Microsoft Word - 1-V8N2(2023)-AITI#9562(81-99).docx Advances in Technology Innovation, vol. 8, no. 2, 2023, pp. 81-99 Tribological Aspects Affecting Surface Durability of Tooth-Sum Altered Spur Gears: A Load Sharing Approach Avil Allwyn Dsa1,*, Joseph Gonsalvis2 1Department of Mechanical Engineering, Don Bosco College of Engineering, Goa, India 2Research Advisor, Mechanical Engineering, St. Joseph Engineering College, Mangalore, India Received 01 May 2022; received in revised form 01 June 2022; accepted 03 June 2022 DOI: https://doi.org/10.46604/aiti.2023.9562 Abstract The performance of tooth-sum altered (ATS) gears is determined by the factors influenced by their profile geometry. This study aims to explore the influence of gear geometry modification on tribological aspects that affect surface wear in ATS spur gears. A computer code is developed to simulate surface wear numerically, using Archard's wear model, Greenwood-Williamson micro-asperity contact model, and Johnson’s load-sharing approach. The outcomes of the study indicate that the low contact ratio ATS gears promote the formation of thick oil film owing to reduced specific sliding and increased speed. However, high contact ratio ATS gears create unfavorable operating conditions resulting in extreme boundary lubrication. The effectiveness of lubricant oil film in reducing wear in ATS gears is associated with its modified profile, sliding velocities, load bearing, operating temperature, and oil viscosity. Keywords: altered tooth-sum gear, wear, lubrication, oil film, specific sliding 1. Introduction The performance and surface durability of gear drives are greatly affected by the gear geometry, material properties, lubrication, and contact conditions. The gear profile is a macroscopic parameter, which affects almost all aspects of the performance of a gear drive. Hence, designers attempt profile modifications to improvise specific design features to fulfill the functional requirements of a gear pair. The tooth-sum altered (ATS) gearing [1-3], is a novel type of profile-shifted gearing system, which provides the flexibility of modifying the profile geometry by accommodating different tooth-sums on the same center distance. Lubrication in ATS gears is influenced by profile modification that affects oil film thickness, sliding velocities, load-bearing, operating temperatures, oil viscosity, and consequently surface wear. A gear tooth contact is a non-conformal engagement under mixed elastohydrodynamic lubrication (EHL) [4], sharing the total load partially between the lubricating oil film and the participating surface asperities. The geometry-driven change in specific sliding and flash temperature at the tooth-contact interface causes variation in oil viscosity conditions, promoting mixed or boundary lubrication with partial metal-to-metal (asperities) surface contact. A favorable fluid film EHL regime can avoid such asperity contacts enhancing surface wear resistance. Surface roughness is also an important parameter that influences gear performance and surface wear. Under high load, the contact asperities undergo elastic and plastic deformation and cause an increase in friction, resulting in wear. The multi-parameter dependence of damage by wear makes it a complex problem that continues to be a common failure mode experienced by gear transmission systems. * Corresponding author. E-mail address: avil.dsa@dbcegoa.ac.in Advances in Technology Innovation, vol. 8, no. 2, 2023, pp. 81-99 82 The objective of this work is to investigate the influence of tooth-sum alteration on lubrication, load bearing, coefficient of friction, and wear along different regions of the tooth flank. In this analysis, a surface wear model based on Archard’s wear formulation [5] and Johnson’s load-sharing concept [6] is used along with classical elastohydrodynamic lubrication theory [4] in predicting the tribological factors that influence surface damage in geometry-modified ATS gearing. 