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Spalling formation mechanism for gears
Wear 254 (2003) 1307–1317
Spalling formation mechanism for gears Yan Ding a,∗ , Neville F. Rieger b a
Department of Mathematics, RMIT University, City Campus GPO Box 2476V, Melbourne 3001, Australia b Stress Technology Incorporated, Rochester, NY, USA Accepted 24 February 2003
Abstract Though the basic phenomenon of wear on gear tooth contact surfaces is the removal of a piece of material from the working surface, the sizes of the wear debris may be different, due to the different physical causes in their formation processes. No common definitions have been established to distinguish spalling from pitting in the literature. This is probably due to the fact that the physical causes of pitting and spalling have not yet been established. In this paper, a brief literature review is presented with the intention to differentiate spalling from pitting. Three types of wear phenomena are defined. Furthermore, the results of a recent experimental study of gear tooth spalling formation in AISI 4340 gears in a test rig are also presented to demonstrate a possible process of spalling due to the development of cracks beneath the tooth contact surfaces and crack linkages in plastically-collapsed metal ligament between the crack tip and the adjacent tooth contact surface. These experimental results substantiated the ligament collapse spalling mechanism proposed by Ding et al. [Y. Ding, R. Jones, B.T. Kuhnell, Elastic–plastic finite element analysis of spall formation in gears, Wear 197 (1996) 197–205; M. Heems, F. Lagarde, R. Courtel, P. Sorin, C. R. Acad. Sci. 257 (3) (1963) 3293]. © 2003 Published by Elsevier Science B.V. Keywords: Spalling; Subsurface cracks; Crack failure; Ligament collapse
1. Introduction Gearing is an essential component of many machines. From aerospace to high-speed automation, from missiles to submarines, few machines can operate without gears. Since gears transmit motion and power through the surface contact, good gearing performance depends on the durability of their teeth surfaces. Generally, there are four basic wear modes: contact fatigue, adhesion, abrasion and corrosion. Under normal operating conditions, contact fatigue is one of the most common failure modes for gear tooth surfaces. Gear tooth interaction causes mild adhesive wear throughout the life of the gear drive. This is called normal rubbing wear and is characterised by particles smaller than 10 m. This is seen as a smoothing of the gear tooth surfaces as a result of mild plastic deformation of asperities. This type of deformation causes a very thin work-hardened surface layer. The thickness of this work-hardened layer is roughly of the order of the asperity widths, i.e. typically less than 10 m [2,3]. Generally, there are two types of surface contact fatigue, namely, pitting and spalling. Pitting appears as shallow craters at contact surfaces. The maximum depth of a pit is about the thickness of the work-hardened layer (≈10 m). ∗ Corresponding author. Tel.: +61-3-9925-2283; fax: +61-3-9925-1748. E-mail address: [email protected] (Y. Ding).
0043-1648/$ – see front matter © 2003 Published by Elsevier Science B.V. doi:10.1016/S0043-1648(03)00126-1
Spalling appears as deeper (typically 20–100 m) cavities at contact surfaces with a depth of 0.25 to 0.35 of the half contact width (usually denoted as “c” in fracture mechanics literature). Fig. 1 illustrates the phenomena of pitting and spalling. It must be noted here that no common definitions have been established to consistently distinguish spalling from pitting in the literature. In much of the literature, spalling and pitting were used indiscriminately, and in some literature, spalling and pitting were used to designate different severities of surface contact fatigue [4,5]. Tallian [6] defined “spalling” as macro-scale contact fatigue caused by fatigue crack propagation and reserved “pitting” as surface damage caused by sources other than crack propagation. One of the reasons for the confusion in the definitions is probably due to the fact that the physical causes of pitting and spalling have not yet been convincingly established. This is one of the major reasons for performing the study described here. In order to discuss the issue on a consistent ground, for this paper, pitting and spalling are defined according to the observed phenomena as discussed above. Pitting is taken to be the formation of shallow craters (<10 m) that are mainly developed from surface-defects, and spalling is taken to be the formation of deeper cavities that are mainly developed from subsurface-defects. Though both spalling and pitting are the common forms of surface contact fatigue, compared
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Fig. 1. Schematic illustration of pitting and spalling phenomena.
to pitting, spalling results in more rapid deterioration of surface durability, and often induces early failure by severe secondary damage. It has been often reported as the most destructive surface failure mode of a gear (e.g. [4]). A detailed understanding of spalling is not only essential for detecting incipient gear failure, before it becomes disastrous and causes expensive secondary damage, but is also central for planning preventative maintenance for gear components. Furthermore, it can also be used to determine the critical parameters for designing gears that satisfy special requirements. One instance is the design of gears with the maximum capacity and the minimum size and weight, for high-speed automation or aerospace power transmissions. Although there has been considerable research devoted to this area over the last half-century, there is still lack of a thorough understanding of the spalling formation process on gears. Most of the relevant previous work concentrated on symmetrical contact problems. The knowledge of subsurface crack behaviour with non-symmetrical contact geometry is very limited. The majority of the previously reported research has focused on either metallurgical studies of the worn material, or on the theoretical analysis of the behaviour of subsurface cracks. There appears little published work aimed to achieve a mutual agreement from the results of these two aspects of the research. Neither much study was focused on the stress state change of the material between the contact surface and subsurface crack tips, which is of great practical interest in regard to the physical process of spalling formation. The objective of this research is to investigate the spalling mechanism in gears by studying the behaviour of subsurface cracks. The behaviour of surface cracks under contact loading is controlled by a different mechanism and needs to be studied separately. 2. Previous research on crack propagation and failure Three stages are involved in the formation process of a spall: crack initiation, crack propagation and failure. It has been well documented that crack initiation is resulted
from an inclusion or a hard particle, as well as material defects such as flaws and pre-existing dislocations. After a crack initiates, the cyclic contact stress produced by repeated rolling or rolling–sliding contacts drives cracks to grow. Eventually, failure of cracks will take place and result in some kind of surface contact damage, such as spalling, pitting, or delamination. In general, the study of surface contact damage reported in literature may be divided into two groups: surface-defect-origin contact fatigue and subsurfacedefect-origin contact fatigue, which are discussed in following subsections. 2.1. Existing theories of surface-defect-origin contact fatigue For decades, there has been a dominant opinion in literature regarding spalling/pitting formation, which considered that, as surface cracks driven by a liquid lubricant, spalling/pitting was the result of surface crack propagation in the direction of contact travel. This opinion was based on Way’s hypothesis [7], which postulated that lubricating oil pre-filled in a surface crack was trapped between the crack surfaces when the approaching contact reached the surface opening and pinched the crack closed. As a result, the crack tip was extended by a hydraulic pressure of the lubricant oil sealed between the crack surfaces. The extensively quoted Way’s hypothesis was not challenged until a half-century later. Keer and Bryant [8] simulated Way’s experiments and found that the dominant mechanism for surface-breaking crack growth was mode II (shear) propagation. Their conclusion is not consistent with Way’s assumption of Mode I (tension) crack propagation. However, they also suggested that the phenomenon of crack curving, i.e. changing its direction to the contact surface to form a crater or cavity, could be due to the influence of tensile rather than shear stress. Bower [9] performed a fracture mechanics analysis of crack propagation in the presence of lubricating oil. His results did not appear to support Way’s hypothesis, either. Furthermore, the experimental results obtained by Cheng et al. [10] showed that the surface crack growth was very slow and the depth of the slowly growing surface cracks was in the
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range of 5–10 m. Therefore, it is almost impossible to form a spall cavity from surface crack growth, unless there is a near-surface inclusion to act as a bridge to significantly accelerate the propagation of the surface crack into the subsurface region. 2.2. Existing theories of subsurface-defect-origin contact fatigue Many researchers have also studied the behaviour of subsurface cracks under contact loads for the purpose of understanding of spalling/pitting mechanisms. Among them, Fleming and Suh [11] were the first ones who utilised fracture mechanics as a method to analyse the propagation of subsurface cracks parallel to the contact surface. Their results showed that the stress intensity factors (SIFs) for Modes I and II were very low. Kaneta et al. [12] studied the growth mechanism of subsurface cracks by numerically analysing the behaviour of a three-dimensional subsurface crack parallel to the contact surface. They concluded that the propagation of subsurface cracks is mainly by Mode II. They also found that the direction of the Mode II propagation was different for the trailing and leading tips of the crack with respect to the direction of the surface traction. The tip at the trailing side of the traction extends along the crack line, and the tip at the leading side extended towards the surface at an angle less than 6.2◦ . Sin and Suh [13] studied the mechanism of subsurface crack propagation in sliding elastic–plastic solids using the finite element analysis. They suggested that crack tip sliding displacement (CTSD) be taken as the propagation rate of subsurface cracks. They also suggested that the direction of the propagation be the direction of the maximum shear stress in front of the crack tip and along an angle between −5 and 5◦ to the crack line, implying that the propagation was almost parallel to the contact surface. They claimed that, based on the CTSDs calculated using FEA, their predicted wear rates compared favourably with the experimentally determined wear rates. More recently, Ding et al. [14] studied the behaviour of subsurface cracks beneath the pitch line of a gear tooth with a view to develop a fundamental understanding of the spalling mechanism in gears. Using the finite element method, they analysed the potential modes of crack propagation and failure, and found that the values of the stress intensity factors of the subsurface cracks were below the critical SIF, Kc . Consequently, ligament collapse at crack tips as the cause of spalling from subsurface cracks was hypothesised. Ding et al. [1] also performed an elastic–plastic finite element analysis that further evaluated the hypothesis as the failure mechanism of spalling in gears. 2.3. Discussion on crack propagation theories The literature presented above inspired the discussion on the following observations.
