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Research Papers: Applications

# Wear and Mechanical Contact Behavior of Polymer GearsPUBLIC ACCESS

[+] Author and Article Information
Khalid Abdulkhaliq M. Alharbi

Mechanical Engineering Department,
Umm Al-Qura University,
Makkah, Saudi Arabia;
School of Engineering,
University of Warwick,
Coventry CV4 7AL, UK
e-mail: kamharbi@uqu.edu.sa

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received July 13, 2017; final manuscript received July 26, 2018; published online August 24, 2018. Assoc. Editor: Xiaolan Ai.

J. Tribol 141(1), 011101 (Aug 24, 2018) (10 pages) Paper No: TRIB-17-1274; doi: 10.1115/1.4041020 History: Received July 13, 2017; Revised July 26, 2018

## Abstract

Extensive investigations have been carried out in the present paper to understand polymer gear performance, i.e., wear and contact behaviors. The experimental results and possible wear mechanisms for polymer gears run against themselves have been presented, especially the wear rate of the polymer gears under different running speeds and loads. The tested samples were made of three different materials (acetal, nylon, and polycarbonate (PC)) and the effects of two different manufacturing techniques were also investigated (i.e., machine-cut and injection-molded polymer gears). The polymer gear performances (wear and life) were recorded using a uniquely designed and built test rig for this purpose. The testing results have been compared with the existing literature for polymer fatigue and wear theory. Further extensive investigations have been carried out to understand the wear phenomena on tooth flank surface profile of these gears and the data obtained have been discussed.

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## Introduction

Recently, polymer gears have been used more widely in engineering applications, due to their low cost, faster and easier to produce, and lighter and quieter in operation than metal gears [1]. In addition, they can be operated without lubrication. For these reasons, they have been partly accounted as metal gear replacement in certain applications. Examples of polymer gears can be found in printers, kitchen electronics and utilities, as well as electric vehicles. A technical project to replace some metal gears and housing of the transmission system of the Visio.M electric vehicle showed good reduction in operating cost and weight, as well as some improvements in production process [2]. Polymer gears' design and rating methods are derived mostly from the rating techniques of metal gears [3,4]. This method is still mainly employed by the British Standard 6168 and other standards as well as the commercial sector [5,6]. The optimum performance in polymer gears is inappropriately achieved using such method of rating, because metal gears rating relies mostly on Lewis formula [7], which calculates gear teeth strength, while polymer gears have been found to be more strongly affected by different factors [8], such as thermal and wear of material [9,10]. Yet, these parameters on polymer gear operation are still under investigation [1114]. On the other hand, other polymer gears' standards involve the effect of thermal phenomena in design of polymer gear, but not in fully accurate temperature prediction [15], as this sector understanding is still under development [16]. Using metal gear rating to rate polymer gears mostly leads to system failures and limitations in their applications. For this reason, an understanding of polymer gear behavior has become very important as a way to understand and employ these mechanical devices more appropriately, and to increasingly gain from their advantages and overcome their limitations.

It has been noted that polymer mechanical properties and tribological characteristics are more strongly affected by temperature change than metals [17,18]. Therefore, some effort has been made to measure wear rate and surface temperature of a gear while it is running [4,10], and to compare these figures with theoretically derived wear rate and temperature calculations [18,19]. Although progress has been made in this sector, there is still some limitations on literature for high-speed running and high-loaded conditions to provide limits that polymer gears can reach before failure [20,21]. As a result of this, the current research will focus more on failure modes and the wear rate of polymer gears, while further deep investigations will be made on heat build-up measurements and calculations.

## Testing Methods and Gear Specifications

The test rig used for this research was uniquely designed and built at the University of Warwick, with the aim of continuous measurement of polymer gear wear and gear wear rate of the tooth flank surfaces (Fig. 1). Its features and specifications have been explained in previous work [22]. Figure 2 shows a schematic diagram for this rig, highlighting its main components. The test rig is of back-to-back setup where tested gears are loaded by a constant mean load, using the torque setting arm. Cut-off switch is attached under the assembly block to automatically stop the test immediately after gear teeth complete damage. Wear is monitored by measuring the vertical component of the displacement of the block using a contact displacement transducer calibrated to an accuracy of 0.1 μm, using highly accurate slip gauges (specified for calibration). This device applies the principle of linear variable differential transformer, which makes it the most reliable displacement measurement device with very accurate resolution and nondisruptive readings. Linear variable differential transformer is connected to a microcomputer to log the displacement change (wear depth) in μm as a function of time in microseconds, allowing accurate wear rate to be defined at any period of time. Figure 3 shows the gear tooth measurement, as quantitatively related to the movement of the assembly block, and the wear measuring location. The measured vertical displacement represents the tooth thickness reduction in addition to a small tooth reformation due to load. This deformation cannot be removed from the logged data using the current test rig. Therefore, two methods were used to overcome this source of error. First, it was found (by running many long running tests) that the tooth deflection occurs at the early stage of running, leaving the next nearly linear set of data as mostly tooth wear reading. Second, the wear rate of the teeth, as a function of the number of cycle, was defined at the nearly linear stage, neglecting the first set of high wear data.

