Effects of lubrication on gear performance: A review

Mechanism and Machine Theory 145 (2020) 103701

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Mechanism and Machine Theory journal homepage: www.elsevier.com/locate/mechmachtheory

Review

Effects of lubrication on gear performance: A review Heli Liu a, Huaiju Liu a,∗, Caichao Zhu a, Robert G. Parker b a b

State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing 400030, China Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA 24061, USA

a r t i c l e

i n f o

Article history: Received 27 August 2019 Revised 19 October 2019 Accepted 6 November 2019 Available online xxx Keywords: Contact fatigue Dynamics Efficiency Gear lubrication

a b s t r a c t Increasingly demanding performance standards and operating requirements are driving the growing interest on lubrication technologies in gear transmission systems. Optimized gear lubrication methods and lubricant compositions are necessary to meet the industrial challenges of higher load, speed, temperature and performance expectations in multiple powertrain applications, including automotive, aeronautical and marine. Numerous theoretical and experimental studies have been dedicated to gear lubrication, especially on lubrication modelling and composition of lubricants. Improvements on lubrication methods and conditions can reduce friction, suppress wear and scuffing, and increase gear flank capacity and fatigue life. In order to compile and categorize key investigations in an expansive field with substantial recent research, this work reviews gear lubrication papers with focus on gear efficiency, contact fatigue and dynamics. Furthermore, some accompanying results obtained by the authors are included. © 2019 Elsevier Ltd. All rights reserved.

1. Background The main aims of gear lubrication are to diminish friction, increase efficiency, reduce wear and contact fatigue of the interacting tooth surfaces and improve durability. Lubrication properties have been addressed in gear tribology since the nineteenth century [1], followed by continuous advances on gear lubrication methods and conditions by many engineers and researchers [2–4]. Sasaki et al. [5] established a fundamental fluid lubrication theory for two rotating cylinders during contact, where the sliding effect was considered. Dowson et al. [6] theoretically analysed the stress distribution during gear meshing by considering elastohydrodynamic lubrication (EHL) theory, which was also mentioned by Johnson [7]. Spikes [8] presented EHL developments over the last few decades, corresponding practical applications (based on EHL theory) [9], and emphasized that EHL investigations were important to the future lubrication work. Fig. 1 displays several types of gear lubrication in engineering practices. In gear applications, mineral oils and other types of lubricants, such as greases, ester oils, etc. are adopted extensively. Differences on the effects of these oil types, together with the variety of lubricant additives, have been reported in literature [11–15]. Cann [16] presented that grease lubrication conditions are dramatically different from oil lubrication, where starvation is a key concern. Martins et al. [17] conducted gear tests to compare the lubrication properties of two industrial gear oils, namely a reference paraffinic mineral oil with a micropitting resistance additive package and a biodegradable non-toxic ester. They found that the ester oil could lead to less gear mass loss while reducing the friction coefficient. Höhn et al. [18] summarized the test methods of gear lubricants based on standard FZG (Forschungsstelle für Zahnräder und ∗

Corresponding author. E-mail address: [email protected] (H. Liu).

https://doi.org/10.1016/j.mechmachtheory.2019.103701 0094-114X/© 2019 Elsevier Ltd. All rights reserved.

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Fig. 1. Gear lubrication in engineering practices [10].

Fig. 2. Schematic diagram of gear lubrication modelling.

Getriebebau) back-to-back gear test rigs and necessary modifications for certain tests. Cardoso et al. [19] designed experiments to evaluate micropitting damages of nitriding steel gears lubricated with a standard mineral oil and two biodegradable ester oils. Results reveal that the ester lubricants give better micropitting resistance than the mineral oil. This research implies the potential value of biodegradable ester lubricants as high-performance and environmentally friendly gear oils. Bartels and Bock [20] summarized that suitable synthetic lubricants, such as poly (alkylene glycols) or synthetic hydrocarbons, generally provide several times longer service life than mineral oils by reducing friction losses and temperature during gear teeth contact. However, the cost of synthetic lubricants is generally much higher. With a view to investigating the lubrication mechanism and its effects on gear engineering, many theoretical studies have been carried out on tribological modelling [21–23]. Among the numerical studies on the effects of lubrication properties on gear performance, the investigations related to EHL/Thermal EHL (TEHL) [24–28], mixed-EHL [29–32] and Plasto-EHL [33,34], that can be divided into statistical [35,36] and deterministic models [37,38], are widely discussed. Fig. 2 shows the diagram of lubrication modelling. Besides the numerical simulations, experimental investigations are essential to understand

