by Korte, W.; Klokow, A.; Bettenworth, J.

This paper presents how Loesche evaluates the rocker arm of a vertical roller mill with the help of S-Life FKM by PART Engineering with respect to static strength and fatigue strength according to the FKM guideline [1]. For this purpose, first the functioning of the vertical roller mill and in detail the function of the rocker arm and its design are described. The load situation is presented and how this is modeled in the interaction between Ansys/Workbench and S-Life FKM. An evaluation of the results and the applied procedure is given.

**Working principle of a roller mill**

Loesche has been manufacturing industrial mills for grinding mineral raw materials such as coal and cement for almost 100 years. So-called vertical roller mills are shown here in more detail (Figure 1).

The raw material falls over the chute (2) onto the center of the grinding table (3). The material to be ground moves to the edge of the grinding table under the effect of the centrifugal force and thus passes under the hydro-pneumatically spring-loaded grinding rollers (4). The material is ground in the gap between the grinding rollers and the grinding table. The grinding rollers (4) are moved up and down in a vertical direction as they roll over the material to be ground (5). This deflects the functional unit consisting of the rocker arm (6) and hydraulic cylinders (7). The material to be ground (5) then rotates by centrifugal force outwards over the edge of the grinding track (8). There, the upwardly directed hot gas flow (9) picks up the mixture of ground material and not yet completely ground material and conveys it to the classifier (10). Material that is too coarse is rejected and falls back over the grit funnel (11) onto the grinding table (3) for regrinding. The finished ground material exits the classifier (10) and is conveyed with the gas stream (12) for further processing. The further illustration focuses on the rocker arm (6), whose mode of operation and design are explained below.

**Working principle and design of the rocker arm**

Figure 2, right, shows the situation at the grinding roller during grinding of the material to be ground. On the one hand, the grinding causes a grinding force in vertical direction on the roller, on the other hand a circumferential force in horizontal direction. Both forces act dynamically due to the distribution of the size and the required breaking forces of the raw material. The hydro-pneumatic operation of the hydraulic cylinders (Figure 2, left) ensures that the average grinding force is as constant as possible, irrespective of the fracture behavior of the material to be ground and the displacement due to the movement of the grinding rollers. The grinding rollers are passively driven by the rotation of the grinding table. Figure 3 shows the design of the rocker arm. The rocker arm consists of the lever and the fork, both of which are firmly connected to each other via press fits on the bolts and the axle. The entire rocker arm unit is supported by the axle in the mill and the support of the roller on the grinding bowl. The vertical grinding force and the forces of the two hydraulic cylinders are in momentum equilibrium. The lever and fork are made of spheroidal cast iron.

**Load cases investigated and FEM modeling**

In addition to the cyclic operating loads resulting from the grinding process, the superimposed static load caused by the assembly of the roller must also be taken into account. Figure 4 and Figure 5 show the bearing conditions and load points used in the model.

The modeling and FEM analysis is done with Ansys/Workbench. The axis is fixed with a fixed-loose bearing. The support of the roller on the grinding path is modeled in such a way that a frictionless contact is defined which does not allow any displacement in the vertical direction, i.e. normal to the grinding path. The circumferential force acting on the roller is applied laterally to the roller. The forces of the two hydraulic cylinders are specified as a cumulative bolt force. The assembly forces due to the roller axle clamping are specified via corresponding axially acting screw forces. These screw forces then lead to a fixed clamping of the roller axle and lever inside the lever via a clamping sleeve design.

The various contact interfaces between pin, lever, fork and the axles are modeled with the respective contact types as Bonded, Frictional or No separation. The material behavior is described linearly-elastically.

In Ansys/Workbench, the combined application of all static preloads, i.e. the screw forces for the roller axle clamping and the nominal forces of the circumferential load and cylinder force, is now carried out in a first load step. In two further load steps, combinations of screw forces + circumferential force and screw forces + cylinder force are then analyzed separately. This is necessary in order to take into account the superimposed cyclic load components later in the strength assessment in S-Life FKM, as will be shown later.

Furthermore, a so-called swing-out load case was investigated, which occurs when the roller is lifted off the grinding table for maintenance purposes by means of a further hydraulic cylinder specially provided for this purpose and moved into a vertical position. This load case has proven to be uncritical and will not be described further.

**Strength assessment with S-Life FKM**

S-Life FKM is a postprocessor that can be used to conduct a strength assessment according to the FKM guideline [1]. S-Life FKM reads the result file of the FEM program, in this case the rst-file of Ansys/Workbench. The strength assessment is then carried out completely in S-Life FKM independently of the FEM program. The workflow is shown in Figure 6.

As a result of the strength assessment, S-Life FKM provides the static and cyclic utilization ratio as a contour plot on the component surface. Furthermore, for the nodes identified as critical, a comprehensive numerical report in pdf format with the complete computation history can be output for validation and documentation of the assessment results. S-Life FKM evaluates the stress values read from the FEM results file nodewise. The standard strength properties of the respective material are taken from the integrated material database in S-Life FKM.

The basic procedure for strength assessment in S-Life FKM is that, in the case of several acting loads, the loads are first analyzed individually and then superimposed using a combination algorithm available in the program. The most critical load combination at each node is automatically determined as the most critical combination of the respective upper and lower loads of the individual loads over the course of the cyclic loading (Figure 7).

Furthermore, a scaling of individual load cases (multiplication by a factor) and a load case subtraction are possible, so that the FEM simulation does not have to be conducted again in case of changed load assumptions. This type of procedure also allows a simple determination of the cyclic load portions, as was done here.