The current study uses four different sets of gears: the first two sets were nylon 66 and acetal gears, manufactured using a machine cut manufacturing process, while the second two sets were nylon 46 and polycarbonate (PC) gears produced in injection molding technique. They were chosen so as to be compared with previous works on polymer gears, as well as previous tribology studies on polymer surfaces operated in nonconformal rolling and sliding contact and pin on disk studies. It is worth clarifying here that in terms of cost, injection-molded gears, when high amount of gears are produced, are very low in cost comparing to machine-cut gears, as cost mostly relies on the manufacturing of the mold itself. Thus, the process of gear molding costs comparably very low (10–20%) compared to machine-cut gears. On the other hand, when a small patch is required, machine-cut gears will be lower in cost, for the same reason (cost of designing and manufacturing the mold). More studies on the operation capability of these two gear types, with different manufacturing techniques, are in progress. The machine-cut gears were manufactured by uniform cuts on extruded bars of nylon 66 and acetal using a uniform cutter to shape the required involute profile following the standards of polymer gears manufacturing [5]. Similarly, injection-molded gears were manufactured using a mold that was designed to the same standard. Spur gear samples were designed to a module of 2 mm, 30 teeth, and face width of 15 mm. The tooth flank forms an involute profile with a pressure angle of 20 degs. The calculated theoretical contact ratio is 1.67, although polymer gears are soft enough to deform and mostly increase this amount [3], which might change the teeth load sharing and pressure angle and consequently affect the contact pressure and highstreetses on gear teeth.

Note that both manufacturing methods lead to some gear dimension instability due to material shrinkage because of manufacturing process, although they are lower in machine-cut gears than in injection-molded gears. In the current research samples, machine-cut acetal gears outer diameter shrunk for an average of 0.18 mm from the original (64 mm), while it was reduced by an average of 0.43 mm in the injection-molded nylon 46 gears. On the other hand, the injection-molded PC gear's outer diameter was increased by the average of 0.83 mm above the theoretical one. Only machine cut nylon 66 gears dimensions were stable enough to satisfy the designed dimensions by around 0.01 mm accuracy. For this reason, the test rig was designed with the capacity for center distance adjustment, according to the tested set of gears, in order to avoid the change of pressure angle, contact ratio, and the required backlash. Finally, it is revealed after several tests that the amount of shrinkage does not affect wear rate results, as they are insignificant compared to wear and deflection measurements. Gears' specifications and four materials properties are presented in Tables 1 and 2, respectively.

## Test Results and Discussion

Each set of gears with certain material has its load and speed endurance capabilities, i.e., maximum load and maximum speed limits. These two capabilities may be defined using the current test rig (explained earlier) by running an incremental load test, initially, by running one pair of gears at certain load, which is increased later by the amount of 0.5 N·m each specified time (half an hour, for example). In addition, this type of test could reveal the amount of wear rate per cycle for each applied load, which leads to a reduction in the number of tests required to reveal such data, and as a result saves more time and cost.

Previously, each amount of load had to be examined by running a separate full test using a pair of polymer gears; this means consuming a higher amount of test samples to clarify the wear rate value of each load. Using the incremental load test method reveals the required wear rate of polymer gears for each amount of load and, at the same time, saves time, effort, and cost by reducing the required number of samples and tests.

Each load wear rate (as a function of number of cycles) has been defined accurately, to a squared correlation coefficient above 99%, for the last set of wear readings (last 10 min) of each load stage and is reflected in Fig. 5 for the above polymer gears wear test results. Because wear rates range widely with respect to load variance, graphs were plotted in a log form to the base of ten.

