requirements to conform with the design. A brief comparison with other bearing types and their response to the effects of magnetic air gap forces are also presented.

The surface of the trunnion deforms under these pressures. Between these members, there is the fluid film lubricant that transfers the load through its pressure. In hydrodynamic bearings, the pressure is created by the viscous forces induced by the rotating journal. In hydrostatic bearings, the pressure is provided by an external lubricant pumping system. In either case, the fluid film thickness distribution between the bearing members plays a critical role in the performance of the bearing.

**Trunnion deformation**

The trunnion deformation pattern is obtained through a structural analysis of the entire SAG mill under its worst possible operating conditions. For the hydrostatic bearing application, the worst case is in the absence of any hydrodynamic action in the bearing when the mill is not rotating, and when the unbalance forces from the wraparound motor are acting vertically downwards. A radial displacement pattern over a very fine mesh at the trunnion area is required for the bearing fluid film analysis.

Since the structural analysis is performed on a stationary mill with a level charge, the axisymmetric type of analysis with non-axisymmetric loadings will provide more accurate results. Industry at large generally accepts the Finite Element Methods. Many FE programs are commercially available and are developed with libraries of elements formulated to solve almost any structural problem in as many cases and options as possible. Yet, the structural analysis for the illustrative example is performed through the author’s developed “NIMAN” program running on PC’s and based on the 4th order accuracy Runge-Kutta Numerical Integration Method.

**Brief description of “NIMAN”**

NIMAN is a high level computer program used exclusively for the structural analysis of grinding mills. It handles arbitrarily shaped axisymmetric shells of revolution subjected to non-axisymmetric loadings. It uses multi-layered (composite) shell elements to allow a reference surface at any arbitrary location rather than precisely at the middle of the section thickness. The method consists of dividing the entire grinding mill structure into a number of cylindrical, radial and conical shell elements of adequate lengths, having continuous first and second derivatives of the fundamental variables.

Forces resulting from the journal bearing reactions, charge loads, weights of different sections and their adjacent liners, drive and thermal loadings, etc., are differently shaped, quite irregular and difficult to assemble in simple acceptable expressions. However, the formulation of the differential equations for the variables, are arranged in such a manner as to contain only first order derivatives; therefore, to simulate the non-symmetrical loading, the principle of superposition, always valid in linear elastic solid mechanics, is used.

**Hydrostatic Bearing Design**

In this step, the following bearing parameters will be defined :

- The machining clearance “C”
- The required flow per recess “Q”
- The nominal recess pressure “Pr”
- The bearing eccentricity ratio “ER”

The machining clearance “C” is defined as the difference between the machined bearing surface radius and the machined

trunnion surface radius in millimeters (or mils). The analysis of the hydrostatic bearing must cover a range of “C” values in order to account for the machining tolerances of both bearing and trunnion.

The distance that the center of the trunnion moves away from the center of the bearing is defined as the bearing eccentricity, and its ratio to the machining clearance is defined as the eccentricity ratio.

**Line A-B :** The maximum film thickness occurs in the recess zone and

the minimum film thickness occurs at the outboard side corner of the bearing surface. In this curve section, the flow is considered overdesigned and the bearing enjoys a good lateral stiffness and stability. The disposition of the maximum and minimum film thicknesses is trying to maintain the lubricant where the bearing carrying action is, i.e. at the recesses and the bottom; sort of holding the escape of the lubricant from the corner at the minimum thickness.

**Hydrostatic Bearing Performance**

In this step, the design parameters obtained from the above paragraph will be used in the performance analysis of the hydrostatic trunnion bearing. In this analysis, the entire bearing surface area and the rotational speed are considered. The performance analysis mainly provides the geometrical arrangement of the centers of the trunnion and bearing, and the (load) angle of its corresponding bearing reaction at the different rotational speeds considered. In addition, more detailed information is provided for the lubricant film thickness, pressure distributions and recess flows, etc.

In fluid film bearing analyses, the major task is to solve the continuity equation derived by Reynolds in 1886. For finite bearings, the variables in Reynolds equation are converted to non-dimensional by using the width of the bearing for the linear dimensions and the bearing reaction for the force dimensions.

**Discussion**

The example used in the above computations was actually based on information available from the Chuquicamata installation in Chile.

During the start-up of this installation, it was found that the trunnion was “climbing” laterally in its bearing to a point exceeding the magnetic air gap limit of the wraparound motor. To solve the problem, “Tilting Pad Satellite Bearings” were added on the drive end at the 3 and 6 o’clock positions. The foundation pier had to be locally raised above the mill center to provide anchor points for these additional fix-ups, which in turn restricted the access to the head liner bolts.

**Sydvaranger VS St. Lawrence Cement**

Both these mills are driven by wraparound motors and are supported by multiple shoe bearings. The effect of the forces from these shoes on the supporting structure or the pedestal is somewhat similar to that of the partial arc hydrostatic bearing in that the forces would tend to “open” the bearing. It is left to the reader of the following details to draw his own conclusions about the Satellite shoes.

**The Sydvaranger SAG mill**

Originally, the mill was supported by five shoes on each side: one at the bottom 6 o’clock position and two on either sides of it. The stability of the bearing was questionable and as in the case of Chuquicamata, the mill was escaping sideways from its bearings.

**The St. Lawrence Cement mill**

Both bearings have 4 shoes each with no “Satellite” shoes at the horizontal 3 and 6 o’clock positions.