Stability Analysis of Nonlinear Models of Nose Landing Gear Shimmy

Shimmy can reduce the service life of the nose landing gear, affect ride comfort, and even cause fuselage damage leading to aircraft crashes. Taking a light aircraft as the research object, the torsional freedom of landing gear around strut axis and lateral deformation of tire are considered. Since the landing gear shimmy is a nonlinear system, a nonlinear mechanical model of the front landing gear shimmy is established. Sobol index method is proposed to analyze the influence of structural parameters on the stability region of the nose landing gear, and Routh-Huritz criterion is used to verify the reliability of the analysis results of Sobol index method. We analyse the effect of torsional stiffness of strut, caster length, rated initial tire inflation pressure, rake angle, and vertical force on the stability region of theront landing gear. And the research shows that the optimization of the torsional stiffness of the strut and the caster length of the nose landing gear should be emphasized, and the influence of vertical force on the stability region of the nose landing gear should be paid attention to.

Statistical Modification Analysis of Helical Planetary Gears based on Response Surface Method and Monte Carlo Simulation

Tooth modification technique is widely used in gear industry to improve the meshing performance of gearings. However, few of the present studies on tooth modification considers the influence of inevitable random errors on gear modification effects. In order to investigate the uncertainties of tooth modification amount variations on system＇s dynamic behaviors of a helical planetary gears, an analytical dynamic model including tooth modification parameters is proposed to carry out a deterministic analysis on the dynamics of a helical planetary gear. The dynamic meshing forces as well as the dynamic transmission errors of the sun-planet 1 gear pair with and without tooth modifications are computed and compared to show the effectiveness of tooth modifications on gear dynamics enhancement. By using response surface method, a fitted regression model for the dynamic transmission error（DTE） fluctuations is established to quantify the relationship between modification amounts and DTE fluctuations. By shifting the inevitable random errors arousing from manufacturing and installing process to tooth modification amount variations, a statistical tooth modification model is developed and a methodology combining Monte Carlo simulation and response surface method is presented for uncertainty analysis of tooth modifications. The uncertainly analysis reveals that the system＇s dynamic behaviors do not obey the normal distribution rule even though the design variables are normally distributed. In addition, a deterministic modification amount will not definitely achieve an optimal result for both static and dynamic transmission error fluctuation reduction simultaneously.

An Exact Analytical Method for Magnetic Field Computation and Electromagnetic Torque in a Concentric Magnetic Gear

准确计算磁力齿轮电磁转矩是设计、分析磁力齿轮的关键,采用二维全局解析法计算同心式磁力齿轮气隙磁场。求解场域划分为内外转子永磁体、内外两层气隙和调磁定子的槽形区域,3类子区域的拉普拉斯方程和泊松方程通过边界连续条件建立联系。得到内外两层气隙区域的矢量磁位磁通密度解析表达式,有利于方便、快速、精确地计算任意转子位置的电磁转矩。计算了内外两层气隙磁场和内外转子电磁转矩,将气隙磁场波形和内外转子电磁转矩波形分别与二维有限元法计算波形作比较,结果吻合,证明了方法的正确性和有效性。

Calculation method of sliding ratios for conjugate-curve gear pair and its application

The calculation method of sliding ratios for conjugate-curve gear pair, generated based on the theory of conjugate curves,is proposed. The theoretical model of conjugate-curve gear drive is briefly introduced. The general calculation formulas of sliding ratios are developed according to the conjugate curves. The applications to the circular arc gears based on conjugate curves and the novel involute-helix gears are studied. A comparison on the sliding coefficient with the conventional corresponding gear drive is also carried out. The influences of gear parameters such as spiral parameter, gear ratio and modulus on the sliding ratios of gear drive are discussed. Brief description of manufacturing method for conjugate-curve gear pair is given. The research results show that the sliding ratios of gear pair become smaller with the increase of spiral parameter and gear ratio, respectively. And it will be greater with the increase of modulus for the tooth profiles. The meshing characteristics of conjugate-curve gears are further reflected and the optimization design of tooth profiles with high performance may be obtained.

