Abstract
Fractal wear behaviour of gears refers to failure mode of gears as a result of contact mechanics, which occurs while in application. Tooth-to-tooth surface damage usually ensues as a result of variation in excitation energy of the gear. This study therefore investigated the nature of fractal wear encountered by gear tooth with a focus on general fatigue wear, temperature-induced wear and different models for wear predictions. The result of the study showed that tooth surface damage such as fatigue, pitting corrosion and scuffing causes gear failure. Failure due to bending fatigue was observed to contribute to the maximum deflection of the gear tooth during rotation, thus resulting in excessive noise and vibration. Further to this, it was possible to predict the material removal rate of a failed gear using some of the highlighted empirical methods in the study. Based on these models, it will be possible to predict the nature of wear on gear tooth surface and use it during gear design.
Access provided by Autonomous University of Puebla. Download conference paper PDF
Similar content being viewed by others
Keywords
1 Introduction
The wear of gear tooth is regarded as a major factor to overall component failure and improvement in the mechanical properties of gear tooth to mitigate or reduce wear, which is important for reliability and availability of machines. Thus, it is necessary to assess the nature of gear failures in order to improve the design. Tooth wear in gears has been associated with misalignment at the tooth profile causing excessive noise and vibration resulting in eventual failure [1]. Miler et al. [2] noted that one major cause of the gear tooth misalignment is the variation in the profile shift, which introduces a stress factor that affects the optimal efficiency of the gear component. Although the profiles are usually specified and designed into the product during manufacturing, they pose a significant wear behaviour due to the alterations during manufacturing in order to meet the satisfaction of the customers [3]. This will cause radial and hoop stress along the tooth leading to crack initiation on the gear surface asperities and the tooth roots of the gear [4,5,6]. Despite numerous efforts by gear designers to predict wear behaviour of the gears using various tribo-dynamic models, the variation in speed of gears has remained a major factor to gear designers [7, 8]. More so, accuracy in wear detection and diagnostic approach has become a major problem at the initial stage of gear failure, thereby mitigating the use of numerical and experimental investigations of the increased tooth wear and acoustic emission monitoring devices [9,10,11]. Further to this, it was reported by Kumar et al. [12] that pitting occurred in gears as a result of increased rolling with sliding motion. The variation in load sharing contributed to gear deflections, which lead to increase in frictional loss along the gear tooth tip [13, 14]. In turn, the loss in frictional power can be increased by the surface roughness along the gear surface in mesh, thus making the oil film less effective in reducing wear [15]. However, there is an extent to which smooth gear surface is affected by surface roughness and once the grinding surface roughness is not well guided during production, it affects the profile of the involute [16, 17]. Based on this statement, it is worthy of noting that most gear failures are associated with error during the manufacturing process. For instance, gear shapers pose geometric and kinematic errors during gear shaping process, which affect the accuracy when compared to standards and cause excessive mesh stiffness that can affect the dynamic action of the gear system [18,19,20]. The variation in the mesh stiffness increases the transmission error between a pair of gear in mesh, thus increasing the torsional effects at the surface of the gears and leading to low performance during operation [21,22,23,24,25]. According to Jolivet et al. [26], the geometry of a finished gear tooth has an effect on the acoustic emission during operation. This will enable a gear specialist to measure the wear behaviour of the gear both in lubrication condition and in dry working condition in order to determine its optimal performance. Inaccurate finishing in tooth geometry causes excessive noise, vibration and eventual micropits on the surface asperities resulting in tooth deformation [27,28,29,30]. In an attempt to reduce wear and improve on gear performance, as well as durability, empirical models have been developed to study the dynamic characteristics of gears in mesh. For instance, Ni et al. [31] employed a numerical approach to improve the mesh behaviour of a bevel gear. However, the high-speed motion in bevel gear transmission was not considered and this can result in reduced bearing capacity of gear tooth surface, but studies have shown that gears of this type will not function well in some applications, which require high pressure due to increased frictional loss and scuffing failure [32,33,34]. In radial loads, lubricant temperature played a major role in the wear behaviour of the gear system [35]. Many experimental attempts have been employed in the treatment of gears in order to reduce wear but still left with great shortcomings. In the light of this, shot peening was adopted to improve the fatigue life of steel gears by Lv et al. [36]. However, the variation in speed and load still remains a major problem during fault detection [37, 38]. Although it was possible to detect faults through the interpretation of the data obtained from the dynamic signals, validation of the detected faults still remains a great challenge [39, 40].
