ABSTRACT:Large-size slewing bearings are usually surface hardened by means of induction heating. The load-carrying capacity of the bearing is dependent on, among others, the depth of the hardened layer, i.e., case depth共CD兲. It is of crucial importance for bearing manufacturers to ensure that sufficient CD is produced to meet the required bearing capacity for the applications. Compared to through-hardened bearings, the calculation method for the load-carrying capacity of surface-hardened bearings, espe-cially the induction-hardened bearings, is not well established. This paper reports on a new calculation method for the static capacity of induction-hardened rings. The method is based on consideration of both the plastic indentation on the raceway and the damage tolerance in the subsurface region. The models for evaluating plastic indentation and subsurface dam-age have been validated with the standing contact fatigue testing.
KEYWORDS: surface induction hardening, case depth, static capacity, slewing bearings, plastic indentation, core crush, cracks, de-fect tolerance
Introduction
Large-size slewing bearings are usually surface hardened by means of induc-tion heating. The load-carrying capacity of the bearing is dependent on, among others, the depth of the hardened layer, i.e., case depth 共CD兲. It is of crucial importance for bearing manufacturers to ensure that sufficient CD is produced
Manuscript received June 19, 2009; accepted for publication August 31, 2009; published online September 2009.
1Senior Research Engineer, SKF Engineering and Research Centre, P.O. Box 2350, 3430 DT Nieuwegein, The Netherlands.
2RKS S.A., SKF Slewing Bearings, BP 137, FR-89204 Avallon Cedex, France.
3SKF Group Technology Development, P.O. Box 2350, 3430 DT Nieuwegein, The Neth-erlands.
Cite as: Lai, J., Ovize, P., Kuijpers, H., Bacchettto, A. and Ioannides, S., ‘‘Case Depth and Static Capacity of Surface Induction-Hardened Rings,’’ J. ASTM Intl., Vol. 6, No. 10.
doi:10.1520/JAI102630.
Copyright © 2009 by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959.
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to meet the required bearing capacity for the applications. However, a hard-ened layer deeper than required should be avoided not only because of the cost involved in induction hardening, but also because of the fact that producing a too deep case increases the risk of surface cracking during induction harden-ing. In order to design and dimension the bearing that fits to the application, the bearing designers need to be able to calculate correctly both the static capacity and dynamic capacity.
For through-hardened bearings, the calculations for static capacity and dy-namic capacity have been well established and accepted in the ISO. The static capacity was referred to as the static load applied to a non-rotating bearing that will result in a permanent raceway indentation of 1⫻10−4Dw 共with Dw being the rolling element diameter兲 at the weaker of the inner or outer raceway con-tacts occurring at the position of the maximum loaded rolling element 关1兴.
Later, the maximum contact pressures of 4000 MPa for line contact and 4200 MPa for point contact were introduced in the ISO关2兴 for the calculation of the static capacity of rolling bearings.
Compared to through-hardened bearings, the calculation method for the load-carrying capacity of surface-hardened bearings, especially the induction-hardened bearings, is not well established. This is due to the complexity that the capacity of a surface-hardened bearing is also dependent on the CD and the strength of the core material. Insufficient CD may result in the so-called core crushing, a severe failure in form of cracking and flaking of the hardened layer due to excessive plastic flow in the core. The present study focuses on the static capacity of induction-hardened bearings.
There have been some published criteria 关3,4兴 for determining the static capacity of surface induction-hardened rings. The major difference among the existing criteria lies in whether or not allowing plasticity in the core of the bearing. Sague and Rumbarger关3兴 postulated that in order to avoid core crush-ing, the maximum shear stress at the case-core interface, arising from a static load, should be lower than the shear yield strength, which was assumed to be 0.425 times the ultimate tensile strength共UTS兲 of the core material. Zwirlein and Wieland 关4兴, however, stated that the equivalent von Mises stress at the case-core interface, resulting from a static load, could be as high as 1.25 UTS for ball bearings and 1.0 UTS for roller bearings. It was further stated in Ref 4 that a raceway plastic indentation of5⫻10−4Dwcaused by a static load had no negative effect on the fatigue strength of the hardened case under the cycling speed usual in slewing bearing applications.
