Über die Beanspruchung oberflächennaher Werkstoffbereiche von Zahnflanken bei Voll‐ und Mangelschmierung

Strengthening of surface‐near‐materials‐zones of gear flanks with plain and deficient lubrication Couplings of gears, as strengthened over long duration, show often ruptures on the flanks. Their distribution and orientation among the surface can be explained by the kinematics of rolling. The cracks show an angle inclined towards the surface between 20 ° and 40 °. They are opposite to the occurring tangential stresses. Only in negative slip zones the ruptures grow to secondary cracks, rupturing occurs mainly at this point. The commonly used calculation of the materials strengthening in surface near zones by the HERTZian distressing conditions applied for tangential stresses does not give any hint to a preferred area of the flank stressed with negatives slip. The various failure phenomena can be explained by the elastohydrodynamic (EHD) – hypothesis. This hypothesis points out that the lubricants flow causes additional strengthening which influences the fatigue endurance and lowers the value determined after HERTZ.     

Die Werkstoffermüdung bei Wälzbeanspruchung – Eine Hypothese zum Mechanismus

Materials fatigue by rolling contact stressing – A hypothesis of the mechanism Research in Rolling contact fatigue produced plenty of experimental observations and theoretical knowledge. By considering all these detailed informations a hypotheses for/describing the mechanism of the fatigue process was developed and will be presented. The fatigue process may be devided up in three phases. In phase 1 and 2 the structure will be deformed microplastically. The strength localy becomes smaller. Residual compressive stresses grow. Added to the load stresses, the stressing continual change. In phase 2 the deformations nearly stop. There is a critical point by material behaviour and stressing when phase 2 attains phase 3. The microplastic deformation changes to a macroplastic deformation. The structure “flows” in the direction of the relative tension stress, more and more (in direction) towards the surface. At both sides of the track vaults arise. In the middle of the track a vault also tends to arise, but it will be smoothed by over rolling. So normal to the raceway residual tensile stresses are created. They become biger and biger. Finally they start the subsurface cracks. By the hypotheses nearly all phenomena detected in rolling contact fatigue research can be explained. The thesis reveals chances, rolling contact systems to optimize.     

Über adiabatic shearbands und die Entstehung der „Steilen Weißen Bänder”︁ in Wälzlagern

About adiabatic shear bands and the generation of “high‐angle white bands” in roller bearings During the rolling motion of roller components structural changes are generated by over‐elastic distressing below the bearing face. Micro‐ and macro‐plastic distortions of the microstructure due to the three‐axial distressing accompany the process of rolling contact fatigue with the start from the first load cycle. They determine the life‐duration of the roller component. Further structural changes in ball bearings besides the plastic deformations are the so called “butterflies” and the so called low‐ and high‐angle “white bands”. The “white bands” you only can detect later, after an extended number of rolling actions. They are inclined to average circumferential angles at ≈ 30 ° respectively ≈ 80 °. Butterflies and white bands develop obviously due to a two‐axial material stressing. An influence on the life duration is not proved. The structure and the mechanism of their generation are under discussion. There exist phenomena of the microstructure which are similar to the white bands, the so called adiabatic shear bands. These generate after a local macro‐shear process of the microstructure, caused by a single, rapid shock‐shear stressing. Flash‐temperatures near the melting point generate in the shear zone of martensitic hardened materials the formations of new hardened zones; these microstructures cannot be etched too. The paper contributes to the question, if there exists a stress‐constellation which causes the adiabatic formation of butterflies and of white bands during the steady and long during process of plastic deformation. If one considers the latest knowledge about rolling contact fatigue and stressing by EHD (elasto‐hydro‐dynamic) flow, he can come to the conclusion, that at least the “high‐angle white bands” are adiabatic shear bands.     