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Fig. 3. General compositions of gear transmission power loss.

the effects of lubrication on gear transmissions, thereby providing verification data for models and reference for engineering design and operation. Lubrication tests of gears or equivalent components are often implemented on multi-disc machines [39], ball-on-disc apparatuses [40], or FZG gear test rigs [41], considering the differences of base oils and additives under various operating conditions. Moreover, crucial parameters, including film thickness [42], surface topography [43,44], microstructural formations [45], temperature [46,47] and more, can be characterized via diverse experimental techniques in comprehensive tribological studies. Over the years, continuous improvements have been made on gear lubrication, and research results have led to practical rules [48–50]. Olver [1] reviewed gear lubrication articles to address the influences of EHL characteristics (i.e. film thickness) and lubrication conditions (i.e. mixed and boundary lubrication) on gear operation. A general conclusion has been made that the oil film thickness predicted under the assumption of fully-flooded, isothermal smooth surface conditions is often overestimated. Errichello [51] published a review on EHL, mainly pointing out that Blok’s flash temperature theory [52–54] was not applicable to the mixed-film or full EHL regime. With more demanding gear operating requirements being proposed by industry, the present work reviews relevant studies, especially experimental investigations, on the effects of lubrication on efficiency, fatigue performance and dynamics, aiming to provide more inclusive references for gear research and engineering. Moreover, recent results obtained by the authors are presented and discussed as supporting evidence. 2. Effect of lubrication on gear mechanical efficiency Predictions and measurements of gear transmission efficiency are crucial during gear system design and operation due to energy sustainability, environmental issues and economic factors [55]. Use of optimized lubricants could give rise to substantial energy conservation and emission reduction of corresponding mechanical systems, including automobiles [56], wind turbines [57], aircrafts [58], etc. The total power loss in gears arises from friction generated between the gear teeth, lubricant churning [59,60] and squeezing [61], and gear windage [62,63]. Fig. 3 displays the compositions of general gear transmission system power loss, where load-dependent (mechanical) and load-independent (oil churning, squeezing, etc.) power losses are included. In order to investigate the efficiency and power losses in gear transmissions, Koffel et al. [64] numerically calculated power losses due to gear friction, considering thermal effects. Gear efficiency tests were conducted for verification, emphasizing that the thermal influence could not be neglected during energy dissipation, which means a thermos-mechanical model is required to precisely capture the lubricant temperature during meshing. Bronshteyn and Kreiner [65] concluded that gear lubricants with improved viscosity-index meaningfully reduced friction and churning losses. In addition, minimal pressure-viscosity dependence of oils leads to significant energy conservation and anti-wear (AW) capacity. Martins et al. [66] evaluated gear transmission efficiency by conducting FZG tests with biodegradable, low-toxicity, ester-based oils compared to commercial mineral oils. Results clearly show that the biodegradable, low-toxicity, ester-based gear oil generates lower gear tooth friction even when operating at high temperatures, consequently leading to a 0.25% efficiency improvement of the FZG gearbox at 10 0 0 rpm compared to the mineral oil case. Höhn and Hinterstoißer [67] confirmed that a potential power loss reduction of 50% in a gearbox was viable depending on the operating conditions and applications. They found that polyalphaolefin lubricants reduce power loss by around 10% compared to mineral oils, whereas a 20% reduction is possible with polyglycol. Ziegltrum et al. [68] proposed TEHL simulations to investigate the gear load-dependent loss for different lubricants. The results were validated by gear lubrication tests. The polyalphaolefin and polyglycol oils presented lower friction, lower maximum fluid temperatures during operation and lower gear power losses compared to mineral oils. Experiments conducted by Marques et al. [69] revealed that lubricants with the same viscosity grade could generate different power loss depending on the base oil type and additive package. Fig. 4 shows the measured power losses under steady state operating temperatures and various working conditions with different types of base oils, namely mineral (MINR), poly-α -olefin (PAOR), mineral+PAMA (MINE) and polyalkylene glycol (PAGD). Based on the experimental results, the PAGD-based lubricant can reduce power loss by about 30% compared to mineral oils. MINR always showed the largest power losses, while PAOR and MINE performed closely in between PAGD and MINR. They also concluded that the operating temperature can be one of the most important limitations on gearbox loading capacity and power conservation, because numerous types of lubricants are sensitive to thermal effects. Furthermore, sufficient and appropriate lubricants should be guaranteed for improving gear operation performances. Lubrication condition is a key influence on total gear meshing efficiency, and improvements have been achieving in gear lubrication modification [70]. Starvation within the contact region must be avoided for better gear meshing performance [71,72]. Many researchers have pointed out that the sliding friction should be one of the main factors of gear