It can be seen from Fig. 5 that acetal gear wear rate is relatively low at applied torque below 7 N·m, and this rate increases dramatically afterward to relatively high wear rates. Therefore, the value of 7 N·m has been assigned as a critical value, and it has been advised that load is preferred not to exceed this limit for longer life acetal gear running. Moreover, it was thought that the reason for the sudden increase after this point was that gears' surface temperature reached the melting point of acetal (165 °C). A similar conclusion was reached by other research [27,28]. Comparing the wear rate of machine-cut acetal gears with the wear rate of injection-molded acetal gears (with similar dimensions and specifications, apart from the face width) done by Hooke et al. [10] could lead to the conclusion that acetal gear wear rate is independent of the followed manufacturing technique, as the wear rates and transition points of the two samples with different manufacturing methods nearly match, and the transition points are happening nearly at the same point, for the same reason that the gear surface is reaching melting point.

A similar wear rate phenomenon was experienced by running two pairs of injection-molded PC gears (Fig. 5), where wear rate was nearly linear at loads below 4.5 N·m before jumping to a relatively high wear rate, which followed by a sudden failure by teeth fracture around the dedendum side and mostly close to the root of the driver gear teeth. Moreover, the wear rate of PC is relatively high at low applied loads, compared to other tested materials, while load endurance is very low (3 to 5 N·m), which is below the start points for other materials. The reason for this was thought to be the higher coefficient of friction of this material compared to others, as well as the low durability of wear and tensile strength (Table 2), which leads to reaching higher surface temperatures, compared to other tested materials. Some molten material was observed on the working surface of the driven PC gear teeth, toward root side. Immediately after stopping the test, this molten material gained its rigidity and shaped some material clots on base circle (Fig. 4(b)).

Injection-molded nylon gear wear rate showed different behavior along the torque incremental test. It may be seen from Fig. 5 that the wear rate is relatively low, at a load of 7.5 N·m and lower. This wear rate suddenly reached a peak when the torque reached 8 N·m before returning to wear rate values relatively lower than the early stage. This peak was followed by a dramatic increase at loads of 9.5 N·m afterward. This wear rate trend was found to be repeatable for many tests that were done, and similar observations were found. Moreover, close achievements were reached on the wear rate of two nylon disks running in nonconformal contact [18], where authors clarified the same wear rate trend with respect to load increase. It was observed while the test was running that when reaching the load of 8.5 N·m, a brown color shield covered the working teeth surface flanks, which was thought to be some molten material from the gears' surfaces that functioned as an internal lubricant, which claimed to be the reason for the sudden decrease in wear rate after reaching a peak at that point. A similar conclusion was reached by Hooke et al. [18]. The earlier low loads range wear rate was relative to gear surface temperature and acted at the same behavior as acetal gears, where wear rate was linear with load increase. Increasing the load afterward led to an elimination of the formed surface shield created at 8.5 N·m torque. This phenomenon revealed the reason for the sudden decrease in wear rate at a certain load, followed by a dramatic increase. The tested injection-molded nylon gears were fractured at load of 9.5 N·m and the fracture normally occurs at the root of the driver gear teeth. Therefore, when designing nylon gear by considering running time and life, one may take into account wear rate of nylon material, especially at loads around peak transition area.

Close achievements were reached when testing machine-cut nylon gears. Figure 5 shows that wear rate of nylon gears is generally low at small loads followed by a relatively high wear rate with dramatic increase at torques above 10 N·m, but with two clear concaves at loads of 6.5 and 9 N·m. The reason for these wear rate decreases shall be for the same reason as the injection-molded nylon gears. Although they have same gear dimensions, similar friction coefficient and close melting temperatures, injection-molded nylon gears fractured at load of 9.5 N·m, while machine-cut nylon gears were able to carry the load for up to 11 N·m. Figures 6 and 7 show the simultaneous thermal analysis (STA) curves for the two materials, which indicate the variance in energy required to melt the sample because of the differences in material crystallinity, which govern the material structure stiffness and, in consequence, the gear load capacity.

All in all, acetal gears show the lowest wear rates at the linear stage comparing to nylon gears and PC gears wear rate is the highest with vast wear amount at low loads, which confirms that it is not a functional material for high-loaded gearing applications. Also, nylon gear wear rates are the most complicated ones, which need to be more investigated to gain the proper understanding for mechanical tribology applications.

