Carrying capacity of hardened raceway

Transcription

1 Carrying capacity of hardened raceway R. Kunc<", I. PrebiF, M. Torkar^ ^ Faculty of mechanical engineering, Askerceva 6, SI-1000 Ljubljana, Slovenia Robert.Kunc@fs.uni-lj.si, Ivan.Prebil@fs.uni-lj.si ^ Institute of Metals and Technology, Lepi pot 11, SI-1000 Ljubljana, Slovenija Matjaz.Torkar@imt.si. Abstract The paper deals with the problem of the actual carrying capacity of a rolling contact in large axial bearings with surface hardened raceway. The carrying capacity of such bearings is usually given with the maximal permissible force on the rolling element with the highest load. The established criteria of maximal permissible plastic displacement of the raceway, and the maximal allowed subsurface stress on the hardened layer boundary give widely varying values for the carrying capacity of the rolling contact. The criterion of allowed permanent displacement is unsuitable, mainly due to the technology. It supposes that both rings are hardened through the whole section, with very high surface hardness - over 63 HRc. The main deficiency of the criterion of allowed shear stress on the edge of the hardened layer is the computation of the subsurface stresses according to Hertz theory. This computation considers only the elastic region of the material deformation curve, and therefore disregards the plastic material hardening. In order to determine the actual carrying capacity of the rolling contact in axial bearings with low speed of rotation, considering base material properties, hardness and thickness of the hardened layer, and the geometry of the contact, we have measured the models of bearing raceways made of 42CrMo4 and C45 materials (ISO 683/1). The loads were low cycle dynamic. We have determined the cyclic curves, limit of fast increase in displacement gradient, and the size of the contact surface. Simultaneously with the experiment, we have checked the sub surface stresses using a FEM model, considering the material non linearities, which we have determined with the experiment.

2 314 Computational Methods in Contact Mechanics Introduction The term "rotational connection" describes a machine structure that allows relative rotating or oscillating motion of two substructures. It is loaded with a combination of axial and radial forces, and a turnover moment, and consists (Fig. 1) of a rolling bearing, screw connection, fixing the bearing rings to supporting and upper structures, and frequently also a gearing, integrated with the inner or outer bearing ring and used to drive the rotating substructure. The external loads are transferred from the upper (rotating) substructure over the bearing rings and rolling elements to the supporting (fixed) structure. The loads are distributed over a large number of rolling elements, so for the purpose of rolling element force calculation, the bearing is considered a statically indeterminate system. In order to calculate the carrying capacity of a bearing, we have to know the actual load distribution over the rolling elements of the bearing (Fig. 2) [1,2]. The actual carrying capacity is determined with the largest contact force on the rolling element with the highest load. Upper structure Screw Connection Toothed Ring \BojKngBearing ^///ng contact: Supporting Structure ~ ^/itecf Force Q, - Deformation, - Max. Hertz stress < Figure 1: Elements of rotational connection and rolling contact * Q, BSS -*- Q, BSS *- Q, BSE * Q, BSE * Q, BSE SM.*. Q, BSE SM BSE BSS = Both Both Structures Structures Elastic Stiff BSE SM - Both Structures Elastic - Simplified geometric Model Position of the rolling element 9 [" Figure 2: Example of load distribution over rolling elements