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2.3.1. Surface crack propagation is most likely to result in pitting or delamination only Despite the controversy over whether Mode I or II is the dominant mode for surface crack propagation, it can be argued that, if Mode I growth of a surface crack is the dominant mode, the crack would extend along the direction of the maximum shear stress at the crack tip. This direction could be determined according to the initial inclined angle of the surface crack. When the initial angle of the crack is equal to or less than 45◦ , the surface crack would propagate either parallel to the surface or at an angle towards the contact surface. As a result, a very shallow pit would form. When the initial inclined angle of the surface crack is greater than 45◦ , the direction of the surface crack would be downwards into the bulk of the material. On the other hand, if the Mode II growth were the dominant mode, a surface crack would extend along the direction of the surface crack line itself. Both analytical and experimental work discussed in Section 2.1 have demonstrated that a surface crack alone is unable to penetrate into the bulk of material by propagation [10,15,16], regardless which mode dominates the growth. Furthermore, when surface roughness is considered, surface crack growth may end up by cutting off asperities, resulting in delamination. Thus, it can be concluded that surface crack growth in both Modes I and II only results in pitting or delamination. 2.3.2. Though subsurface cracks propagate in Mode II, they do not appear to fail by crack propagation As the general perception shown in the literature, spalling and pitting are assumed to be the result of propagation of a crack until it reaches a critical size. O’regan et al. [17] defined the critical size as a/d = 1, where a is the half crack length and d the depth of the crack from the contact surface. However, the literature discussed previously has demonstrated that subsurface crack growth is very slow. According to the concept of brittle fracture, the SIFs for Modes I and II, obtained by Fleming and Suh [11], were too small to be the driving force for subsurface crack growth. The results of Kaneta et al. [12] showed that, for the case of low coefficients of friction between contact surfaces, i.e. 0 < f < 0.1, the values of SIFs in Mode II, KII , were just in the threshold stress intensity range: KII,th ∼ = 1.5 MPa m1/2 . These results indicated that the growth of a subsurface crack would be very slow, particularly for the case of low friction contact, such as gears. The results of CTSD obtained Sin and Suh [13] also implied a very slow growth of subsurface crack propagation. Besides, the CTSD criterion for crack propagation in elastic–plastic solids proposed by Sin and Suh [13] and Bastias et al [18] lacks support according to available data for such complex loading conditions. Moreover, their work only suites the cases of high surface traction (f ≥ 0.25), such as in abrasive or adhesive sliding wear, but not for the case of gear tooth contact in which f ∼ = 0.06, since the influence of surface traction on subsurface crack propagation is detrimental [19]. Furthermore, the direction of the crack propagation reported in the literature
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Table 1 The maximum values of SIF ( KII ) at subsurface crack tips [1] d/c
0.177 0.237 0.296 0.355 0.414 0.532 0.887
a/c = 0.11
a/c = 0.33
a/c = 0.5
a/c = 0.67
a/c = 0.89
Trailing tip
Lead tip
Trailing tip
Lead tip
Trailing tip
Lead tip
Trailing tip
Lead tip
Trailing tip
Lead tip
3.9677 3.790 3.823 4.571 1.427 1.239 1.393
3.925 3.624 4.469 4.236 1.595 1.177 0.996
6.950 10.657 6.810 6.494 5.840 4.085 –
7.199 7.670 4.314 1.853 1.643 2.504 –
13.402 11.198 15.124 19.926 15.669 13.541 –
18.050 10.763 8.516 11.309 9.793 9.954 –
8.863 8.608 16.174 7.549 11.707 – –
5.818 7.042 12.602 5.141 7.284 – –
13.922 12.009 11.345 8.796 9.602 9.727 –
10.789 15.711 12.880 7.372 6.526 6.992 –
was almost parallel to the contact surface. This does not explain the orientations of the walls of a spall cavity. Although Miller [20] recognized the incapability of Mode II propagation resulting in spalling and attempted to explain such failure as subsurface crack branching in Mode I, the tendency of crack branching shown in Miller’s results did not appear to confirm this theory. Using a realistic asymmetrical gear tooth FE model, Ding et al. [1,14] investigated the behaviour of subsurface cracks under a gear tooth in contact with a heavy contact load and low surface traction. They calculated the stress intensity factors for both Modes I and II of the subsurface cracks beneath a gear tooth surface with normalised size: a/c = 0.89, 0.67, 0.50, 0.11, at normalised depth: d/c = 0.118, 0.177, 0.237, 0.296, 0.355, 0.414, 0.532, 0.887 (where a is the half crack length, c the half contact width, and d the depth of the crack from the contact surface). The highest value of KI obtained was 4.54 MPa m1/2 , which did not exceed the threshold value. On the other hand, the stress intensity factor range in Mode II, KII , was more appealing. As shown in Table 1, the values of KII are generally greater than the threshold value KII,th . However, the highest value of KII is 19.9 MPa m1/2 , less than the suggested critical stress intensity of crack failure Kc ∼ = 20 MP m1/2 by Blake and Cheng [21]. It should be noted here that this value of Kc is conservative. For gear material, the value of Kc should be significantly greater. In summarising the findings from literature, it can be concluded that (1) surface crack propagation only results in pitting or delamination; (2) spalls are developed from subsurface cracks; (3) the growth of a subsurface crack is in Mode II; and (4) a subsurface crack beneath a gear tooth contact surface does not fail by crack propagation. In another word, spalling is not caused by the failure of subsurface cracks.
3. Ligament collapse spalling mechanism 3.1. The hypothesis In searching for the possible cause of spalling, Ding et al. [1] used a general fracture mechanics based approach to investigate the subsurface crack failure by checking if the remaining ligament between the crack tip and the contact
surface had failed. This was done using the following equation: ysurface σe dy ytip (1) σm = ysurface − ytip where σ m is the mean stress in a ligament region, σ e the von Mises stress caused by the contact load, the ligament length: (ysurface −ytip ) is the shortest distance from the crack tip to the contact surface. Comparing σ m to the material ultimate strength, σult = 1207 MPa, it was found that the material in the ligament (ysurface − ytip ) failed during a load cycle for most of the crack cases investigated, and that the crack with size of a/c = 0.5 at the depth of d/c = 0.355 was the most severe case. Based on these results, ligament collapse spalling mechanism for gears was hypothesised as the failure mode of subsurface cracks resulting in spalling. 3.2. Experimental apparatus In order to verify Ding’s hypothesis, an experimental investigation was conducted in the Department of Mechanical Engineering, Monash University, Australia. The aims of the experimental work were to investigate the important phenomenon and interdependencies, as well as to examine experimental evidence to test the proposed gear ligament collapse spalling mechanism. Fig. 2 shows the schematic diagram of the experimental apparatus of the single stage spur gear test rig. As indicated in Fig. 2, the hydraulic gear pump provided input load for the gear set. The load control system included a pressure control valve, a pressure relief valve, two pressure transducers, and amplifiers. The input load was controlled by adjusting the pressure control valve, and monitored constantly by the two pressure transducers. The pressure relief valve installed between the pressure transducers and the control valve for safety. The calibration for the reading of the amplifier meter Re , in terms of the input hydraulic pressure pinput of the pump, was carefully conducted, and the relation between pinput and Re was obtained using the straight line of best fit: pinput (psi) = 2.43 + 420.29Re
(2)
Consequently, the relation between the input hydraulic pressure pinput of the pump and the contact load F on gear tooth
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Fig. 2. Schematic diagram of the gear test rig.
surfaces was derived: F (N) = 43.1 + 0.76pinput
(3)
The lubricating system consisted of an oil pump, an oil filter (3 m pore size), an oil relief valve, an oil jet feeder, and a large oil tank. The oil circulated by the oil pump was first pumped through the oil filter, then injected directly onto the meshing area of the gear teeth through the oil feeder situated on the top of the gear box as shown in Fig. 3. The oil, then, flowed back to the large oil tank where it was cooled down and then re-circulated. In order to keep the oil temperature within the room temperature range, the ratio of the oil volume in the gearbox to that in the tank was 1:20. The brand of the lubricating oil was Spirax hd80w/90, which was additive free. It should be noted that gear lubricants often contain several additives to improve gear life. For example, in the cases
of heavily loaded contacts, as occur in hypoid gear drives, EP (extreme pressure) additives are adopted. However, for this study the lubricant was chosen to be adequate in that it would provide a lubrication film in the elasto-hydrodynamic regime, but in view of the need in minimising the test time, it was not chosen to provide significant increase in life of the gears. The test conditions were deemed to be fair as far as the tooth spalling phenomenon was concerned and subsequent observation proved that the spalling of the test gear teeth was typical of that found in heavily loaded in-service gear drives. 3.3. Gear sets Three pairs of spur gear sets, identical in dimensions, manufacturing process and material, were used in this investigation. Fig. 4 shows one pair of them. The dimension
Fig. 3. The gear transmission and lubrication system with the oil jet feeder.