Allowing no plasticity in the core 关3兴 eliminates the risk of the core-crushing failure. However, it normally requires a thick case layer with respect to the rolling element diameter, which is costly to produce and may even be beyond the capacity of the induction heating facility if the bearing is large and exceeds a certain size. The rules allowing plasticity in the core, such as those published in Ref 4, were mainly based on experience, which might be correct for a certain range of bearings with specific material and heat treatment. Their validity to other ranges of induction-hardened bearings remains questionable.
It is thus of technical significance to understand and, desirably, to be able to determine the limit of plasticity caused by a static load, which will not endan-ger the raceway integrity and the fatigue strength of the bearings. Such a limit
must be related to bearing geometry, CD, and the mechanical properties of the core material.
Summarizing the aforementioned arguments, we can conclude that in order to determine the static capacity of a surface-hardened bearing, two as-pects resulting from the applied static loading have to be considered: The per-manent raceway indentation and the subsurface damage. The former is to guar-antee the smoothness of bearing motion, such as blade pitching in wind turbines, whereas the latter is to ensure the integrity of the bearing raceway or to avoid the core-crushing failure.
The objective of the present study is to develop a calculation method for the static capacity of induction-hardened bearings, which is based on consider-ation of both the limit for raceway permanent indentconsider-ation and the tolerance for subsurface damage. The development of the static capacity model involves the following:
• The description of the plastic indentation and subsurface residual stress, each being related to bearing geometry, CD, and material proper-ties;
• The damage tolerance for core to exclude the risk of core-crushing fail-ure; and
• Model validation by experiment.
Finite Element Analysis
Elasto-plastic finite element analysis was performed to study the plastic defor-mation of an induction-hardened surface and subsurface stress, resulting from indentation of a ball or roller subjected to static loading. The general-purpose finite element共FE兲 package ABAQUS 关5兴 is employed for this study. In the FE model共Fig. 1兲, the indenter 共ball or roller兲 was modeled as a through-hardened component, and the ring was modeled as a layered body containing a hardened case layer of depth CD, a soft core, and a transition layer with a thickness of 0.1 CD between the case and the core, as shown in Fig. 2共a兲. The stress-strain curves were measured from compression tests 关6兴 of several medium-carbon steels both in soft and hardened states. The soft specimens were machined from blocks cut from forged rings with hardness ranging from 190 Hv to 308 Hv. The hard specimens were martensitically heat treated to hardness of about 670 Hv, corresponding to the required hardness of the hardened cases in slew-ing bearslew-ings. The measured stress-strain curves for the soft and hardened ma-terials were used for the case layer and the core in the FE model. The consti-tutive共elasto-plastic兲 behaviour of the transition layer is assumed to be a result of linear interpolation between the end of the case and the start of the core, as schematically shown by Fig. 2共b兲. The von Mises yield criterion and isotropic hardening were employed for the description of the elasto-plastic behaviour of the materials. Simulation was done for one loading followed by unloading.
Parametric study was made to calculate plastic indentation ␦ for two ex-treme contact cases: Circular point contact 共CPC兲 and cylindrical line contact 共CLC兲. The parameters considered include 共i兲 load in terms of the maximum Hertzian pressurep0,共ii兲 rolling element diameter Dw, and共iii兲 CD.
Figures 3 and 4 show the plastic indentation ␦resulting from indenting a ball and roller, respectively, onto a flat surface induction hardened with differ-ent CDs. In the graphs both␦and CD are normalized by the indenter diameter Dw. Calculations were made also for different applied loads in terms of the maximum Hertzian pressure p0 normalized by the yield strength of the core material y. Obviously, plastic indentation decreases with an increase in CD.
Under a specific load level, the plastic indentation ceases to decrease with CD if CD exceeds a certain value. In this situation, the stress in the core is below its yield strength, and plasticity occurs only in the hardened case, a situation equivalent to a through-hard component. It can also be seen that the “through hard” can be achieved at a lower load and less deep CD 共Fig. 3兲 under CPC, compared to the CLC 共Fig. 4兲. This is owing to the difference in subsurface stress distribution between the two contact conditions. The maximum von Mises stress in CPC is located at a shallower depth than that in the CLC.
