Design and Durability Rating of Plastic Gears

1. Introduction

Plastic gears have been in use since the 1960s, initially serving simple motion transmission purposes. Over time, advancements in plastic materials led to their adoption in power transmission applications. Historically, plastic gear drives were limited to power levels up to 1 kW. However, recent efforts have explored the use of high-performance plastics in gear drives capable of handling power levels beyond 10 kW.
Plastic gears are increasingly replacing metal gears across various applications due to the numerous advantages they offer. These include reduced weight, elimination of lubrication requirements, cost-effective mass production, significantly improved NVH performance, and excellent resistance to chemicals and corrosion. Most plastic gears are manufactured through injection molding, which provides remarkable design flexibility. This method allows for integrating multiple machine elements into a single molded component and enables modifications to gear geometry, such as enhanced root rounding or altered profile shapes [1].
Compared to steel gears, polymer gears also come with certain drawbacks. The most notable are their lower load-bearing capacity, reduced thermal conductivity, lower temperature stability, and inferior manufacturing precision. Among these, load-bearing capacity stands out as the most critical property. To address this limitation, numerous studies have been conducted, focusing on enhancements through specialized gear designs [2] or the development of improved materials [3].
The wider adoption of polymer gears could be significantly advanced if standardized design methodologies were established and relevant material data became readily accessible. Currently, no international standard exists to formalize the calculations, design principles, and guidelines specific to polymer gears. Some national standards address this topic, such as the Japanese JIS B 1759:2013 [4], British BS 6168:1987 [5] and Chinese GB/T 44846-2024 [6]. Additionally, various engineering associations have published guidelines. Among these, VDI 2376:2014 [7], provides the most detailed framework for plastic gear design. There are also some guidelines provided by AGMA [8,9], however these focus primarily on potential materials and gear configurations, without addressing design models or the critical material data necessary for polymer gear development.

2. Design rating of plastic gears

To ensure a reliable operation of the gearbox each gear needs to be appropriately designed in order to avoid failure within the required lifespan and operating conditions. Plastic gears can fail due to different failure modes, i.e. fatigue fracture, wear or plastic deformation, which is usually thermally induced. Examples of the possible failure modes are shown in Fig. 1. The fatigue failure mode can result in root fracture (Fig. 1a), flank fracture, or in some cases also pitting. Out of the three, the most common fatigue failure mode is root fracture, while flank fracture is often correlated with unfavorable contact characteristics of the gear pair, and pitting is usually only observed in oil lubricated cases. Wear, shown in Fig. 1b is another common failure mode for plastic gears. The degree of wear the gear exhibits depends on a variety of factors, e.g. operating temperature, lubrication, load, material of the mating gear, etc… Notable wear of the flank profile, deviating it from the involute shape, leads to an elevated level of transmission error and worse NVH performance. As the wear progresses significantly, it also results in the breaking of teeth, with cracks originating from the worn tooth profile. The acceptable extent of wear varies depending on the specific use case. In applications demanding high precision (such as robotics and sensors), minimal wear is permissible, whereas in applications with lower precision requirements (like household appliances, power tools, and e-bike drives), a relatively substantial degree of wear is acceptable, involving a reduction in tooth thickness within the range of 20-30% of the gear module.

VDI 2736:Part 2 proposes a framework considering a process to rate the spur and helical gear design, against all recognized failure modes (Fig. 2). While the proposed procedures are feasible, the real problem arises as each control model requires some gear-specific material data, which is to date very limited.

The framework proposes several control steps, enabling a design rating procedure for each failure mode.

Step 1. Calculate the operating temperature for the gear pair under design

In order to ensure a reliable operation of a plastic gear, its operating temperature needs to be lower than the permissible temperature for a continuous load. Coefficient of friction for the selected material pair is needed in this step in order to be able to calculate the heat generated by friction.