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Fig. 4. A pair of the tested gear sets.
Table 2 Dimension parameters of the tested gear sets Gears
Pitch diameter (mm)
Teeth num. (z)
Diametral pitch (z/D)
Base Diameter (mm)
Outer diameter (mm)
Pinion Gear
38.1 50.8
24 32
16 16
35.8 47.7
40.6 53.3
parameters of the gears are given in Table 2. They were generated from AISI 4340, a typical through-hardening, annealed steel for gears, of which the material property is given in Table 3. The surface finish of the gear teeth was below 1.6 m roughness, which is the typical smoothness of tooth surface for in-service applications. In order to avoid the phenomenon of case crushing, no case-hardened gears were used. 3.4. Experimental procedure Three sets of the gear pairs were tested with different loading conditions and different operating periods. Before the test, the lubricating oil was filtered through a 3 m filter, then, circulated in the lubricating system of the rig until
a filtergram analysis indicated that there were no particles larger than 3 m in the lubricant. In order to examine the spalling progress on the same teeth at the end of each operation step, three teeth of each gear were chosen randomly and labelled A, B, and C, respectively, as shown in Fig. 4. The test procedure of the first gear set was as follows: (1) Initially, the gears were run for 1 h at a pinion rotation speed of 300 rpm and a low contact load (10 N), in order to smooth the original machine-finished teeth surfaces. (2) Then, the gears were run for 8 h with the operation conditions as the loading stage 1 shown in Table 4, and then stopped. (3) After being removed from the rig, the gears were washed in acetone first, then soaked in Shell X55 solvent in an
Table 3 Material properties of the gears Material
Approximate carbon (%)
Hardness BHN
Modulus of elasticity (GPa)
Yield strength (MPa)
Tensile strength (MPa)
AISI 4340
0.4
350
197
1145
1207
Table 4 Operating and loading conditions of the first gear set Load stage
Pinion speed (RPM)
Contact ratio
Input pressure of the pump (psi)
Contact load (N)
Maximum Hertzian pressure (MPa)
Operating hours
Total test hours
1 2 3 4
1200 1200 1200 1200
1.6 1.6 1.6 1.6
250 500 500 500
233.1 437.7 437.7 437.7
656 898 898 898
8 8 16 32
8 16 32 64
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(4)
(5)
(6)
(7)
(8) (9)
ultrasonic bath for 1 h to remove all of the wear particles, and then dried in a desiccator. The three teeth labelled A, B, and C, on both the pinion and gear were examined using the scanning electron microscope (SEM). The gears were re-assembled into the rig, then set to run for another 8 h. The operating condition was the loading stage 2 as shown in Table 4. Steps 3 and 4 were repeated. Then, the gears were assembled again to the rig and set to run for a further 16 h with the same load (see loading stage 3 in Table 4). Step 6 was repeated with the exception of the running time, which was extended to 32 h for the final operating stage (see loading stage 4 in Table 4). Steps 3 and 4 were repeated to obtain the final surface damage of the gear teeth. After the final SEM examination on the worn surfaces, each selected tooth (labelled A, B, and C) was sawed off from the gear together with the two adjoining teeth, and then cross-sectioned for the preparation of metallographic samples. A spark erosion wire-cutting machine, Hansvedt EDM model serial SM-150B, was used to carry out the cross-section procedure. In order to avoid artefacts, special care was taken to ensure the direction of the cutting, which must be from a worn surface into the bulk of the tooth. The sectioned samples were then carefully mounted, grinded, and polished, following procedures described in ASM Metals Handbook by Knechtel et al. [22]. Fig. 5 shows some of the completed samples. These samples were finally examined in SEM to observe the characteristics of spalls.
The test procedures of the second and third sets of gears followed the same steps as described above but with different operating and loading conditions as shown in Table 5. 3.5. Experimental results According to the different stages of the test, the experimental results are presented in the following two groups: • Spalling features on gear tooth surfaces due to different loading conditions. • Profiles of spall cavities due to different loading conditions. 3.5.1. Spalling features on contact surfaces of gear teeth Although a number of studies of the spalling phenomenon were conducted (e.g. [6,23,24]), there has been no thorough
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Fig. 5. Some cross-sectioned samples.
investigation that focused on the process between the phenomenon and its causes. The first objective of this experimental study was to investigate the variation of spalling features due to the variation of loading conditions. The second objective was to examine the development of spalling from the initiation to the completion. The intent was to encapsulate different stages of the spalling process by observing ‘snapshots’ of random spalling events. It is not possible to ‘snap’ various stages of the progression of a single spall because that the process requires intrusive metallographic sectioning and, anyway, the final creation of a spall (after the period of crack initiation) is thought to take place in a very short interval of time. As outlined in Tables 4 and 5, the maximum Hertzian pressure on the three gear sets were 898, 1503, and 1885 Mpa, respectively. From all the SEM examined contact surfaces, spalls were found to concentrate in a band right across a tooth flank in the region from the pitch line spreading towards the dedendum. Figs. 6–8 reveal the spalling band and some typical spalls on a tooth surface from each set of gears. It is evident that the features of the majority of spall cavities, although randomly different in individual details, are very similar in overall form that seems falling into a pattern, i.e. the cavity of the spalling is formed by a shallow wall and a steep wall along the load rolling direction. The shallow wall lies at the tail of the spall cavity in relation to the load rolling direction and the steep wall lies at the head of the spall cavity. Another common feature of spalling is that all
Table 5 Operation and loading conditions of the second and third gear sets Gear set no.
Pinion speed (RPM)
Contact ratio
Input pressure of the pump (psi)
Contact load (N)
Maximum Hertzian pressure (MPa)
Operating hours
Total test hours
2 3
1200 1200
1.6 1.6
1500 2500
1226.8 1929.7
1503 1885
4 2
4 2
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Fig. 6. Scanning electron micrographs of the wheel in gear set 1 showing the spalling phenomenon after 4.32 × 105 contact cycles under the maximum Hertzian pressure of 898 MPa.
Fig. 7. Scanning electron micrographs of the pinion in gear set 2 showing the spalling phenomenon after 2.88 × 105 contact cycles (4 h engagement) under the maximum Hertzian pressure of 1503 MPa.
the spall cavities have zigzag surfaces. The only difference in spalling phenomenon is that the depth of spalls appeared to become deeper and the size of them be larger as the load increased. 3.5.2. Spalling features observed from sections of gear teeth Though spalling features have been clearly revealed from the worn surfaces, certain aspects of them still need to be further established, such as the depth of a cavity and the slopes of the cavity walls. Furthermore, the formation pro-
cess of a spall cavity, in terms of whether a spall starts to develop from the surface or subsurface, also needs further study. In order to observe these phenomena, some samples of gear tooth cross-sections prepared and examined in SEM. Figs. 9–11 present some of the SEM results. From the SEM results, the features of spalling can be summarised as: (1) spalls are concentrated in the dedendum vicinity of the pitch line (DVP); (2) a spalling cavity consists of a shallow wall and a steep wall; (3) the slope of the shallow wall is about 20–30◦ from the bottom crack line at the trailing tip towards the contact surface, and the slope
Fig. 8. Scanning electron micrographs of the pinion in gear set 3 showing the spalling phenomenon after 1.44 × 105 contact cycles (2 h engagement) under the maximum Hertzian pressure of 1885 MPa.
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Fig. 9. Scanning electron micrographs taken from the gear teeth sections of gear set 1 showing profiles of spall cavities and different stages of spall formation process. The maximum Hertzian pressure for the gear set 1 was 898 MPa.
Fig. 10. Scanning electron micrographs taken from the gear teeth sections of gear set 2 showing profiles of spall cavities and different stages of spall formation process. The maximum Hertzian pressure for the gear set 2 was 1503 MPa.
