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.

Effect of Ball-Milling Time on the Performance of Ni-Al2O3 Catalyst for 1,4-Butynediol Hydrogenation to Produce 1,4-Butenediol

The Ni-Al2O3 catalyst was prepared by the mechanochemical method in combination with a planetary ballmilling machine.Effect of milling time on the crystal structure,the reduction characteristics and the catalytic performance of Ni-Al2O3 catalyst for hydrogenation of 1,4-butynediol to produce 1,4-butenediol were investigated.The catalysts were characterized by PSD,EDX,XRD,H2-TPR,BET,TEM,and NH3-TPD methods.Results showed that the MCt2.5 catalyst treated at a ball milling time of 2.5 h could form a smallest particle size of 191.0 nm.The evaluation experiments revealed that the activity of the prepared catalyst increased at first and then reached a constant value with the extension of ballmilling time.The BYD conversion,BED selectivity and yield on the MCt2.5 catalyst reached 35.63%,33.48%and 32.46%,respectively,which were higher than those obtained by other samples.The excellent performance of MCt2.5 sample is mainly related to the following three reasons from characterization results.Firstly,it has a smallest particle size of 191.0 nm;and then,the surface acidity(in terms of strong acids)of the catalyst was weaker than other catalysts;and eventually,the loading amount(23.84%)of the active component Ni exceeded the theoretical value(20%).

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。

复杂行星表面着陆避障增广曲率制导方法

针对复杂行星表面安全着陆问题,提出避障增广曲率制导方法。在基本曲率制导律的基础上引入障碍规避增广项。该方法利用着陆器着陆空间区域划分的思想,在障碍附近易发生碰撞区域建立膨胀预警区,基于膨胀预警区推导连续解析的障碍规避制导律,在满足几何凸轨迹状态约束的同时,考虑着陆器与障碍的相对位置关系,能够快速引导着陆器远离障碍,提高着陆器着陆过程中的安全性。仿真结果表明,该方法能够有效规避复杂行星表面的地形障碍,实现在行星表面定点软着陆,具有良好的灵活性和可靠性。

地球与行星内源磁场建模研究进展

太阳系绝大多数行星都拥有随星体自转而共转的内源磁场.随着人类不断地进行深空探测,人们已经对所有已知具有内源磁场的太阳系星体建立起了其对应的行星磁场模型.行星磁场建模是深入研究行星内部动力学过程、探究行星演化历史、理解行星磁场与太阳风相互作用、认识行星磁场对高能带电粒子的屏蔽效应等多种研究方向的重要基础.同时,行星磁场建模也是一项多学科交叉的研究工作,其涉及到行星磁场建模理论、内外源磁场场源分离、参数反演方法与方程优化等多方面的研究.本文综述了地球与太阳系其他行星,包括月球以及木卫三两颗卫星在磁场建模方向的研究进展,描述了行星内源磁场的特征,整理了太阳系行星最准确的全球磁场模型.本文首先从行星磁场的数学建模方法开始,梳理了自高斯时代以来磁场建模技术的发展历史,介绍了行星磁场建模研究的热点方法.文章最后展望了未来行星磁场建模研究的发展趋势,以及我国未来的深空探测计划对行星磁场建模研究的可能贡献.

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。

混合动力电动汽车构型优化设计方法研究

针对行星齿轮汽车结构特性与动态特性的关系,提出了混合动力汽车动力系统构型的理论设计方法.首先,将构型中所有连接分为3类,采用矩阵表示法表示这些连接,以反映系统动力学和构型的物理结构.接着,在此基础上提出了构型自动设计的矩阵表示方法,通过矩阵运算得到转速方程进而得到汽车双行星齿轮结构的各种构型.最后,通过仿真验证了该方法的有效性.结果表明,在矩阵表示方法的支持下,可以通过计算机自动完成最优构型的选择,避免了人工计算和比较,节省了大量的精力和时间.