Step 2. Root strength control

To avoid root fatigue fracture, which is a fatal failure, the actual stress in the tooth's root σ_F needs to be lower than the material’s fatigue strength limit σ_Flim for the required operating lifespan – translated to number of load cycles (1 rotation of gear is 1 load cycle on each tooth) (see Fig. 3). To account for unexpected effects some additional safety S_F is usually also included. Knowledge on the material's fatigue strength is crucial to complete this step.
 

Step 3. Flank strength control against pitting

This step is usually performed only for plastic gear pairs running in oil, as this is the only operating condition where pitting on plastic gears is sometimes observed. For dry running or grease lubricated plastic gears, usually root fatigue or wear are the most frequent failure modes.

Step 4. Wear control

Wear is a common damage mode for dry run and also some grease-lubricated applications with plastic gears. It can lead to a fatal failure where teeth are worn to the degree that they break instantly under load or that fatigue cracks originate at the worn section (Figure 5). Wear factor for the material pair of choice is required to conduct this step.

 

Step 5. Teeth deflection control

Excessive deflection of teeth should be avoided in order to prevent teeth jamming and irregular meshing. Elastic modulus is required in this step in order to be able to calculate the tooth's deflection.

Step 6. Control of the static load

In some applications the gears are loaded with a high static load, e.g. holding some weight in a defined position. In that case the gears need to be rated against a static load and knowledge on material’s tensile strength is required.

It is not necessary to always conduct all of the design rating steps. From the above presented procedure Step 1, Step 2 and Step 4 are advised to be always conducted, while others are case dependent.

3. Testing methodologies – Generation of Crucial Material Data

3.1. S-N curve generation

The information on the material’s fatigue strength can be summarized in an S-N curve. To generate an S-N curve, several test repetitions need to be conducted at various loads, and all the samples need to be tested until a fatigue induced failure occurs as shown in Fig. 5. For gears, the S-N curves can be generated by extensive testing in a gear-on-gear application or by a single tooth bending test on a pulsator test stand. Both methods have their pros and cons. While operating, the gears heat up. Friction between the meshing teeth and hysteretic effects are the main reasons for the temperature increase in plastic gears. The rate of the heat generation and the resulting temperature rise depend on several factors, e.g. torque, rotational speed, coefficient of friction, lubrication, thermal conductivity, convection, gear geometry, etc. The mechanical properties (strength, hardness, elastic modulus) of polymers and polymer composites are strongly temperature dependent. Therefore, several S-N curves, generated for different temperatures of the tested sample, are required for the design of plastic gears. Precise temperature control of tested gear samples is therefore crucial for characterization of S-N curves for plastic gears. Advanced stopping algorithms need to be applied as well since the test needs to be stopped instantly once the first tooth is fractured, see Fig. 5.

3.4. Wear characterization

Wear behavior of plastic gears can be best studied by conducting gear tests. Simple tribological tests, e.g. disk-on-disk can provide basic information about materials behavior in a rolling-sliding motion under non-conformal contact, but for an in-deep understanding of the wear behavior in the gear contact, gear testing needs to be conducted. 

The contact conditions between the two meshing flanks consist of rolling and sliding motion. The direction of sliding and the frictional force are reversed when passing through the pitch point C. On the driven gear, the direction of sliding points always towards the pitch point C, so the kinematic line is usually clearly visible on the worn gear surface. The main difference, when compared to the disk-on-disk test, is that with the disk-on-disk test, the sliding rate is constant all the time and also the direction of the frictional force remains the same. The pin on disk test is even less suitable, since there is only sliding motion present in contact without any rolling. 

Different wear characterization methods can be employed. The most commonly used ones are the gravimetric method, and the tooth thickness reduction method. When employing the gravimetric method wear is characterized as the loss of mass, while in the tooth thickness reduction method the wear is determined as the reduced tooth’s chordal thickness. Several advanced methods can also be used, e.g. image processing or optical measurements, however these are more cost and labor expensive. The wear can be tracked during testing by conducting regular checkpoints or the wear is measured after a specified number of load cycles. Different stages of wear a presented in Fig. 6.