3 Computational Methods in Contact Mechanics 315 Mainly large static loads and material fatigue cause damage appearing on large, slowly running bearings [3,4]. Too high static loads on bearings during standstill periods cause plastic displacement in the contact of rolling element and raceway, and consequently the movement of the rotational connection becomes uneven. Low cycle loading can be the cause of material fatigue. To assure normal operation of a slowly running rotational connection during its predetermined lifetime, two criteria have been established to evaluate the static carrying capacity of a large axial bearing: Criterion of allowed permanent displacement - it determines the maximal static contact force on the element with the highest load such that the maximal permanent displacement does not exceed 0.01% of the rolling element diameter [5,6]. Criterion of allowed shear stress on the edge of the hardened layer - determines the largest static load on the element with the highest load such that the largest principal shear stress on the boundary of the hardened layer does not exceed the plasticity limit of the core [7,8]. Both criteria consider the mechanical properties of the weaker body in contact, i.e. the raceway. But the conditions for the use of the criterion of allowed permanent displacement and the criterion of allowed shear stress on the edge of the hardened layer are in the case of large dimension rolling bearings not completely fulfilled, mainly due to the technology. The manufacturing technology comprises bending and welding of rings, machining of the raceway, drilling of the screw holes, manufacturing of the gearing, hardening of the raceways. The material for rotational bearings must be sufficiently soft to facilitate the manufacturing process (low carbon steels C45, 42CrMo4 -ISO 683/1). These materials are soft and do not reach the required surface carrying capacity to insure resistance against impressions. The surface carrying capacity is increased with suitable heat treatment, i.e. hardening of the raceway. The criterion of allowed permanent displacement supposes that both rings are hardened through the whole section, with very high surface hardness - over 63 HRc. The main deficiency of the criterion of allowed shear stress on the edge of the hardened layer is the computation of the subsurface stresses according to Hertz theory. This computation considers only the elastic region of the material deformation curve, and therefore disregards the plastic material hardening. Shown are the results for an induction hardened raceway of a tempered base material 42CrMo4 (Fig. 3); with raceway radius % = 8.13mm and rolling element diameter d = mm.

4 316 Computational Methods in Contact Mechanics 1UUU ^ n -? $ _..._» -* " \ "*" HV osl -HV 3 J JOUU 3000 ct^ 2500 E 2000 & _ n depth z [mm] Figure 3: Depth and hardness of the hardened layer of the tempered material 42CrMo4 and a section of the bearing raceway 2 Determination of the contact carrying capacity Because the listed criteria are not completely satisfactory, we would like with the experiment and numeric calculation to determine the allowable contact force. Therefore we have to do: Experimental determination of the carrying capacity of the contact - allowable contact force and Computation of subsurface stress on the edge of the hardened layer with the use of the FEM (Finite Element Method) model and experimentally derived low cycle properties on various stages of the heat treatment of the C45 and 42CrMo4 materials [10]. 2.1 Experimental determination of the carrying capacity of the contact The growth of the contact displacement as a function of the number of oscillations varies with the type of the specimen and the load magnitude. Therefore it is not possible to give a reliable function for the contact displacemet or the hardening/softening of the raceway. The largest part of the displacement occurs normally during the first ten oscillations (Fig. 5). The largest part of the plastic displacement within a single oscillation occurs during the first oscillation. This can be seen as a pronounced hysteresis (i.e. change of the slope of the displacement function) under 6.5 kn load (Fig. 4). After that, the displacement function remains stable. There is no marked difference between the oscillations. The hysteresis loop is not pronounced and the increase or decrease of the displacement (i.e. softening or hardening) is indicates by the movement of the hysteresis loop. The loop also narrows with increased number of oscillations. Despite the increase of the contact load the displacement (permanent and total) remains more or less constant (Fig. 6). The decrease in displacement growth is

5 Computational Methods in Contact Mechanics 317 caused by hardening of the base material under the hardened layer, that has already been subjected to the plastic displacement (the stress exceeded the elasticity limit aj. Further increase of the contact force causes an increase of the displacement with similar intensity as at the beginning of the permanent displacement. Figure 4: Hysteresis functions - Specimen contact displacement Figure 5: Permanent displacement function (def. at F = 1 kn) 0.07 Figure 6: Permanent displacement for the specimen B-l-P as a function of the rolling element size - osculation 2.2 Checking of shear stresses It is not possible to measure the stresses on the hardened layer boundary and to determine the initial damage under the surface. To overcome this difficulty we have used a numerical model (FEM) that allows us to calculate simultaneously the deformations and displacements of the bodies in contact and stress under the surface of the hardened layer of the raceway (Fig. 7). The results of the numeric computation of sub surface stresses show all the properties of the sub stress distribution computed according to the extended Hertz theory i.e. maximum of the principal normal stresses on the surface, their decrease with the depth, appearance of the maximal principal shear stress,