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Fig. 4. Measured power losses with different lubricants under various operating conditions [69].

transmissions power losses, indicating the crucial role of lubrication conditions [73,74]. Li et al. [75] analytically studied the impact of lubrication parameters on gear frictional power consumption and efficiency for rough surfaces with full-oil/starved lubrication. The results suggest that increasing oil film thickness and length increases efficiency whereas the friction power consumption declines. It can also be inferred from this work that establishing ideal EHL working conditions is difficult in practice. Liu et al. [76] summarized that the friction coefficient would increase as the inlet film thickness decreased, causing greater frictional power losses. When the inlet film thickness starts to rise, the friction coefficient reaches a steady value that corresponds to fully-flooded conditions. Nutakor et al. [77] performed a two-disc test to measure the friction coefficient under sliding-rolling contacts based on the characteristics of isotropic, super-finished and axially ground wind turbine gears. Results show that the increased film thickness provides lower friction coefficient and thus leads to high meshing efficiency. Compared with the super-finished specimen, the rough surface contact (axially ground contacts) exhibits high friction. Differences can be observed in gear efficiency among several lubrication methods, such as dip lubrication and jet lubrication, even with similar lubricants. Hence, the appropriate lubrication method would be selected via optimization of the gear transmission efficiency. Höhn et al. [78] experimentally showed that the power losses, especially the load-independent losses, decline with decreased oil immersion depth. When the lubricant level decreased from the central line to three times the gear module, the load-independent losses dropped to around 50% at the low pitch line velocity and to about 35% at the high pitch line velocity. Similar conclusions can be deduced from their previous work [79]. Handschuh et al. [80] carried out experimental comparison of gear meshing efficiency between an oil-mist system (employing two different lubricants) and a grease injection system (two different grease types). The results demonstrate that grease injection is a feasible gear lubrication approach for energy conservation and fatigue life enhancement. Andersson et al. [81] conducted spur gear tests to compare the influences of dip lubrication and spray lubrication on efficiency under various contact pressures. It was found that spray lubrication provided much higher total gearbox efficiency than dip lubrication, whereas no obvious differences were observed between the effect of these two lubrication methods on gear mesh efficiency when the pitch velocity ranged from 0.5 to 15 m/s. 3. Effect of lubrication on gear fatigue Many theoretical and experimental studies on gear fatigue performance seek to obtain the contact fatigue life and the relevant S-N curves [82,83]. Meanwhile, the mechanisms of typical gear fatigue failure modes have been analysed [84]. Gear fatigue performance, especially contact fatigue resistance, is directly and prominently impacted by the conditions of the interacting gear surfaces, such as lubrication and surface topographies, since the distributions of the contact pressure and the resultant stresses/strains can be significantly affected. 3.1. Effect on gear contact fatigue life Gear fatigue life and reliability relate closely to lubrication properties. Studies on lubrication effects on gear fatigue life primarily focus on the types of lubricants and additives, largely through gear fatigue tests. Early in the 1980s, researchers at NASA studied the effects of lubrication on gear fatigue life via amounts of gear fatigue tests. Scibbe et al. [85] implemented gear tests trying to reveal the effects of lubricant with extreme-pressure (EP) additives on surface fatigue life of spur gears made of AISI 9310. The fatigue life of gears with EP lubricants presented 10–50% enhancement compared to gears lubricated with reference oils. However, more tests needed to be conducted for statistical significance. Townsend and Zaretsky [86] evaluated the influence of five lubricants (with similar viscosity and pressure-viscosity coefficients) on the fatigue life of AISI 9310 carburized spur gears. Results suggest that the phosphorus AW additive may have beneficial effect on surface

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Fig. 5. Contact life cycles of tests under jet and dip lubrication conditions (deduced from the results in Ref. [96]).