2. Literature Review In recent years, a few researchers reported the benefits of gear profile modification by tooth-sum alteration of non-lubricated gears with smooth surfaces operating on a fixed center distance. Sachidananda et al. [1] showed it is possible to obtain either low, normal, or high contact ratio gear drives by altering the tooth-sum of a gear pair. They experimentally investigated the surface damage of non-lubricated spur gear contacts and confirmed the design benefits and flexibility of ATS gears. Sachidananda et al. [2] studied the effects of sliding velocity in ATS gears and concluded that negative tooth-sum alterations are better than standard or positive alterations in tooth-sum. Dsa and Gonsalvis [3] extended the tooth-sum alteration technique to asymmetric gears and studied surface wear in non-lubricated contacts. Earlier, Johnson et al. [6] proposed a theoretical approach for studying highly loaded lubricated contacts by combining the established elastohydrodynamic theory and Greenwood and Williamson’s [7] theory of rough random contact surfaces. They proposed the concept of the total load being shared between hydrodynamic pressure and surface asperity contacts. Gelinck and Schipper [8] used the load-sharing idea and developed a mixed lubrication model to obtain the Stribeck curves for line contact problems to predict transitions between lubrication regimes. Akbarzadeh and Khonsari [9] used the load-sharing approach to develop a model for predicting the performance of spur gears. They validated their model by comparing their predictions with published theoretical and experimental data. Ebrahimi Serest and Akbarzadeh [10] presented a model for predicting the performance of helical gears, using the load-sharing concept for accounting for the contribution of surface roughness and the lubricant in bearing the applied load. Kimiaei and Akbarzadeh [11] used the load-sharing model to evaluate the performance of So and S+/- profile shifted gears. Simon [12-14] reported the results of his extensive work on full EHL analysis in different types of gears, investigating the influence of gear design, operating conditions, and lubricant on gear performance characteristics. Over the years, researchers on surface wear of spur gears have mainly focused on developing prediction models, enhancing wear resistance by geometry modification and material properties. Archard’s general wear equation [5] is a popular choice among researchers for wear prediction in gears having parameters with complex inter-dependency due to its simplicity and reasonably realistic estimate. Flodin and Andersson [15] proposed a numerical wear simulation model based on Archard’s wear formulation employing the single-point contact observation technique. Prabhu Sekar and Sathishkumar [16] reported the possibility of enhancing the wear resistance in spur gears by profile shift. In a study on the wear of asymmetric gears, Karpat and Ekwaro-Osire [17] found that tooth tip relief given could reduce induced dynamic load and wear depth. Brandão et al. [18] determined the roughness shape of the pinion tooth flank surface using a combined wear and surface contact fatigue damage model. Zhang et al. [19] experimentally investigated the wear and contact fatigue of modified involute gears under minimum lubrication, considering tooth wear evolution. Ristivojevic et al. [20] studied the impact of geometric and operational parameters on surface wear and reported lesser wear on the addendum flank and higher wear on the dedendum. Ding and Kahraman [21] in their work on the interaction between gear dynamics and surface wear presented a set of simulations to demonstrate a two-way relationship between non-linear gear dynamics and surface wear. Reviewing the literature on ATS spur gears, the study of the tribological aspects affecting surface wear is identified as a research gap. In addition, Johnson’s load-sharing concept which combines the classical EHL theory and micro-asperity contact model is identified as an efficient method to solve the mixed EHL problem with fairly good accuracy. Advances in Technology Innovation, vol. 8, no. 2, 2023, pp. 81-99 83 3. Gear Geometry Modification by Tooth-Sum Alteration It is possible to accommodate different tooth-sums and gear ratios on a specified center distance. While the module � is a parameter that is critical for the magnitude of power transmitted, the gear ratio is important to maintain the required output speed. For a standard gear pair with reference tooth-sum ��� , the operating pressure angle �� and center distance � are the same as the standard pressure angle � and center distance ��� . Keeping the center distance