Werkstoffanstrengung bei Wälzbeanspruchung – Einfluß von Reibung und Eigenspannungen

Material Stressing under Rolling Contact – Influence of Friction and Residual Stresses Material stressing of parts in rolling contact is in the main made up by the normal load to be transmitted, by surface friction due to slippage of the body in rolling contact and by residual stresses. The effects of varying slippage rates are described as well as the additional influence of residual stresses on magnitude, position and direction of load. By the aid of mere mechanical reflections the formation of flat and steep White Bands can be interpreted which are observed in long-lived ball bearings subjected to high stresses. The report shows that residual stresses and friction must not be neglected when describing the material stressing by rolling contact. This especially applies to residual stresses originating from rolling contact.     

Slip‐rolling resistance of ta‐C and a‐C coatings up to 3,000 MPa of maximum Hertzian contact pressure

The slip‐rolling resistances of hard and stiff thin films under high Hertzian contact pressures can be improved by optimizing the “coating/substrate systems”. It is known from former investigations that the so‐called “egg‐shell” effect is no general hindrance for high slip‐rolling resistance of thin hard coatings. The coating stability depends more on specific deposition process and coating/substrate interface design. In this article it is experimentally shown, that pure amorphous carbon thin films with hardness between 15 and 63 GPa can be slip‐rolling resistant several million load cycles under a maximum Hertzian contact pressures of up to 3.0 GPa. Whereas all coatings were stable up to 10 million load cycles in paraffin oil at room temperature, reduced coating lifetime was found in SAE 0W‐30 engine oil at 120°C. It was shown how the coating hardness and the initial coating surface roughness influence the running‐in process and coating lifetime. No clear correlation between coating hardness and coating lifetime could be observed, but friction coefficients seem to be reduced with higher coating hardness. Very low friction down to ?0.03 in unmodified engine oils was found for the hardest ta‐C film.     

Grundsätzliche Betrachtungen zur Oberflächen-Ermüdung

Rolling Contact Fatigue . Wear, rolling contact fatigue, fatigue – calculation of stresses – stresses caused by normal load – influence of friction – influence of surface roughness – influence of residual stresses – influence of temperature – influence of pressure profile in EHL-contacts – influence of material – influence of lubricants – influence of additives – size effect – investigation of damages.     

Materialbeanspruchungsanalyse und ihre Anwendung auf Prüfstandsversuche zum Oberflächenausfall (Nierlich‐Schadensmodus) von Wälzlagern

Material Response Analysis and its Application to Rig Tests for the Surface Failure (Nierlich Damage Mode) of Rolling Bearings The material response analysis according to Nierlich using X‐ray diffraction represents an important physical examination technique for the evaluation of material stressing and the lifetime estimation of rolling bearings and other highly loaded machine parts. The method is presented and employed for the evaluation of automobile gearbox rig tests. The extensively described damage modes of the practically predominating surface and the classical sub‐surface failure of rolling bearings can be distinguished that way. In gearboxes, lubricating oil contaminated by metal abrasion of the cogwheels usually appears. Penetrating foreign particles produce indentations at the ring raceways and rolling elements of the rolling bearings, which promotes surface fatigue. The results of the X‐ray diffraction measurements confirm this damage mode. Evaluation of the occurred material stressing permits a more detailed characterization of the surface failure of rolling bearings.     

Finite‐Element analysis of a rolling contact model with anisotropic elastic material properties

The elastic properties of a material are an important factor for the designing and dimensioning of structural and functional components with respect to the dimensional stability, the spring‐back behavior or the fatigue properties. The present work is focused on the impact of the elastic anisotropy on a rolling contact loading of a severely deformed ferritic steel. Linear profiles produced by the newly developed forming process called linear flow splitting are considered to be well suitable as linear guides, due to their reduced surface roughness and highly increased surface hardness. Orientation data obtained by EBSD measurements are used for the calculation of the elastic tensors of the severely deformed parts applying the geometric mean in addition to the classical Voigt and Reuss approaches. The produced profiles exhibit a strong elastic anisotropy in the plane parallel to the desired rolling contact surface showing a strong gradient in forming rate. The evaluation of the stresses in the rolling contact area of the formed microstructure is estimated by the implementation of the determined compliance tensors into a finite element rolling‐contact model. In comparison to results with a homogeneous and isotropic material model the results are analyzed with respect to the rolling contact loading based on the von Mises failure criterion.     