Low wear rate ranges in Fig. 5 may be compared and reflected by the wear volume formula developed by Archard [29] and modified by Friedrich and Reinicke [30] using thrust bearing testing method. The wear volume $Vw$ was represented, as Display Formula

(1)$Vw=ksFs$

where $ks$ is the specific wear rate, $F$ is the normal force, and $s$ is the sliding distance.

In reforming above equation for the tooth profile of the spur gear, one can wright the specific wear rate $ks$, as Display Formula

(2)$ks=Qbd2TN$

where $Q$ is the wear depth (as measured in test), $b$ is the gear face width, $d$ is the gear pitch circle diameter, $T$ is the torque transmitted, and $N$ is the number of cycles corresponding to the wear $Q$.

Applying the previous equation to the tested gears gives the specific wear rate of $5.14×10−15$, $4×10−13,$ and $4.1×10−13$ (m3 N−1 m−1) for machine-cut acetal gears, injection-molded nylon 46 gears, and machine-cut nylon 6 gears, respectively. These results may be compared with Friedrich results for different polymer materials against steel, which are $3×10−15$, $1.05×10−15$, and $4.32×10−7$ (m3 N−1 m−1) for acetal, cast nylon 6, and extruded nylon 6, respectively. The previous equation applies to wear rates below the critical wear transition points and specifically at low wear rate values, while the after-transition point wear rate is not predicted, as it is affected by high temperatures, which changes the material physical and mechanical properties. Both results and formula are in agreement that wear rate is in positive correlation with torque and number of cycles.

In most polymer materials under mechanical tribology, there is a transition point where wear rate is suddenly greatly increased. This phenomenon was thought to be the result of polymer surfaces under friction reaching melting temperature. A theoretical form to calculate the maximum teeth temperature of a pair of gears in mesh was developed previously by Mao et al. [28]. This maximum surface temperature ($θmax$) is the combination of ambient temperature ($θa$), body temperature ($θb$), and flash temperature ($θf$), i.e., Display Formula

(3)$θmax=θa+θb+θf$

(4)$θmax=θa+k1T+k2T3/4$

where

$k1=3.927μbcρZra2−r2andk2=1.11μV11/2−V21/22r3/4b3/4kρcπER1/4$

Here $T$ is transmitted torque, μ is coefficient of friction, $c$ is specific heat, $ρ$ is specific gravity, Z is number of teeth, $ra$ is outside radius, $r$ is reference radius (see Fig. 8), $b$ is gear face width,$k$ is thermal conductivity, and $V1$ and $V2$ are sliding velocity for gear 1 and gear 2, respectively.

Applying the earlier equation to the tested four different materials polymer gears at the running speed of 1000 rpm and the specified gear geometry (Table 1), the theoretical maximum load that intersects with the maximum surface temperature of each material (Table 2) may be defined and compared with the experimental results in Fig. 5, as in Table 3. It may be seen that close agreements were achieved between the maximum tested load capacity of different materials polymer gears and the theoretical calculations that predict the load capacity of a gear at the maximum surface temperature point. In general, one can conclude that polymer gears mostly fail at the highest torque due to the thermal wear effect. Loading gears at torques below the relative load capacity leads to relatively low wear rates and consequently increases the running life of such mechanical devices.

Number of tests have been setup for different types of material with the aim of getting wear measurements at certain loads and speeds to extensively understand wear rate behavior as a function of load and speed change, as well as understanding the surface behavior of each material under rolling and sliding contact (gears in mesh) by investigating the tooth worn surface using scanning electron microscope (SEM). For this aim, number of tests was conducted on acetal and nylon gears.

###### Machine-Cut Acetal Gears.

Figure 9 shows the wear test result on acetal gears at a load of 7 N·m and a speed of 1000 rpm. After stopping the test rig, gears tooth showed some regain from its deflected form (by the applied load) as a result of cooling down from the higher running temperature.

Monitoring acetal gears test along running time revealed that wear debris were falling in very few amounts during both wear stages (running in and linear). Similar behavior was observed at injection-molded acetal gears in the previous work by Mao et al. [28]. Pictures were taken, and gear samples and some debris were collected to be investigated under microscope.

It was revealed from SEM investigation (Fig. 10(b)) that there was some friction at the pitch point of the driver and driven of polymer gears, which does not agree with the theoretical assumption that friction at pitch point is zero (where the only motion is rolling with no sliding). This sliding motion at this specific point is due to low polymer material strength, causing some gear tooth bending, while at mesh with other gear that slightly changes the rolling and sliding theoretical motions.