the same and altering the reference tooth-sum by a factor to ���, causes the operating pressure angle to change (refer to Fig. 1). Such gear pairs require a total profile shift coefficient �� to be included for proper meshing [22]. Tooth topping of addendum radii of the mating gears by a factor: called tooth topping coefficient ensures adequate root clearance [23]. Fig. 1 Standard tooth-sum and altered tooth-sum gears The ratio of profile shift coefficient �� on the driver to that of the total profile shift coefficient �� for a gear pair is defined as the profile shift factor �. If the tooth-sum [3] and the center distance of a reference gear pair are altered by a factor and � respectively, it can be shown that: cos cos wφ α φ β = (1) ( ) 2 tan a s w s mZ inv inv B X m φ φ α β φ − − = (2) ( ) 2 r s s Z Y X α β= + × − (3) 1 s x X κ = (4) For a standard tooth-sum (STS) normal contact ratio (NCR) gear pair, � � � 1. For the ATS gear system, 0.96 � � 1.04 and � � 1. For the S± profile shifted system, 0.96 � � � 1.04 and � 1. The performance characteristics of altered tooth-sum gears can be studied under a constant load or constant speed condition. The equation for tooth load on a pair of gears transmitting a power P at speed N under constant load can be expressed as: 2 r a t t b P F F Nrπ = = (5) Advances in Technology Innovation, vol. 8, no. 2, 2023, pp. 81-99 84 Altering the tooth-sum of a gear pair on a fixed center distance changes the radius of the base circles. To maintain constant load, the speed of the ATS gear pair should be changed. The equation for speed relation between the ATS and the STS gear pair is given by: r r a rb t a a b t r F N N r F = × × (6) where N, Ft, and rb represent the speed, normal load, and radius of the base circles, respectively. The superscripts r and a represent reference gear and altered gear pairs, respectively. For a constant load using ��� � ��� Eq. (6) reduces to: r a rb a b r N N r = × (7) 4. Load Sharing and Friction Coefficient in ATS Gears under Boundary Lubrication In ATS gears operating under a boundary lubrication regime, the total load transmitted is assumed to be shared between the oil film and the contacting asperities [6]. The dynamic load ��� shared by a tooth pair at any arbitrary location is equal to the sum of the load carried by the asperities �� and oil film � !, and it can be expressed as: dx hy c f f f= + (8) Dividing throughout by ��� Eq. (8) can be written as: 1 hy c dx dx f f f f + = (9) Defining 1/#� and 1/#$ as load sharing factors for the hydrodynamic part and asperities contact part respectively, Eq. (9) can be written as: 1 2 1 1 + =1 γ γ (10) Similarly, the total friction force %��� at any location is the sum of the oil film friction force �& ! and asperities contact friction force %���. Mathematically: dx hy c c f f fµµ µ= + (11) Dividing Eq. (11) throughout by ��� and using the definition of 1/#$ from Eq. (10), the total friction coefficient % is given by: 2 hy c dx f f µ µ µ γ = + (12) From Newton’s law of viscosity, the hydrodynamic friction force �& ! per unit, face width is given by: 1 22 r r hy c v v f a h µ η − = (13) where a is the Hertzian half-width of contact, ' is the dynamic viscosity at contact pressure, (� is the rolling velocity of gears and ℎ� is the oil film thickness. Using simplified Roeland’s equation, lubricant viscosity at any contact pressure and temperature can be found. Advances in Technology Innovation, vol. 8, no. 2, 2023, pp. 81-99 85 ( ) ( ) 0 02.303 1 1 135 z SiG p c t eη η + + ∞= × (14) where zi is called the viscosity pressure index assumed to be 0.6 for mineral oils, '* � 6.315 × 10./01. 23�, and the value of � � 196451. G0 and S0 are dimensionless numbers for lubricant viscosity grade and slope. The Hertzian half-width of contact is given by: 8 dx f a E ρ π ′ = ′ (15) 1 2 1 2 ρ ρ ρ ρ ρ ′ = + (16) 2 2 1 2 1 2 1 12 v v E E E − − = + ′ (17) where, using the modulus of elasticity E and the poisons ratio 6, the equivalent modulus of elasticity 78 is defined using Eq. (17). Using the radius of curvature 9 at any contact location, the equivalent radius of curvature 98 is defined using Eq. (16). 