A rolling contact fatigue crack driven by squeeze fluid film

ABSTRACT A new model of surface breaking rolling contact fatigue (RCF) crack driven by a coupled action of a squeeze oil film built up in the crack interior and a pressure exerted at the external contact interface was developed. The model can be applied to the ‘nominally dry’ contact couples with an occasional presence of liquid in the crack interior (wheel/rail contact) as well as to the elastohydrodynamic lubrication (EHL) conditions. In the first case, the contact load is a result of solid/solid interaction and can be determined by solving the FE contact problem, but the liquid contained in the crack interior forms a thin film between the crack faces changing their interaction into the type of liquid/solid. This liquid is being periodically squeezed under contact load and acts as a ‘squeeze film’ known from the lubrication theory. In the second case, the liquid (lubricating oil) is permanently present in the contact area and consequently in the vicinity of the crack mouth. This creates conditions for filling the crack with oil. Similarly as in the first case, the ‘squeeze oil film’ is built between the crack faces. The contact load in this case results from a liquid/solid interaction and can be approximated by the pressure and traction distributions obtained from the numerical solution of the elastohydrodynamic contact problem. In both cases the model can be used to determine the Linear Elastic Fracture Mechanics (LEFM) crack tip stress intensity histories during cyclic loading and consequently to predict the crack growth rate and direction. An example of applying the model to the EHL case is given to explain the mechanisms and phenomena leading to the crack front loading. The cycle of rolling a roller over the crack was numerically simulated to obtain the mixed mode (I and II) SIF histories. In the analysis, the EHD pressure and traction were determined through the full solution of the EHD line contact problem accounting for the presence of a crack, whilst the pressure in the crack was found with the use of the wedge shaped squeeze oil film (SOF) model. Possible effects of the mode I and mode II stress intensity cycles on crack growth rate and direction are discussed. The solution indicates high pressure in the neighbourhood of the crack tip, exerted on the crack faces by the squeeze oil film. This leads to the ranges of the mode I and mode II SIF variations, which are larger than for the ‘dry’ and ‘fluid entrapment’ models, and can be an explanation for the crack growth rate observed in practice     

Schäden wälzbeanspruchter DLC‐Schichten auf Stahlsubstraten unterschiedlicher Härte

Damages of slip‐rolling tested DLC coatings on steel substrates of different hardness Extremely hard diamond coatings on hard SSiC substrates, various hard DLC coatings on 100Cr6 substrates (HRC60) as well as selected DLC coatings on unhardened steel substrates (HRC20) were tested under slip‐rolling conditions. Unadditivated paraffin oil was used as a lubricant. The tests were carried out in an Amsler type twin disc tester at initial maximum pressures of P₀=2.3 GPa according to Hertz. The tests were terminated after n=1.000.000 revolutions (endurance tests: n=10.000.000 revolutions) or if a coherent damaged area of A>1 mm² occurred. The slip‐rolling tests showed that the SSiC had a supportive influence on the diamond coatings which, however, failed due to fractures in the substrate. At least two of the DLC coatings on 100Cr6 substrates (HRC60) withstood the slip‐rolling test for up to n=10.000.000 revolutions with nearly no visible damage. These coatings deposited onto a soft, nitrogen alloyed steel (HRC20) were able to adjust to the deformation of the substrate without major damaged areas (A>1 mm²).     