It may be seen in Fig. 10(c) that some thin chips are starting to separate from the tooth surface and then their edges are forming narrow long debris, which are starting to rotate as a result of the friction forming scratches on tooth surface all along the tooth profile from pitch point to tooth root (friction direction), where debris are gathered before being thrown out of gear mesh. Most of the collected debris from below the tested gears had a long and twisted shape.

On the addendum side of tooth surface, the friction along tip side of the acetal driver gear seems to be higher in SEM investigations. It may be seen from Fig. 10(a) that debris that were formed at the pitch point are moved along the direction of the tip, but some of them are pressed along the way as a result of the higher pressure than the root side, making them flat in shape rather than long and twisted in shape (as in root side). Some flat chip debris was found below the tested gears.

In contrast, tooth tip edge is an open end that cannot collect the pulled out of mesh debris, as in tooth root, which makes the debris drop straight away out of the mesh.

It can be revealed that in acetal gears scratch wear is the most prevalent form of wear that occurred all along the tooth profile of the tested driver acetal gear, as a result of the moving debris between the two rubbing surfaces. In addition, some micropitting wear was discovered as a result of the Hertzian load on gear teeth along gear running time.

On the other hand, the acetal driven gear shows different wear phenomena; as the sliding directions are different (from tip to pitch and from root to pitch). This gives the opposite direction of debris movements, but the same scratch wear type as a result of debris rubbing between the two surfaces. Figure 11 shows the sever wear happed to the surface, in line with movement direction from top to bottom (tip to pitch).

###### Injection-Molded Nylon Gears.

Nylon material shows good promising in mechanical typological applications, although it has unsteady wear rate with load changes. Therefore, more investigations were needed to gain more understanding on how nylon gears will behave in real applications. Figure 12 shows the wear trend of injection-molded nylon gears rotating for around 5 × 105 cycles, which were loaded by 6 N·m and were running to the speed of 1000 rpm.

Nylon gears were investigated during the test, and it was observed that there was nearly no wear debris during the running in stage, which might lead to the conclusion that most of the measured displacement at this stage is the result of tooth bending by the applied load. While on the next linear wear stage, debris amount started to increase, although it was still very small.

Similar conclusion was reached by Hooke et al. using two rolling disks made of injection-molded nylon and running at different slip ratios [18]. Their results showed that the wear of nylon disks with respect to cycles were nearly linear all during running test. These results fairly match the linear stage of a pair of nylon gears showed earlier. The early running in stage did not appear in their results for the reason of differences in specimen body shape (gear shape compared with disk). In disk results, they found an initial negative reading of wear which they explained as disk expansion as a result of body temperature increase due to surface friction. While in this work, results reveal that early stage high increase in displacement reading is the result of tooth deflection. Similarly, the wear rate of the final stage has a high sudden increase in polymer gears, while it is not always the case in polymer disks, though the linear stage time is relatively shorter in gears than in disks, for the same shape reason. Therefore, the linear stage of polymer gear wear results is the only stage that could be compared with polymer disks results, which shows close agreements. In contrast with disk results, dry running nylon gears showed relatively low-wear rate results compared with other materials when running at low-load range. This means that they are functional for low-torque applications.

A microscope analysis was carried out on the dry tested nylon gears at a load of 6 N·m and a speed of 1000 rpm. Results showed different conclusion compared to dry running acetal gears in case of failure mode. Figure 13(a) shows an SEM general view for the driver gear tooth surface after running for 8 h. It can be seen that generally the most common failure mode is scuffing and plastic flow, where the surface of the material is softened by high load and temperature and is welded to the contact surface of flow toward the contact direction. In contrast to acetal gears, there were no debris that were sliding between the two rubbed surfaces which caused high wear at acetal gears, but here in nylon gears debris were mostly formed at the edges, and sometimes from the middle of contact surfaces toward the directions of the plastic flow. As it can be seen, some of the contact surfaces were trimmed away, as a result of scuffing, forming some wear debris. The collected debris was in two shapes: small chips and rounded fibers (Fig. 13(c)).