In the FEM analysis, the following load steps were analyzed with Ansys/Workbench:

1. load step: roller clamping

2. load step: roller clamping + nominal circumferential force + nominal cylinder force

3. load step: roller clamping + nominal cylinder force

4. load step: roller clamping + nominal circumferential force

From this, the following assessment load cases are then defined in S-Life FKM with the load case processing options described above:

1. load case: static preloads = 2. load step; R_{Load} = 1

2. load case: cyclic portion of cylinder force = (3. load step MINUS 1. load step) x K_{dyn,Cyl}; R_{Load} = -1

3. load case: cyclic portion of circumfer. force = (4. load step MINUS 1. load step) x K_{dyn,Circ}; R_{Load} = -1

The cyclic load portions for cylinder force and circumferential force were determined via corresponding dynamic factors K_{dyn}, which relate in each case to the static nominal forces minus the roller clamping forces. Since no cyclic load portion results from the roller clamping, as this acts purely statically, it must be subtracted from load steps 3 and 4 of the FEM analyses before multiplication by the dynamic factor.

Furthermore, the loads in the assessments 1 to 3 have to be characterized with regard to their time history. For this purpose, the load ratios R_{Load} (ratio of lower load to upper load analogous to the stress ratio) must be specified in S-Life FKM. Assessment 1 is therefore assumed to be purely static and assessments 2 and 3 purely alternating. Since all loads act simultaneously during operation of the mill, the loads and the resulting stresses are superimposed to determine the relevant static and cyclic load factor.

S-Life FKM can take into account both proportional or synchronous stresses as well as stresses acting non-proportionally. In this case, the assumption was made that the stresses act synchronously, i.e. the static preload is superimposed on the two cyclic load cases, which in turn act proportionally to each other. This assumption is justified here, since it can be assumed that the grinding roller always experiences maxima in grinding force and circumferential force at the same times, e.g. when a larger particle enters the grinding gap.

The prerequisite for the described features of load case combination and load case scaling or subtraction is that the FEM analysis is carried out with a linear material model, as prescribed by the FKM guideline anyway.

Figure 8 shows contour plots of the static and cyclic utilization ratios of the rocker arm. According to the FKM guideline, the utilization ratio is defined as the ratio of stress, i.e. (equivalent) stress, to strength, including a possible safety factor. If the utilization ratio remains below one or 100 %, the strength is proven. The utilization ratios are therefore per FE node for the most critical combination of the defined load cases at this node. For the static case, this refers to the combination of upper and lower load of the individual load cases, which then leads to the highest static utilization ratio at this node in the superposition. For the cyclic case, this refers to the combination of load amplitudes of the individual load cases, which then leads to the highest cyclic utilization ratio at this node in the superposition.

The most critical combination can be different per node. Also, the positions of the highest utilization ratios are not necessarily identical with the positions of the highest stresses. Since the FKM guideline works with so-called local component strengths, there is not only a distribution of stresses in the component, but also a distribution of component strength. The component strength changes locally as a result of, for example, the local state of multi-axiality (static strength) or the local stress gradient (cyclic strength).

**Conclusion**

Since both stresses and strengths in the component are locally varying, the most critical position in the component with regard to failure, i.e. the one with the highest utilization ratio, cannot necessarily be determined by evaluating the position of the highest stress. In the usual approach in a standard FEM postprocessor, the local component strengths are usually unknown or would have to be determined manually by iterative and node-by-node procedures. Alternatively, it is of course also possible to calculate homogeneously in the entire component with the conservative assumption of the most unfavorable component strength.

If multiple loads are present, there is the additional challenge of determining which load combination, in terms of combinations of positive or negative load directions, will result in the highest utilization ratios. The FEM analysis of all theoretically possible combinations at load level and their subsequent individual assessment is already time-consuming for a comparatively small number of loads. For example, even three cyclic loads acting proportionally to each other lead to eight possible load combinations per node. Intuitively, for complex components and load situations, it will only be clear in the rarest of cases how an FEM analysis is to be set up with regard to the load directions to be selected for cyclic loads in order to determine the most critical condition from the outset.

S-Life FKM solves these difficulties in a user-friendly way. S-Life FKM automatically calculates the most critical combination per node for multiple acting loads and outputs the local utilization ratios on the component surface for this purpose. In this way, the most critical position of the highest utilization ratio in the component can be identified with certainty.

Loesche uses S-Life FKM as standard for strength assessment of machine and plant components. This saves a lot of time compared to manual assessment and increases the reliability of the assessment. The standardized procedure and the simple application of S-Life FKM reduce sources of error. The representation of the static and cyclic utilization ratios as well as the comprehensive numerical assessment report for the critical node are used for documentation purposes (Figure 9, left). The FKM guideline represents the state of the art for the assessment of machine components made of steel, cast iron and aluminum materials. S-Life FKM contains a material database with more than 1500 material grades corresponding to the material tables of the guideline (Figure 9, right). The guideline is completely reflected in S-Life FKM for unwelded components and thus guarantees the user that a strength assessment can be carried out that corresponds to the state of the art.

*[1] N.N: Analytical Strength Assessment of Components in Mechanical Engineering in its 6th revised edition, Forschungskuratorium Maschinenbau, VDMA Verlag, Frankfurt am Main, Germany, 2012*

**The Authors**

Dr. Wolfgang Korte is Managing Director at PART Engineering GmbH, Bergisch Gladbach, Germany

Alexander Klokow is Development Engineer at Loesche GmbH, Düsseldorf, Germany

Jörg Bettenworth is Head of Advanced Development at Loesche GmbH, Düsseldorf, Germany