5. Flash Temperature and Oil Film Thickness The operating condition at the contact interface depends upon gear geometry, loading conditions, and lubricant properties as the point of contact glides along the pressure line. The sliding motion in a gear contact increases the temperature of its contact interface, which can break down the lubricating oil film. Flash temperature is defined as the instantaneous rise in surface temperature when contact between gear teeth occurs. Blok’s flash temperature equation formulated by AGMA is given as: ( ) ( ) 0.5 0.5 1 20.5 0.8 dl f r r m x F T v v B a µ = − (18) Temperature changes the oil viscosity, consequently affecting oil film formation. The central oil film thickness calculation is based on Moe’s equation [4]. The following dimensionless numbers are used in defining Moe’s numbers. dxf W E ρ = ′ ′ (19) ( )0 1 2r rv v U E η ρ Σ + = ′ ′ (20) ehlG Eα ′= (21) where W is the dimensionless load parameter, :∑ is the dimensionless speed parameter, < = is called the Barus pressure viscosity coefficient. The dimensionless Moe’s numbers are defined as: 1 2c c h H U ρ − Σ= ′ (22) 1 2M WU− Σ= (23) 1 4L GUΣ= (24) Moe’s equation for central oil film thickness modified by Gelinck and Schipper [8] using Johnson’s load-sharing method is given as: Advances in Technology Innovation, vol. 8, no. 2, 2023, pp. 81-99 86 ( ) ( ) 1 3 7 2 7 2 7 3 14 15 7 3 2 7 2 7 2 1 2 1 1 1 1 s s s s s c ri ei rp ep H H H H Hγ γ γ γ −− − − − = + + +   (25) 13 ri H M−= (26) 1 52.621 ei H M −= (27) 2 31.287 rp H L= (28) ( )1 8 3 41.311 ep H M L−= (29) 2 5 12 1 7 8 5 ei ri H H s e γ − −   = +     (30) The subscripts ri, rp, ei, and ep denote rigid-isoviscous; rigid-piezoviscous; elastic-isoviscous, and elastic-piezoviscous, respectively. The type of lubrication regime is determined based on the value of the roughness parameter given by: c rms h σ Λ = (31) The value of Λ > 3 represents full oil film, 1 � Λ � 3 represents mixed lubrication regime, and Λ � 1 represents boundary lubrication. According to Greenwood-Tripp’s asperity contact model [24], the average contact pressure can be expressed as: ( ) 2 5 2 8 2 15 rms c d c rms rms h d p n E F σ π β σ β σ − ′ ′ ′= ′ (32) where @8 is the density, �8 is the radius of curvature of the asperities, and A�B� is the composite root mean square surface finish. The �//$ function can be approximated by: ( ) ( ) 6.8045 5 2 44.4068 10 4 >40 HH F H for H σσ σ σ − ≤× − = (33) Applying Johnson’s concept of load sharing, Gelinck and Schipper have shown that central pressure is a good quantity to characterize the pressure distribution of rough line contact. Mathematically: ( ) 0.5882 1.7 0.442 0.0337 0.4757 2 2 1 1 1.558 rms c fc p n W σ σ γ ρ β ρ γ ρ −−−     ′ ′ ′ ′= +    ′      (34) 2 dx fc f E σ πρ ′ = ′ (35) where Eq. (35) gives the variation of contact stress AC� along the line of action. 6. Static and Dynamic Load Factors Evaluation of static and dynamic loading patterns for ATS gears with different values of tooth-sum alteration factors is essential to identify the effect of gear geometry modification on various performance parameters. If D� is the mesh stiffness [25] at any arbitrary contact location for tooth load intensity per unit face width ��, then static load factor �= is defined as the ratio of location-based mesh stiffness to that of equivalent mesh stiffness D 1), and low contact ratio (LCR) ATS gears with negative tooth alterations ( < 1), all pairs running on the same center distance (refer to Fig. 3(a)). Speed and contact ratio affect dynamic load factors in STS as well as ATS gears. Plots of dynamic load factors of NCR STS gears and LCR ATS gears for profile shift factors 0.25 < � < 0.75 show one region of single tooth contact and two regions of double tooth contact (refer to Figs. 3(b)-(d)). Larger zones of single tooth contact represent a lower contact ratio, and reducing the roll angle of single tooth contact shows improvement in the contact ratio. Plots of dynamic load factors of HCR ATS gears with CR > 2, show three regions of triple teeth contact and two regions of double tooth contact, indicating an improvement in the load-bearing capacity (refer to Figs. 3(e)-(f)). Spikes are observed at the transition zones between double to single tooth contact and triple to double tooth contact. As the speed increases, the dynamic load as a function of contact position differs appreciably from the static load. Dynamic load in a gear system decreases with an increase in contact ratio at any given speed because