含误差的直齿轮的齿廓修形

依据齿轮传动载荷与轮齿变形的关系,推导出定载荷条件下,修形直齿轮静态传动误差与齿对综合修形参数的关系表达式。提出含制造误差修形齿轮修形参数的确定原则:理论设计修形齿轮的最大综合修形量应能消除含误差齿廓轮齿在啮入和啮出位置产生的几何干涉,理论设计修形齿轮的静态传动误差应保持最小的变化。给出了合制造误差修形直齿轮修形参数的计算公式,阐述了相应的确定方法。系统动态响应计算表明该方法所获得的修形齿轮具有良好的减振效果。     

直齿轮减振修形优化设计

为了提高齿轮副实际齿面啮合性能,设计齿廓修形曲面,与理论齿面叠加构造了直齿轮实际修形齿面,结合TCA、LTCA技术,建立考虑啮入冲击、刚度激励的直齿轮弯扭耦合的多齿对振动模型,以传动误差幅值、啮合冲击、啮合线向相对加速度均方根最小进行多目标优化,设计了最佳修形齿面。研究表明:无修形齿轮的传动误差幅值随载荷增加而增大,修形后随载荷增加重合度逐渐增大,幅值会产生波动,然后保持稳定,修形后直齿轮啮入啮出端载荷明显降低,因此啮合冲击降低;该方法确定的齿轮修形参数精确、有效,能大幅度减小齿轮的振动。     

天文望远镜传动直齿轮齿廓修形设计

采用高次幂、短修形方式设计望远镜传动直齿轮,既满足重合度要求,又可改善齿轮的静传动误差,还能消除齿顶刮行现象,避免应力集中。定义空载传动误差设计曲线为齿廓修形参数,根据虚拟加工过程,建立修形齿廓方程。采用轮齿接触分析理论,结合有限元法,计算了空载传动误差曲线、齿轮承载变形曲线以及静传动误差曲线、并计算了定载荷情况下,考虑齿距误差的齿廓修形方程。结合仿真算例,对比未修形齿轮与修形齿轮的静传动误差以及主动轮齿顶处的应力,表明修形效果明显。     

修形直齿轮的啮合干涉与啮合间隙

修形直齿轮因误差因素在齿对的啮入和啮出位置会出现啮合干涉或啮合间隙。本文利用齿对的啮合变形与齿廓法向修形量、齿廓误差的关系,推导了啮合齿对在啮合线的啮入和啮出位置所存在的几何干涉或啮合间隙,得到了啮合重合度小于2和3的齿轮副啮合齿对的最大干涉量或间隙量的计算表达式,为分析修形直齿轮的啮合状态和修正齿轮修形参数奠定了基础。     

考虑轴线平行度误差及热变形的齿轮修形设计

以渐开线直齿圆柱齿轮副为研究对象,基于改进的摩擦热量离心抛射扩散模型计算齿面对流换热系数,综合有限元仿真及摩擦生热分析求得齿面热流量,计算了考虑轴线平行度误差的齿轮副本体温度,进而建立热-结构耦合分析模型,研究轴线平行度误差、温度影响下齿轮副的修形量,给出了确定合理齿廓及齿向修形量的方法。结果表明,温度对修形量有一定影响,轴线平行度误差使得齿轮副齿向两端啮入/啮出干涉量不同,存在偏载的齿轮副应按齿廓齿向综合修形方式对齿轮副修形。     

渐开线直齿轮修形的有限元分析与研究

针对不同修形曲线对齿轮修形产生不同效果的问题,首先推导出了渐开线参数方程和修形曲线的齿廓参数方程,然后应用Pro/E建立了标准渐开线直齿轮与修形齿轮的三维模型,最后利用ANSYS Workbench的瞬态动力学模块对其进行了有限元分析;通过仿真得出了渐开线直齿轮和修形齿轮在啮合过程中的齿面接触应力的变化曲线.研究结果表明,在齿轮传动时的单双齿啮合交替时及啮入/啮出时,Walker修形曲线较直线修形曲线具有更好的修形效果,但同时两种修形曲线都导致了齿轮重合度的降低,增加了单齿啮合区,为修形齿轮的设计提供了数值实验依据.     

