1. Introduction
In the realm of mechanical engineering, gears play a crucial role in power transmission and motion control. Among various types of gears, modified helical cylindrical gears are widely used, especially in applications where space is limited and high – performance requirements are imposed. When dealing with the cloning design of these gears, accurately determining their parameters is of utmost importance. This article delves into the detailed process of clone design and calculation of modified helical cylindrical gears, aiming to provide a comprehensive guide for engineers and researchers in this field.
2. Structure and Working Principle of Electric Vehicle Glass Lifter
2.1 Structure Overview
The electric vehicle glass lifter is a complex mechanical system. As shown in Figure 1, it mainly consists of a DC motor, a worm shaft, left and right tooth – worm dual – links, a large gear, a spline shaft, a pulley, and a steel rope. The worm shaft has two – section worm teeth at its upper end, with one section on the left and the other on the right. The left and right tooth – worm dual – links are composed of a worm gear and a gear integrated together, and they mesh with the large gear respectively.
| Component | Function |
|---|---|
| DC motor | Provides power for the operation of the glass lifter |
| Worm shaft | Transmits the rotational motion of the motor to the left and right tooth – worm dual – links |
| Left/right tooth – worm dual – link | Converts the rotational motion of the worm shaft into the rotational motion of the gear, and then transmits it to the large gear |
| Large gear | Drives the spline shaft and pulley to rotate, thereby controlling the movement of the steel rope and the glass |
| Spline shaft | Connects the large gear and the pulley, ensuring the synchronous rotation |
| Pulley | Wraps the steel rope, and its rotation controls the up – and – down movement of the glass |
| Steel rope | Connects the glass and the pulley, transmitting the pulling force |
2.2 Working Principle
When the DC motor is activated, it drives the worm shaft to rotate. When the worm shaft rotates clockwise, the right – hand worm teeth engage with the worm gear teeth of the right – hand tooth – worm dual – link, causing it to rotate. At the same time, the left – hand worm teeth disengage from the worm gear teeth of the left – hand tooth – worm dual – link, so no motion is transmitted on the left side. Conversely, when the worm shaft rotates counter – clockwise, the left – hand worm teeth engage with the left – hand tooth – worm dual – link, and the right – hand side is in a disengaged state.
The rotation of the tooth – worm dual – link gears is then transmitted to the large gear. The large gear, in turn, drives the spline shaft and pulley to rotate. The pulley’s rotation causes the steel rope to wind or unwind, which ultimately controls the up – and – down movement of the glass. When the glass reaches its limit position, the increased resistance causes the steel rope to slip on the pulley, protecting the electric lifter from damage.
3. Observation and Measurement of Transmission Components in Electric Lifters
3.1 Observation of Left and Right Gears
The left and right gears in the electric lifter are helical cylindrical gears, each with 8 teeth. In gear manufacturing, there is a limit to the minimum number of teeth to avoid root – cutting. For a standard involute gear, when using a rack – type cutter to cut teeth, the minimum number of teeth \(Z_{min}\) for a non – root – cutting straight – tooth cylindrical gear can be calculated by the formula \(Z_{min}=\frac{2f}{\sin^{2}\alpha_{0}}\) when \(i_{q}=\infty\). In practical applications, an allowable minimum number of teeth \(Z_{min}’=\frac{5}{6}Z_{min}\) is often adopted.
For example, when \(\alpha_{0} = 20^{\circ}\), \(f = 1\), and \(m>1\), the minimum number of teeth for an external – meshing straight – tooth cylindrical gear without root – cutting is 17. When \(m\leq1\), the non – root – cutting minimum number of teeth is 14, and the actual minimum number of teeth can be 12. Since the left and right gears in the electric lifter have only 8 teeth, they will definitely experience root – cutting during the cutting process if they are not modified.
Modified gears use the principle of moving the tooth profile to avoid root – cutting. By moving the cutting tool away from or closer to the workpiece center, the non – involute part of the gear root is reduced, and an involute tooth surface is added at the tooth tip. This changes the tooth thickness on the pitch circle and the tooth root height. Comparing the tooth shape of the left and right gears with that of a known modified gear (as shown in Figure 2), it can be qualitatively determined that they are modified gears.
3.2 Detection of Left Gear, Right Gear, Large Gear, and Gear Box
To determine whether the gears are modified or not, it is necessary to measure the tooth tip circle diameter of the left gear, right gear, and large gear, as well as the center distances between the worm and worm gear, and between the left/right gears and the large gear in the gear box.
The measured values and non – modified theoretical values of these parameters are shown in Table 1.
| Parameter | Left/Right Gear Tooth Tip Circle Diameter \(D_{w}\) (mm) | Large Gear Tooth Tip Circle Diameter \(D_{w}\) (mm) | Center Distance between Left/Right Gears and Large Gear \(A\) (mm) | Center Distance between Worm and Worm Gear \(A\) (mm) |
|---|---|---|---|---|
| Measured Value (Sample) | 11.86 | 47.44 | 27.80 | 15.20 |
| Theoretical Value (Non – Modified) | 10.88 | 47.55 | 26.96 | 14.90 |
| Table 1: Comparison of Measured and Non – Modified Theoretical Values of Transmission Components |
It can be clearly seen from Table 1 that the actual tooth tip circle diameter of the left and right gears is 11.86 mm, which is 0.98 mm larger than the non – modified theoretical value of 10.88 mm. The actual tooth tip circle diameter of the large gear is 47.44 mm, which is 0.11 mm smaller than the non – modified theoretical value of 47.55 mm. In addition, the actual center distance between the left/right gears and the large gear is 27.8 mm, which is 0.84 mm larger than the non – modified value of 26.96 mm. These differences indicate that the left/right gears and the large gear are modified.
