Journal of Jilin University(Engineering and Technology Edition) ›› 2024, Vol. 54 ›› Issue (4): 865-873.doi: 10.13229/j.cnki.jdxbgxb.20221060

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Numerical simulation and experiment of non-circular gear transmission error and backlash

Chang-bin DONG(),Long-kun LI,Yong-ping LIU,Wang-peng PEI   

  1. School of Mechanical and Electrical Engineering，Lanzhou University of Technology，Lanzhou 730050，China
  • Received:2022-08-18 Online:2024-04-01 Published:2024-05-17

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Abstract:

The difficulty in establishing the transmission error model of non-circular gears and obtaining the backlash limit its application in precision occasions. In order to improve the transmission accuracy of non-circular gears， the non-circular gear transmission error model and backlash model under bidirectional transmission are established based on the meshing line incremental method considering the eccentricity error. The influence of eccentricity and eccentricity error on bidirectional transmission error and backlash are analyzed， and the correctness of theoretical analysis is verified by transmission test. The analysis shows that the backlash of the non-circular gear can be obtained by the bidirectional transmission error. With the increase of eccentricity and eccentricity error， the two-way transmission error shows an increasing trend. Optimizing the initial phase can reduce the transmission error and backlash to a certain extent. As the load increases， the transmission error and backlash also show an increasing trend. And due to the existence of gear tooth deformation， there is a certain cumulative value of the backlash.

Key words: mechanical manufacturing and automation, non-circular gear, meshing line increment, transmission error, gear backlash, transmission experiment

CLC Number: 

  • TH132.4

Fig.1

Non-circular gear reversing device for pumping unit"

Fig.2

Meshing line increment when driving gear rotates counterclockwise"

Fig.3

Meshing line increment when driving gear rotates clockwise"

Table 1

Non-circular gear pair parameters"

名称数值
模数m/mm3
中心距a/mm150
顶隙系数C*0.25
偏心率k0.2
齿数Z47
齿顶高系数ha*1
齿宽B/mm30
节曲线方程r64.6671±0.3287cos?θ

Fig.4

Variation law of non-circular gear transmission error with eccentricity"

Fig.5

Variation law of non-circular gear transmission error with eccentricity error"

Fig.6

Relationship between transmission error of non-circular gears and backlash"

Fig.7

Effect of initial phase on transmission error and backlash of non-circular gears"

Fig.8

Comparison of backlash of non-circular gears after phase optimization"

Fig.9

Distribution law of non-circular gear transmission error and backlash after phase optimization"

Fig.10

Non-circular gear transmission test rig"

Table 2

Detailed configuration information of non-circular gear transmission test rig"

部件名称型号规格
转矩传感器YH-502

测量量程：20 N·m和2000 N·m；测量精度：±0.1%；

电源电压：24 V DC；输出信号：10±5 kHz；扭矩精度：<±0.1%F?S；频率响应：100?μs

噪声传感器RS-ZS-V05-2量程：30~120 dB；频率范围：0.02~12.5 kHz；测量误差：±1.5 dB
红外温度传感器CK-01A

温度范围：-20~300 ℃；光谱范围：8~14?μm；

测量精度：±1%；响应时间：50~300 ms可选；

振动传感器CA-YD-107频率响应：0.5~6000 Hz；最大横向灵敏度：≤5%；轴向灵敏度：50?PC/g；磁灵敏度：2 g/T；基座应变：0.2?mg/μg
圆光栅K-100电源电压：24 V DC；分辨率：48 000 P/R；防护等级：IP50
交流伺服电动机MSME504G额定转速：3000 r/min；额定电压：400 V AC（三相）；转矩：15.9 N·m；防护等级：IP67
伺服电动机驱动器MFDTA464额定电压：400 V AC（三相）
PLCS7-200SMART电源电压：220 V AC；I/O点：30；AO通道：4
数据采集卡NI-6351采样率：1.25 MS/s；AI通道：16；A/D精度：16位；AO通道：2；DIO通道：24；计数通道：4

Fig.11

Distribution law of transmission error under two kinds of steering obtained by test"

Fig.12

Influence of load on transmission error"

Fig.13

Effect of load on tooth backlash"

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