斜齿轮的齿廓修形的实验研究

本文以一对斜齿轮传动为对象,设计了这对齿轮在传动误差幅值最小时的齿廓修形曲线。作者进一步在齿轮实验台上,实际测量了该对齿轮在修形和未修形时的传动误差波形,与计算波形作了对比,并测量了该对齿轮在实际工况下的相对扭振加速度,证明了齿廓修形方法在齿轮系统减振设计中的突出效用。     

直齿轮齿距误差与齿高修形综合设计

定义空载传动误差设计曲线为齿高修形参数,根据虚拟加工过程,建立修形齿廓方程,以最小化静传动误差波动幅值为目的,推导定载荷条件下,无齿距误差齿轮的齿高修形参数公式.采用轮齿接触分析理论求解包含齿距误差的空载传动误差,建立包含齿距误差的修形齿轮有限元模型,计算各啮合位置因承载变形引起的传动误差,在满足无齿距误差齿高修形参数公式的基础上,以设计平滑的静传动误差曲线为目的,建立齿距误差与齿高修形参数的约束方程.算例中,含齿距误差的无修形齿轮静传动误差曲线有阶跃误差,通过修形设计,消除阶跃误差,获得平滑的静传动误差曲线.     

望远镜方位锁转频率分析与动力学模型简化

定义空载传动误差设计曲线为齿高修形参数,根据虚拟加工过程,建立修形齿廓方程,以最小化静传动误差波动幅值为目的,推导定载荷条件下,无齿距误差齿轮的齿高修形参数公式.采用轮齿接触分析理论求解包含齿距误差的空载传动误差,建立包含齿距误差的修形齿轮有限元模型,计算各啮合位置因承载变形引起的传动误差,在满足无齿距误差齿高修形参数公式的基础上,以设计平滑的静传动误差曲线为目的,建立齿距误差与齿高修形参数的约束方程.算例中,含齿距误差的无修形齿轮静传动误差曲线有阶跃误差,通过修形设计,消除阶跃误差,获得平滑的静传动误差曲线.     

直齿轮传动多工况多目标修形优化设计

针对直齿轮多工况使用情况,研究了小轮修形齿面理论建模方法和直齿轮传动多工况多目标修形优化方法,进行了两种工况下直齿轮传动多工况多目标修形优化设计,并进行了修形和不修形齿轮的齿面啮合仿真,通过对比分析,验证了齿面优化修形后达到了较好的综合性能,两种工况下的承载传动误差波动幅值和最大闪温均明显下降.研究成果为提高直齿轮综合性能的修形设计奠定了基础.     

三环齿轮传动的非线性动力学模型

振动大、噪声高是三环齿轮传动存在的突出问题,线性的振动模型无法完全解释其动力学行为。在考虑输入轴和支承轴的弹性、齿轮啮合综合误差、时变啮合刚度以及齿侧间隙的情况下,建立了三环齿轮传动的弯扭耦合非线性动力学模型。采用适当的坐标变换,将线性恢复力和非线性恢复力共存的动力学方程组转化为统一的矩阵形式,并对方程进行量纲一化处理,为进一步研究三环齿轮传动的非线性动力学行为打下基础。     

Performance improvement method for Nylon 6 spur gears

Plastic gears made of Nylon 6 are especially susceptible to failure due to extreme heat accumulation in the single tooth mesh area, which results in damage that consequently shortens gear teeth life and causes transmission errors. In this experimental study, the teeth width of plastic spur gears made of Nylon 6 were modified and investigated. The values of load sharing, F/b, in single and double tooth meshing areas were leveled by widening the single tooth zone along the meshing area, and the performances of both modified and unmodified gears were studied experimentally under three different loadings. It was observed that modified Nylon 6 gears exhibit lower tooth temperatures, which results in a decrease in wear rate as compared to unmodified gears. Consequently, teeth width modification helps to increase Nylon 6 gear performance.     

Mesh relationship modeling and dynamic characteristic analysis of external spur gears with gear wear

Gear wear is one of the most common gear failures, which changes the mesh relationship of normal gear. A new mesh relationship caused by gear wear affects meshing excitations, such as mesh stiffness and transmission error, and further increases vibration and noise level. This paper aims to establish the model of mesh relationship and reveal the vibration characteristics of external spur gears with gear wear. A geometric model for a new mesh relationship with gear wear is proposed, which is utilized to evaluate the influence of gear wear on mesh stiffness and unloaded static transmission error (USTE). Based on the mesh stiffness and USTE considering gear wear, a gear dynamic model is established, and the vibration characteristics of gear wear are numerically studied. Comparison with the experimental results verifies the proposed dynamic model based on the new mesh relationship. The numerical and experimental results indicate that gear wear does not change the structure of the spectrum, but it alters the amplitude of the meshing frequencies and their sidebands. Several condition indicators, such as root-mean-square, kurtosis, and first-order meshing frequency amplitude, can be regarded as important bases for judging gear wear state.     