fatigue life. In contrast, the sulphur additive exhibits no obvious influence on the surface fatigue life. Still, more tests are necessary to statistically quantify the effects of lubricants on gear fatigue life. Similar conclusions can be derived from the experimental results of Townsend et al. [87], where lubricants with 0.1% wt% sulphur and 0.1% wt% phosphorus EP additive established reactive films that were 20 0–40 0 A˚ thick covering the gear contact region. Recently, Krantz [88] reported on the correlation between the gear surface fatigue life and lambda ratio (ranging from 0.66 to 7.4). A total of 258 group tests were conducted, and the main results indicate that generally the gear surface life increases with the rise of lambda ratio, namely the improving lubrication condition. Superfinishing can dramatically enhance the gear surface fatigue resistance, resulting in longer surface fatigue life. Höhn and Michaellis [89] experimentally investigated the effects of lubricant ageing caused by temperature rise on gear fatigue. The results indicate that pitting resistance deteriorates whereas wear performance improves, and the viscosity rises with oil ageing. Moreover, the micropitting resistance declines with mild oil ageing but is enhanced with severe oil ageing. Krantz and Kahraman [90] experimentally investigated the effects of gear lubricant viscosity on wear rate and contact fatigue life. The results reveal that larger lubricant viscosity leads to larger lambda ratio, and thus leads to longer gear surface fatigue life. However, the wear rate decreases with the increased lubricant viscosity. The above studies both demonstrate that the wear performance can be improved by applying high viscosity lubricants, whereas give different conclusions on surface fatigue resistance. Consequently, the gear surface fatigue failures, such as gear micropitting, should be given special attention when lubrication properties are incorporated, otherwise confused and one-sided conclusions may be summarized. Querlioz et al. [91] experimentally investigated gear contact fatigue life using a twin disc machine under starved lubrication conditions based on the fact of unpredictable lubricant supply. The results show that starvation can aggravate thermal effects, leading to severe scuffing failure. For a lubricant flow-rate of 50%, the contact fatigue life was about 50% of that with full flow-rate, which was an impressive decline. These results correspond well with the work by Dowson [92], which regarded the lambda ratio [93] as the main factor affecting contact fatigue life. Based on the work of Errichello [94], lubricants with superior micropitting resistance may give a shorter macro-pitting life than lubricants with inferior micropitting resistance. Johansson et al. [95] predicted pitting life considering the oil physical properties using rolling four-ball test configuration. According to the experimental data, the fatigue life with poly-alpha-olefin (PAO) base oil was more than twice that with mineral base oil, whereas the friction modifiers had negligible effects on pitting life enhancement. Moss et al. [96] implemented an experimental investigation to quantify the effects of lubrication methods on spur gear macro-pitting fatigue life. Both high and low velocity jet lubrications were applied into-the-mesh and out-of-mesh compared with dip lubrication conditions. Fig. 5 summarizes the contact life cycles of all tests under jet and dip lubrication conditions deduced from results listed in Ref. [96]. The jet lubrication (nozzle diameter of 6.83 mm, jet velocity of 21 m/s) generally gives longer fatigue life than dip lubrication (half-immersed), unless the jet velocity is relatively low (0.28 m/s), preventing oil impingement across the entire tooth flank. It is also reported in this investigation that the spin losses are more significant

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Fig. 6. A schematic diagram of gear sliding-rolling and fluid pressurization phenomenon [94,110].