偏载状态下轧机轴承接触力学模型研究

该文针对板带轧制过程偏载工况下滚动轴承接触力学模型进行研究。建立了支承辊四列圆柱滚子轴承的Hertz理想接触模型、基于柔度矩阵法的轴承偏载接触力学模型。针对辊间不同载荷进行了模型数值求解,仿真模拟了理想及偏载接触过程。研究表明:偏载运行状态严重影响各列轴承载荷分布,15°~30°位置角的滚动体承载最大,最大接触应力呈“M”形分布;仿真结果与数值模拟结果吻合程度较好,误差不超过15%,且略小于数值求解结果,在实际工程应用范围内;随着轧制载荷的增大,轴承同一列上的总径向力不断增大,偏载程度越来越严重。研究为延长轴承使用寿命、保证轧机安全稳定运行提供理论依据,具有重要工程意义。     

Simulation der Wärmebehandlung von Stählen am Institut für Werkstoffkunde I

Simulation of the heat treatment of steels at the Institut für Werkstoffkunde I The simulation of manufacturing processes is an important tool in simultaneous engineering. The aim is to cut the time necessary for development and to optimize processes by simulation of the complete manufacturing chain. The field of heat treatment offers a large variety of applications for the use of simulation tools. The geometry of the part, the composition of the material, the heat treatment process as well as the initial state of the parts interact with each other in complex ways and have an influence on the distortion of the part. The calculation of the microstructure and of the hardness distribution helps to determine suitable charging and quenching conditions as well as plant engineering. Calculated residual stresses and distortions can be taken into account in the development and construction of new parts. The Institut für Werkstoffkunde I of the Universität Karlsruhe (TH) is engaged in research programms in this field dealing with numerical as well as experimental problems for almost 30 years.     

On the temperature in the wheel–rail rolling contact*

The flash temperature in an asperity of the rail due the wheel–rail rolling contact is investigated. First the contact configuration and the total heat produced are explained. Then approaches to heat partitioning between the two contacting bodies are discussed. A new heat partitioning factor is derived for the case of frictional heating and heating due to plastic deformation, thereby taking into account the roughness of the contacting surfaces by a contact intensity factor distribution as well as the local pressure intensification by individual asperities. Several roughness distributions are studied. Finally, an explicit calculation is outlined of the asperity flash temperature at the end of the contact, expressed by two temperatures and two factors contributing to the partitioning of heat between the contacting bodies.     

Stress‐dependent fatigue mechanisms of CrC–NiCr coatings in rolling contact

The rolling contact fatigue (RCF) behaviour of the plasma‐sprayed CrC–NiCr cermet coatings under different tribological conditions of contact stress was investigated. Four sets of fatigue life data of coatings were characterized by Weibull distributions. The failure modes of the coatings were classified on the basis of worn surface observations of the failed coatings. Results showed that the failure mode of the coating was related to the magnitude of contact stress. The RCF life data of the coatings tested at high contact stresses exhibited high scattering, because the bimodal distribution of the fatigue life data was seen in the Weibull plot. Generally, when the contact stress was relatively low, the coatings were prone to fail in spalling and cohesive delamination. However, at high contact stress, the coatings often failed due to interfacial delamination. At different contact stress levels, the maximum shear stress amplitude was the main reason for the generation of spall and delamination.     

The Morphology of Rolling Contact Fatigue Fracture of Hardened Steels

Rolling Contact Fatigue(RCF) is a cumulativedamage phenomenon when metals are subjectedto repeated contact stresses. The fomationof pitting on the contact surface is the resultof the rolling contact fatigue. The morphologiesof rolling contact fatigue fracture of the har-dened steels (86CrHoV7, 42CrMo) show that strongresemblance in fractuye mechanisms exists betweenrolling contact fatigue and uni-axial fatigue.Since fatigue striations are hardly observedin hardened steels under uni-axial fatigue,it is interesting to note that the state ofstress in rolling contact fatigue is more favor-able to ductile fractures than in uni-axialfatigue.     

Werkstoffanstrengung im Hertz'schen Kontakt infolge Last- und Eigenspannungen

Material Stressing in a Hertzian Contact – Influence of Load and Internal Stresses For the analysis of the material stressing in a Hertzian Contact due to elliptically distributed normal load it is sufficient to calculate the stresses at z ≥ 0, × = y = 0. At this point the maximum stress occurs in the contact surface as well as in the stressed volume. From the center to the rim of the contact the stress decreases. In the case of residual stresses in the material it is necessary to calculate the resulting stresses in the entire contact area. The superposition of stresses due to load and internal stresses can cause stressings of the material with a maximum in the region of the rim of the contact area. The calculation of the conditions in the center alone can lead to misinterpretations.     