6 318 Computational Methods in Contact Mechanics computed according to the theory of maximal shear stresses, under the point of contact in the depth of up to 1 mm (Fig. 8). With a load increase the material shows signs of plasticity (Fig. 7). Because the hardened layer is too thin, the plasticity first appears in the base material on the boundary of the hardened layer. This can be clearly seen in the distribution of the plastic deformation in the principal contact axis (Fig. 9). The second and third principal stresses also increase in the region of the most intense plastification on the boundary of the hardened layer. The increase of the stress over the elasticity limit can be seen in nearly constant reference stress and in increase of the permanent displacement (Fig. 10). With further increase in contact load the plastification causes an increase in plastic deformation and spreads further into the base material and also in the hardened layer. When the hardened layer has sufficient thickness, a broad region of maximal stresses appears in the hardened layer. Plastification appears only in the hardened layer. When the hardened layer is thin, the plastification appears early and only in the base material. Its region spreads very fast and deep in the base material. Most probably the damage will appear on the hardened layer boundary and will spread towards the surface. Such damage is typical for bearings with surface hardened raceways with either too soft a core or too thin hardened layers. In order to check the contact carrying capacity and initial damage, the function of the reference stress according to the hypothesis of maximal shear stresses is the most important factor. 3 4 depth z [mm] Figure 7: Reference stress function Ss for FEM model at F - 50 kn Figure 8: Stress function Si, 83, 83 and a, at F = 50 kn

7 Computational Methods in Contact Mechanics 319 Figure 9: Plastic deformation as a function of load Figure 10: Growth of permanent displacement as a function of load and rolling element size 3 Conclusion The computation of the allowed contact force considering the criterion of permissible permanent displacement (0.01% d) is not suitable for rolling bearings with surface hardened raceway, because the criterion does not account for falling hardness along the depth of the relatively thin hardened layer. Derived contact forces are too high and cause a significant plastification of the base material on the hardened layer boundary. This can lead to sub surface cracks typical for bearings with hardened rolling surface, resulting in cracking and chipping of the hardened layer. If the minimal thickness of the hardened layer equals or exceeds 20% of the rolling element diameter, the contact forces computed with various criteria are similar. In this way we can avoid excessive plastification of the base material on the boundary of the hardened layer. For the computation of the permissible contact force and for the displacement of minimal geometric and material properties of the rolling contact we could drop out the load maxima provided that their number is small, and the load spectrum is known. The load maxima cause only the creation of initial cracks that do not spread under subsequent lower loads. The cracks virtually "lock" themselves up. The indicated methodology and derived results are part of large scale measurements, augmented with analytical computations of sub surface stress (FEM). Determination of the carrying capacity of the rolling contact is the basis for determination of the actual carrying capacity and usable life span of low speed large dimension axial rolling bearings. In the future it will be necessary to investigate also the roll-on influence.

8 320 Computational Methods in Contact Mechanics 4 Literature [1] Brandlein, J.: Lastiibertragung durch Grofiwalzlager bei elastischen Ringtragern als Unter und Oberkonstruktion, Fordern und Heben, 30,1980 [2] Prebil,I.;Zupan,S.;Lucic,P.: Lastverteilung auf Walzkorper von Drehverbindungen, Konstrukcion, 47, 1995, 11 [3] Eschman,P.; Hasbargen, L.; Weigand, K.: Ball and Roller Bearings, John Wiley & Sons Inc., New York, 1985 [4] Harris, T. A.: Rolling Bearing Analysis - 3rd edition, John Wiley & Sons Inc., New York, 1991 [5] ISO 76, Rolling bearings - Static load ratings, 1987 [6] Yhland, E.: Static load carrying capacity, Ball Bearing Journal, 211, 1982 [7] Pallini, R. A.; Sague, J. E.: Computing Core-Yeild Limits for Case- Haredened Rolling Bearings, ASLE Trans., 28, 1985, 1, [8] Thomas, H. R.; Hoersch, V. A.: Stresses due to the Preasute of one elastic Solid upon Another, University of Illinois, Bull. 212, [9] KUNC, Robert, PREBIL, Ivan, TORKAR, Matjaz. Determination of low cycle carrying capacity of rolling contact, Kovine zlit. tehnol, 32, 1999,