in dip-lubricated gear systems than that with jet-lubrication. This is due to the oil churning, which corresponds well with the aforementioned test results. 3.2. Effect on gear fatigue failure mode Most gear fatigue failure modes are sensitive to variations in characteristics of the interacting surfaces, especially the surface initiated failures such as micropitting and wear [97–101]. More specifically, the likelihood of micropitting can be roughly determined by the lubrication conditions together with the surface topography [102,103]. Several studies combined with the authors’ work are illustrated below for clearer demonstration of the investigated phenomena. In order to explore the influence of friction modifier additives on surface initiated failures, Lainé et al. [104] added molybdenum bis-diethylhexyl dithio-carbamate (MoDTC) and zinc dialkyl dithio phosphate (ZDDP) to mineral base-stock. The results indicated that, compared to the samples with added MoDTC, micropitting is more efficiently suppressed by adding ZDDP to the base oil. Schultheiss et al. [105] designed groups of gear tests aiming to study the influence of NLGI 00 grease on wear performance. The test results confirm the excellent effect of grease on wear resistance compared with traditional mineral oils even under boundary lubrication conditions. Liu et al. [71] studied spur gear contact behaviour considering starved lubrication characteristics. The results point out that the minimum oil film thickness may occur around the highest point of single tooth contact instead of the engage-in point in the full-film case, implying that starved lubrication will notably affect the contact fatigue initiation position. Engelhardt et al. [106] performed experiments with a FZG gear test rig on the effect of an “unconventional type of additive” in lubricants, namely the water contamination, on contact behaviour. No obvious influence of water contamination was observed on wear or micropitting performance. However, a different conclusion was reached by Errichello [94], stating that water contamination can promote gear micropitting and weaken corrosion resistance. Stump et al. [107] designed a bench-scale rolling-sliding test to study rear axle lubrication involving hypoid gears. The results reveal that lubricant temperature can have a significant effect on the surface contact fatigue performance. Higher oil temperature induces more surface damage, larger friction coefficient and even more noticeable vibrations compared with cooler oils. Stump et al. [108] experimentally explored the mitigation effect of oil-soluble ionic liquid (IL) on gear contact fatigue failures. Results show that a type of phosphonium-phosphate IL, namely the [P8888 ][DEHP], could protect the contact surface from wearing and rolling contact fatigue (RCF) failures. Furthermore, surface characterization revealed that the film oil of [P8888 ][DEHP] was about 3 times thicker than that of other commercial gear lubricants, such as SAE 75W-90. Sarita and Senthilvelan [109] conducted gear tests to evaluate the effect of lubricants on injection moulded PA66 gears. Results clearly show that lubrication could effectively dissipate heat and reduce surface pitting compared with dry contact condition. With respect to fatigue crack propagation, after formation of the original, tiny fatigue cracks driven by the contact stress field, the pressure generated by fluid entrainment into the high-pressure contact region causes flow into the cracks, forcing them to open, which is referred as fluid pressurization [110]. This mechanism can explain the fact that the motion direction in the contact zone has decisive impact on crack propagation, which can be schematically seen in Fig. 6. A similar conclusion can be deduced from Ref. [94], that is, like macro-pitting evolutions, micropitting cracks propagate mainly opposite the sliding direction on the tooth surface. Hence, the initiated cracks converge toward the pitch line of the driving gear and diverge away in the driven gear. Additionally, according to RCF tests using different lubricants carried out by Kürten et al. [111], the hydrogen composition may induce RCF failures in the form of white etching area (WEA) or dark etching region (DER) due to lubricant degradation. These results indicate that the application of lubrication is not always beneficial to the contact conditions since lubrication combines with chemical issues. Thus, evaluation of lubrication effects on gear transmissions is complicated and needs further exploration [112]. Theoretically, just like micropitting, wear [113] and scuffing damage [114] can be eliminated with effective lubrication, which is the formation of oil film whose thickness exceeds the combined heights of tooth surface roughness within the contact region [1]. As reported by Yoon and Cusano [115], the severity of lubricant starvation on scuffing was experimentally examined as a function of sliding velocity. Scuffing performance improves with increasing the lubricant sup-

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Fig. 7. Wear and friction test results with different lubricants (deduced from the results in Ref. [122]).