At the pitch point of the driver nylon gear (Figs. 14(a) and 14(b)), it appears that there was less scuffing and plastic flow, as surfaces slide at lower speed at this point, although it was expected to find some microcracks or pitting around this area due to high contact load and high stresses from Hertzian pressure, which form larger crack later, leading to gear failure with pitch point fracture. The fracture point at nylon gears was still unpredicted, as it varied between pitch point and tip of the teeth. Some other tested gears were fractured at the tip point, leading to the conclusion that in these tested gears pitting and microcracks were not the reason for gear tooth failure, as was concluded in nylon disks tests [18], although nylon gears were run to a close load and sliding speed conditions. Further investigations were carried out by slicing one of the teeth to look at the side under the SEM (Figs. 14(a) and 14(c)). It may be seen that no microcracks appear at the pitch point or anywhere else on the contact surface, which leads to the conclusion that injection-molded nylon gears do not fracture because of microcrack formation, but for thermal reasons.

On the other hand, driven gear tooth SEM showed nearly similar wear characteristics (Figs. 14(d)14(f)). It can be seen that there is a thin surface film, which covers most of the contact surface, which was formed as a result of thermal and high loaded pressure, leading to some surface scuffing and plastic flow, but toward the pitch point direction. Therefore, the detached chips from the surface travels toward the pitch point and be rotated and formed to a rounded debris before they gathered at that point.

Number of different running speed tests was carried out for the aim to validate the achieved results at different speeds. Figure 15 shows the wear of injection-molded nylon gear pairs running continually at different torques and the speed of (a) 500 rpm, (b) 1000 rpm, and (c) 2000 rpm. It was found from the three curves that the wear rates at the torque of 6 N·m were 0.0029 mm/cycle × 105, 0.0067 mm/cycle × 105, and 0.0125 mm/cycle × 105 for speeds of 500, 1000, and 2000 rpm, respectively, with a relative linear increase of wear rate with respect of running speed. Figure 16 shows the wear rate of the injection-molded nylon gears against (a) running speed and (b) torque. Two forms of wear can be found at all the tested speed: the low-wear rate form and the severe wear form. It was thought that the reason for the wear form transition can be for the same reason of the surface temperature change. To conclude, at the low-wear rate form and different speeds, one may say that the aforementioned specific wear rate equation (Eq. (1)) can be rewritten, with respect to running speed, as follows: Display Formula

(5)$ks=Qbd2TNvv0$

where $v$ is the new gear rotation velocity (rpm) and $v0$ is the earlier gear rotation velocity (rpm).

## Conclusion

Polymer gears' wear against time was tested using a uniquely designed test rig for this purpose. Four different patches of gears with different materials and two types of manufacturing methods were tested continually at different loads and speeds to find out the wear and wear rate of each condition. The revealed data were analyzed and compared with the available literature. Fairly close matches were found.

It was found that acetal and nylon gears wear rate was independent of the manufacturing process, as both materials' wear showed close agreement despite of the production technique. Acetal gear wear rate increase, with respect to load increase, was mostly linear at low loads, but this trend was changed by high sudden increase at specific torque, which defined as transition point. Nylon gears wear rate trend with load was found to be more complicated than acetal gears, with variable trends along torque increment. This phenomenon was further investigated as the high change in wear rate trend of nylon gears is quite different from the linearity trend of acetal gears wear rate. It may be concluded from the present research that this high change in wear rate trend of nylon gears was caused by a tribological phenomenon, whereby a thin film of molten material (for the reason of the high temperature) was formed at some load ranges, which acts as an internal lubricant. Further investigations using SEM were carried out with results that validate polymer gear wear rate results.

The effect of polymer gears' rotation speed change on wear rate was investigated, and the results showed a linear relation, which led to rewriting the specific wear rate equation accordingly.

## Acknowledgements

The author would like to thank the University of Warwick for providing the research facilities and Umm Alqura University for funding this research work.

## Nomenclature

• $b$ =

gear face width

• $c$ =

specific heat

• $d$ =

gear pitch circle diameter

• $F$ =

normal force (applied on gear tooth)

