Leakage Analysis and Volumetric Efficiency of Symmetrical Multiple Output Gear Motors
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摘要: 为了研究对称型多输出齿轮马达的泄漏与容积效率，通过对称型多输出齿轮马达的内部结构计算出内外马达不同连接方式下的几何排量，分析了马达的主要泄漏途径，通过建立泄漏的数学模型归纳不同连接下泄漏的一般表达式；同时搭建试验平台测试对称型多输出齿轮马达的容积效率. 研究结果表明：当马达的进出口压力由0.9 MPa增加至5.9 MPa时，内马达工作时容积效率由94.2%下降至80.2%，外马达容积效率由92.5%下降至73.6%，内外马达同时工作时容积效率由88.8%下降至63.2%，差动连接时容积效率由86.0%下降至62.7%；当进出口压差为5.9 MPa时，内马达单独工作容积效率最高为80.2%，差动连接下马达的容积效率最低为62.7%.Abstract: In order to study the leakage and volumetric efficiency of a symmetrical multi-output geared motor, the geometric displacements of the internal and external motors under different connection modes were calculated based on the internal structure of the symmetric multi-output gear motor. The main leakage paths of the motor were analyzed. By establishing a mathematical model of the leakage, general expressions of leakage under different connections were summarized. At the same time, an experimental platform was built to test the volumetric efficiency of the symmetrical multi-output geared motor. The results show that when the inlet and outlet pressure of the motor increase from 0.9 MPa to 5.9 MPa, the volumetric efficiency of the internal motor decreases from 94.2% to 80.2%, and the volumetric efficiency of the external motor decreases from 92.5% to 73.6%. The efficiency drops from 88.8% to 63.2%, and the volumetric efficiency decreases from 86.0% to 62.7% during differential connection. When the pressure difference between the inlet and outlet is 5.9 MPa, the volumetric efficiency of the internal motor alone is 80.2%, and the volumetric efficiency of the motor is 62.7%.
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Key words:
- hydraulic motor /
- leakage /
- geometric displacement /
- volumetric efficiency /
- test
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图 2 齿轮马达齿顶与壳体的径向间隙泄漏
Figure 2. Radial clearance leakage between gear motor top and housing
表 1 不同连接方式下马达的泄漏量
Table 1. Leakage of the motor under different connection modes
马达工作方式 泄漏量 内马达 外马达 工作 不工作 $\Delta {Q_2} + \Delta {Q'_2}$ 不工作 工作 $\Delta {Q_1} + \Delta {Q'_1}$ 工作 工作 $\Delta {Q_1} + \Delta {Q'_1} + \Delta {Q_2} + \Delta {Q'_2}$ 
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表 2 马达的共齿轮设计参数
Table 2. Co-gear design parameters of the motor
主要设计参数 取值 共齿轮齿宽/mm 40 共齿轮的外齿轮高压腔的包角/rad π/4 共齿轮的内齿轮高压腔的包角/rad π/2 共齿轮的外齿轮齿顶圆半径/mm 37.5 共齿轮的内齿轮齿顶圆半径/mm 15.8 共齿轮的外齿轮齿根圆半径/mm 30.8 共齿轮的内齿轮齿根圆半径/mm 19.1 共齿轮的外齿轮齿轴半径/mm 27 共齿轮的内齿轮齿轴半径/mm 24 共齿轮外齿轮齿顶厚度/mm 2.1 共齿轮内齿轮齿顶厚度/mm 1.7 共齿轮外齿轮过渡区的齿数/个 17 共齿轮内齿轮过渡区的齿数/个 11
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表 3 马达的大齿轮设计参数
Table 3. Large Motor gear design parameters
主要设计参数 取值 大齿轮齿宽/mm 40 大齿轮高压腔的包角/rad π/3 大齿轮齿顶圆半径/mm 27 大齿轮齿根圆半径/mm 20.3 大齿轮齿轴半径/mm 17 大齿轮齿顶厚度/mm 2 大齿轮过渡区的齿数/个 11
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表 4 马达的小齿轮设计参数
Table 4. Design parameters of motor pinion
主要设计参数 取值 小齿轮齿宽/mm 40 小齿轮高压腔的包角/rad 2π/3 小齿轮齿顶圆半径/mm 12 小齿轮齿根圆半径/mm 12 小齿轮齿轴半径/mm 8.6 小齿轮齿顶厚度/mm 1 大齿轮过渡区的齿数/个 5 齿轮马达的端面间隙/mm 0.015 齿轮马达的径向间隙/mm 0.03
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表 5 理论与实际泄漏对比
Table 5. Comparison of theoretical and actual leakage
工作
方式理论泄漏/（L•min−1） 理论容积效率/% 实际泄漏/（L•min−1） 实际容积效率/% 内马达 1.6 91.6 3.8 80.2 外马达 2.7 85.8 4.3 73.6 内外马达同时 4.2 78.1 7.0 63.2 内外马达差动 4.5 76.4 7.6 60.7
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表 6 内马达工作试验数据
Table 6. Test data of internal motors working
压差
/MPa输入流量
/（L•min−1）理论流量
/（L•min−1）容积效率
/%0.9 5.2 4.9 94.2 2.2 7.2 6.7 93.1 3.1 9.2 8.4 91.3 3.9 12.3 10.8 87.8 5.1 15.4 12.9 83.5 5.9 19.1 15.3 80.2
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表 7 外马达工作试验数据
Table 7. Test data of external motors working
压差
/MPa输入流量
/（L•min−1）理论流量
/（L•min−1）容积效率
/%0.9 5.2 4.7 92.5 2.2 7.2 6.5 90.0 3.1 9.2 8.0 87.2 3.9 12.3 10.1 82.9 5.1 15.4 12.1 78.9 5.9 19.1 14.8 73.6
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表 8 内外马达同时工作试验数据
Table 8. Test data of internal and external motors working simultaneously
压差
/MPa输入流量
/（L•min−1）理论流量
/（L•min−1）容积效率
/%0.9 5.2 4.6 88.8 2.2 7.2 6.2 86.5 3.1 9.2 7.7 84.0 3.9 12.3 9.7 78.2 5.1 15.4 11.1 72.0 5.9 19.1 12.1 63.2
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表 9 内外马达差动工作试验数据
Table 9. Test data of internal and external motor differential working
压差
/MPa输入流量
/（L•min−1）理论流量
/（L•min−1）容积效率
/%0.9 5.2 4.6 86.0 2.2 7.2 6.2 83.5 3.1 9.2 7.7 80.8 3.9 12.3 9.7 74.2 5.1 15.4 10.1 70.0 5.9 19.1 12.0 62.7
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