The Metallicity Dimension of the Super Earth-cold Jupiter Correlation

The correlation between close-in super Earths and distant cold Jupiters in planetary systems has important implications for their formation and evolution.Contrary to some earlier findings,a recent study conducted by Bonomo et al.suggests that the occurrence of cold Jupiter companions is not excessive in super-Earth systems.Here we show that this discrepancy can be seen as a Simpson’s paradox and is resolved once the metallicity dependence of the super-Earth-cold Jupiter relation is taken into account.A common feature is noticed that almost all the cold Jupiter detections with inner super-Earth companions are found around metal-rich stars.Focusing on the Sun-like hosts with super-solar metallicities,we show that the frequency of cold Jupiters conditioned on the presence of inner super Earths is 39_(-11)^(+12)%,whereas the frequency of cold Jupiters in the same metallicity range is no more than 20%.Therefore,the occurrences of close-in super Earths and distant cold Jupiters appear correlated around metal-rich hosts.The relation between the two types of planets remains unclear for stars with metal-poor hosts due to the limited sample size and the much lower occurrence rate of cold Jupiters,but a correlation between the two cannot be ruled out.

核电循环泵行星齿轮热弹流润滑研究

核电齿轮箱的良好润滑性能是核电循环泵可靠运行的重要保障,充分考虑齿面形貌和齿廓修形等因素对内/外啮合齿轮副的影响是准确评估其润滑特性的前提。建立典型工况下核电循环泵行星传动系统斜齿轮热弹流润滑模型,首先将斜齿轮副的啮合状态几何等效为圆锥滚子的接触问题,然后考虑斜齿轮接触变形和齿廓偏差,计算得到内/外啮合齿轮副接触区域不同位置的油膜厚度、承载压力、摩擦应力和闪温等参数。考虑齿面磨合作用,采用移动平均滤波方法对未经磨合的初始形貌进行光滑处理,分析了齿面形貌对润滑行为的影响,最后采取齿廓修形改善润滑特性。结果表明:粗糙度和齿廓修形均会对润滑特性产生明显的影响,齿面粗糙形貌会造成油膜厚度减小,进而影响其润滑特性,弱化润滑油膜的承载能力;通过齿廓修形可以改善齿轮啮合边界处的几何过渡,降低该区域的应力集中和表面温度,从而明显改善啮合线终端的润滑状态。

行星传动系统均载与动载系数试验测量改进设计

试验测量行星传动系统均载与动载系数的精准度是评价系统动态性能的基础。针对现有行星传动系统均载与动载系数测量方法存在灵敏度与精度欠佳、系数测试算法缺失、测试应力点存误等问题,本文提出了一种方便、实用且具有高精度的行星传动系统均载与动载系数测试方法,定义了系统系数的测试算法与概念,明确了精确应力测试位置点及不同位置间差异性,采用应变片电桥传感器串并联设计,实现了拉压应力叠加、温度补偿以及繁琐标定免除等优点,为精准测取行星传动系统均载与动载性能提供了重要的理论基础和技术手段。

基于改进迁移学习的行星齿轮箱故障自动诊断

传统机器学习故障诊断方法依赖专业经验选取统计特征,导致诊断结果误差较大。为此,提出了基于改进迁移学习的行星齿轮箱故障自动诊断。采集行星齿轮箱的振动信号,对振动信号进行去噪处理,利用深度学习改进迁移学习构建故障诊断模型,对采集信号进行分类识别,实现了行星齿轮箱故障自动诊断。结果表明,该设计方法下不同类型的行星齿轮箱故障诊断精度为96.09%,证实了该方法的性能良好。

人字齿行星齿轮系统激励参数二维域界特性

为探究人字齿行星齿轮系统激励参数二维域界特性,课题组构建了系统的平移-扭转动力学模型,运用Runge-Kutta法对消除刚体位移和量纲一化的系统微分方程组进行数值求解,基于离散空间域胞映射法绘制了啮合阻尼比与太阳轮输入转速和太阳轮输入功率构成的二维域界图,并结合位移分岔图、FFT频谱图、相图和Poincaré映射对系统激励参数二维域界特性进行分析。结果表明:在满足系统工况条件下,适当增大啮合阻尼比可使系统由混沌运动转变为周期运动;啮合阻尼比较小时,系统对太阳轮输入转速变化敏感,提高太阳轮输入转速可使系统进入稳定1周期运动,减轻系统振动响应;太阳轮输入功率较小时,系统处于大范围混沌运动区域,通过增加太阳轮输入功率,系统更趋向于稳定周期运动,提高系统运行稳定性。研究结果可为人字齿行星齿轮系统选择稳定运行的激励参数范围提供参考。