Fig. 11. Scanning electron micrographs taken from the gear teeth sections of gear set 3 showing profiles of spall cavities and different stages of spall formation process. The maximum Hertzian pressure for the gear set 3 was 1885 MPa.
of the steep wall is about 50 ◦ from bottom crack line at the lead tip towards the contact surface; (4) the orientation of spalling is sensitive to the direction of the contact load movement, i.e. the shallow wall always lies at the tail of the spall cavity and the steep wall lies at the head of the spall cavity in relation to the load rolling direction; (5) both the shallow and steep walls have jagged surfaces; (6) the depth of a spall cavity increases as the normal contact load increases. Furthermore, Figs. 10a and 11b also indicate that spalling is initiated from subsurface cracks. It should be noted that overwhelming SEM micrographs obtained have substantiated this argument. Unfortunately, they are unable to be presented here due to the restriction of the paper length.
4. Discussions Based on the experimental results presented in Sections 3.5.1 and 3.5.2, it is clear that the features of spall cavities, regarding the pattern, orientation, and morphology, are very similar in overall form. These findings are consistent with the prediction of spall formation process, which was proposed by the authors on the basis of the hypothesis of ligament collapse spalling mechanism. It is also observed that the surface morphology of spall cavities is very rough. Figs. 6–8 clearly revealed the jagged wall surfaces. This feature implies that spalling was not caused by brittle fracture. According to the ligament collapse
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hypothesis of the spalling mechanism, a separation plane that forms a wall of a spall cavity should have the feature of jagged surfaces because the actual formation of the separation plane is processed by highly concentrated microcracks joining with each other. These microcracks have formed along the direction of the maximum shear stress in the ligament-collapsed region during the early stage of the contact. All spall images observed from the worn surfaces clearly showed jagged surfaces as one of the features of spalling. Moreover, since that the normal contact load acting in the vicinity of tooth pitch line reaches the maximum, spalling would occur in this region that includes dedendum vicinity of pitch line and addendum vicinity of pitch line (AVP), if the contact load were the only influential factor for the initiation of the microcracks. However, a spalling band was found only in DVP, not AVP. This phenomenon can be explained by dislocation theory (e.g. [25]). According to the theory, two major factors mutually contribute to the initiation of subsurface cracks. One is the magnitude of the loading, which increases the density of dislocations. The other one is whether these dislocations are mobile or non-mobile. Mobile dislocations generally result in plastic deformation, whereas non-mobile dislocations result in crack initiation. Due to the kinematics of gear tooth contact, highly concentrated non-mobile dislocations in DVP are inevitable. The fact that spalls were observed only concentrated in the DVP of a tooth further substantiates the validity of the ligament collapse spalling mechanism. Furthermore, it was also found that the shallow wall of a spall cavity had formed before the formation of the steep wall, as shown in Figs. 6–8. The formation process of a cavity appeared to be caused by the material between subsurface crack(s) and contact surface-breaking out from the cavity. This process seemed to initiate from the trailing section of a cavity, then gradually extend to the head section of the cavity until the completion of the spall formation. Fig. 7c showed the final phase of the formation process and revealed the last piece of the material in a nearly developed spall cavity. When a heavy contact load was applied, the formation of the head part of the spall cavity appeared to be rather catastrophic as shown in Fig. 8c, in which the piece of the surface material in the head part of the cavity collapsed into the cavity. The micrographs in Figs. 9a, 10b and 11a showed that the shallow wall of a cavity is formed at the beginning of the cavity developing stage and before the formation of the steep wall. Fig. 11b showed that the material, between the contact surface and the main crack plane had been ruptured into several chunky-shaped particles. All the spall profiles presented in Figs. 9–11 showed that the angles of the shallow-wall were found in the range of 18–33◦ and the majority is about 30◦ . This agreed well with the slope of the predicted angle of the shallow wall: 33◦ [1]. These are again consistent with the prediction of spall formation process based on the ligament collapse spalling mechanism.
5. Conclusions The following conclusions were drawn based on the predictions of the spalling phenomenon from the application of finite element analysis and the experimental verifications: (1) The position of the spalls could be predicted, as could the initiation of spalls from subsurface cracks, the depth of spalling, and the geometry of the spalling cavity. (2) Results provided plausible support for the hypothesis that ligament collapse associated with subsurface cracks is a primary mechanism of spalling. (3) The current analysis and results clarify much of the past confusion as regards the spalling phenomenon, and they establish a basis for future spalling prediction based on the cyclic-loading induced initiation, collapse, and the interaction of subsurface cracks in the plastically-collapsed region. References [1] Y. Ding, R. Jones, B.T. Kuhnell, Elastic–plastic finite element analysis of spall formation in gears, Wear 197 (1996) 197–205. [2] M. Heems, F. Lagarde, R. Courtel, P. Sorin, C. R. Acad. Sci. 257 (3) (1963) 3293. [3] A.M. Kumar, G.T. Hahn, V. Rubin, Elasto-plastic finite element analyses of two-dimensional rolling and sliding contact deformation of bearing steel, J. Tribol. Trans. ASME 111 (1989) 309–314. [4] L.E. Alban, Systematic Analysis of Gear Failures, ASM International, Metals Park, OH, 1985. [5] R. I. Widner, Rolling Bearing Failures, ASM Metals Handbook, ninth ed., vol. 11, Failure Analysis and Prevention, ASM International, Metals Park, OH, 1986, pp. 490–511. [6] T.E. Tallian, Failure Atlas for Hertz Contact Machine Elements, New York, 1992. [7] S. Way, Pitting due to rolling contact, J. Appl. Mech. Trans. ASME 2 (1935) A49. [8] L.M. Keer, M.D. Bryant, A pitting model for rolling contact fatigue, J. Lubr. Technol. Trans. ASME 105 (1983) 198–205. [9] A.F. Bower, The influence of crack face friction and trapped fluid on surface initiated rolling contact fatigue cracks, Trans. ASME, JOT 110 (1988) 704–711. [10] H.S. Cheng, L.M. Keer, T. Mura, Analytical modelling of surface pitting in simulated gear-teeth contacts, SAE Technical Paper, No. 841086, 1984, pp. 4.987–4.995. [11] J.F. Fleming, N.P. Suh, Mechanics of crack propagation in delamination wear, Wear 44 (1977) 39–56. [12] K. Kaneta, Y. Murakami, T. Okazaki, Growth mechanism of subsurface crack due to Hertzian contact, J. Tribol. Trans. ASME 108 (1986) 134–139. [13] H.-C. Sin, N.P. Suh, Subsurface crack propagation due to surface traction in sliding wear, J. Appl. Mech. Trans. ASME 51 (1984) 317–323. [14] Y. Ding, R. Jones, B.T. Kuhnell, Numerical analysis of subsurface crack failure beneath the pitch line of a gear tooth during engagement, Wear 185 (1995) 141–149. [15] M. Kaneta, H. Yatsuzuka, Y. Murakami, Mechanism of crack growth in lubricated rolling/sliding contact, ASLE Trans. 28 (1985) 407–414. [16] T.M. Clarke, G.R. Miller, L.M.. Keer, H.C. Cheng, The role of near-surface inclusions in the pitting of gears, ASLE Trans. 28 (1) (1985) 111–116. [17] B.D. O’regan, G.T. Hahn, C.A. Rubin, The driving force for Mode II crack growth under rolling contact, Wear 101 (1985) 333–346.
Y. Ding, N.F. Rieger / Wear 254 (2003) 1307–1317 [18] P.C. Bastias, G.T. Hahn, C.A. Rubin, Finite element modelling of subsurface Mode II cracks under contact loads, Eng. Fracture Mech. 33 (1) (1989) 143–152. [19] L.M. Keer, M.D. Bryant, G.K. Haritos, Subsurface and surface cracking due to Hertzian contact, J. Lubr. Technol. Trans. ASME 104 (1982) 347–351. [20] G.R. Miller, A preliminary analysis of subsurface crack branching under a surface compressive load, J. Tribol. Trans. ASME 110 (1988) 292–296. [21] J.W. Blake, H.S. Cheng, A surface pitting life model for spur gears. Part I. Life prediction, J. Tribol. Trans. ASME 113 (1991) 712– 718.
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[22] H.E. Knechtel, W.F. Kindle, J.L. McCall, R.D. Buchheit, Metallographic Methods, ASM Metal Handbook, eighth ed., vol. 8, American Society of Metals, Metals Park, OH, 1973, pp. 1–14. [23] M.L. Atkin, R.A. Cummins, G.P. Sharp, A Study of Gear Wear in a Model Gearbox, Mechanical Engineering Transactions, The Institute of Engineers, Australia, 1979, pp. 40–52. [24] X.Z. Jin, N.Z. Kang, A study on rolling bearing contact fatigue failure by macro-observation and micro-analysis, in: Proceedings of the International Conference on Wear of Materials, Denver, CO, USA, 1989, pp. 205–213. [25] D.C. Stouffer, L.T. Dame, Inelastic Deformation of Metals: Models, Mechanical Properties, and Metallurgy, Wiley, New York, 1996.