• $k$ =

thermal conductivity

• $ks$ =

specific wear rate

• $N$ =

number of cycles corresponding to the wear $Q$

• $r$ =

• $ra$ =

• $s$ =

sliding distance

• $Q$ =

tooth wear depth

• $T$ =

transmitted torque

• $V1,V2$ =

sliding velocity for gear 1 and gear 2, respectively

• Z =

number of teeth

• μ =

coefficient of friction

• $v$ =

gear rotation velocity

• $ρ$ =

specific gravity

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Mao, K. , Langlois, P. , Hu, Z. , Alharbi, K. , Xu, X. , Milson, M. , Li, W. , Hooke, C. J. , and Chetwynd, D. , 2015, “ The Wear and Thermal Mechanical Contact Behaviour of Machine Cut Polymer Gears,” Wear, 332, pp. 822–826.
Ensinger, 2014, “ Polyamide 66 Data Sheet,” AGRO AG, Hunzenschwil.
DuPont Engineering Polymers, 2008, “ Acetal 500P Data Sheet,” DELRIN®, Meadowlands, Boulevard.
DSM Engineering Plastics, 2011, “ Polyamide 46 Data Sheet,” DSM, Birmingham, MI.
Bayer Material Science LLC, 2008, “ Polycarbonate Data Sheet,” RTP Co., St, Winona, MN.
Lancaster, J. K. , 1971, “ Estimation of the Limiting PV Relationships for Thermoplastic Bearing Materials,” Tribology, 4(2), pp. 82–86.
Mao, K. , 2007, “ A New Approach for Polymer Composite Gear Design,” Wear, 262(3–4), pp. 432–441.
Archard, J. F. , 1953, “ Contact and Rubbing of Flat Surfaces,” J. Appl. Phys., 24(8), pp. 981–988.
Friedrich, K. , and Reinicke, P. , 1998, “ Friction and Wear of Polymer-Based Composites,” Mech. Compos. Mater., 34(6), pp. 503–514.
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## References

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Gauvin, R. , Girard, P. , and Yelle, H. , 1980, “ Investigation of the Running Temperature of Plastic/Steel Gear Pairs,” ASME Paper No. 80-C1.
BSI, 1987, “ Specification for Non-Metallic Spur Gears,” British Standards Institution, London, UK, Standard No. BS6168.
AGMA, 1997, “ Tooth Proportions for Plastic Gears,” AGMA, Alexandria, VA, Standard No. ANSI/AGMA 1006-A97.
Radzevich, S. P. , 2013, Theory of Gearing: Kinematics, Geometry, and Synthesis, CRC Press, Boca Raton, FL.
Walton, D. , and Shi, Y. W. , 1989, “ A Comparison of Ratings for Plastic Gears,” Proc. Inst. Mech. Eng. Part C, 203(1), pp. 31–38.
Mao, K. , 1993, “ The Performance of Dry Running Non-Metallic Gears,” Ph.D. thesis, The University of Birmingham, Birmingham, UK.
Hooke, C. J. , Mao, K. , Walton, D. , Breeds, A. R. , and Kukureka, S. N. , 1993, “ Measurement and Prediction of the Surface Temperature in Polymer Gears and Its Relationship to Gear Wear,” ASME J. Tribol., 115(1), pp. 119–124.
Evans, S. M. , and Keogh, P. S. , 2016, “ Efficiency and Running Temperature of a Polymer-Steel Spur Gear Pair From Slip/Roll Ratio Fundamentals,” Tribol. Int., 97, pp. 379–389.
Mertens, A. J. , Kumar, P. , and Senthilvelan, S. , 2016, “ The Effect of the Mating Gear Surface Over the Durability of Injection-Molded Polypropylene Spur Gears,” Proc. Inst. Mech. Eng. Part J, 230(12), pp. 1401–1414.
Yousef, S. , Osman, T. A. , Abdalla, A. H. , and Zohdy, G. A. , 2015, “ Wear Characterization of Carbon Nanotubes Reinforced Acetal Spur, Helical, Bevel and Worm Gears Using a TS Universal Test Rig,” JOM, 67(12), pp. 2892–2899.
Senthilvelan, S. , and Gnanamoorthy, R. , 2004, “ Damage Mechanisms in Injection Molded Unreinforced, Glass and Carbon Reinforced Nylon 66 Spur Gears,” Appl. Comp. Mater., 11(6), pp. 377–397.
Verein Deutscher Ingenieure Standards, 2014, “ Part 2: Thermoplastic Gear Wheels—Cylindrical Gears—Calculation of the Load-Carrying Capacity,” VDI, Düsseldorf, Germany, Standard No. VDI 2736.
Pogačnik, A. , and Tavčar, J. , 2015, “ An Accelerated Multilevel Test and Design Procedure for Polymer Gears,” Mater. Des., 65, pp. 961–973.
Kukureka, S. N. , Hooke, C. J. , Rao, M. , Liao, P. , and Chen, Y. K. , 1999, “ The Effect of Fibre Reinforcement on the Friction and Wear of Polyamide 66 Under Dry Rolling–Sliding Contact,” Tribol. Int., 32(2), pp. 107–116.
Hooke, C. J. , Kukureka, S. N. , Liao, P. , Rao, M. , and Chen, Y. K. , 1996, “ The Friction and Wear of Polymers in Non-Conformal Contacts,” Wear, 200(1–2), pp. 83–94.
Takanashi, S. , and Shoji, A. , 1980, “ On the Temperature Rise in the Teeth of Plastic Gears,” International Power Transmission and Gearing Conference, San Francisco, CA.
Wright, N. , and Kukureka, S. , 2001, “ Wear Testing and Measurement Techniques for Polymer Composite Gears,” Wear, 251(1–12), pp. 1567–1578.
Mertens, A. J. , and Senthilvelan, S. , 2016, “ Surface Durability of Injection-Moulded Carbon Nanotube–Polypropylene Spur Gears,” Proc. Inst. Mech. Eng. Part L, (accepted).
Mao, K. , Langlois, P. , Hu, Z. , Alharbi, K. , Xu, X. , Milson, M. , Li, W. , Hooke, C. J. , and Chetwynd, D. , 2015, “ The Wear and Thermal Mechanical Contact Behaviour of Machine Cut Polymer Gears,” Wear, 332, pp. 822–826.
Ensinger, 2014, “ Polyamide 66 Data Sheet,” AGRO AG, Hunzenschwil.
DuPont Engineering Polymers, 2008, “ Acetal 500P Data Sheet,” DELRIN®, Meadowlands, Boulevard.
DSM Engineering Plastics, 2011, “ Polyamide 46 Data Sheet,” DSM, Birmingham, MI.
Bayer Material Science LLC, 2008, “ Polycarbonate Data Sheet,” RTP Co., St, Winona, MN.
Lancaster, J. K. , 1971, “ Estimation of the Limiting PV Relationships for Thermoplastic Bearing Materials,” Tribology, 4(2), pp. 82–86.
Mao, K. , 2007, “ A New Approach for Polymer Composite Gear Design,” Wear, 262(3–4), pp. 432–441.
Archard, J. F. , 1953, “ Contact and Rubbing of Flat Surfaces,” J. Appl. Phys., 24(8), pp. 981–988.
Friedrich, K. , and Reinicke, P. , 1998, “ Friction and Wear of Polymer-Based Composites,” Mech. Compos. Mater., 34(6), pp. 503–514.