2 Critical Problems Associated with Gear Wear Prediction Models
The frequent transmission error occurring during gear meshing has necessitated the application of several engineering models to predict the gear performance and the wear behaviour. Basically, the variation in impact load between meshing tooth can result in bending fatigue and pitting on the working surface. Although it was possible to predict the surfaces or teeth that are missing during operation using some simple empirical models, however, the failed gear tooth will show some evidence of material removal causing distortions on the involute profile. Models to predict this material removal rate are quite not easy to develop [41]. To this end, model development will need critical analysis of the thermal stress on the contact surface by considering the various points of acoustic emissions causing pitting at the tooth surfaces, which make the material susceptible to eventual deformation before adequate prediction of material removal rate can be ascertained [42,43,44,45,46]. Morales-Espejel and Gabelli [47] proposed a model for analysing the fatigue life of gears based on the load-carrying capacity of the machine. The model adopted a Weibull method to analyse the strength of the material and the Lundberg–Palmgren principle to investigate the load-bearing capacities. However, transmission error reduction requires a good surface finish and accurate microgeometry during gear manufacturing. The pressure distribution during contact is also a factor to surface fatigue prediction, which becomes a major challenge, especially in production of gears that have non-circular shape [48,49,50,51,52]. Technically, the developed model was possible for backlash reduction, especially on worm wheel gears, but to what extent would this improve the optimal working efficiency of the gear remains a major problem, unless the complex nature of the gear tooth kinematic geometry is well understood, which is a function of the nonlinear and acoustic behaviours of the gear system [53,54,55,56,57]. Based on this, Dhamande and Chaudhari [58] developed a statistical model for diagnosing the vibration of gears on the basis of speed and load condition in order to predict fatigue on the surfaces of the gear tooth. This is limited by the type of contact stress causing fatigue failure due to the fact that it is impossible to identify the stress in real-life situation [59]. More so, studies have revealed that simulations or experiments would give a better result because the parameters for vibration monitoring can be controlled overtime; however, in real-life applications, operation conditions are prone to these errors, thus making it impossible to get the exact point of stress causing incessant fatigue failure. In addition, complex mechanism of operation of the gear component limits the chances of fundamental fatigue, which causes the fracture of the tooth surfaces [60,61,62,63]. A number of researches have been carried out on the way to predict failures in gears by synchronizing the gear components with gear monitoring devices. For instance, Palermo et al. [64] suggested that a digital encoder can be integrated into the system to measure the transmission error during vibration. Besides, Li et al. and Ren et al. [65, 66] reported that angular displacement of gears during operation causes gear deflection along the path of travel and this will result in variation in the meshing mechanism of the gear. The studies further proposed that this problem can be monitored using angular displacement sensor to detect faults. Obviously, data obtained from angular signals are limited by variation in the speed of the machine and dynamic responses of the rotary component [67]. Reduction in degree of freedom and accurate gear mesh simulation might be of interest in reducing the surface fatigue [68].
3 Temperature-Induced Gear Wear
Heat generation exists at the interface of meshing teeth due to increased torque transmission, which constitutes a temperature zone, which can be referred to as bulk and flash temperature point on the gear tooth [69]. It was possible to say that the heat flux distribution along the path of contact induces thermal stress on the material resulting in thermal failure of the gear tooth [70]. The unsteady state temperature distribution can result in frictional heat generation and increased temperature rise on the gear tooth surface, which eventually reduces the transmission efficiency [71]. According to Castro and Seabra [72], the viscosity of the oil is a function of temperature and a coefficient of friction between a pair of gears in mesh. This, however, affects the scuffing load capacity of the gears. Bulk flash temperature variation is usually directed to the vertical tooth surface, which reduces transmission efficiency and increases the thermal deformation at the meshing interface [73, 74]. More so, the flash temperature at the tooth surfaces of gears can be predicted using a nonlinear model, which can estimate the temperature of the tooth overtime that can cause the surface deformation; thus, temperature is suitable for monitoring the performance of the gear, especially when elastohydrodynamic technique is used [75,76,77,78,79,80]. Thus, it was needful to say that temperature formed a dominant parameter in analysing fatigue failures of gears [81].