Spalling formation mechanism for gears Yan Ding a,∗ , Neville F. Rieger b a
Department of Mathematics, RMIT University, City Campus GPO Box 2476V, Melbourne 3001, Australia b Stress Technology Incorporated, Rochester, NY, USA Accepted 24 February 2003
Abstract Though the basic phenomenon of wear on gear tooth contact surfaces is the removal of a piece of material from the working surface, the sizes of the wear debris may be different, due to the different physical causes in their formation processes. No common definitions have been established to distinguish spalling from pitting in the literature. This is probably due to the fact that the physical causes of pitting and spalling have not yet been established. In this paper, a brief literature review is presented with the intention to differentiate spalling from pitting. Three types of wear phenomena are defined. Furthermore, the results of a recent experimental study of gear tooth spalling formation in AISI 4340 gears in a test rig are also presented to demonstrate a possible process of spalling due to the development of cracks beneath the tooth contact surfaces and crack linkages in plastically-collapsed metal ligament between the crack tip and the adjacent tooth contact surface. These experimental results substantiated the ligament collapse spalling mechanism proposed by Ding et al. [Y. Ding, R. Jones, B.T. Kuhnell, Elastic–plastic finite element analysis of spall formation in gears, Wear 197 (1996) 197–205; M. Heems, F. Lagarde, R. Courtel, P. Sorin, C. R. Acad. Sci. 257 (3) (1963) 3293]. © 2003 Published by Elsevier Science B.V. Keywords: Spalling; Subsurface cracks; Crack failure; Ligament collapse
1. Introduction Gearing is an essential component of many machines. From aerospace to high-speed automation, from missiles to submarines, few machines can operate without gears. Since gears transmit motion and power through the surface contact, good gearing performance depends on the durability of their teeth surfaces. Generally, there are four basic wear modes: contact fatigue, adhesion, abrasion and corrosion. Under normal operating conditions, contact fatigue is one of the most common failure modes for gear tooth surfaces. Gear tooth interaction causes mild adhesive wear throughout the life of the gear drive. This is called normal rubbing wear and is characterised by particles smaller than 10 m. This is seen as a smoothing of the gear tooth surfaces as a result of mild plastic deformation of asperities. This type of deformation causes a very thin work-hardened surface layer. The thickness of this work-hardened layer is roughly of the order of the asperity widths, i.e. typically less than 10 m [2,3]. Generally, there are two types of surface contact fatigue, namely, pitting and spalling. Pitting appears as shallow craters at contact surfaces. The maximum depth of a pit is about the thickness of the work-hardened layer (≈10 m). ∗ Corresponding author. Tel.: +61-3-9925-2283; fax: +61-3-9925-1748. E-mail address: [email protected] (Y. Ding).
0043-1648/$ – see front matter © 2003 Published by Elsevier Science B.V. doi:10.1016/S0043-1648(03)00126-1
Spalling appears as deeper (typically 20–100 m) cavities at contact surfaces with a depth of 0.25 to 0.35 of the half contact width (usually denoted as “c” in fracture mechanics literature). Fig. 1 illustrates the phenomena of pitting and spalling. It must be noted here that no common definitions have been established to consistently distinguish spalling from pitting in the literature. In much of the literature, spalling and pitting were used indiscriminately, and in some literature, spalling and pitting were used to designate different severities of surface contact fatigue [4,5]. Tallian [6] defined “spalling” as macro-scale contact fatigue caused by fatigue crack propagation and reserved “pitting” as surface damage caused by sources other than crack propagation. One of the reasons for the confusion in the definitions is probably due to the fact that the physical causes of pitting and spalling have not yet been convincingly established. This is one of the major reasons for performing the study described here. In order to discuss the issue on a consistent ground, for this paper, pitting and spalling are defined according to the observed phenomena as discussed above. Pitting is taken to be the formation of shallow craters (<10 m) that are mainly developed from surface-defects, and spalling is taken to be the formation of deeper cavities that are mainly developed from subsurface-defects. Though both spalling and pitting are the common forms of surface contact fatigue, compared
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Fig. 1. Schematic illustration of pitting and spalling phenomena.
to pitting, spalling results in more rapid deterioration of surface durability, and often induces early failure by severe secondary damage. It has been often reported as the most destructive surface failure mode of a gear (e.g. [4]). A detailed understanding of spalling is not only essential for detecting incipient gear failure, before it becomes disastrous and causes expensive secondary damage, but is also central for planning preventative maintenance for gear components. Furthermore, it can also be used to determine the critical parameters for designing gears that satisfy special requirements. One instance is the design of gears with the maximum capacity and the minimum size and weight, for high-speed automation or aerospace power transmissions. Although there has been considerable research devoted to this area over the last half-century, there is still lack of a thorough understanding of the spalling formation process on gears. Most of the relevant previous work concentrated on symmetrical contact problems. The knowledge of subsurface crack behaviour with non-symmetrical contact geometry is very limited. The majority of the previously reported research has focused on either metallurgical studies of the worn material, or on the theoretical analysis of the behaviour of subsurface cracks. There appears little published work aimed to achieve a mutual agreement from the results of these two aspects of the research. Neither much study was focused on the stress state change of the material between the contact surface and subsurface crack tips, which is of great practical interest in regard to the physical process of spalling formation. The objective of this research is to investigate the spalling mechanism in gears by studying the behaviour of subsurface cracks. The behaviour of surface cracks under contact loading is controlled by a different mechanism and needs to be studied separately. 2. Previous research on crack propagation and failure Three stages are involved in the formation process of a spall: crack initiation, crack propagation and failure. It has been well documented that crack initiation is resulted
from an inclusion or a hard particle, as well as material defects such as flaws and pre-existing dislocations. After a crack initiates, the cyclic contact stress produced by repeated rolling or rolling–sliding contacts drives cracks to grow. Eventually, failure of cracks will take place and result in some kind of surface contact damage, such as spalling, pitting, or delamination. In general, the study of surface contact damage reported in literature may be divided into two groups: surface-defect-origin contact fatigue and subsurfacedefect-origin contact fatigue, which are discussed in following subsections. 2.1. Existing theories of surface-defect-origin contact fatigue For decades, there has been a dominant opinion in literature regarding spalling/pitting formation, which considered that, as surface cracks driven by a liquid lubricant, spalling/pitting was the result of surface crack propagation in the direction of contact travel. This opinion was based on Way’s hypothesis [7], which postulated that lubricating oil pre-filled in a surface crack was trapped between the crack surfaces when the approaching contact reached the surface opening and pinched the crack closed. As a result, the crack tip was extended by a hydraulic pressure of the lubricant oil sealed between the crack surfaces. The extensively quoted Way’s hypothesis was not challenged until a half-century later. Keer and Bryant [8] simulated Way’s experiments and found that the dominant mechanism for surface-breaking crack growth was mode II (shear) propagation. Their conclusion is not consistent with Way’s assumption of Mode I (tension) crack propagation. However, they also suggested that the phenomenon of crack curving, i.e. changing its direction to the contact surface to form a crater or cavity, could be due to the influence of tensile rather than shear stress. Bower [9] performed a fracture mechanics analysis of crack propagation in the presence of lubricating oil. His results did not appear to support Way’s hypothesis, either. Furthermore, the experimental results obtained by Cheng et al. [10] showed that the surface crack growth was very slow and the depth of the slowly growing surface cracks was in the
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range of 5–10 m. Therefore, it is almost impossible to form a spall cavity from surface crack growth, unless there is a near-surface inclusion to act as a bridge to significantly accelerate the propagation of the surface crack into the subsurface region. 2.2. Existing theories of subsurface-defect-origin contact fatigue Many researchers have also studied the behaviour of subsurface cracks under contact loads for the purpose of understanding of spalling/pitting mechanisms. Among them, Fleming and Suh [11] were the first ones who utilised fracture mechanics as a method to analyse the propagation of subsurface cracks parallel to the contact surface. Their results showed that the stress intensity factors (SIFs) for Modes I and II were very low. Kaneta et al. [12] studied the growth mechanism of subsurface cracks by numerically analysing the behaviour of a three-dimensional subsurface crack parallel to the contact surface. They concluded that the propagation of subsurface cracks is mainly by Mode II. They also found that the direction of the Mode II propagation was different for the trailing and leading tips of the crack with respect to the direction of the surface traction. The tip at the trailing side of the traction extends along the crack line, and the tip at the leading side extended towards the surface at an angle less than 6.2◦ . Sin and Suh [13] studied the mechanism of subsurface crack propagation in sliding elastic–plastic solids using the finite element analysis. They suggested that crack tip sliding displacement (CTSD) be taken as the propagation rate of subsurface cracks. They also suggested that the direction of the propagation be the direction of the maximum shear stress in front of the crack tip and along an angle between −5 and 5◦ to the crack line, implying that the propagation was almost parallel to the contact surface. They claimed that, based on the CTSDs calculated using FEA, their predicted wear rates compared favourably with the experimentally determined wear rates. More recently, Ding et al. [14] studied the behaviour of subsurface cracks beneath the pitch line of a gear tooth with a view to develop a fundamental understanding of the spalling mechanism in gears. Using the finite element method, they analysed the potential modes of crack propagation and failure, and found that the values of the stress intensity factors of the subsurface cracks were below the critical SIF, Kc . Consequently, ligament collapse at crack tips as the cause of spalling from subsurface cracks was hypothesised. Ding et al. [1] also performed an elastic–plastic finite element analysis that further evaluated the hypothesis as the failure mechanism of spalling in gears. 2.3. Discussion on crack propagation theories The literature presented above inspired the discussion on the following observations.
