Plastic worm and crossed helical gears are increasingly utilized in various applications due to their distinct advantages over traditional metal worm gear drives. These advantages include lower weight, reduced noise, and corrosion resistance, making them ideal for automotive, consumer electronics, and medical devices. However, plastic gears also come with limitations such as lower load-bearing capacity and higher susceptibility to temperature variations and wear. The design and calculation of plastic crossed-helical gears (often referred to simply as worm gears) are defined in guidelines like VDI 2736, which provides comprehensive methods for material selection, dimensioning, and performance prediction. Experimental testing, also thoroughly described in VDI 2736, includes procedures to evaluate the durability and efficiency of these drives under realistic operating conditions. In most applications, plastic worm gear pairs are composed of a metal worm paired with a polymer worm wheel. In terms of load-carrying capacity, several types of failure modes typically determine the service life of a plastic worm gear pair. Out of these, fatigue is one of the most detrimental and often exhibited failure modes in worm gear drives. Polymer worm wheel fatigue was studied by Nomura et al. (Ref. 1), who tested polymer worm wheels in pairs with various metal worm geometries. Kim et al. (Ref. 2) additionally tested the durability of a glass fiber-reinforced polyamide polymer worm wheel used in a car steering system. They identified root fatigue with cracks forming slightly above the root to be the driving failure mode. Marshek et al. (Ref. 3) noted that polymer worm gear drives can fail due to multiple failure modes simultaneously, e.g., fatigue combined with wear. Wear was studied in more detail using SEM microscopy by the same author (Ref. 4), who noted that pitting and ridge formation are two types of flank damage phenomena often related to wear on polymer worm wheels. In the already noted study by Kim et al. (Ref. 2), wear, as a function of running cycles, was also studied. Wear was measured as a function of angle loss during meshing. Additionally, the NVH (noise vibration and harshness) behavior of polymer gears is often of interest, since one of the key goals of polymer gear drives is to reduce the noise level in a gear transmission. Chakroun et al (Ref. 5) presented a numerical model, based on the Generalized Maxwell Model (GMM), a widely adopted type of viscoelastic constitutive mechanical model, to analyze the influence of the non-elastic mechanical characteristics of the polymer wheel on the frequency-spectrum vibration response of the meshing gear drive. Despite these advancements, achieving higher performance in plastic worm gear drives remains challenging. Current research is focused on enhancing material properties, improving manufacturing precision, and developing more robust predictive models to bridge the performance gap compared to their metal counterparts. The study presented focuses on the implementation of the state-of-the-art worm gear calculation methods, exemplified by the VDI 2736 guideline and the experimental testing aspects correlated with this implementation. Via an executed case study, the work outlines suitable testing methodologies for the characterization of worm wheel limiting strength parameters. These parameters are essential for the implementation of the calculation methods defined in the guideline. Additionally, practical aspects related to the implemented testing procedures are discussed. Worm Geometry Variants Several variations of worm gear drives exist, each offering distinct advantages and disadvantages. The possible combinations are schematically shown in Figure 1 and include: Cylindrical crossed-helical gear pair Cylindrical worm paired with enveloping (globoid) worm wheel Cylindrical worm paired with semi-enveloping (semi-globoid) worm wheel Enveloping worm paired with cylindrical worm wheel Enveloping worm paired with enveloping worm wheel
The most common type is the cylindrical crossed-helical gear pair, where both the “worm” and the “worm wheel” are cylindrical and hold a helical lead profile. This simple design is relatively straightforward to manufacture, also using plastic processing methods like injection molding. The main drawback of this gearing geometry is that it results in a theoretical point contact during meshing and consequently offers a lower load-carrying capacity due to a less favorable load distribution across a small contact area on the active flank. For improved load-carrying capacity, durability and smoother operation, enveloping worm gears can be produced. This design offers an improved line-contact load distribution, potentially leading to reduced wear and a longer service life. Two main variations exist: cylindrical worm/enveloping (globoid) worm wheel and enveloping worm / cylindrical worm wheel. In the former, the worm wheel has a curved profile, matching the worm’s curvature of the helix, which prolongs the path of contact. The latter features a curved, hourglass-shaped worm gear meshing with a straight-toothed worm wheel. Both offer improvements over the basic cylindrical pair, but the cylindrical worm / globoid worm wheel generally boasts the highest efficiency due to its deeper tooth engagement. On the other hand, both geometries increase the complexity and cost of production. A globoid worm wheel is especially problematic for plastic injection molding since it exhibits negative draft angles, which hampers the possibility for part ejection from the molding tool. To amend this problem, a semi-enveloping (semi-globoid) worm wheel geometry can be introduced that provides partial line contact and avoids negative draft angles that undermine part ejection in the globoid geometry. Finally, the least common variant is the enveloping worm / enveloping worm wheel. Both the worm and the worm wheel have curved profiles, maximized tooth contact and achieved the best load distribution among all these designs. However, these benefits come at the cost of increased manufacturing difficulty, as already discussed above. Our further analysis will entirely be based on cylindrical crossed-helical gear pairs, since this geometry is by far the most commonly used in plastic worm gear drives and the VDI 2736: Part 3 guideline also provides calculation methods for this type of gear pair. To simplify communication, in subsequent sections, the words “worm” and “worm wheel” will be used to denote the pinion and gear of the analyzed crossed-helical gear pair.