Multiaxial fatigue life calculation model for components in rolling‐sliding line contact with application to gears

Important components such as gears, rollers, or bearings operate in rolling‐sliding contact loading conditions. Determination of their fatigue lives remains a challenging task due to complex states of stress and strain in the contact region, as well as complex contact conditions such as variable loading amplitude and complex geometry of contact. A mathematical model of rolling‐sliding line contact combined with a multiaxial fatigue life calculation model based on the Fatemi‐Socie critical plane crack initiation criterion is proposed. The developed model was applied to gears' teeth in mesh and compared with fatigue lives of gears reported in the literature. Good agreement was determined confirming the validity of the proposed model. A further advantage is obtaining locations of initiated cracks and the orientation of critical plane(s), which can subsequently be used for the estimation of crack shapes in initial phases of their growth and the damage type that they can be expected to develop into.     

Surface crack growth of silicon nitride bearings under rolling contact fatigue

Surface crack growth of silicone nitride ceramic bearings under rolling contact fatigue has been investigated from the viewpoints of contact stresses (ring crack model) and fluid pressure (wedge effect model). The mechanisms of these two models have been investigated independently; however, it was impossible to separate the effects of contact stresses and fluid pressure on surface crack growth. In this paper the effects of contact stresses (ring crack model) on surface crack growth are investigated. In the ring crack model the crack growth is caused by contact stresses around the circumference of the contact circle. The growth of surface cracks located inside and outside the contact track was observed in order to obtain data from which we could reexamine the ring crack model. The outside cracks under rolling contact fatigue were propagated by contact stresses alone and also the inside cracks grew as slowly as the outside cracks. We concluded that the cracks are propagated by the single effect of contact stresses. Preliminary observations of surface crack growth showed that the cracks were unaffected by wear and residual stresses.     

惯性载荷对高速角接触球轴承最优预紧力的影响分析

高速角接触球轴承拟静力学模型是轴承内部载荷分布的有效分析手段,是动力学分析的基础.对受轴向载荷的高速角接触球轴承的具体算例进行了求解计算,得出了不同转速下钢球与沟道接触力随预紧力的变化规律.计算结果表明:在低转速范围内,钢球与外沟道接触力随着轴向预紧力的增大而线性增大;随着转速的升高,该接触力会呈现非线性变化,表现出先减小后增大的变化趋势.对这一变化规律进行了详细的分析,并从接触疲劳寿命和陀螺转动摩擦生热的角度,提出了确定高速角接触球轴承最佳预紧力的双重约束条件,为高速角接触球轴承的设计与使用提供参考依据.     

Rechnerischer Festigkeitsnachweis der Ermüdungstragfähigkeit von vergüteten und einsatzgehärteten Stirnrädern

The work presents a calculative proof of strength for compensated and case hardened spur gears taking into account the different stress conditions in the tooth root and on the tooth flank. The basis of the proof of stregth is the local comparision of the occured stresses and the allowed stresses in the spur gear. The complex stress condition on the tooth flank is illustrated. On the flank occours a three dimensional stress condition with turnig principial stress systems. Furthermore the influences on this stress condition of residual stresses and of the contact of technical surfaces are discussed. Especially the described complex stress condition on the tooth flank asks for a calculation with an adequate criterion of failure. For this purpose a variant of the Schubspannungsintensitätshypothese (SIH) is proposed. The applicability of the proposed model is verified with numerous results of experiments. Some of the calculations are presented here. Altogether there is a good conformity between the test results and the calculated results especially for the ammount of the fatigue limit, the kind of damage (e.g. tooth root breackage, pitting, tooth breackage in the region of the flank) and the position of the beginning of the damage.