1.The design and manufacturing of modified helical cylindrical gears, especially in applications with narrow widths and small moduli (e.g., electric vehicle glass lifters), require precise parameter determination. This paper presents a systematic approach to clone these gears using measured data such as modulus, center distance, and tooth tip circle diameter. Key challenges include avoiding root cutting, optimizing tooth strength, and ensuring dimensional consistency with samples. Through theoretical analysis and experimental validation, this study demonstrates the critical role of modification coefficients and geometric calculations in achieving accurate clone designs.
2. Introduction
2.1 Background
Modified helical gears are widely used in compact mechanical systems, such as electric vehicle glass lifters, due to their ability to reduce root cutting, improve load capacity, and adjust center distances. However, cloning these gears from samples poses significant challenges, especially when direct parameter measurement is infeasible.
2.2 Problem Statement
For gears with modulus (m) ≤ 1 mm and 齿数 (Z) < 12, traditional non-modified designs often result in root cutting, compromising strength and performance. The goal is to derive all geometric parameters (e.g., tooth tip diameter, center distance) using limited measured data to ensure clone accuracy.
3. Design Methodology
3.1 Qualitative Analysis
- Root Cutting Identification: Gears with Z < 17 (for α = 20°) are prone to root cutting. For m ≤ 1 mm, the minimum 齿数 to avoid root cutting is Z = 14, but practical designs allow Z = 12 with controlled modification.
- Modification Type: Table 1 summarizes the selection criteria for modification types (height vs. angle modification) based on center distance (A) and 齿数 sum (Z₁ + Z₂).
| 齿数 Z₁ | 齿数和 Z₁+Z₂ | 中心距 A | 变位系数 ξ | 变位方法 | 主要目的 |
|---|---|---|---|---|---|
| Z₁ < 17 | ≥34 | A = A₀ | ξ₁ = -ξ₂ | 高度变位 | 避免根切 |
| Z₁ < 17 | ≥34 | A ≠ A₀ | ξ₁ + ξ₂ ≠ 0 | 角度变位 | 避免根切 |
| Z₁ ≥ 17 | >34 | A = A₀ | ξ₁ = -ξ₂ | 高度变位 | 改善啮合性能 |
Table 1: Gear Modification Selection Criteria
3.2 Quantitative Calculation
3.2.1 Key Parameters
- 法向模数 (mₙ): Derived from the sample (e.g., mₙ = 1 mm).
- 螺旋角 (β): Typically 22° for compact designs.
- 变位系数 (ξₙ): Determined to avoid root cutting and ensure tooth tip thickness (Figure 1).
3.2.2 Geometric Formulas
- 分度圆直径 (d_f):\(d_f = Z \cdot m_s \quad \text{where} \quad m_s = \frac{m_n}{\cos \beta}\)
- 齿顶圆直径 (d_w):\(d_w = d_f + 2 \cdot (f_{on} + \xi_n – \sigma_n) \cdot m_n\)
- 中心距 (A):\(A = \frac{Z_1 + Z_2}{2} \cdot m_s \cdot \cos \alpha_{os}\)
4. Experimental Validation
4.1 Measurement Setup
- 样品测量:
- 齿顶圆直径 (D_w): Left/right gears = Φ11.86 mm, large gear = Φ47.44 mm.
- 中心距 (A): Left/right gears with large gear = 27.80 mm, 蜗杆与蜗轮 = 15.20 mm.
4.2 Results Comparison
Table 2 compares measured values with non-modified and angle-modified theoretical results.
| 参数 | 测量值 | 非变位理论值 | 角度变位理论值 |
|---|---|---|---|
| 左 / 右齿轮齿顶圆直径 (mm) | 11.86 | 10.88 | 11.70 |
| 大齿轮齿顶圆直径 (mm) | 47.44 | 47.55 | 47.80 |
| 中心距 (mm) | 27.80 | 26.96 | 27.80 |
Table 2: Measured vs. Theoretical Values
4.3 Tooth Profile Analysis
- 非变位齿轮 (ξ = 0): 明显根切 (Figure 2a).
- 变位齿轮 (ξ = +0.3): 无可见根切 (Figure 2b).
5. Application Case Study: Electric Vehicle Glass Lifter
5.1 System Overview
The glass lifter mechanism (Figure 3) uses a worm gear drive to control window movement. Key components include:
- 蜗杆轴 (Z_left=1, Z_right=1)
- 右齿蜗双联 (Z_gear=8, Z_worm=40)
- 大齿轮 (Z=42)
5.2 Clone Design Process
- qualitative analysis:
- Left/right gears (Z=8) require modification to avoid root cutting.
- 大齿轮 (Z=42) uses negative modification to adjust center distance.
- Quantitative calculations:
- The total coefficient of normal displacement (ξₙ_Σ): Calculated as 0.914.
- Assign a displacement factor: ξₙ₁ = 0.614 (left/right gears), ξₙ₂ = 0.3 (large gear).
6. Conclusion
Accurate clone design of modified helical gears relies on systematic parameter calculation and experimental validation. Key findings include:
- Root Cutting Prevention: Modification coefficients must be ≥0.353 for Z=8 gears.
- Center distance adjustment: Angle modification effectively adjusts center distance to match sample specifications.
- Tooth top thickness verification: Ensure tooth tip width ≥0.4 mm to avoid breaking.
Future work should explore advanced optimization algorithms and material selections to enhance gear performance in high-load applications.