A Method for Gear Fault Diagnosis Based on the Empirical Mode Decomposition

According to the characteristics of gear fault vibration signals, a methodfor gear fault diagnosis based upon the empirical mode decomposition (EMD) is proposed in thispaper. By using EMD, any complicated signal can be decomposed into a finite and often small numberof intrinsic mode functions (IMFs) , which are based upon the local characteristic time scale of thesignal. Thus, EMD is perfectly suitable for non-stationary signal processing and faultcharacteristics extracting. It is well known that a gear vibration signal consists of a number offrequency family components, each of which is a modulated signal. Thus, we can use EMD to decomposea gear fault vibration signal into a number of IMF components, some of which correspond to thefrequency families, and the others are noises. Therefore, the frequency families can be separatedand the noise can be decreased at the same time. The proposed method has been applied to gear faultdiagnosis. The results show that both the sensitivity and the reliability of this method aresatisfactory.

Calculating method of contact stress for non-circular gears

According to Hertz theory, the difference of contact stress for non-circular gears and equivalent gears is compared in the paper, a calculating method of contact stress for non-circular gears by using equivalent gears is researched, and computing formulas of power and rotation speed for equivalent gears are deduced. A numerical simulation of contact stress for non-circular gears has also been conducted based on the finite element method. By the comparison of fitting curves, the feasibility of using equivalent gears instead of non-circular gears to calculate the contact stress is testified.

Tooth surface geometry optimization of spiral bevel and hypoid gears generated by duplex helical method with circular profile blade

In order to effectively improve meshing performance of spiral bevel and hypoid gears generated by the duplex helical method, the effects of straight lined and circular cutting edges profile on meshing and contact of spiral bevel and hypoid gears were investigated analytically. Firstly, a mathematical model of spiral bevel and hypoid gears with circular blade profile was established according to the cutting characteristics of the duplex helical method. Based on a hypoid gear drive, the tooth bearings and the functions of transmission errors of four design cases were analyzed respectively by the use of the tooth contact analysis(TCA), and the contact stresses of the four design cases were analyzed and compared using simulation software. Finally, the curvature radius of the circular profile blade was optimized. The results show that the contact stresses are availably reduced, and the areas of edge contact and severe contact stresses can be avoided by selecting appropriate circular blade profile. In addition, the convex and concave sides are separately modified by the use of different curvature radii of inside and outside blades, which can increase the flexibility of the duplex helical method.

Perturbation Theory Combined with Boundary Element Method for Analysis of Gear Contact Problems

This paper combines the perturbation theory with the boundary element methodfor contact problems of three-dimensional elasticity mechanism to analyse the effect oferrors on the shape of the contact area and pressure distribution in gear drive through theperturbation of a cubic order geometry,there by greatly bringing down both computationwork volume and cost and providing a powerful tool for engineering study on the effectof errors on structural strength.

ERROR PROCESSING METHOD OF CYCLOIDAL GEAR MEASUREMENT USING 3D COORDINATES MEASURING MACHINE

An error processing method is presented based on optimization theory and microcomputer technique which can be successfully used in the cycloidal gear measurement on three dimensional coordinates measuring machine (CMM). In the procedure, the minimum quadratic sum of the normal deviation is used as the object function and the equidistant curve is dealed with instead of the teeth profile. CMM is a high accurate measuring machine which can provide a way to evaluate the accuracy of the cycloidal gear completely.

Quasi Ellipsoid Gear Surface Reconstruction Based on Meshless Local Petrov-Galerkin Method and Transmission Characteristic