4 Conclusion
In the design of power transmissions, the major factors, which affect the system when in application, are noise and vibration emission. The variation in the transmission error distribution has a major impact on the noise behaviour. This study has shown that the noise emission and temperature flash are associated with transmission error due to gear excitation. Further investigation into the material failure of gears, the chemical composition, strength and surface fracture showed that fatigue is one major factor, which usually leads to gear tooth failure. Thus, the outcome of this study can be adopted to improve on the gear tooth design.
References
Sekar RP, Sathishkumar R (2017) Enhancement of wear resistance on normal contact ratio spur gear pairs through non-standard gears. Wear 380:228–239
Miler D, Lončar A, Žeželj D, Domitran Z (2017) Influence of profile shift on the spur gear pair optimization. Mech Mach Theory 117:189–197
Karpuschewski B, Beutner M, Köchig M, Härtling C (2017) Influence of the tool profile on the wear behaviour in gear hobbing. CIRP J Manuf Sci Technol 18:128–134
Hu Z, Mao K (2017) An investigation of misalignment effects on the performance of acetal gears. Tribol Int 116:394–402
Salawu EY, Ajayi OO, Olatunji OO (2015) Theoretical modelling of thermal-hoop stress around the tooth of a spur gear in a filler machine. J Multidiscip Eng Sci Technol (JMEST) 2(2):1635–1640
Salawu EY, Okokpujie IP, Ajayi OO, Agarana MC (2018) Analytical technique for the determination of hoop stress and radial stress on the tooth spur gear under vertical loading in a food packaging machine
Ouyang T, Huang H, Zhang N, Mo C, Chen N (2017) A model to predict tribo-dynamic performance of a spur gear pair. Tribol Int 116:449–459
Li S, Anisetti A (2017) A tribo-dynamic contact fatigue model for spur gear pairs. Int J Fatigue 98:81–91
Brethee KF, Zhen D, Gu F, Ball AD (2017) Helical gear wear monitoring: modelling and experimental validation. Mech Mach Theory 117:210–229
Sharma RB, Parey A, Tandon N (2017) Modelling of acoustic emission generated in involute spur gear pair. J Sound Vib 393:353–373
Sánchez MB, Pleguezuelos M, Pedrero JI (2017) Approximate equations for the meshing stiffness and the load sharing ratio of spur gears including hertzian effects. Mech Mach Theory 109:231–249
Kumar P, Hirani H, Agrawal A (2017) Fatigue failure prediction in spur gear pair using AGMA approach. Mater Today Proc 4(2):2470–2477
Diez-Ibarbia A, Fernandez-del-Rincon A, de-Juan A, Iglesias M, Garcia P, Viadero F (2017) Frictional power losses on spur gears with tip reliefs. The load sharing role. Mech Mach Theory 112:240–254
Diez-Ibarbia A, Fernandez-del-Rincon A, de-Juan A, Iglesias M, Garcia P, Viadero F (2018) Frictional power losses on spur gears with tip reliefs. The friction coefficient role. Mech Mach Theory 121:15-27
Huang K, Xiong Y, Wang T, Chen Q (2017) Research on the dynamic response of high-contact-ratio spur gears influenced by surface roughness under EHL condition. Appl Surf Sci 392:8–18
Clarke A, Jamali HU, Sharif KJ, Evans HP, Frazer R, Shaw B (2017) Effects of profile errors on lubrication performance of helical gears. Tribol Int 111:184–191
Wang Y, Liu Y, Chu X, He Y, Zhang W (2017) Calculation model for surface roughness of face gears by disc wheel grinding. Int J Mach Tools Manuf 123:76–88
Khusainov RM, Khaziev RR (2017) Mathematical model for assessing the accuracy of processed gears on gear shaping machines. Proc Eng 206:1087–1092
Saxena A, Chouksey M, Parey A (2017) Effect of mesh stiffness of healthy and cracked gear tooth on modal and frequency response characteristics of geared rotor system. Mech Mach Theory 107:261–273