基于改进天牛须算法的永磁电机过载转矩分析

定子铁心饱和以及电枢反应等因素极大地影响永磁无刷直流电机(BLDC)的过载能力,无法满足足式机器人运动时的转矩需求。因此,设计一台具有高过载能力的减速电机。从电机关键结构参数出发,分析极槽配合、齿槽宽度以及磁钢厚度对BLDC过载转矩的影响;进一步利用有限元及响应面法构建过载转矩和转矩波动的优化模型,并采用改进天牛须算法进行多目标优化设计;对比优化前、后电机的电磁性能和过载输出转矩,并分析行星减速器结构对电机影响。最后,根据电磁设计进行样机研制,并进行转矩转速试验。结果表明:优化后平均过载转矩从1.99 N·m增加到2.05 N·m,转矩脉动从6.78%降低到6.34%,减小了0.44%,电机过载输出性能更好,且样机实验与仿真结果相接近,验证了所提方法的合理性。

Finite Element Analysis of Internal Gear in High-Speed Planetary Gear Units

The stress and the elastic deflection of internal ring gear in high-speed spur planetary gear units are investigated. A rim thickness parameter is defined as the flexibility of internal ring gear. Six evenly spaced linear springs are used to describe the fitting status between internal ring gear and the gearcase. The finite element model of the whole internal ring gear is established by means of Pro/E and ANSYS. The loads on meshing teeth of internal ring gear are applied according to the contact ratio and the load-sharing coefficient. With the finite element analysis (FEA), the influences of flexibility and fitting status on the stress and elastic deflection of internal ring gear are predicted. The simulation reveals that the principal stress and deflection increase with the decrease of rim thickness of internal ring gear. Moreover, larger spring stiffness helps to reduce the stress and deflection of internal ring gear. Therefore, the flexibility of internal ring gear must be considered during the design of high-speed planetary gear transmissions.

Translational - torsional coupled model based nonlinear dynamic analysis of an NGW planetary gear train

This paper aims to investigate the nonlinear dynamic behaviors of an NGW planetary gear train with multi-clearances and manufacturing/assembling errors. For this purpose, an analytical translational- torsional coupled dynamic model is developed considering the effects of time-varying stiffness, gear backlashes and component errors. Based on the proposed model, the nonlinear differential equations of motion are derived and solved iteratively by the Runge-Kutta method. An NGW planetary gear reducer with three planets is taken as an example to analyze the effects of nonlinear factors. The results indicate that the backlashes induce complicated nonlinear dynamic behaviors in the gear train. With the increment of the backlashes, the gear system has experienced periodic responses, quasi-periodic response and chaos responses in sequence. When the planetary gear system is in a chaotic motion state, the vibration amplitude increases sharply, causing severe vibration and noise. The present study provides a fundamental basis for design and parameter optimization of NGW planetary gear trains.

Design and Dynamic Analysis of the Recirculating Planetary Roller Screw Mechanism

The recirculating planetary roller screw mechanism(RPRSM)is a transmission mechanism that engages the screw and nut threaded by multiple grooved rollers.In this paper,frstly,the design method of RPRSM nut threadless area is proposed,and the equations related to the structural parameters of nut threadless area are derived.On this basis,the cross-section design method of roller,screw and nut is constructed according to the actual situation of engagements between the screw/nut and the roller.By adjusting the gap between the two beveled edges and that between the arc and the beveled edge,the accuracy of the thread engagements between the screw/nut and the roller can be improved.Secondly,to ensure the engagements of the screw/nut and the roller,the distance equation from the center surface of the diferent rollers to the end surface of cam ring is given.Thirdly,combined with the working principle and structural composition of RPRSM,the component model is established according to its relevant structural parameters,and the virtual assembly is completed.Finally,the 3D model is imported into the ADAMS simulation software for multi-rigid body dynamics.The dynamic characteristic is analyzed,and the simulated values are compared with the theoretical values.The results show that the contact forces between the screw/nut and the roller are sinusoidal,mainly due to the existence of a small gap between the roller and the carrier.The maximum collision forces between the roller and cam ring are independent from load magnitude.Normally,the collision force between the roller and the carrier increases as the load increases.When RPRSM is in the transmission process,the roller angular speed in nut threadless area begins to appear abruptly,and the position of the maximum change is at the contact between the roller and the convex platform of cam ring.The design of the nut threadless area and the proposed virtual assembly method can provide a theoretical guidance for RPRSM research,as well as a reference for overall performance optimization.