Special transmission 3D model simulation must be based on surface discretization and reconstruction, but special transmission usually has complicated tooth shape and movement, so present software can＇t provide technical support for special transmission 3D model simulation. Currently, theoretical calculation and experimental method are difficult to exactly solve special transmission contact analysis problem. How to reduce calculation and computer memories consume and meet calculation precision is key to resolve special transmission contact analysis problem. According to 3D model simulation and surface reconstruction of quasi ellipsoid gear is difficulty, this paper employes meshless local Petrov-Galerkin （MLPG） method. In order to reduce calculation and computer memories consume, we disperse tooth mesh into finite points--sparseness points cloud or grid mesh, and then we do interpolation reconstruction in some necessary place of the 3D surface model during analysis. Moving least square method （MLSM） is employed for tooth mesh interpolation reconstruction, there are some advantages to do interpolation by means of MLSM, such as high precision, good flexibility and no require of tooth mesh discretization into units. We input the quasi ellipsoid gear reconstruction model into simulation software, we complete tooth meshing simulation. Simulation transmission ratio during meshing period was obtained, compared with theoretical transmission ratio, the result inosculate preferably. The method using curve reconstruction realizes surface reconstruction, reduce simulation calculation enormously, so special gears simulation can be realized by minitype computer. The method provides a novel solution for special transmission 3D model simulation analysis and contact analysis.

Research on Design Method of Non-Circular Gear Pair with Double Generating Angles

In order to enhance the bearing capacity of non-circular gear pair, the non-circular gear pair with double generating angles is proposed based on the design idea of unsymmetrical gear with double pressure angles. The tooth profile is designed by generating cutting theory, the pure rolling mathematic model that the center line of unsymmetrical rack roll along non-circular pitch curve is built, the digital model of non-circular gear with double generating angles is created through the second development method of CAD software, and then the drive characteristic and tooth strength are analyzed. The results show that the design method for double generating angles non-circular gear proposed in this paper is feasible, which is significant to improve the bearing capacity of non-circular gear pair.

METHOD FOR PRECISE CALCULATION OF ROOT STRESS OF SPIRAL BEVEL GEARS

A method for precise calculation of tooth root stress of spiral bevel gears is presentedand developed. On the basis of the machine settings analysis, tooth geometry anaysis and loadedtooth contact analysis, by using the tooth surface distribution load from tooth load analysis, thecalculation model is established and the root stress is calculated by means of finite element meth-od. The method mentioned is verified by a tested gears example.

面齿轮展成磨削表面残余应力优化方法

面齿轮展成磨削表面残余应力优化是一个复杂的非线性问题,传统的优化算法无法实现高效率和高精度的求解。因此,文章提出了以齿面磨削实验数据为驱动的面齿轮表面残余应力智能优化方法。通过设计系列实验获取齿面残余应力数据集,建立以基础数据为驱动的响应曲面模型,实现了以齿面残余应力和磨削效率为优化目标的智能粒子群多目标优化,解决了面齿轮表面残余应力的优化问题。实验表明该方法的相对误差介于0.89%~1.61%,证明了面齿轮展成磨削表面残余应力优化方法的有效性。分析发现:齿面残余压应力与磨削深度和工件速度呈正相关,与砂轮速度和砂轮分度角呈负相关。从敏感性角度分析,齿面残余应力对磨削深度的敏感性最大,其次是砂轮分度角,而齿面残余应力对砂轮速度和工件速度的敏感性相对较小。

Chaos control of gear system with elastomeric web based on multi-parameter multi-step method

This paper employs a multi-parameter multi-step chaos control method, which is built up on the OGY method, to stabilize desirable UPOs of a gear system with elastomeric web as a high-dimensional and non-hyperbolic chaotic system, and the analyses are carried out. Three types of relations between components of a certain control parameter combination are defined in a certain control process. Special emphasis is put on the comparison of control efficiencies of the multi-parameter multi-step method and single-parameter multi-step method. The numerical experiments show the ability to switch between different orbits and the method can be a good chaos control alternative since it provides a more effective UPOs stabilization of high-dimensional and non-hyperbolic chaotic systems than the single-parameter chaos control, and according to the relation between components of each parameter combination, the best combination for chaos control in a certain UPO stabilization process are obtained.