ply rate. Moreover, even a dimple or groove is detrimental to lubricant capacity when the contact regime is severely starved. Studies about the above issues are primarily related to the appropriate compositions of gear lubricants [12,116,117], thus this aspect remains an important topic for further research. Bartz [118] concluded that an optimal concentration should be determined when adding solid lubricants (e.g. MoS2 , graphite) to liquid or paste lubricants in order to prevent gear tooth surface wear. Sharif et al. [119] considered the impact of elastohydrodynamic film thickness on a worm gear wear model based on Archard’s wear equation [120]. The wear rate was computed under low lambda-ratio conditions, and the wear pattern on the gear surface was predicted. Numerical results illustrate that wear is very sensitive to the oil film thickness, which concentrates wear on the central zone of the wheel tooth area. Gear material will be removed continuously from this area until the local pressure is relieved, and then reduces the wear rate. Thus, the relation between film thickness and wear rate is an essential prerequisite in practical predictions. Khalil et al. [121] added various concentrations of multi-walled carbon nanotubes (MWCNTs) nanoparticles (0.1, 0.5, 1 and 2% wt%) as additives into mobil gear 627 and paraffinic mineral oils to evaluate the AW properties. As for the results, MWCNTs exhibit a relatively efficient influence on AW, and the characterized Worn Scar Diameters (WSD) are reduced by nearly 68% and 39% in the mobil gear 627 oil and mineral oil bases, respectively, compared to the case lubricated only with mineral oil. Meanwhile, the average friction coefficient decreases due to the influence of MWCNTs. Kotia et al. [122] experimentally estimated the tribological performance by testing industrial gear oils with nanoparticle additives (Al2 O3 and SiO2 ) on a pin-disc test rig. As shown in Fig. 7, the lubricant with 0.6% Al2 O3 /gear oil nanoparticle can create much larger wear scar diameter while the others are relatively beneficial for gear wear resistance. Moreover, a larger percentage of nanoparticles additives leads to a larger friction coefficient under the same loading condition. Several types of AW additives in lubricants may protect the tooth surface topography from wear but lead to other notable contact fatigue failures (e.g. micropitting) [123]. Morales-Espejel et al. [124,125] defined this as the competitive phenomenon between surface fatigue failures and mild wear. This concept was further explained by Brandão [126] and Vrcek [127]. As stated by Brechot et al. [128], adopting EP and AW additives can prevent wear damage but may promote micropitting. Benyajati et al. [129] carried out micropitting tests by employing a new miniature gear test-rig. Results illustrate that a PAO base stock with ZDDP AW additive may be detrimental to micropitting resistance, because the gear surface topography will be kept relatively intact due to the superior AW effect. Ochoa et al. [130] analysed the effects of different EP and AW additives in a low viscosity polyalphaolefin base on micropitting through an FZG gear tester. They found that the EP and AW additives increase the friction coefficient by protecting the initial surface roughness, which may lead to micropitting. As a consequence, the compositions of gear lubricants should be carefully designed with comprehensive consideration of both the anti-wear ability and micropitting resistance in real industrial applications. Current studies about the “competitive mechanism” mainly focus on the composition of lubricant additives, while this complicated issue still requires further study to better reveal the underlying physical and chemical phenomena. The authors conducted groups of experiments to identify the failure modes of poly(ether-ether-ketone) (PEEK) steel spur gear pairs under dry and lubricated conditions [131]. Normally, polymer gears are self-lubricated. In order to make more extensive use of polymer gears in demanding applications, lubrication may become an effective way for them to survive high-load, high-speed, and high-temperature operations. Hence, as an important part of the experimental schedule, the PEEK gear fatigue performance under dry contact and jet lubricated conditions were predicted. The driven wheel adopted in this work is manufactured with unfilled PEEK material (PEEK 450G) through mechanical hobbing. The mating driving pinion is fabricated with traditional C45 gear steel. Sixteen PEEK gears have been manufactured and tested on a typical FZG enclosed power flow gear test rig. The durability tests continued until final tooth fracture appeared. The tooth surface morphology was captured by a 3D microscope. The lubricant is MOBILGEAR SHC 627, which is classified as ISO-VG100 due to its extraordinary extreme pressure characteristic [132]. Fig. 8 compares the contact fatigue performance between dry and jet lubricated conditions under a moderate input torque of 15 Nm. It clearly exhibits that severe thermal damages occurred on the PEEK gear surface after 50,0 0 0 cycles under dry contact conditions. After 30,0 0 0 loading cycles, thermal damage could be easily observed on the tooth flanks,

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Fig. 8. Comparison of fatigue behaviour of dry contact and jet lubricated conditions in PEEK gears [131].

which was identified by oxidation colouring and cracks. The damage appeared at the location between the pitch line and the tooth root mainly because of the considerable local sliding effect [133]. As meshing proceeds, the thermal damage becomes more severe, leading to deterioration such as softening and melting, even under moderate working conditions. Additionally, mild scratches on the tooth tips occurred after about 1,0 0 0 cycles. With regard to jet lubricated conditions, only a few slight pits were observed on the lubricated flanks after 10,0 0 0 cycles. More pits were generated around the pitch line and the tooth tip with increased loading cycles, while bearing surfaces were protected from the thermal impact. Although pitting is unlikely to be avoided, the lubrication effectively protects the polymer gear surface from severe thermal damage, and significantly prolongs the gear service life as well. These test results correspond well with the investigations of Alencar et al. [134] and Düzcükog˘ lu [135].