of the narrow single or triple contact zone, which passes quickly, leaving no time for the system to respond. (a) κ = 0.25 and β = 1 (b) κ = 0.5 and β = 1 (c) κ = 0.75 and β = 1 Fig. 4 Effective radius of curvature for ATS gears 0.96 < < 1.04 (a) κ = 0.25 and β = 1 (b) κ = 0.5 and β = 1 (c) κ = 0.75 and β = 1 Fig. 5 Contact stresses for ATS gears 0.96 < < 1.04 ATS gear geometry modification influences dynamic loads, contact pressure, and sliding velocities, consequently affecting flash temperature, oil viscosity, and film thickness. For a given load, the contact stress in ATS gears solely depends on the effective radius of curvature of the tooth (refer to Fig. 4). The effective radius of curvature is larger in LCR ATS and smaller in HCR ATS than the NCR STS. The effect of profile shift factor 0.5 < � is to reduce the effective radius of curvature of the point of engagement in LCR ATS gears and increase the same at the point of disengagement in HCR ATS gears. Profile shift factor � > 0.5 reduces the effective radius of curvature of the point of disengagement in LCR ATS gears and increases the same at the point of engagement in HCR ATS gears. Consequently, LCR ATS gears have lower magnitudes of contact Advances in Technology Innovation, vol. 8, no. 2, 2023, pp. 81-99 92 stresses than NCR STS, but the variation from single to double tooth contact region is significant. In HCR ATS, the highest magnitude of contact stress is comparable with LCR ATS, and the variation from two to three teeth contact region is comparatively less (refer to Fig. 5). (a) κ = 0.25 and β = 1 (b) κ = 0.5 and β = 1 (c) κ = 0.75 and β = 1 Fig. 6 Specific sliding in ATS gears 0.96 < < 1.04 Specific sliding, contact stresses, and dynamic load factors are important indicators useful in contact wear analysis to quantify and compare damage by failure-promoting mechanisms such as fatigue, pitting, and abrasion in ATS gears. NCR STS and LCR ATS gears exhibit lower sliding velocities but higher dynamic loads. In contrast, HCR ATS gears show higher sliding speeds but lower dynamic loads (refer to Figs. 3(b)-(f) and Fig. 6). In any ATS gear pair, profile shift factor � < 0.5 increases the specific sliding at the start point of mesh in LCR ATS and the endpoint in HCR ATS. On the contrary, the ATS gear pair with profile shift factor � > 0.5 increases the specific sliding at the endpoint in LCR ATS and the start point of mesh in HCR ATS. For all the values of tooth-sum alteration factor α, the flash temperatures obtained using Blok’s contact temperature expression show the least value at the pitch point and gradually increase towards the beginning and end of the tooth mesh (refer to Fig. 7). Flash temperatures are affected by speed, dynamic load factors, and coefficient of friction. Specific sliding reduction or increase is associated with the speed and radius of curvature that influences flash temperature. (a) κ = 0.25 and β = 1 (b) κ = 0.5 and β = 1 (c) κ = 0.75 and β = 1 Fig. 7 Flash temperature for ATS gears 0.96 < < 1.04 ATS gears with profile shift factor � = 0.5, irrespective of the value of their tooth-sum alteration factor α, have symmetric temperature distribution about the pitch point. Flash Temperature distribution about the pitch point in LCR and HCR ATS gears operating with profile shift factor, � = 0.5 can be compared with NCR STS gears under constant load conditions. Reduced relative sliding and higher oil film thickness due to higher speeds cause a reduction in the coefficient of friction, which helps reduce the flash temperature in ATS LCR gears. Higher relative sliding velocity and reduced oil film thickness due to lower operational speeds increase the coefficient of friction and flash temperature in HCR ATS gears. In any ATS gear pair, varying the profile shift factor � alters the temperature distribution about the pitch point. In an LCR ATS gear pair, the relative sliding velocity increases at the point of engagement and disengagement for gears operating with profile shift factor � < 0.5 and � > 0.5, respectively. In an HCR ATS gear pair, the relative sliding velocity increases at the point of disengagement and engagement for gears operating with profile shift factor � < 0.5 and � > 0.5, Advances in Technology Innovation, vol. 8, no. 2, 2023, pp. 81-99 93 respectively. Increased relative sliding