Dogruer CU, Pirsoltan AK (2017) Active vibration control of a single-stage spur gearbox. Mech Syst Signal Process 85:429–444
Barrios MLR, Montero FEH, Mancilla JCG, Marín EP (2017) Application of lock-in amplifier on gear diagnosis. Measurement 107:120–127
Yu W, Mechefske CK, Timusk M (2017) The dynamic coupling behaviour of a cylindrical geared rotor system subjected to gear eccentricities. Mech Mach Theory 107:105–122
Karpuschewski B, Beutner M, Koechig M, Wengler M (2017) Cemented carbide tools in high speed gear hobbing applications. CIRP Ann 66(1):117–120
Singh PK, Singh AK (2017) An investigation on the effects of the various techniques over the performance and durability of polymer gears. Mater Today Proc 4(2):1606–1614
Ramanjaneyulu S, Suman KNS, Kumar SP, Babu VS (2017) Design and development of graphene reinforced acetal copolymer plastic gears and its performance evaluation. Mater Today Proc 4(8):8678–8687
Jolivet S, Mezghani S, El Mansori M, Vargiolu R, Zahouani H (2017) Experimental study of the contribution of gear tooth finishing processes to friction noise. Tribol Int 115:70–77
Mallipeddi D, Norell M, Sosa M, Nyborg L (2017) Influence of running-in on surface characteristics of efficiency tested ground gears. Tribol Int 115:45–58
Kimme S, Bauer R, Drossel WG, Putz M (2017) Simulation of error-prone continuous generating production processes of helical gears and the influence on the vibration excitation in gear mesh. Proc CIRP 62:256–261
Garambois P, Donnard G, Rigaud E, Perret-Liaudet J (2017) Multiphysics coupling between periodic gear mesh excitation and input/output fluctuating torques: application to a roots vacuum pump. J Sound Vib 405:158–174
Xiao H, Zhou X, Liu J, Shao Y (2017) Vibration transmission and energy dissipation through the gear-shaft-bearing-housing system subjected to impulse force on gear. Measurement 102:64–79
Ni G, Zhu C, Song C, Du X, Zhou Y (2017) Tooth contact analysis of crossed beveloid gear transmission with parabolic modification. Mech Mach Theory 113:40–52
Yoon Y, Park BH, Shim J, Han YO, Hong BJ, Yun SH (2017) Numerical simulation of three-dimensional external gear pump using immersed solid method. Appl Therm Eng 118:539–550
Nutakor C, Kłodowski A, Sopanen J, Mikkola A, Pedrero JI (2017) Planetary gear sets power loss modeling: application to wind turbines. Tribol Int 105:42–54
Wang Y, Tang W, Chen Y, Wang T, Li G, Ball AD (2017) Investigation into the meshing friction heat generation and transient thermal characteristics of spiral bevel gears. Appl Therm Eng 119:245–253
Benedetti M, Fontanari V, Torresani E, Girardi C, Giordanino L (2017) Investigation of lubricated rolling sliding behaviour of WC/C, WC/C-CrN, DLC based coatings and plasma nitriding of steel for possible use in worm gearing. Wear 378:106–113
Lv Y, Lei L, Sun L (2017) Effect of microshot peened treatment on the fatigue behavior of laser-melted W6Mo5Cr4V2 steel gear. Int J Fatigue 98:121–130
Feng K, Wang K, Ni Q, Zuo MJ, Wei D (2017) A phase angle based diagnostic scheme to planetary gear faults diagnostics under non-stationary operational conditions. J Sound Vib 408:190–209
Aouabdi S, Taibi M, Bouras S, Boutasseta N (2017) Using multi-scale entropy and principal component analysis to monitor gears degradation via the motor current signature analysis. Mech Syst Signal Process 90:298–316
Baron P, Kočiško M, Blaško L, Szentivanyi P (2017) Verification of the operating condition of stationary industrial gearbox through analysis of dynamic signal, measured on the pinion bearing housing. Measurement 96:24–33