4. Effect of lubrication on gear dynamics Studies of gear system dynamics developed from linear to linear time-varying, and then to nonlinear time-varying dynamics. Furthermore, the systems studied evolved from single gear pairs to multi-stage gear pairs and then, to entire transmission systems [136,137]. In recent years, the interactions between lubrication and dynamic behaviour are increasingly important in improving gear fatigue life and transmission efficiency. Discussions on this active scientific problem primarily focus on the dynamic effects on gear lubrication [138–140] and evaluations of gear vibrations and rattling [141,142] via the establishment of tribo-dynamic model [143,144]. Therefore, the influence of lubrication on dynamic response (e.g., vibration and noise), including tribo-dynamic coupling effects, which has hitherto not attracted sufficient attention, and requires further experimental exploration. One of the important steps in dynamic gear analysis is the inclusion of the lubrication parameters to obtain the dynamic response, including friction [145–147], film stiffness [148,149] and film damping [150–152]. Vibrations or impacts of the gear teeth during meshing generally result from the mesh stiffness variations, gear backlash, fluctuations of the external load and rotation speed, manufacturing errors and misalignment [153]. Noise radiation is a by-product of vibrations due to periodic gear meshing [154]. Lubrication provides beneficial effects to diminish vibration and noise through friction reduction [155], and subsequently contributes to gear life extension [156]. Several numerical and experimental investigations are explained as follows. Houser et al. [155] carried out experiments to study the tribological effects on vibration and noise in a test gearbox. The results show that lubricants with higher viscosity significantly reduce vibration and noise, and a smoother gear surface gives better vibro-acoustic performance. Cheon [157] addressed the influences of hydrodynamic and friction forces on the dynamic behaviours. Results indicate that the hydrodynamic effect stimulates the nonlinearity and damping but decreases elastic deformation and tooth reaction force, but further experimental verification is highly required. Fietkau and Bertsche [158] theoretically and experimentally highlighted the effect of tribological factors on gear structure-borne noise during meshing. They explained that noise decreases with the rise of oil viscosity due to increased drag torque. However, the test transmission only contained one gear stage, so the influence of oil viscosity is limited. Mohammadpour et al. [142] developed a tribodynamic model to capture the dynamic response of differential hypoid gear pairs. Results suggest that the formation of lubricant film is vital to Noise, Vibration and Harshness (NVH) performance. Paouris [159] developed a tribodynamic model to predict transmission efficiency and dynamic response of a hypoid gear pair, incorporating temperature variation (employing a thermal network model and the Time Temperature Superposition method) and measured gear surface topography. Results show that vibrations are suppressed by rising lubricant viscosity. Cao et al. [160] pointed out that the

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Fig. 9. Experimental rig and results for the gear rattle index (IGR) under dry contact, boundary lubrication and oil jet lubrication conditions [163].

tribological properties could have significant effect on gear nonlinear dynamic performance, especially in vicinity resonance. The gear dynamic properties also play an important role in spiral gear lubrication and fatigue life. Gear rattle is usually generated from the gear teeth meshing in the presence of backlash under lightly loaded or unloaded conditions [161], and the impact of lubrication cannot be neglected [162]. Russo et al. [163] experimentally studied the effect of oil lubricant on idle rattle in automotive manual transmissions. Fig. 9 illustrates the test rig arrangement and gear rattle index (IGR) measurements under dry contact, boundary lubrication and oil jet lubrication conditions. They concluded that neglecting the lubricant damping leads to overestimation of the rattle problem, indicating that damping reduces rattle vibrations. Several studies on lubricated gear rattle have been conducted as well [164,165]. Theodossiades et al. [166] proposed a methodology incorporating the lubricated contacts for idle gear rattle in automotive manual transmission systems. They concluded that the lubricants behave like a nonlinear spring damper, whose properties dramatically influence the gear rattle response. Tangasawi et al. [167] investigated rattle in automotive transmission systems considering tribo-dynamics. The results reveal that rattle increases when the oil viscosity drops due to the rising temperature in the teeth contact. Moreover, the squeeze film motion plays a crucial role in the variation of gear rattle, which was further confirmed in [168]. FernandezDel-Rincon et al. [169] analytically evaluated the effects of lubrication on gear rattle behaviour under low-level torques. The lubrication regime was hydrodynamic under these loading conditions. They emphasized the decisive impact of the lubricant entrance in the contact area on gear dynamics rattle. Then the same team highlighted the effect of lubricant viscosity on the gear rattle phenomenon considering both the entraining and squeezing fluid effects [170]. They concluded that decreasing the fluid viscosity could lead to the alleviation of oscillation amplitude in high frequencies. The fluid entraining effect is more obvious than the squeezing effect on dynamic behaviours within the contact region, and the viscosity effect is more decisive than the external effect.

5. Conflicting gear performances and lubrication requirements Higher lubrication quality improves gear transmission performance. To this end, frequent renewal of the lubricant and sufficient amount of oil reaching the tooth contact regions are necessary. However, a conflicting fact is rising as for certain gear systems and operating requirements, frequent service is impractical. This is especially true in large-scale and heavyduty transmissions (e.g. wind turbines), or gearboxes with limited available space. According to the engineering practice in gear industries, replacement of the wind turbine gearbox lubricant occurs every five years if no problem appears during annual inspections. Compact transmission structures have disadvantages in terms of heat dissipation and airflow, which may degrade the lubricant. Some rotate vector reducers employed in industrial robots with compact structures require grease replacement after a long operating period, such as approximately 10,0 0 0 h, if no high temperature issue appears during quarterly inspections. Another potentially conflicting gear performance and lubrication requirements should be mentioned, namely the possible conflict between transmission efficiency improvement and noise, vibration and harshness (NVH) refinement reported in the