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2.3.1. Surface crack propagation is most likely to result in pitting or delamination only Despite the controversy over whether Mode I or II is the dominant mode for surface crack propagation, it can be argued that, if Mode I growth of a surface crack is the dominant mode, the crack would extend along the direction of the maximum shear stress at the crack tip. This direction could be determined according to the initial inclined angle of the surface crack. When the initial angle of the crack is equal to or less than 45◦ , the surface crack would propagate either parallel to the surface or at an angle towards the contact surface. As a result, a very shallow pit would form. When the initial inclined angle of the surface crack is greater than 45◦ , the direction of the surface crack would be downwards into the bulk of the material. On the other hand, if the Mode II growth were the dominant mode, a surface crack would extend along the direction of the surface crack line itself. Both analytical and experimental work discussed in Section 2.1 have demonstrated that a surface crack alone is unable to penetrate into the bulk of material by propagation [10,15,16], regardless which mode dominates the growth. Furthermore, when surface roughness is considered, surface crack growth may end up by cutting off asperities, resulting in delamination. Thus, it can be concluded that surface crack growth in both Modes I and II only results in pitting or delamination. 2.3.2. Though subsurface cracks propagate in Mode II, they do not appear to fail by crack propagation As the general perception shown in the literature, spalling and pitting are assumed to be the result of propagation of a crack until it reaches a critical size. O’regan et al. [17] defined the critical size as a/d = 1, where a is the half crack length and d the depth of the crack from the contact surface. However, the literature discussed previously has demonstrated that subsurface crack growth is very slow. According to the concept of brittle fracture, the SIFs for Modes I and II, obtained by Fleming and Suh [11], were too small to be the driving force for subsurface crack growth. The results of Kaneta et al. [12] showed that, for the case of low coefficients of friction between contact surfaces, i.e. 0 < f < 0.1, the values of SIFs in Mode II, KII , were just in the threshold stress intensity range: KII,th ∼ = 1.5 MPa m1/2 . These results indicated that the growth of a subsurface crack would be very slow, particularly for the case of low friction contact, such as gears. The results of CTSD obtained Sin and Suh [13] also implied a very slow growth of subsurface crack propagation. Besides, the CTSD criterion for crack propagation in elastic–plastic solids proposed by Sin and Suh [13] and Bastias et al [18] lacks support according to available data for such complex loading conditions. Moreover, their work only suites the cases of high surface traction (f ≥ 0.25), such as in abrasive or adhesive sliding wear, but not for the case of gear tooth contact in which f ∼ = 0.06, since the influence of surface traction on subsurface crack propagation is detrimental [19]. Furthermore, the direction of the crack propagation reported in the literature
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Table 1 The maximum values of SIF ( KII ) at subsurface crack tips [1] d/c
0.177 0.237 0.296 0.355 0.414 0.532 0.887
a/c = 0.11
a/c = 0.33
a/c = 0.5
a/c = 0.67
a/c = 0.89
Trailing tip
Lead tip
Trailing tip
Lead tip
Trailing tip
Lead tip
Trailing tip
Lead tip
Trailing tip
Lead tip
3.9677 3.790 3.823 4.571 1.427 1.239 1.393
3.925 3.624 4.469 4.236 1.595 1.177 0.996
6.950 10.657 6.810 6.494 5.840 4.085 –
7.199 7.670 4.314 1.853 1.643 2.504 –
13.402 11.198 15.124 19.926 15.669 13.541 –
18.050 10.763 8.516 11.309 9.793 9.954 –
8.863 8.608 16.174 7.549 11.707 – –
5.818 7.042 12.602 5.141 7.284 – –
13.922 12.009 11.345 8.796 9.602 9.727 –
10.789 15.711 12.880 7.372 6.526 6.992 –
was almost parallel to the contact surface. This does not explain the orientations of the walls of a spall cavity. Although Miller [20] recognized the incapability of Mode II propagation resulting in spalling and attempted to explain such failure as subsurface crack branching in Mode I, the tendency of crack branching shown in Miller’s results did not appear to confirm this theory. Using a realistic asymmetrical gear tooth FE model, Ding et al. [1,14] investigated the behaviour of subsurface cracks under a gear tooth in contact with a heavy contact load and low surface traction. They calculated the stress intensity factors for both Modes I and II of the subsurface cracks beneath a gear tooth surface with normalised size: a/c = 0.89, 0.67, 0.50, 0.11, at normalised depth: d/c = 0.118, 0.177, 0.237, 0.296, 0.355, 0.414, 0.532, 0.887 (where a is the half crack length, c the half contact width, and d the depth of the crack from the contact surface). The highest value of KI obtained was 4.54 MPa m1/2 , which did not exceed the threshold value. On the other hand, the stress intensity factor range in Mode II, KII , was more appealing. As shown in Table 1, the values of KII are generally greater than the threshold value KII,th . However, the highest value of KII is 19.9 MPa m1/2 , less than the suggested critical stress intensity of crack failure Kc ∼ = 20 MP m1/2 by Blake and Cheng [21]. It should be noted here that this value of Kc is conservative. For gear material, the value of Kc should be significantly greater. In summarising the findings from literature, it can be concluded that (1) surface crack propagation only results in pitting or delamination; (2) spalls are developed from subsurface cracks; (3) the growth of a subsurface crack is in Mode II; and (4) a subsurface crack beneath a gear tooth contact surface does not fail by crack propagation. In another word, spalling is not caused by the failure of subsurface cracks.
3. Ligament collapse spalling mechanism 3.1. The hypothesis In searching for the possible cause of spalling, Ding et al. [1] used a general fracture mechanics based approach to investigate the subsurface crack failure by checking if the remaining ligament between the crack tip and the contact
surface had failed. This was done using the following equation: ysurface σe dy ytip (1) σm = ysurface − ytip where σ m is the mean stress in a ligament region, σ e the von Mises stress caused by the contact load, the ligament length: (ysurface −ytip ) is the shortest distance from the crack tip to the contact surface. Comparing σ m to the material ultimate strength, σult = 1207 MPa, it was found that the material in the ligament (ysurface − ytip ) failed during a load cycle for most of the crack cases investigated, and that the crack with size of a/c = 0.5 at the depth of d/c = 0.355 was the most severe case. Based on these results, ligament collapse spalling mechanism for gears was hypothesised as the failure mode of subsurface cracks resulting in spalling. 3.2. Experimental apparatus In order to verify Ding’s hypothesis, an experimental investigation was conducted in the Department of Mechanical Engineering, Monash University, Australia. The aims of the experimental work were to investigate the important phenomenon and interdependencies, as well as to examine experimental evidence to test the proposed gear ligament collapse spalling mechanism. Fig. 2 shows the schematic diagram of the experimental apparatus of the single stage spur gear test rig. As indicated in Fig. 2, the hydraulic gear pump provided input load for the gear set. The load control system included a pressure control valve, a pressure relief valve, two pressure transducers, and amplifiers. The input load was controlled by adjusting the pressure control valve, and monitored constantly by the two pressure transducers. The pressure relief valve installed between the pressure transducers and the control valve for safety. The calibration for the reading of the amplifier meter Re , in terms of the input hydraulic pressure pinput of the pump, was carefully conducted, and the relation between pinput and Re was obtained using the straight line of best fit: pinput (psi) = 2.43 + 420.29Re
(2)
Consequently, the relation between the input hydraulic pressure pinput of the pump and the contact load F on gear tooth
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Fig. 2. Schematic diagram of the gear test rig.
surfaces was derived: F (N) = 43.1 + 0.76pinput
(3)
The lubricating system consisted of an oil pump, an oil filter (3 m pore size), an oil relief valve, an oil jet feeder, and a large oil tank. The oil circulated by the oil pump was first pumped through the oil filter, then injected directly onto the meshing area of the gear teeth through the oil feeder situated on the top of the gear box as shown in Fig. 3. The oil, then, flowed back to the large oil tank where it was cooled down and then re-circulated. In order to keep the oil temperature within the room temperature range, the ratio of the oil volume in the gearbox to that in the tank was 1:20. The brand of the lubricating oil was Spirax hd80w/90, which was additive free. It should be noted that gear lubricants often contain several additives to improve gear life. For example, in the cases
of heavily loaded contacts, as occur in hypoid gear drives, EP (extreme pressure) additives are adopted. However, for this study the lubricant was chosen to be adequate in that it would provide a lubrication film in the elasto-hydrodynamic regime, but in view of the need in minimising the test time, it was not chosen to provide significant increase in life of the gears. The test conditions were deemed to be fair as far as the tooth spalling phenomenon was concerned and subsequent observation proved that the spalling of the test gear teeth was typical of that found in heavily loaded in-service gear drives. 3.3. Gear sets Three pairs of spur gear sets, identical in dimensions, manufacturing process and material, were used in this investigation. Fig. 4 shows one pair of them. The dimension
Fig. 3. The gear transmission and lubrication system with the oil jet feeder.