Dust growth in protoplanetary disks-a comprehensive experimental / theoretical approach

More than a decade of dedicated experimental work on the collisional physics of protoplanetary dust has brought us to a point at which the growth of dust aggregates can - for the first time - be self-consistently and reliably modeled. In this article, the emergent collision model for protoplanetery dust aggregates, as well as the numerical model for the evolution of dust aggregates in protoplanetary disks, is reviewed. It turns out that, after a brief period of rapid collisional growth of fluffy dust aggregates to sizes of a few centimeters, the protoplanetary dust particles are subject to bouncing collisions, in which their porosity is considerably decreased. The model results also show that low-velocity fragmentation can reduce the final mass of the dust aggregates but that it does not trigger a new growth mode as discussed previously. According to the current stage of our model, the direct formation of kilometer-sized planetesimals by collisional sticking seems unlikely, implying that collective effects, such as the streaming instability and the gravitational instability in dust-enhanced regions of the protoplanetary disk, are the best candidates for the processes leading to planetesimals.

Simulation of a Laboratory Scale Ball Mill via Discrete Element Method Modelling

Discrete Element Method (DEM) is a powerful tool for simulating different types of mills. It also used for computing different types of particles such as rocks, grains, and molecules. DEM has been widely used in the field of rock mechanics. In the present work, DEM approach is applied to model the milling media (powder particles and balls) inside a planetary ball mill and to estimate the distribution of particles of a dry powder during milling. In fact, the efficiency of the DEM strongly depends on the input parameters. The DEM simulation results indicated that DEM is a promising tool for the simulation of the dynamic particles motion and interactions within planetary ball mill. These results could be utilized to further develop the synthesis performance, anticipate the reaction, and reduce the wear in the dry milling reactions.

The dynamical architecture and habitable zones of the quintuplet planetary system 55 Cancri

We perform numerical simulations to study the secular orbital evolution and dynamical structure of the quintuplet planetary system 55 Cancri with the self-consistent orbital solutions by Fischer and coworkers. In the simulations, we show that this system can be stable for at least 108 yr. In addition, we extensively investigate the planetary configuration of four outer companions with one terrestrial planet in the wide region of 0.790AU 〈 a 〈 5.900AU to examine the existence of potential asteroid structure and Habitable Zones （HZs）. We show that there are unstable regions for orbits about 4：1, 3：1 and 5：2 mean motion resonances （MMRs） of the outermost planet in the system, and several stable orbits can remain at 3：2 and 1：1 MMRs, which resembles the asteroid belt in the solar system. From a dynamical viewpoint, proper HZ candidates for the existence of more potential terrestrial planets reside in the wide area between 1.0 AU and 2.3 AU with relatively low eccentricities.

An investigation of planetary nebulae accompanying PG 1159 central stars,based on Gaia DR2 measurements

This article discusses the physical and kinematical characteristics of planetary nebulae accompanying PG 1159 central stars.The study is based on the parallax and proper motion measurements recently offered by the Gaia space mission.Two approaches were used to investigate the kinematical properties of the sample.The results revealed that most of the studied nebulae arise from progenitor stars in the mass range 0.9-1.75 M⊙.Furthermore,they tend to live within the Galactic thick disk and move with an average peculiar velocity of 61.7±19.2 km s^(-1) at a mean vertical height of 469±79 pc.The locations of the PG 1159 stars on the H-R diagram indicate that they have an average final stellar mass and evolutionary age of 0.58±0.08 M⊙and 25.5±5.3×103 yr,respectively.We found a good agreement between the mean evolutionary age of the PG 1159 stars and the mean dynamical age of their companion planetary nebulae(28.0±6.4×103 yr).