4. Selection of Modification Methods for Automotive Lifter Transmission Components
4.1 Types of Modified Cylindrical Helical Gear Transmissions
There are two main types of modified cylindrical helical gear transmissions: height modification and angular modification.
- Height Modification: When the center distance \(A\) of height – modified meshing is equal to the center distance \(A_{0}\) of non – modified meshing, i.e., \(A = A_{0}\), and the modification coefficients satisfy \(\xi_{1}=\xi_{2}\), so \(\xi_{\sum}=\xi_{1}+\xi_{2}=0\). In this case, one gear has a positive modification coefficient (\(\xi_{1}>0\)) and the other has a negative modification coefficient (\(\xi_{2}<0\)).
- Angular Modification: Angular modification can be further divided into positive – angular modification and negative – angular modification. Each type can be classified into three situations according to the values of the modification coefficients \(\xi\) of the two meshing gears.
4.2 Determination of the Modification Method for the Electric Lifter Gears
For the electric lifter, the center distance \(A = 27.8\) mm, and the non – modified center distance \(A_{0}=26.96\) mm. Since \(A\neq A_{0}\), it does not belong to the height – modified type.
Based on the selection table of gear modification methods (Table 2), when \(Z_{1}<17\), \(Z_{1}+Z_{2}=50>34\), and \(A\neq\frac{m}{2}(Z_{1}+Z_{2})\), the purpose is to avoid root – cutting through angular modification, and \(\xi_{1}+\xi_{2}\neq0\). Therefore, the left/right gears and the large gear in the electric lifter adopt the positive – angular modification method.
5. Geometric Calculation of Modified Helical Cylindrical Gear Meshing
5.1 Limiting Conditions for Modification Coefficients
- Minimum Modification Coefficient \(\xi_{min}\): To ensure that the gear does not produce root – cutting or allows for a slight amount of root – cutting without reducing the expected contact ratio or shortening the effective part of the tooth profile. When \(f = 1\) and \(\alpha_{on}=20^{\circ}\), the minimum modification coefficient for non – root – cutting is \(\xi_{min}=\frac{17 – Z_{1}}{17}\). For an 8 – tooth gear, \(\xi_{min}=\frac{17 – 8}{17}\approx0.529\). The minimum modification coefficient for allowing a slight amount of root – cutting is \(\xi_{min}=\frac{14 – Z_{1}}{17}=\frac{14 – 8}{17}\approx0.353\).
- Maximum Modification Coefficient \(\xi_{max}\): As the modification coefficient increases, the tooth shape gradually becomes pointed. When \(f = 1\), \(\alpha_{0m}=20^{\circ}\), and \(Z = 8\), through looking up the table, \(\xi_{max}=0.565\) and \(\xi_{min}=0.255\). The modification coefficient should satisfy \(\xi_{max}\geq\xi\geq\xi_{min}\). If \(\xi\) exceeds \(\xi_{max}\), it is necessary to check the tooth tip width \(S_{w}\).
- Checking the Tooth Tip Width \(S_{w}\): For open – type and easily – worn gears, \(S_{w}>0.4 – 0.5\) mm. First, calculate the equivalent tooth number \(Z_{l1}=\frac{Z_{1}}{\cos^{3}\beta_{f}}\). For example, when \(Z_{1}=8\) and \(\beta_{f}=22^{\circ}\), \(Z_{l1}=\frac{8}{\cos^{3}22^{\circ}}\approx10\). Then, according to the equivalent tooth number and the modification coefficient, look up the value of \(S_{w1}\) in the table. Calculate the reduction amount of the tooth tip height based on the obtained values.
5.2 Geometric Parameter Calculation of Non – Modified Helical Cylindrical Gear Transmission
Given the known conditions of non – modified helical cylindrical gear design: \(Z_{1}=8\), \(Z_{2}=42\), \(m_{on}=1\) mm, \(\alpha_{on}=20^{\circ}\), \(\beta_{f}=22^{\circ}\), \(f_{an}=1\), \(C_{en}=0.25\), the geometric parameters can be calculated.
6. Design of Modified Helical Cylindrical Gears
The outer – shape design of modified helical cylindrical gears depends on the measured data of the sample. The tooth parameters are calculated based on the center – distance data of the installation holes of the large gear and the left/right tooth – worm dual – links in the gear box and gear cover, as well as the modulus, number of teeth, and large – diameter data of the sample gears. The design diagrams of the large – modified gear and the left/right modified gears.
7. Conclusion
In gear – meshing transmission mechanisms, for gears with \(Z<17\) teeth and a modulus \(m\leq1\), especially when \(Z<14\) for small – modulus gears, the modification method must be used in calculation, design, and manufacturing to avoid root – cutting. For cloned products of such gears, it is necessary to conduct actual measurements. After comparative calculations, determine their nature and modification types. Only after quantitatively calculating various geometric dimensions can product drawing design, mold design, and manufacturing be carried out. Otherwise, rework will be inevitable, resulting in unnecessary economic losses.
In modern manufacturing, with the continuous development of technology, the requirements for the accuracy and performance of gears are also increasing. The clone design and calculation of modified helical cylindrical gears are key links in ensuring the quality of gear – related products. By following the methods and principles described in this article, engineers can more accurately design and manufacture modified helical cylindrical gears to meet the needs of different mechanical systems. Future research can focus on further optimizing the modification coefficient selection method, improving the accuracy of geometric parameter calculation, and exploring new manufacturing processes for modified gears to enhance their performance and durability.