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Fig. 4. A pair of the tested gear sets.
Table 2 Dimension parameters of the tested gear sets Gears
Pitch diameter (mm)
Teeth num. (z)
Diametral pitch (z/D)
Base Diameter (mm)
Outer diameter (mm)
Pinion Gear
38.1 50.8
24 32
16 16
35.8 47.7
40.6 53.3
parameters of the gears are given in Table 2. They were generated from AISI 4340, a typical through-hardening, annealed steel for gears, of which the material property is given in Table 3. The surface finish of the gear teeth was below 1.6 m roughness, which is the typical smoothness of tooth surface for in-service applications. In order to avoid the phenomenon of case crushing, no case-hardened gears were used. 3.4. Experimental procedure Three sets of the gear pairs were tested with different loading conditions and different operating periods. Before the test, the lubricating oil was filtered through a 3 m filter, then, circulated in the lubricating system of the rig until
a filtergram analysis indicated that there were no particles larger than 3 m in the lubricant. In order to examine the spalling progress on the same teeth at the end of each operation step, three teeth of each gear were chosen randomly and labelled A, B, and C, respectively, as shown in Fig. 4. The test procedure of the first gear set was as follows: (1) Initially, the gears were run for 1 h at a pinion rotation speed of 300 rpm and a low contact load (10 N), in order to smooth the original machine-finished teeth surfaces. (2) Then, the gears were run for 8 h with the operation conditions as the loading stage 1 shown in Table 4, and then stopped. (3) After being removed from the rig, the gears were washed in acetone first, then soaked in Shell X55 solvent in an
Table 3 Material properties of the gears Material
Approximate carbon (%)
Hardness BHN
Modulus of elasticity (GPa)
Yield strength (MPa)
Tensile strength (MPa)
AISI 4340
0.4
350
197
1145
1207
Table 4 Operating and loading conditions of the first gear set Load stage
Pinion speed (RPM)
Contact ratio
Input pressure of the pump (psi)
Contact load (N)
Maximum Hertzian pressure (MPa)
Operating hours
Total test hours
1 2 3 4
1200 1200 1200 1200
1.6 1.6 1.6 1.6
250 500 500 500
233.1 437.7 437.7 437.7
656 898 898 898
8 8 16 32
8 16 32 64
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(4)
(5)
(6)
(7)
(8) (9)
ultrasonic bath for 1 h to remove all of the wear particles, and then dried in a desiccator. The three teeth labelled A, B, and C, on both the pinion and gear were examined using the scanning electron microscope (SEM). The gears were re-assembled into the rig, then set to run for another 8 h. The operating condition was the loading stage 2 as shown in Table 4. Steps 3 and 4 were repeated. Then, the gears were assembled again to the rig and set to run for a further 16 h with the same load (see loading stage 3 in Table 4). Step 6 was repeated with the exception of the running time, which was extended to 32 h for the final operating stage (see loading stage 4 in Table 4). Steps 3 and 4 were repeated to obtain the final surface damage of the gear teeth. After the final SEM examination on the worn surfaces, each selected tooth (labelled A, B, and C) was sawed off from the gear together with the two adjoining teeth, and then cross-sectioned for the preparation of metallographic samples. A spark erosion wire-cutting machine, Hansvedt EDM model serial SM-150B, was used to carry out the cross-section procedure. In order to avoid artefacts, special care was taken to ensure the direction of the cutting, which must be from a worn surface into the bulk of the tooth. The sectioned samples were then carefully mounted, grinded, and polished, following procedures described in ASM Metals Handbook by Knechtel et al. [22]. Fig. 5 shows some of the completed samples. These samples were finally examined in SEM to observe the characteristics of spalls.
The test procedures of the second and third sets of gears followed the same steps as described above but with different operating and loading conditions as shown in Table 5. 3.5. Experimental results According to the different stages of the test, the experimental results are presented in the following two groups: • Spalling features on gear tooth surfaces due to different loading conditions. • Profiles of spall cavities due to different loading conditions. 3.5.1. Spalling features on contact surfaces of gear teeth Although a number of studies of the spalling phenomenon were conducted (e.g. [6,23,24]), there has been no thorough
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Fig. 5. Some cross-sectioned samples.
investigation that focused on the process between the phenomenon and its causes. The first objective of this experimental study was to investigate the variation of spalling features due to the variation of loading conditions. The second objective was to examine the development of spalling from the initiation to the completion. The intent was to encapsulate different stages of the spalling process by observing ‘snapshots’ of random spalling events. It is not possible to ‘snap’ various stages of the progression of a single spall because that the process requires intrusive metallographic sectioning and, anyway, the final creation of a spall (after the period of crack initiation) is thought to take place in a very short interval of time. As outlined in Tables 4 and 5, the maximum Hertzian pressure on the three gear sets were 898, 1503, and 1885 Mpa, respectively. From all the SEM examined contact surfaces, spalls were found to concentrate in a band right across a tooth flank in the region from the pitch line spreading towards the dedendum. Figs. 6–8 reveal the spalling band and some typical spalls on a tooth surface from each set of gears. It is evident that the features of the majority of spall cavities, although randomly different in individual details, are very similar in overall form that seems falling into a pattern, i.e. the cavity of the spalling is formed by a shallow wall and a steep wall along the load rolling direction. The shallow wall lies at the tail of the spall cavity in relation to the load rolling direction and the steep wall lies at the head of the spall cavity. Another common feature of spalling is that all
Table 5 Operation and loading conditions of the second and third gear sets Gear set no.
Pinion speed (RPM)
Contact ratio
Input pressure of the pump (psi)
Contact load (N)
Maximum Hertzian pressure (MPa)
Operating hours
Total test hours
2 3
1200 1200
1.6 1.6
1500 2500
1226.8 1929.7
1503 1885
4 2
4 2
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Fig. 6. Scanning electron micrographs of the wheel in gear set 1 showing the spalling phenomenon after 4.32 × 105 contact cycles under the maximum Hertzian pressure of 898 MPa.
Fig. 7. Scanning electron micrographs of the pinion in gear set 2 showing the spalling phenomenon after 2.88 × 105 contact cycles (4 h engagement) under the maximum Hertzian pressure of 1503 MPa.
the spall cavities have zigzag surfaces. The only difference in spalling phenomenon is that the depth of spalls appeared to become deeper and the size of them be larger as the load increased. 3.5.2. Spalling features observed from sections of gear teeth Though spalling features have been clearly revealed from the worn surfaces, certain aspects of them still need to be further established, such as the depth of a cavity and the slopes of the cavity walls. Furthermore, the formation pro-
cess of a spall cavity, in terms of whether a spall starts to develop from the surface or subsurface, also needs further study. In order to observe these phenomena, some samples of gear tooth cross-sections prepared and examined in SEM. Figs. 9–11 present some of the SEM results. From the SEM results, the features of spalling can be summarised as: (1) spalls are concentrated in the dedendum vicinity of the pitch line (DVP); (2) a spalling cavity consists of a shallow wall and a steep wall; (3) the slope of the shallow wall is about 20–30◦ from the bottom crack line at the trailing tip towards the contact surface, and the slope
Fig. 8. Scanning electron micrographs of the pinion in gear set 3 showing the spalling phenomenon after 1.44 × 105 contact cycles (2 h engagement) under the maximum Hertzian pressure of 1885 MPa.
Y. Ding, N.F. Rieger / Wear 254 (2003) 1307–1317
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Fig. 9. Scanning electron micrographs taken from the gear teeth sections of gear set 1 showing profiles of spall cavities and different stages of spall formation process. The maximum Hertzian pressure for the gear set 1 was 898 MPa.
Fig. 10. Scanning electron micrographs taken from the gear teeth sections of gear set 2 showing profiles of spall cavities and different stages of spall formation process. The maximum Hertzian pressure for the gear set 2 was 1503 MPa.