## Figures

Fig. 1

Polymer gears test rig

Fig. 2

Schematic diagram for polymer gear test rig

Fig. 3

Tooth wear measurement method and location

Fig. 4

Wear of (a) machine-cut acetal, (b) injection-molded polycarbonate, (c) injection-molded nylon 46, and (d) machine-cut nylon 66 gear pairs at 1000 rpm and step loading

Fig. 5

Wear rate of the four tested polymer gears

Fig. 6

STA curve for nylon (PA46) (injection molded)

Fig. 7

STA curve for nylon (PA66) (machine-cut)

Fig. 8

Fig. 9

Wear of machine-cut acetal gear pair

Fig. 10

Scanning electron microscope for driver acetal gear tooth at (a) addendum side, (b) pitch point, and (c) dedendum side (7 N·m, 1000 rpm)

Fig. 11

Scanning electron microscope of acetal driven gear tooth addendum side (7 N·m, 1000 rpm)

Fig. 12

Wear of injection-molded nylon gear pair

Fig. 13

Scanning electron microscope for driver nylon gear (a) general view, (b) addendum, and (c) debris (at 6 N·m, 1000 rpm and 8 h)

Fig. 14

Scanning electron microscope for nylon gear (a) driver side, (b) driver pitch point, (c) driven side, (d) driven pitch point, (e) driven addendum, and (f) driven dedendum (6 N·m, 1000 rpm, and 8 h)

Fig. 15

Wear results of injection-molded nylon gears, at different torques and the speed of (a) 500 rpm, (b) 1000 rpm, and (c) 2000 rpm

Fig. 16

Wear rate of injection-molded nylon gears against (a) running speed and (b) torque

## Tables

Table 1 Gear specifications
Table 2 Gears' four material properties [2326]
Table 3 Theoretical and experimental load capacity of polymer gears for different materials

## Errata

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