and comparatively larger dynamic loads due to opposing friction forces consequently increase flash temperature and reduce dynamic viscosity and oil film thickness when operating the gears under constant load and speed conditions. Even though HCR ATS gears have lower dynamic loads, larger sliding velocities result in higher magnitudes of flash temperatures than LCR ATS gears. (a) κ = 0.25 and β = 1 (b) κ = 0.5 and β = 1 (c) κ = 0.75 and β = 1 Fig. 8 Dynamic viscosity ATS gears 0.96 < < 1.04 The dynamic viscosity for LCR and HCR ATS gears with profile shift factor 0.25 < � < 0.75 are plotted using Roeland’s temperature-pressure-viscosity relation shows the largest magnitude at the pitch point and starts reducing on either side of it (refer to Eq. (14), Fig. 8). Dynamic viscosity is lower at the locations of higher flash temperatures and pressures with the least magnitudes at the beginning and end of contact in HCR ATS gears. Lower flash temperatures and pressures result in a comparatively smaller range of variation in viscosity in ATS LCR gears. Even though the HCR ATS gears have a higher load-carrying capacity than their LCR ATS counterparts, for a given load, a drop in viscosity results in reduced oil film thickness (refer to Fig. 9). (a) κ = 0.25 and β = 1 (b) κ = 0.25 and β = 1 (c) κ = 0.75 and β = 1 Fig. 9 Oil film thickness ATS gears 0.96 < < 1.04 (a) κ = 0.25 and β = 1 (b) κ = 0.5 and β = 1 (c) κ = 0.75 and β = 1 Fig. 10 Load on oil film ATS gears 0.96 < < 1.04 The reduction in oil film thickness causes the asperities to take a considerable portion of the load and vice versa, especially at the start point and the endpoint of contact (refer to Fig. 10). The load sharing graphs indicate a maximum of 60% load taken up by the oil film at the pitch point, and the same reduces to below 10% at the extreme ends of mesh for HCR ATS gears. A more Advances in Technology Innovation, vol. 8, no. 2, 2023, pp. 81-99 94 significant portion of the load taken up by asperities due to thin oil film can cause the HCR ATS gears to operate under extreme boundary lubrication conditions. Improved oil film thickness in LCR ATS gears share a higher load of above 90% at the pitch point, reducing to 50% at the extreme ends of the mesh. The reduced oil film thickness causes a higher load share on the asperities resulting in a higher coefficient of friction in HCR ATS gears and vice versa in LCR ATS gears (refer to Fig. 11). (a) κ = 0.25 and β = 1 (b) κ = 0.5 and β = 1 (c) κ = 0.75 and β = 1 Fig. 11 coefficient of friction ATS gears 0.96 < < 1.04 The higher the percentage of load taken by the oil film, the lesser the load on the surface asperities, and the better will be the life of the gear (refer to Fig. 12). Hence, LCR ATS gears will have a better life under the given loading conditions due to relatively thicker oil film formation than HCR ATS gears. The oil film thickness can be maintained by changing the oil or the operating speeds. Under the given operating conditions, the service life of HCR ATS can be improved by using oil of higher viscosity. However, using higher viscosity oil to avoid surface damage may increase power loss. Speed, dynamic load, and specific sliding are the important factors influencing the formation of the oil film and consequently the load distribution and wear. Plots of accumulated wear in NCR ATS gears operating under constant load and speed conditions are presented in Fig. 13. (a) κ = 0.25 and β = 1 (b) κ = 0.5 and β = 1 (c) κ = 0.75 and β = 1 Fig. 12 Tooth life estimate ATS gears 0.96 < < 1.04 (a) α = 1 and β = 1 of pinion (b) α = 1 and β = 1 of gear Fig. 13 Wear plots STS gears α = 1 for 2 × 10r cycles Varying the profile shift factor � of any LCR ATS gear pair alters the mesh zone about its pitch point. The Profile shift factor � < 0.5 makes the drive approach dominant by reducing the length of the path of recess and increasing the length of the approach. The specific sliding increases at the point of engagement and decreases at disengagement for both the pinion and the Advances in Technology Innovation, vol. 8, no. 2, 2023, pp. 81-99 95 gear, compared with the ATS LCR gears with profile shift factor, � = 0.5. Increased specific sliding and relatively larger dynamic loads due to opposing friction forces eventually raise the flash temperature reducing dynamic