Parra J, Vicuña CM (2017) Two methods for modeling vibrations of planetary gearboxes including faults: comparison and validation. Mech Syst Signal Process 92:213–225
Mark WD, Isaacson AC, Wagner ME (2019) Transmission-error frequency-domain-behavior of failing gears. Mech Syst Signal Process 115:102–119
Singh PK, Singh AK (2018) An investigation on the thermal and wear behavior of polymer based spur gears. Tribol Int 118:264–272
Mehta G, Somani M, Babu TN, Watts T (2018) Contact stress analysis on composite spur gear using finite element method. Mater Today Proc 5(5):13585–13592
Sharma RB, Parey A (2018) Modelling of acoustic emission generated due to pitting on spur gear. Eng Fail Anal 86:1–20
Morales-Espejel GE, Rycerz P, Kadiric A (2018) Prediction of micropitting damage in gear teeth contacts considering the concurrent effects of surface fatigue and mild wear. Wear 398:99–115
Singh AK (2018) Noise emission form functionally graded materials based polypropylene spur gears-a tribological investigation. Mater Today Proc 5(2):8199–8205
Morales-Espejel GE, Gabelli A (2018) A model for gear life with surface and subsurface survival: tribological effects. Wear 404:133–142
Petare AC, Jain NK (2018) On simultaneous improvement of wear characteristics, surface finish and microgeometry of straight bevel gears by abrasive flow finishing process. Wear 404:38–49
Zhou C, Wang H (2018) An adhesive wear prediction method for double helical gears based on enhanced coordinate transformation and generalized sliding distance model. Mech Mach Theory 128:58–83
Zheng F, Xinghui H, Hua L, Zhang M (2018) Design and manufacture of new type of non-circular cylindrical gear generated by face-milling method. Mech Mach Theory 122:326–346
Ouyang T, Huang H, Zhou X, Pan M, Chen N, Lv D (2018) A finite line contact tribo-dynamic model of a spur gear pair. Tribol Int 119:753–765
Tong D, Gu J, Totten GE (2018) Numerical investigation of asynchronous dual-frequency induction hardening of spur gear. Int J Mech Sci 142:1–9
Kacalak W, Majewski M, Budniak Z (2018) Innovative design of non-backlash worm gear drives. Arch Civil Mech Eng 18(3):983–999
Peng Y, Zhao N, Zhang M, Li W, Zhou R (2018) Non-Newtonian thermal elastohydrodynamic simulation of helical gears considering modification and misalignment. Tribol Int 124:46–60
Ma Z, Luo Y, Wang Y, Mao J (2018) Geometric design of the rolling tool for gear roll-forming process with axial-infeed. J Mater Process Technol 258:67–79
Zhou C, Xiao Z (2018) Stiffness and damping models for the oil film in line contact elastohydrodynamic lubrication and applications in the gear drive. Appl Math Model 61:634–649
Hu X, Hu B, Zhang F, Fu B, Li H, Zhou Y (2018) Influences of spline assembly methods on nonlinear characteristics of spline–gear system. Mech Mach Theory 127:33–51
Dhamande LS, Chaudhari MB (2018) Compound gear-bearing fault feature extraction using statistical features based on time-frequency method. Measurement 125:63–77
Li W, Liu B (2018) Experimental investigation on the effect of shot peening on contact fatigue strength for carburized and quenched gears. Int J Fatigue 106:103–113
Praveenkumar T, Sabhrish B, Saimurugan M, Ramachandran KI (2018) Pattern recognition based on-line vibration monitoring system for fault diagnosis of automobile gearbox. Measurement 114:233–242
Cerrada M, Li C, Sánchez RV, Pacheco F, Cabrera D, de Oliveira JV (2018) A fuzzy transition based approach for fault severity prediction in helical gearboxes. Fuzzy Sets Syst 337:52–73
Everitt CM, Alfredsson B (2018) Contact fatigue initiation and tensile surface stresses at a point asperity which passes an elastohydrodynamic contact. Tribol Int 123:234–255
