﻿ 二级直齿轮空间驱动机构传动误差分析

# 二级直齿轮空间驱动机构传动误差分析Analysis of Transmission Error of Two-Stage Spur Gear Space Driving Mechanism

Abstract: To improve the transmission accuracy of the two-stage spur gear system of a certain type of space drive mechanism, solving the nonlinear disturbance problem in the operation of system operation, the profile error and the pitch error was described by simple harmonic function and the influence of profile error and pitch error on the overall transmission error of gear system was analyzed. The results show that the pitch error of the second stage gear pair has a great influence on the transmission error, and the gear 4 has a greater effect than the gear 3, and the influence of the pitch error is greater than that of the profile error. This paper enriches the research on the transmission error of the two-stage spur gear system, and provides an important reference for the actual design of the gear system.

1. 引言

2. 两级直齿轮传动模型

1) 忽略轴承的摩擦；

2) 认为齿轮减速系统的输入扭矩为固定值：

3) 轮齿始终沿啮合线方向进行啮合。

Figure 1. Transmission diagram of two-stage spur gear

3. 齿型误差和齿距误差

${e}_{pf}={a}_{1}\mathrm{sin}\left(\alpha \right)+{b}_{1}\mathrm{sin}\left(2\alpha \right)+{c}_{1}\mathrm{sin}\left(3\alpha \right)$ (1)

${e}_{pt}={a}_{2}\mathrm{sin}\left(\theta \right)+{b}_{2}\mathrm{sin}\left(2\theta \right)+{c}_{2}\mathrm{sin}\left(3\theta \right)$ (2)

${e}_{pf},{e}_{pt}$ ——齿形误差和齿距误差；

${a}_{1},{b}_{1},{c}_{1}$ ——齿形误差各阶谐波的幅值系数；

${a}_{2},{b}_{2},{c}_{2}$ ——齿距误差各阶谐波的幅值系数；

$\alpha$ ——啮合角；

$\theta$ ——齿轮转角。

${e}_{t}={e}_{pf}+{e}_{pt}$ (3)

4. 齿形齿距误差对传动误差的影响

4.1. 第一级与第二级齿轮副的对比

Figure 2. Curve of profile error

Figure 3. Curve of pitch error

Figure 4. Transmission error curve under different profile error and pitch error combination

Figure 5. Comparison of different error combination and default combination (1)

Table 1. Basic parameters of two-stage spur gear

Table 2. Different profile error and pitch error combination (1)

Table 3. Transmission error amplitude under different combinations (1)

4.2. 第二级齿轮中齿轮3与齿轮4的对比

4.3. 第二级齿轮中齿形误差与齿距误差的对比

Figure 6. Comparison of different error combination and default combination (2)

Figure 7. Comparison of different error combination and default combination (3)

Table 4. Different profile error and pitch error combination (2)

Table 5. Transmission error amplitude under different combinations (2)

Table 6. Different profile error and pitch error combination (3)

Table 7. Transmission error amplitude under different combinations (3)

5. 结论

1) 分析了齿形齿距误差对齿轮系统传动误差的影响，分析结果表明，第二级齿轮的齿形齿距误差对传动误差影响较大，而且相比于齿轮3，齿轮4的影响更大，相比于齿形误差，齿距误差的影响更大。

2) 在实际设计二级直齿轮传动系统时，为了提高传动精度，应优先提高第二级齿轮的精度等级。在齿轮的制造和加工过程中，应将齿轮4的齿形齿距误差控制在一定范围内，尤其是齿距误差。在保证传动精度的前提下，为了降低成本，可适当降低第一级齿轮的精度等级，对齿轮系统的传动误差影响较小。

3) 本文丰富了二级直齿轮系统传动误差方面的研究，为实际设计齿轮系统提供重要参考依据。

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