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Ref. [142,171]. It is said that lubrication can have conflicting effects on NVH and efficiency. Velex and Cahouet [172] experimentally and numerically studied the effect of tooth friction on the spur and helical gear dynamics, which led them to conclude that the transmission characteristics and tooth friction need simultaneous consideration when studying noise reduction. De la Cruz et al. [173] concluded that loose gear pairs were the main sources of NVH, whereas the thermomechanical efficiency was dominated by the engaged gear pairs. Consequently, a full gear transmission tribo-dynamic model is essential for in-depth analysis of transmission efficiency and operational refinement. Later, Fatourehchi et al. [174] proposed a combined tribo-dynamic model to evaluate the NVH and transmission efficiency of a wheel hub planetary system. Although a near optimal solution may be reached by mesh phasing of the gear contacts, a coupled optimization approach is desired to simultaneously refine transmission efficiency and NVH performance. Mohammadpour et al. [142] investigated the combined efficiency and NVH refinement of a hypoid gear pair in a light van differential. Results indicate that the NVH performance deteriorates during transient acceleration, which at speeds away from resonance (where friction is low due to the relatively thick oil film) increases gear transmission efficiency. After that, Mohammadpour et al. [175] developed a six degree-of-freedom, torsional, multi-body dynamic model for planetary gear-sets of hybrid-electric-vehicle configurations that incorporated a tribological contact model. Their objective was to improve NVH performance while improving transmission efficiency in a hybrid powertrain comprising an electric motor and an internal combustion engine. Results show that compared to the internal combustion engine drive mode of these specific configurations, the electric motor drive mode can give better NVH performance but provide worse transmission efficiency at lower vehicle speeds. A possible explanation of this conflicting behaviour is probably that transmission efficiency and NVH refinement are combined through friction in modern gear transmission systems [172,173]. On the one hand, tooth friction behaves like an energy sink mechanism that can effectively decrease the excessive supplied energy of the gear systems, and creates vibration damping that reduces NVH. On the other hand, the unavoidable gear friction losses contribute to transmission inefficiency [175]. Therefore, the lubrication conditions are particularly crucial when seeking an optimally balanced condition for gear transmission efficiency and NVH. 6. Conclusions The present work reviews analytical and experimental investigations on the effects of lubrication on gear meshing efficiency, contact fatigue and dynamic behaviour. Moreover, investigations proposed by the authors are presented for further illustration. The key conclusions can be summarized as follows: (1) The power losses in gears comprise contributions of friction, lubrication (i.e., churning, squeezing) and gear windage. Ester gear oil and grease enhance efficiency even when operating at high temperature, yet thermal influences cannot be neglected. A viscosity-improved lubricant leads to better energy conservation and anti-wear performance. Generally, spray lubrication provides higher gearbox efficiency than dip lubrication. Starvation significantly increases friction and power loss. (2) Anti-wear and extreme-pressure oil additives, and higher viscosity lubricants give greater gear surface fatigue life. Starvation aggravates thermal effects, leading to severe scuffing and wear damage. Jet lubrication gives longer fatigue life than dip lubrication unless the jet velocity is low. The lubricant fluid flow may force fatigue cracks to propagate according to sliding-rolling conditions. Oil degradation may induce failures in the form of white etching or dark etching regions. (3) Gear lubricants with appropriate higher viscosity can reduce vibration and noise. The lubricant temperature rise that decreases oil viscosity can cause rattle oscillations. In addition, neglecting the lubricant damping can lead to overestimation of rattle, suggesting that damping reduces rattle vibrations. Starvation conditions are detrimental to gear dynamics. According to the aforementioned studies, the gear meshing performance such as mechanical efficiency, contact fatigue, dynamics are all significantly influenced by lubricants, lubrication conditions or lubricating methods. Experimental investigations remain critically important for future gear lubrication research because some lubrication theories may not be suitable for current industrial oils or operating conditions. Moreover, gear tribology and contact fatigue are not only about mechanical and physical problems, but also chemical issues, indicating the huge challenges to comprehensively describe their characteristics with numerical or analytical models. The compositions of lubricants remain of great interest to researchers and engineers in order to enhance micropitting and wear resistances of gears. In fact, numerical simulation is still beneficial to reveal the gear contact mechanism, such as the competitive phenomenon occuring between contact fatigue failures and wear damage, where lubrication is one of the key factors. Acknowledgements This work was funded by the National Natural Science Foundation of China (No. 51975063) and National Key R&D Program of China (No. 2018YFB2001300). The present research has been supported by Prof. Stephanos Theodossiades, Loughborough University, UK, whose valuable contribution is gratefully acknowledged.

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