viscosity and oil film thickness. Consequently, there is a proportional increase in wear on the pinion than on the gear in the approach engagement region and vice versa in the recess engagement region (refer to Figs. 14(a)-(b) & Figs. 15(a)-(b)), while the gears are operating under constant load condition. For profile shift factor � = 0.5, the LCR ATS gears, irrespective of their tooth-sum alteration factor α, attain equal approach-recess action. Accumulated wear is comparatively lesser than NCR STS gears (refer to Figs. 14(c)-(d) and Figs. 15(c)-(d)). Reduced specific sliding and improved oil film thickness due to increased speed help reduce wear rates in ATS LCR gears. Alternatively, increasing the profile shift factor � > 0.5 decreases the path of approach and proportionately increases the path of recess, making the drive recess dominant. The specific sliding decreases at the engagement point and increases at disengagement for both pinion and gear. Higher specific sliding on the gear than on the pinion at the point of disengagement causes an increase in flash temperature, consequently reducing dynamic viscosity and oil film thickness. This leads to a relative increase in wear on gear than on the pinion in the recess engagement region and vice versa (refer to Figs. 14(e)-(f) and Figs. 15(e)-(f)) in the approach engagement region while operating the gears under constant load condition. (a) α = 0.96, κ = 0.25, and β = 1 of pinion (b) α = 0.96, κ = 0.25, and β = 1 of gear (a) α = 0.98, κ = 0.25, and β = 1 of pinion (b) α = 0.98, κ = 0.25, and β = 1 of gear (c) α = 0.96, κ = 0.5, and β = 1 of pinion (d) α = 0.96, κ = 0.5, and β = 1 of gear (c) α = 0.98, κ = 0.5, and β = 1 of pinion (d) α = 0.98, κ = 0.5, and β = 1 of gear (e) α = 0.96, κ = 0.75, and β = 1 of pinion (f) α = 0.96, κ = 0.75, and β = 1 of gear (e) α = 0.98, κ = 0.75, and β = 1 of pinion (f) α = 0.98, κ = 0.75, and β = 1 of gear Fig. 14 Wear plots ATS gears α = 0.96 for 2 × 10r cycles Fig. 15 Wear plots ATS gears α = 0.98 for 2 × 10r cycles For tooth-sum alteration factor > 1, the contact transforms from NCR STS to HCR ATS gears, significantly reducing dynamic load factors over ATS gears with lower values due to reduced unit tooth load and the minimal dimension of the transition zone. Just as in the case of LCR ATS gears, varying the profile shift factor � alters the mesh zone about the pitch Advances in Technology Innovation, vol. 8, no. 2, 2023, pp. 81-99 96 point in HCR ATS gears. However, unlike the LCR ATS gears, the profile shift factor � < 0.5 for any HCR ATS reduces the length of the approach path and increases the recessed path, making the drive recess dominant. The specific sliding decreases at the point of engagement and increases at disengagement for both the pinion and the gear, compared with the ATS HCR gears with profile shift factor � = 0.5. Significantly higher specific sliding and very thin oil film in the root region of the gear causes a higher wear rate on the gear than on the pinion (refer to Figs. 16(a)-(b) and Figs. 17(a)-(b)). The HCR ATS gears with profile shift factor � = 0.5 have equal approach-recess action. The root regions of both the pinion and the gear have higher specific sliding and lower oil film thickness than the NCR STS gears under constant load conditions. Consequently, the accumulated wear (refer to Figs. 16(c)-(d) and Figs. 17(c)-(d)) is comparatively greater than NCR STS under constant load conditions. The HCR ATS gears with shift factor � > 0.5 have significantly higher specific sliding at the pinion root causing higher wear (refer to Figs. 16(e)-(f) and Figs. 17(e)-(f) on the pinion than on the gear. Increased specific sliding and reduced oil film thickness due to reduced operating speed cause higher wear rates in HCR ATS gears. (a) α = 1.02, κ = 0.25, and β = 1 of pinion (b) α = 1.02, κ = 0.25, and β = 1 of gear (a) α = 1.04, κ = 0.25, and β = 1 of pinion (b) α = 1.04, κ = 0.25, and β = 1 of gear (c) α = 1.02, κ = 0.5, and β = 1 of pinion (d) α = 1.02, κ = 0.5, and β = 1 of gear (c) α = 1.04, κ = 0.5, and β = 1 of pinion (d) α = 1.04, κ = 0.5, and β = 1 of gear (e) α = 1.02, κ = 0.75, and β = 1 of pinion (f) α = 1.02, κ = 0.75, and β = 1 of gear (e) α = 1.04, κ = 0.75, and β = 1 of pinion (f) α = 1.04, κ = 0.75, and β = 1 of gear Fig. 16 Wear plots ATS gears α = 1.02 for 2 × 10r cycles Fig. 17 Wear plots ATS gears α = 1.04 for 2 × 10r cycles Tooth tip relief modification is considered one of the well-known ways to reduce dynamic loads and wear in spur gears. To investigate the effectiveness of the tip relief modification in reducing tooth wear in ATS gears, the variations of tip relief for the contact points are integrated into tooth profile deviations as wear (refer to Eq. (45)). The amount of relief is configured based on the design load and the tooth deflection for a test case on LCR ATS with tooth-sum alteration factor = 0.96 and Advances in Technology Innovation, vol. 8, no. 2, 2023, pp. 81-99 97 profile shift factor � = 0.5 (refer to Fig. 18). Referring to Figs. 14(c)-(d) and Fig. 19 for comparison of wear on gear and pinion with and without tip relief, the reduction in wear on the latter reflects the reduction in dynamic loads, which is particularly pronounced at the beginning and the end of the mesh. Different gear ratios of ATS gears of a given tooth-sum also alter the tooth geometry, just like profile shift factors alter the gear geometry since their base circles are different. Superimposing magnitudes of gear ratios and profile shift factors push the start or end of tooth contact very near to the point of tangency to the base circles which may cause extreme sliding operating conditions. Therefore, LCR or HCR ATS gears with GR > 1 should be paired with profile shift factors � < 0.5 to avoid higher specific sliding. Similarly, LCR or HCR gears with GR < 1 should be paired with profile shift factors � > 0.5 to avoid extreme operating conditions. α = 0.96, κ = 0.5, and β = 1 (a) α = 0.96, κ = 0.5, and β = 1 of pinion (b) α = 0.96, κ = 0.5, and β = 1 of gear Fig. 18 Tooth with relief modification Fig. 19 Wear plots for ATS gears with tip relief 11. Conclusions ATS gear drives are geometry-modified and, kinematically compatible sets of gear pairs capable of operating at a specified center distance. LCR and HCR ATS gear pairs can be obtained by altering the tooth-sum of an NCR STS gear pair with the tooth-sum alteration factor 1 < < 1, respectively. Based on the comparative study of the supportive and detrimental effects of tribological aspects affecting surface durability in ATS gears under constant load, the following conclusions are drawn: (1) The effects of tooth-sum alteration on surface wear are influenced by meshing parameters such as dynamic load factors, specific sliding, and material properties. (2) Specific sliding is an important parameter that is associated with the radius of curvature and speed ratio. (3) Zones of higher specific sliding are associated with higher flash temperature, reduced oil viscosity, and increased coefficient of friction. (4) LCR ATS gears operating at higher speeds help in the formation of better oil film, and lower specific sliding causes reduced flash temperature that prevents excessive reduction in dynamic viscosity and promotes better oil film thickness. Therefore, the oil film takes up a more significant portion of the load, reducing the coefficient of friction and surface wear, and increasing pitting life. (5) Lower operating speeds in HCR ATS and high specific sliding at the start or endpoint of mesh are responsible for higher flash temperatures and reduced dynamic viscosity, which results in very thin oil film formation. Consequently, much of the load is taken up by the asperities causing increased surface wear, higher coefficient of friction, and lower pitting life. (6) While operating ATS gears with gear ratios other than unity, it is preferable to use gear ratio and profile shift factor combinations that lower the specific sliding for the reasons mentioned above. On a concluding note, the study on ATS gears reveals the influence of profile modification resulting from tooth-sum alteration on surface wear and other interdependent parameters. ATS gearing offers flexible design features often unavailable in STS gear design. However, experimental studies on this methodology of gear design are proposed as a scope for future work. LPSTC HPSTC (10 )linear relief mµ Modified profile Trueinvolute profile Tooth center line Advances in Technology Innovation, vol. 8, no. 2, 2023, pp. 81-99 98 Nomenclature Tooth-sum alteration factor � Center distance � Center distance alteration factor �