## 5 Load Distribution Model  
It is well-known that cylinder gears need to be modified when a high load is carried. Figure 2 shows the correct method to alter the cylinder gear. This is always true when the meshing number is not more than two [17]. In some applications, such as window lift, three to four teeth carry the load in the steel worm and plastic helical gear train. Here, the working torque is further lowered than the maximum torque (stall torque). During the life test at a high temperature (\(\sim\)90 \({}^{\circ}\)C), the plastic helical gear is easily broken when maximum torque is applied. Sometimes, a creep test is required in the case of a window lift. During these tests, the deformation of the plastic gear is inevitable, and the NONE breakage component is the key judgment rule. In other words, the deformation of the helical gear is permitted. The traditional tip relief and the root relief cannot satisfy the large deformations. Thus, to enhance the load capacity of the current steel worm and helical worm gear/helical gear, further modification is needed. From the traditional relief theory, it can be drawn that equal-stress displacement is expected when the load is carried at some temperature [18]. In this optimized design, the typical window lift is selected as the test platform, and a higher creep load capacity is the key aim. The creep rupture of Delrin(r)100 is listed in Figure 8.  
The common requirement for a window lift is 12.74 Nm for 840 h (Window lift test standard). According to this, the same rate of deformation for all the teeth is expected to have the maximum load capacity. The same deformation rate can be obtained by modifications. A different pitch is selected to achieve the same rate of deformation. The traditional design is shown in Figure 9. The normal pitch of the worm and the helical gear is the same. The tooth pair 2-2\({}^{\prime}\)3-3\({}^{\prime}\)4-4\({}^{\prime}\) will be in contact in a while when the worm moves along the direction of the arrow. If only the load capacity is considered, the worm gear can be fixed. Figure 7: The schematic diagram of the research flow. The analysis is based on the following assumptions: The worm gear is strong enough that it would not be deformed. The material of helical gear/worm gear is Delrin(r)100. The structure of helical gear/worm gear is too strong to deform. In other words, the deformation is only limited at the tooth area. At the beginning of the meshing, the tooth pair 2-2\({}^{\prime}\), 3-3\({}^{\prime}\), 4-4\({}^{\prime}\) will be in contact for a while. With the increasing load, teeth 2, 3, and 4 will deform by the same distance. Based on such assumptions, the bending deformation rate can be calculated according to the following formula [19],  
\[\varepsilon\ =\ \frac{\delta}{h} \tag{20}\]  
where \(\varepsilon\) is deformation rate; \(\delta\) is bending deformation (axial moveable distance), mm, \(h\) is the distance between the contact point and root circle, mm. In this load model, \(\delta_{1}\), \(\delta_{2}\), \(\delta_{3}\) are the same, and \(h_{1}\), \(h_{2}\), \(h_{3}\) increase in this order. Correspondingly, \(\varepsilon_{1}\), \(\varepsilon_{2}\), \(\varepsilon_{3}\) decrease in the given sequence. Let us suppose that \(\delta_{1}=\delta_{2}=\delta_{3}=0.06\) mm, \(h_{1}=0.6\) mm, \(h_{2}=1.2\) mm, \(h_{3}=3\) mm. According to the calculation, the deformation rate \(\varepsilon_{1}\), \(\varepsilon_{2}\), and \(\varepsilon_{3}\) are 10%, 5%, and 2%, respectively, when the highest load is carried. The tooth \"2\" carries more than fifty-eight percent of the load. The root stress is highest for the plastic tooth, which contacts the tooth root, and the root stress is smallest for the plastic tooth, which contacts the tooth tip. The distribution of stress is shown in Figure 10.  
Figure 8: Creep rupture in Delrin®100. Figure 9: Traditional meshing between steel worm & helical gear (a = b = c).