基于自助法的弧齿锥齿轮齿面修正

为了降低弧齿锥齿轮在批量加工制造中存在的齿面偏差,提出一种基于自助法的弧齿锥齿轮齿面修正方法。以同一批次小样本弧齿锥齿轮作为研究对象,在自助法统计齿面偏差检测数据的基础上,得到大量的齿面偏差数据;利用NURBS曲面拟合方法构建齿面的均值差曲面,将它作为实际加工齿面,建立齿面偏差的数字化预控补偿模型,对它进行优化求解,得到批量齿面数控加工的机床修正参数,然后不断调整机床加工参数,实现齿面的预控修正补偿;最后对修正前、后齿面偏差作对比分析。结果表明:小轮齿面偏差比修正前降低了76.66%,验证了自助法齿面修正理论的有效性,对指导弧齿锥齿轮批量齿面修正提供了理论依据。

用Gear法求解病态的引信球转子运动常微分方程组

应用欧拉角及欧拉动力学方程、欧拉运动学方程所建立的描述引信球转子转正运动的数学模型,为强非线性的病态常微分方程组。为了准确、高效地分析球转子的运动过程,以某火炮引信球转子为例,针对不同参量和积分精度,对比地应用了Gear方法和Runge-Kutta方法,对该方程组进行了数值模拟。Gear方法比Runge-Kutta方法易于获得准确解,并且耗用机时也短。

小模数航空锥齿轮全工序法铣齿印痕模拟研究

针对小模数航空螺旋锥齿轮全工序铣齿技术应用展开研究,采用KIMOS软件对齿轮印痕进行仿真,调整齿轮印痕,生成调整卡,采用国产机床加工,并参照测量结果进行大轮反调。加工后,通过验证实现小模数航空齿轮的全工序铣齿,取代五刀法,保证齿轮加工精度的同时提高加工效率。

某金属带式无级变速器振动仿真分析与多工况下试验验证

为分析某金属带式无级变速器(CVT)振动产生机理,采用集中参数法建立双级行星齿轮非线性扭转动力学模型,应用四阶龙格库塔方法进行动态响应求解,利用ADAMS软件进行动力学仿真,对动态响应进行验证,进行CVT振动台架试验测试。研究结果表明:四阶龙格库塔方法与ADAMS动态仿真得到的动态响应结果基本一致;台架试验结果表明前进挡转速为2500 r/min时,低速挡输入轴轴向位置的振动加速度最大为0.623 m/s^(2),转速为1000 r/min时,低速挡输入轴轴向位置的加速度最大为0.309 m/s^(2);倒挡工况下,转速为2500 r/min时,倒挡输入轴轴向位置的振动加速度最大为0.703 m/s^(2),转速1000 r/min时,倒挡输入轴轴向位置的加速度最大为0.504 m/s^(2);倒挡工况下的振动加速度幅值比前进挡高12.85%;倒挡阶次谱中54.4阶和108.8阶振动信号最为明显,挡位切换过程中双级行星齿轮啮合次数增多,啮合间隙是CVT在倒挡动力传递中振动增大的主要原因。

三轴环板式永磁齿轮气隙磁场及转矩计算

利用标量磁位法获得了三轴环板式永磁齿轮(Triple-shaft Ring-plate Magnet Gear,TRMG)的气隙磁场数理模型,根据磁场叠加原理建立了内、外永磁圈间气隙磁场及其相应的电磁转矩模型;由于所有计算均基于TRMG的平面磁场建立,因此,所建模型与二维有限元结果间具有较高的准确度(误差≤5%);其计算速度远快于三维有限元法,且与二维及三维有限元分析具有较好的吻合度与趋势性,验证了所建模型的准确性,可适用于三轴以上的多轴环板式永磁齿轮的磁场分析与结构动力学计算。

考虑啮合误差的复式行星传动系统均载特性研究

为研究复式行星传动系统的均载特性及影响均载特性的因素,通过势能法建立齿轮刚度求解模型,求解了传动系统的时变啮合刚度;计入阻尼、时变啮合刚度、啮合误差等因素影响,采用集中质量法建立了系统的平移-扭转耦合动力学模型,利用Newmark-β积分法求解了系统的动态响应,以均载系数量化均载性能,分析了转速、负载及单构件和多构件偏心误差对系统均载性能的影响。分析结果表明,提高转速会降低系统的均载性能,增加负载会提高系统的均载性能;偏心误差的增大会使系统的均载性能降低,当偏心误差同时作用在内啮合的构件上时会使均载系数下降3.1%;当同类行星轮的偏心误差以旋转中心作用时,会有效降低偏心误差对系统均载性能的影响。