Fig. 11. Scanning electron micrographs taken from the gear teeth sections of gear set 3 showing profiles of spall cavities and different stages of spall formation process. The maximum Hertzian pressure for the gear set 3 was 1885 MPa.
of the steep wall is about 50 ◦ from bottom crack line at the lead tip towards the contact surface; (4) the orientation of spalling is sensitive to the direction of the contact load movement, i.e. the shallow wall always lies at the tail of the spall cavity and the steep wall lies at the head of the spall cavity in relation to the load rolling direction; (5) both the shallow and steep walls have jagged surfaces; (6) the depth of a spall cavity increases as the normal contact load increases. Furthermore, Figs. 10a and 11b also indicate that spalling is initiated from subsurface cracks. It should be noted that overwhelming SEM micrographs obtained have substantiated this argument. Unfortunately, they are unable to be presented here due to the restriction of the paper length.
4. Discussions Based on the experimental results presented in Sections 3.5.1 and 3.5.2, it is clear that the features of spall cavities, regarding the pattern, orientation, and morphology, are very similar in overall form. These findings are consistent with the prediction of spall formation process, which was proposed by the authors on the basis of the hypothesis of ligament collapse spalling mechanism. It is also observed that the surface morphology of spall cavities is very rough. Figs. 6–8 clearly revealed the jagged wall surfaces. This feature implies that spalling was not caused by brittle fracture. According to the ligament collapse
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hypothesis of the spalling mechanism, a separation plane that forms a wall of a spall cavity should have the feature of jagged surfaces because the actual formation of the separation plane is processed by highly concentrated microcracks joining with each other. These microcracks have formed along the direction of the maximum shear stress in the ligament-collapsed region during the early stage of the contact. All spall images observed from the worn surfaces clearly showed jagged surfaces as one of the features of spalling. Moreover, since that the normal contact load acting in the vicinity of tooth pitch line reaches the maximum, spalling would occur in this region that includes dedendum vicinity of pitch line and addendum vicinity of pitch line (AVP), if the contact load were the only influential factor for the initiation of the microcracks. However, a spalling band was found only in DVP, not AVP. This phenomenon can be explained by dislocation theory (e.g. [25]). According to the theory, two major factors mutually contribute to the initiation of subsurface cracks. One is the magnitude of the loading, which increases the density of dislocations. The other one is whether these dislocations are mobile or non-mobile. Mobile dislocations generally result in plastic deformation, whereas non-mobile dislocations result in crack initiation. Due to the kinematics of gear tooth contact, highly concentrated non-mobile dislocations in DVP are inevitable. The fact that spalls were observed only concentrated in the DVP of a tooth further substantiates the validity of the ligament collapse spalling mechanism. Furthermore, it was also found that the shallow wall of a spall cavity had formed before the formation of the steep wall, as shown in Figs. 6–8. The formation process of a cavity appeared to be caused by the material between subsurface crack(s) and contact surface-breaking out from the cavity. This process seemed to initiate from the trailing section of a cavity, then gradually extend to the head section of the cavity until the completion of the spall formation. Fig. 7c showed the final phase of the formation process and revealed the last piece of the material in a nearly developed spall cavity. When a heavy contact load was applied, the formation of the head part of the spall cavity appeared to be rather catastrophic as shown in Fig. 8c, in which the piece of the surface material in the head part of the cavity collapsed into the cavity. The micrographs in Figs. 9a, 10b and 11a showed that the shallow wall of a cavity is formed at the beginning of the cavity developing stage and before the formation of the steep wall. Fig. 11b showed that the material, between the contact surface and the main crack plane had been ruptured into several chunky-shaped particles. All the spall profiles presented in Figs. 9–11 showed that the angles of the shallow-wall were found in the range of 18–33◦ and the majority is about 30◦ . This agreed well with the slope of the predicted angle of the shallow wall: 33◦ [1]. These are again consistent with the prediction of spall formation process based on the ligament collapse spalling mechanism.
5. Conclusions The following conclusions were drawn based on the predictions of the spalling phenomenon from the application of finite element analysis and the experimental verifications: (1) The position of the spalls could be predicted, as could the initiation of spalls from subsurface cracks, the depth of spalling, and the geometry of the spalling cavity. (2) Results provided plausible support for the hypothesis that ligament collapse associated with subsurface cracks is a primary mechanism of spalling. (3) The current analysis and results clarify much of the past confusion as regards the spalling phenomenon, and they establish a basis for future spalling prediction based on the cyclic-loading induced initiation, collapse, and the interaction of subsurface cracks in the plastically-collapsed region. References [1] Y. Ding, R. Jones, B.T. Kuhnell, Elastic–plastic finite element analysis of spall formation in gears, Wear 197 (1996) 197–205. [2] M. Heems, F. Lagarde, R. Courtel, P. Sorin, C. R. Acad. Sci. 257 (3) (1963) 3293. [3] A.M. Kumar, G.T. Hahn, V. Rubin, Elasto-plastic finite element analyses of two-dimensional rolling and sliding contact deformation of bearing steel, J. Tribol. Trans. ASME 111 (1989) 309–314. [4] L.E. Alban, Systematic Analysis of Gear Failures, ASM International, Metals Park, OH, 1985. [5] R. I. Widner, Rolling Bearing Failures, ASM Metals Handbook, ninth ed., vol. 11, Failure Analysis and Prevention, ASM International, Metals Park, OH, 1986, pp. 490–511. [6] T.E. Tallian, Failure Atlas for Hertz Contact Machine Elements, New York, 1992. [7] S. Way, Pitting due to rolling contact, J. Appl. Mech. Trans. ASME 2 (1935) A49. [8] L.M. Keer, M.D. Bryant, A pitting model for rolling contact fatigue, J. Lubr. Technol. Trans. ASME 105 (1983) 198–205. [9] A.F. Bower, The influence of crack face friction and trapped fluid on surface initiated rolling contact fatigue cracks, Trans. ASME, JOT 110 (1988) 704–711. [10] H.S. Cheng, L.M. Keer, T. Mura, Analytical modelling of surface pitting in simulated gear-teeth contacts, SAE Technical Paper, No. 841086, 1984, pp. 4.987–4.995. [11] J.F. Fleming, N.P. Suh, Mechanics of crack propagation in delamination wear, Wear 44 (1977) 39–56. [12] K. Kaneta, Y. Murakami, T. Okazaki, Growth mechanism of subsurface crack due to Hertzian contact, J. Tribol. Trans. ASME 108 (1986) 134–139. [13] H.-C. Sin, N.P. Suh, Subsurface crack propagation due to surface traction in sliding wear, J. Appl. Mech. Trans. ASME 51 (1984) 317–323. [14] Y. Ding, R. Jones, B.T. Kuhnell, Numerical analysis of subsurface crack failure beneath the pitch line of a gear tooth during engagement, Wear 185 (1995) 141–149. [15] M. Kaneta, H. Yatsuzuka, Y. Murakami, Mechanism of crack growth in lubricated rolling/sliding contact, ASLE Trans. 28 (1985) 407–414. [16] T.M. Clarke, G.R. Miller, L.M.. Keer, H.C. Cheng, The role of near-surface inclusions in the pitting of gears, ASLE Trans. 28 (1) (1985) 111–116. [17] B.D. O’regan, G.T. Hahn, C.A. Rubin, The driving force for Mode II crack growth under rolling contact, Wear 101 (1985) 333–346.
Y. Ding, N.F. Rieger / Wear 254 (2003) 1307–1317 [18] P.C. Bastias, G.T. Hahn, C.A. Rubin, Finite element modelling of subsurface Mode II cracks under contact loads, Eng. Fracture Mech. 33 (1) (1989) 143–152. [19] L.M. Keer, M.D. Bryant, G.K. Haritos, Subsurface and surface cracking due to Hertzian contact, J. Lubr. Technol. Trans. ASME 104 (1982) 347–351. [20] G.R. Miller, A preliminary analysis of subsurface crack branching under a surface compressive load, J. Tribol. Trans. ASME 110 (1988) 292–296. [21] J.W. Blake, H.S. Cheng, A surface pitting life model for spur gears. Part I. Life prediction, J. Tribol. Trans. ASME 113 (1991) 712– 718.
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[22] H.E. Knechtel, W.F. Kindle, J.L. McCall, R.D. Buchheit, Metallographic Methods, ASM Metal Handbook, eighth ed., vol. 8, American Society of Metals, Metals Park, OH, 1973, pp. 1–14. [23] M.L. Atkin, R.A. Cummins, G.P. Sharp, A Study of Gear Wear in a Model Gearbox, Mechanical Engineering Transactions, The Institute of Engineers, Australia, 1979, pp. 40–52. [24] X.Z. Jin, N.Z. Kang, A study on rolling bearing contact fatigue failure by macro-observation and micro-analysis, in: Proceedings of the International Conference on Wear of Materials, Denver, CO, USA, 1989, pp. 205–213. [25] D.C. Stouffer, L.T. Dame, Inelastic Deformation of Metals: Models, Mechanical Properties, and Metallurgy, Wiley, New York, 1996.