基于平行连杆机构加工的圆弧齿线圆柱齿轮啮合特性研究
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摘要
以圆弧齿线圆柱齿轮为研究对象,基于平行连杆机构加工原理,推导齿轮齿面方程,并完成三维建模,进而建立动力学分析模型,分析齿宽、齿线半径、负载及转速对圆弧齿线圆柱齿轮啮合特性的影响。研究结果表明,随着齿宽增加,最大啮合力、平均啮合力以及啮合力均方根均先减小后增加;随着齿线半径的增加,最大啮合力、平均啮合力以及啮合力均方根均先减小后增大,RT=120～240 mm时达到最优,平均啮合力和啮合力均方根波动范围小,最大啮合力波动范围大;啮合力随着负载的增加而逐渐增加,但正向/负向波动幅度随着负载的增加而减小,在低负载时传动平稳性差,甚至出现脱啮现象;随着转速增加,齿轮平均啮合力、最大啮合力增加,最小啮合力减小,即齿轮啮合力的波动越剧烈,齿轮传动冲击越大。
The cylindrical gear with arcuate tooth trace is regarded as the research object. Based on the processing principle of parallel link mechanism,the gear tooth surface equation is derived,and the 3 D model of gear is established,and the dynamics analysis model of gear pair is further established. Through the dynamics analysis simulation,the influence of tooth line radius,tooth width,load and speed on the meshing characteristics is analyzed. The results show that, the maximum meshing force,average meshing force and RMS of meshing force all decrease first and then increase with the increase of the tooth width. The maximum meshing force,average meshing force and RMS of meshing force all decrease first and then increase with the increase of tooth line radius,it's optimum at RT=120～240 mm,the fluctuation range of average meshing force and RMS of meshing force is small,while that of maximum meshing force is large. The meshing force increases gradually with the increase of load,but the positive/negative fluctuation amplitude decreases with the increase of load. The transmission stability is poor at low loads,and even the gear transmission appears to be out of mesh. With the increase of rotating speed,the average meshing force and maximum meshing force increase,while the minimum meshing force decreases,that is,the more severe the fluctuation of gear meshing force,the greater the impact of gear transmission.
The cylindrical gear with arcuate tooth trace is regarded as the research object. Based on the processing principle of parallel link mechanism,the gear tooth surface equation is derived,and the 3 D model of gear is established,and the dynamics analysis model of gear pair is further established. Through the dynamics analysis simulation,the influence of tooth line radius,tooth width,load and speed on the meshing characteristics is analyzed. The results show that, the maximum meshing force,average meshing force and RMS of meshing force all decrease first and then increase with the increase of the tooth width. The maximum meshing force,average meshing force and RMS of meshing force all decrease first and then increase with the increase of tooth line radius,it's optimum at RT=120～240 mm,the fluctuation range of average meshing force and RMS of meshing force is small,while that of maximum meshing force is large. The meshing force increases gradually with the increase of load,but the positive/negative fluctuation amplitude decreases with the increase of load. The transmission stability is poor at low loads,and even the gear transmission appears to be out of mesh. With the increase of rotating speed,the average meshing force and maximum meshing force increase,while the minimum meshing force decreases,that is,the more severe the fluctuation of gear meshing force,the greater the impact of gear transmission.
引文
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[11]肖华军,侯力,董璐,等.旋转刀盘母面成形的弧齿线圆柱齿轮数学建模[J].四川大学学报(工程科学版),2013,45(3):171-175.
[12]赵斐,侯力,段阳,等.旋转刀盘圆弧齿轮成形理论分析及数字化建模研究[J].四川大学学报(工程科学版),2016,48(6):119-125.
[13]宋爱平,吴伟伟,高尚,等.弧齿圆柱齿轮理想几何参数及其加工方法[J].上海交通大学学报,2010,44(12):1735-1740.
[14]吴伟伟,宋爱平,王召垒,等.渐开线弧齿圆柱齿轮的应力分析[J].机械传动,2010,34(11):38-44.
[2] TSENG R T,TSAY C B. Contact characteristics of cylindrical gears with curvilinear shaped teeth[J]. Mechanism and Machine Theory,2004,39(9):905-919.
[3] TSENG R.T,TSAY C B. Mathematical model and undercutting of cylindrical gears with curvilinear shaped teeth[J]. Mechanism and Machine Theory,2001,36(11):1189-1202.
[4] TSENG R.T,TSAY C B. Mathematical model and surface deviation of cylindrical gears with curvilinear shaped teeth cut by a hob cutter[J]. Journal of Mechanical Design,2005,127(5):982-987.
[5]祝海林,邹旻,胡爱萍.圆弧齿线圆柱齿轮啮合理论的研究[J].机械,1996,23(5):7-10.
[6]马振群,王小椿,沈兵.对称弧形齿线圆柱齿轮的真实齿面接触分析研究[J].西安交通大学学报,2005,39(7):722-726.
[7]狄玉涛,洪晓晖,陈明.弧齿线圆柱齿轮齿面形成原理[J].哈尔滨轴承,2006,27(3):58-61.
[8] FUENTES A A,RUIZ O R,GONZALEZ P I. Comparison of spur,helical and curvilinear gear drives by means of stress and tooth contact analyses[J]. Meccanica,2017,52(7):1721-1738.
[9] FUENTES A,RUIZ O R,GONZALEZ P I. Computerized design,simulation of meshing,and finite element analysis of two types of geometry of curvilinear cylindrical gears[J]. Computer Methods in Applied Mechanics&Engineering,2014,272(2):321-339.
[10]马登秋,侯力,王虹,等.面向制造的弧齿线圆柱齿轮建模及动力学分析[J].机械设计与制造,2017(11):9-12.
[11]肖华军,侯力,董璐,等.旋转刀盘母面成形的弧齿线圆柱齿轮数学建模[J].四川大学学报(工程科学版),2013,45(3):171-175.
[12]赵斐,侯力,段阳,等.旋转刀盘圆弧齿轮成形理论分析及数字化建模研究[J].四川大学学报(工程科学版),2016,48(6):119-125.
[13]宋爱平,吴伟伟,高尚,等.弧齿圆柱齿轮理想几何参数及其加工方法[J].上海交通大学学报,2010,44(12):1735-1740.
[14]吴伟伟,宋爱平,王召垒,等.渐开线弧齿圆柱齿轮的应力分析[J].机械传动,2010,34(11):38-44.