Vučković K, Galić I, Božić Ž, Glodež S (2018) Effect of friction in a single-tooth fatigue test. Int J Fatigue 114:148–158
Palermo A, Britte L, Janssens K, Mundo D, Desmet W (2018) The measurement of gear transmission error as an NVH indicator: theoretical discussion and industrial application via low-cost digital encoders to an all-electric vehicle gearbox. Mech Syst Signal Process 110:368–389
Li L, He K, Wang X, Liu Y (2018) Sensor fault-tolerant control for gear-shifting engaging process of automated manual transmission. Mech Syst Signal Process 99:790–804
Ren X, Lu Z, Tian G (2018) Sensor fault-tolerant control for gear-shifting engaging process of electric-drive mechanical transmission. In: Proceedings of the 6th international conference on control, mechatronics and automation. ACM, pp 21–28
Li B, Zhang X, Wu T (2018) Measurement of instantaneous angular displacement fluctuation and its applications on gearbox fault detection. ISA Trans 74:245–260
Liu JP, Shu XB, Kanazawa H, Imaoka K, Mikkola A, Ren GX (2018) A model order reduction method for the simulation of gear contacts based on Arbitrary Lagrangian Eulerian formulation. Comput Methods Appl Mech Eng 338:68–96
Fernandes CM, Rocha DM, Martins RC, Magalhães L, Seabra JH (2018) Finite element method model to predict bulk and flash temperatures on polymer gears. Tribol Int 120:255–268
Stark S, Beutner M, Lorenz F, Uhlmann S, Karpuschewski B, Halle T (2013) Heat flux and temperature distribution in gear hobbing operations. Proc Cirp 8:456–461
Li W, Tian J (2017) Unsteady-state temperature field and sensitivity analysis of gear transmission. Tribol Int 116:229–243
Castro J, Seabra J (2018) Influence of mass temperature on gear scuffing. Tribol Int 119:27–37
Shi Y, Yao YP, Fei JY (2016) Analysis of bulk temperature field and flash temperature for locomotive traction gear. Appl Therm Eng 99:528–536
Luo B, Li W (2017) Influence factors on bulk temperature field of gear. Proc Institut Mech Eng Part J J Eng Tribol 231(8):953–964
Gou X, Zhu L, Qi C (2017) Nonlinear dynamic model of a gear-rotor-bearing system considering the flash temperature. J Sound Vib 410:187–208
Touret T, Changenet C, Ville F, Lalmi M, Becquerelle S (2018) On the use of temperature for online condition monitoring of geared systems–a review. Mech Syst Signal Process 101:197–210
Zhang JG, Liu SJ, Fang T (2017) Determination of surface temperature rise with the coupled thermo-elasto-hydrodynamic analysis of spiral bevel gears. Appl Therm Eng 124:494–503
Taburdagitan M, Akkok M (2006) Determination of surface temperature rise with thermo-elastic analysis of spur gears. Wear 261(5–6):656–665
Li S, Anisetti A (2016) On the flash temperature of gear contacts under the tribo-dynamic condition. Tribol Int 97:6–13
Evans SM, Keogh PS (2016) Efficiency and running temperature of a polymer–steel spur gear pair from slip/roll ratio fundamentals. Tribol Int 97:379–389
Kalin M, Kupec A (2017) The dominant effect of temperature on the fatigue behaviour of polymer gears. Wear 376:1339–1346
Acknowledgements
The authors would like to thank the management of Covenant University for the partial sponsorship of this research.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Salawu, E.Y., Inegbenebor, A.O., Ajayi, O.O., Akinlabi, S.A., Akinlabi, E.T. (2020). Fractal Wear Behaviour of Gear Tooth: A Review. In: Emamian, S.S., Awang, M., Yusof, F. (eds) Advances in Manufacturing Engineering. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-5753-8_5
Download citation
DOI: https://doi.org/10.1007/978-981-15-5753-8_5
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-5752-1
Online ISBN: 978-981-15-5753-8
eBook Packages: EngineeringEngineering (R0)