In order to gain some insight into the core crushing in surface induction-hardened rings, the subsurface response in terms of plasticity and residual stress was investigated. If the stress resulting from a static load exceeds the yield strength of the core material, the core undergoes plastic flow. The plastic flow causes damage in the subsurface in the form of residual stress. Consider, for example, a situation of a shallow case 共CD/Dw= 2%兲 and applied contact pressurep0is 5.4 times the yield strength of the core material. It can be seen from Fig. 5 that if the applied load is high and/or the CD is shallow, a high tensile residual stress will be generated in the case-core transition region, which may cause cracking or delamination at the case and core interface.
Severe plasticity in the core also weakens the support of the core to the case layer and, as a result, the case will be subjected to severe bending by the load.
FIG. 1—FE model for indentation of an induction-hardened surface by a ball or roller.
共a兲 Global model; 共b兲 local mesh near the contact.
FIG. 2—Schematics of hardness profile of a surface induction-hardened component共a兲 and the stress-strain curves for the material in the hard case, soft core, and the transi-tion zone between the case and the core共b兲.
FIG. 3—FE results of surface plastic indentation共␦兲 as a function of CD in CPC.
FIG. 4—FE results of surface plastic indentation共␦兲 as a function of CD in CLC.
The bending of the case may be significant if the case layer is shallow, as shown in Fig. 6. The bending of the case layer may lead to cracking of the case if the bending stress in the case is too high. Core crushing is actually a consequence of deterioration of the core due to plastic flow, which weakens the support to the case layer.
The tensile stress in the subsurface, resulting from a high load, is an indi-cation of potential failure of core crushing, which must be accounted for in the static capacity model.
Experimental Study
Testing Methodology
The standing contact fatigue 共SCF兲 testing was employed to experimentally study the relevant failure mechanisms and to generate data for validating the proposed static capacity model. The SCF testing involves cyclically indenting a flat specimen with a ball or roller共see Fig. 7共a兲兲 in which the load applied on the indenter pulsates betweenPminandPmax共Fig. 7共b兲兲. A minimum load Pminwas FIG. 5—Subsurface damage in form of plasticity-induced residual tensile stress 共per-pendicular to surface兲 due to a static load. CD/Dw= 0.02, p0= 5.4y.
chosen to keep the load applied on the same spot on the specimen. The meth-odology of the SCF was proposed and published by Alfredsson and Olsson关7兴 from the Royal Institute of Technology.
The reason for choosing the SCF testing was twofold. It may reproduce the damaging cracks relevant to the core-crushing failure of induction-hardened rings. Moreover, the standing contact load, i.e., standing-still roller or ball pressed cyclically to the specimen, is also a loading condition relevant for slew-ing bearslew-ings in some slewslew-ing bearslew-ing applications.
Test Specimens and Equipment
The material used for the testing specimen is 42CrMo4. The chemical compo-sition of the material is given in Table 1.
The testing specimens were cut from a forged ring and machined to blocks with a dimension of120⫻130⫻50 mm3. The forged ring was tough tempered.
The specimens were surface hardened by induction heating with two CDs, namely, a shallow CD of 0.5 mm and a deep CD of 1.1 mm. The surface hard-ness was around 670 Hv.
FIG. 6—Subsurface damage in the form of plasticity-induced residual tensile bending stress共parallel to the surface兲 due to a static load. CD/Dw=0.02, p0= 5.4y.
FIG. 7—Schematic of the SCF testing:共a兲 Test set-up; 共b兲 load history.
The indenter used for the SCF testing was a through-hard crowned roller of a diameter of 10 mm and a crowning radius of 98 mm. For each test, a new roller was used. The indentation of the roller onto the testing block forms an elliptical共point兲 contact with b/a ratio of 6.84 共b and a are the semi axes of the contact ellipse兲.