Investigation of the Thermal Behaviour of Non‐metallic Curved‐Face‐Width Spur Gears

This paper describes a curved‐face‐width spur gear, specially designed for manufacture from non‐metallic materials. The benefits of this gear are the higher contact ratio, bending and Hertzian contact resistance, and greater tooth stiffness compared to standard spur gears. A modified geometry is proposed for the gear tooth, the height of which varies along the gear face width. Due to the reduction in tooth height, in sections away from the gear centre, lower sliding friction is expected, with consequences for the gear's thermal behaviour. The complex gear geometry makes the design of a die difficult; therefore the gears were cut on a milling machine, using a special kinematic generation process and related equipment. The tooth flank profile, an involute or near involute in sections away from the gear half‐width plane, as well as the flank surface quality determined by the single‐cutter tool used for gear manufacture, influence the meshing condition, and can be detrimental to the thermal behaviour of the gear. Experimental tests were carried out to examine the influence of load and speed on the temperature of the curved‐face‐width spur gears with modified geometry. The measured temperature of the non‐standard gear is further compared with the predicted temperature of plastic standard spur gears of the same specification.     

齿面综合研磨率分析与研齿性能试验

首次通过对研齿过程的轮齿接触仿真,齿面瞬时接触应力、齿面滑动系数与齿面研磨概率的研究分析,建立了齿面综合研磨率的评价指标,并进行了研齿性能试验。结果表明,准双曲面齿轮齿面中部研磨要严重一些,靠齿根稍重些,靠齿顶稍轻些,这与传动误差变化规律一致。研齿能一定程度上降低齿形、齿距误差,尤其对轮齿的实际啮合精度改善明显,振动噪声均有较大下降。     

Simulation of meshing for the spur gear drive with modified tooth surfaces

The authors have proposed methods (lead crowning and profile modification) for modifying the geometry of spur gears and investigated the contact pattern as well as the transmission errors to recommend the appropriate amount of modification. Based on the investigation, dynamic load of the modified spur gear drive has been calculated, which is helpful to predict the life of the designed gear drive. Computer programs for simulation of meshing, contact and dynamics of the modified spur gears have been developed. The developed theory is illustrated with numerical examples.     

直齿锥齿轮齿廓修形

根据啮合刚度和噪声之间的关系,以修形减振降噪为目的,用旋转渐开线曲线对直齿锥齿轮进行齿廓修形.以减小齿轮传动误差和啮合刚度的波动大小为衡量标准,同时确保载荷变化呈平稳过渡.静态计算结果表明,直齿锥齿轮齿廓长修形具有较好的减振效果.直齿锥齿轮采用冷精锻进行齿廓修形,显著地降低了成本,这为齿轮传动系统的修形、减振、降噪和设计提供了一种新的研究方法.     

基于ANSYS/LS-DYNA的齿轮动力学接触仿真分析

针对渐开线直齿轮容易出现的载荷突变及噪声问题,需对齿轮进行齿廓方向的磨削修形。利用ANSYS/LS-DYNA中的APDL语句实现标准齿轮和修形齿轮的建模及动力学接触分析,并对分析结果进行比较,验证其修形的必要性。     

基于齿背接触刚度的高速斜齿轮瞬态振动特性

为了分析基于齿背接触刚度的高速斜齿轮瞬态振动放大特性,针对高转速瞬态工况下斜齿轮齿面啮合-脱啮-齿背接触的齿面实际承载接触状态,建立了同时考虑啮合时间与齿面振动位移耦合机理的斜齿轮动态啮合刚度。在细化考虑齿背啮合机理、基于齿背实际啮合刚度的模型基础上,进一步建立斜齿轮啮合型瞬态振动模型,并在此基础上展开不同齿侧间隙以及齿背接触对系统瞬态振动特性影响分析研究。搭建封闭功率流式斜齿轮瞬态扭转振动测试试验台,对基于齿背接触刚度的斜齿轮瞬态振动特性进行了验证。该研究具有较好的理论研究意义,有利于斜齿轮传动系统在航空传动、新能源传动系统上的应用推广,进一步提升高转速齿轮系统的瞬态振动噪声品质。