## 2 Literature Review  
Worm and Worm gear train is widely used in cross shaft transmission. It has many advantages, such as small volume, big speed ratio, low noise, simple structure, etc. [8]. The key points of the meshing between worm and worm gear are as follows [9]:  
1. The axial module of the worm is equal to the transverse module of the worm gear.
2. The pressure angle of the Worm and Worm gear is the same.  
According to the first key item, the worm pitch is the same as the pitch of the worm gear. This is always true when there is a steel worm meshing in the bronze worm gear. Commonly, a cutter is used to cut the bronze worm gear with the same parameters as that of the meshing worm.  
The tooth thickness and the tooth addendum height of the cutter are small and different from the meshing worm owing to the tip clearance and backlash requirement [10].  
In some appliances such as window lift, steel worm, and plastic helical gear train is widely used owing to its low cost, low noise, self-locking ability, and compact volume. According to DuPont's suggestion, the helical gear strength should be calculated based on the sheer strength under the worst condition.  
There are many appliances where the gear must be designed to withstand a stall torque loading significantly higher than the normal running torque. In some cases, the stall torque governs the gear design. To determine the stall torque a given gear design can handle, the material yield strength is taken into account at the expected operating temperature under stall conditions. Only a small safety factor (S = 1.3-1.5) needs to be applied if the material to be used is either Zytel(r) nylon resin (Dupont company, Eleutherian Mills, DE, USA) or Delrin(r)100 (Dupont company, Eleutherian Mills, DE, USA). The resilience of these materials allows the stall load to be distributed over several teeth [11].  
Appliances like window lift gears for cars, use a steel worm, and a plastic helical gear (=worm gear), where the tooth thickness of the steel worm has been reduced in favor of the tooth thickness of the plastic gear.  
In this case, the gear strength may be limited by the shear strength of the loaded teeth, as given by the following equation [12],  
\[F_{\text{max}}\ =\ n\cdot f\cdot t\cdot\tau \tag{1}\]  
where \(n\) = number of teeth in (full) contact;\(f\) = tooth width (mm); \(t\) = tooth thickness (mm),  
\[\tau\ =\ \text{shear strength}\ =\ \sigma_{y}/(1.7\times S)\ (\text{MPa}) \tag{2}\]  
where \(\sigma_{y}\) = yield strength at design temperature (MPa).  
The characteristic of plastic widely varies with changing temperature. The typical strain-stress curve of POM is presented in Figure 1.  
Plastic can show higher deformation than steel (Figure 1). According to DuPont, Delrin100 (POM) can withstand 48 MPa at \(10^{6}\) times under room temperature, which implies that the deformation is \(\sim\)2.5%. For steel gear, the maximum deformation allowed is about 0.2%, which forms the basis of the gear design [13].  
Steel gear carrying high load must be modified according to the load. Accordingly, plastic gear should be adjusted according to the load because the deformation of plastic gear is much larger than that of the steel gear.  
According to the suggestion from American Gear Manufacture Association (AGMA), the plastic gear tooth profile is shown in Figure 2[14].