The tests were conducted on a servo-hydraulic testing machine, MTS 100 kN, equipped with digital controllers.
As shown in Fig. 7, the specimen was positioned and fixed to a support plate. A cyclic load varying as a sine function with time was applied on the indenter. The minimum load was constant at 0.05 kN in order to keep the roller at the same contact location.
Results
In the SCF tests on both shallow- and deep-case specimens, three types of cracks were observed and identified as the lateral crack, the median crack, and the edge crack, as schematically shown in Fig. 8共a兲. The lateral crack developed at the case-core transition region; the edge occurred at the edges of the contact, whereas the median crack initiated from the upper surface of the lateral crack and grew vertically towards the surface. Figure 8共b兲 shows a fully developed lateral crack, whereas no edge and median cracks are formed. The location and the shape of the lateral crack shown in Fig. 8共b兲 correlate well with the plasticity-induced tensile residual stress calculated from FE analysis 共see Fig.
5兲. The edge and the median cracks indicated in Fig. 8共a兲 seem also to coincide with the predicted damage zones shown in Fig. 6.
It was found in the present experiments that the required load to develop the edge cracks and the median cracks was substantially higher than the load to develop the lateral cracks. Furthermore, the edge cracks were formed later than the lateral cracks. The median cracks could only be formed if lateral cracks were present.
The phenomenon that the required load for generating the lateral cracks is lower than the required load for generating the edge cracks and the median, can be understood from the FE analysis. The stresses in the positions of the edge crack and the median crack, as shown in Fig. 6, vary slightly around a high residual共static兲 stress, when an alternating load is applied. In other words, in those regions, the stress amplitude is pretty low, but the mean stress is high.
In the case-core transition region where the lateral crack develops, the stress varies from compression to tension, thus with a big range/amplitude upon ap-plication of alternating loading. Therefore, the load required to trigger the lat-eral crack is lower than that to initiate the edge and median cracks.
In view of the fact that the lateral crack can be generated at a lower load than the other two types of cracks, it is reasonable to consider the load for the
TABLE 1—Chemical composition共wt %兲 of 42CrMo4.
C Mn P Si S Cr Ni Mo Cu V Al Ti Nb
0.404 0.83 0.01 0.25 0.006 1.02 0.19 0.22 0.21 0.003 0.033 0.0043 0.003
formation of the lateral cracks as the fatigue load limit. For the shallow-case specimen the fatigue load limit is 7 kN, corresponding to a nominal Hertzian contact pressure of 3.98 GPa, while for the deep-case specimen, the fatigue load limit is 18 kN, corresponding to a nominal Hertzian contact pressure of 5.46 GPa.
Residual surface deformation after the SCF testing, as well as the perma-nent plastic indentation from a single load, was measured using the Talysurf equipment.
FIG. 8—Indication of three types of cracks observed in the specimens in the SCF test-ing: The lateral crack, the edge cracks, and the median crack共a兲 and a picture of a well developed lateral crack at the case-core transition zone of the specimen共b兲.
Formulation of Surface Indentation and Subsurface Damage
Surface Permanent Indentation
The permanent indentation of the raceway due to static loading is an important aspect to be considered for the static capacity of bearings. The evaluation of the plastic indentation, however, is not a trivial task. It relies on accurate measur-ing equipment and/or a theoretical model that accounts for the subsurface stress resulting from applied load and the resilience of the material to plastic straining. Calculation of plastic indentation is even more difficult for surface-hardened bearings in that the depth of the case layer as well as the material properties of both core and case can influence the magnitude of the surface indentation.
An early published model for estimating plastic indentation in bearings was due to Palmgren 关9兴. Based on empirical data for bearing quality steel through hardened between 63.5 and 65.5 Rockwell, such as those in Ref 8, Palmgren关9兴 developed the following formula to describe the total permanent indentation␦t共for both contact bodies兲 for point contact:
␦t= 1.3⫻ 10−7P2
Dw共I1+II1兲共I2+II2兲 共1兲 where:
P = applied load,
Dw= diameter of indenter共body I兲,
I1= curvature of body I, and so on.
I1= curvature of body I, and so on.