随机事元及其在解决矛盾问题中的应用

通过建立随机事件的可拓模型,给出了随机事元、随机事元的概率、随机事元集和可拓事件集的概念。在对随机事元可拓性研究的基础上给出了随机事元的拓展概率的概念。利用随机事元的多特征性,讨论了当随机事元的某一个或若干个特征及其量值改变时,由可拓变换的传导性,将在随机事元的各要素之间产生传导效应,从而导致随机事元概率的改变,进而为涉及随机事件发生的概率的矛盾问题的解决提供了有效途径。最后举例说明了利用概率的改变处理矛盾问题的方法。     

装配偏置误差对正交面齿轮传动接触特性的影响

 分析装配误差对正交面齿轮传动的影响是开展面齿轮传动工程应用的重要基础理论之一。为了分析装配偏置误差对正交面齿轮传动接触特性的影响,建立了考虑装配偏置误差影响的点接触正交面齿轮传动坐标系;推导了正交面齿轮齿廓和过渡曲面方程以及考虑装配偏置误差影响的接触点方程,分析了装配偏置误差对传动中正交面齿轮上接触点位置的影响;根据曲面上任意点处主方向和主曲率的求解方法,分析了装配偏置误差对接触点处主曲率的影响;利用布希涅斯克问题的解法,推导了传动中正交面齿轮上接触点处接触特性方程,分析了装配偏置误差对正交面齿轮上接触点处接触特性的影响。     

基于弹流润滑理论的深沟球轴承动态虚拟仿真

润滑油膜对轴承的胶合、擦伤和接触疲劳有重要影响.而以往对轴承的仿真均忽略了润滑油膜的存在,误差较大.首先在刚性套圈假设的前提下,基于Hertz接触理论,运用拟动力学法建立球轴承在径向、轴向载荷作用下的力学模型,以Newton-Raphson法为主要计算工具对模型进行求解,获得轴承在联合载荷作用下的接触载荷和变形,并求取了各个滚珠与内、外圈之间的接触刚度.基于弹性流体动力润滑(EHL)理论考虑润滑油膜对轴承动态特性的影响,求取滚动轴承油膜刚度.提出等效综合刚度的概念并求其值,在此基础上运用ADAMS软件对轴承进行准确的动力学仿真.      

基于逆最优问题的最优制导律及特性分析

在典型的能量最优制导律基础上,将制导律的2个特征根从有限的点/线区域扩展到所有可能的正实根区域,进而提出制导律中的逆最优问题。详细讨论了逆最优问题中性能指标加权矩阵的构造过程,给出了加权矩阵和Riccati矩阵的计算公式;将控制权矩阵选为time-to-go的负n次幂的形式,对加权矩阵的求解进行了举例说明。对8组不同的特征根研究结果表明,尽管每一对可能的特征根取值都能找到最优解释,但这并不能保证与其对应的制导律都能达到与典型能量最优制导律类似的制导性能,特征根取值越靠近典型能量最优制导律,则相对应的制导特性也越接近。     

Design and analysis of an extended mission of CE-2: From lunar orbit to Sun–Earth L2 region

Chang’E-2 (CE-2) has firstly successfully achieved the exploring mission from lunar orbit to Sun–Earth L2 region. In this paper, we discuss the design problem of transfer trajectory and at the same time analyze the visible segment of Tracking, Telemetry & Control (TT&C) system for this mission. Firstly, the four-body problem of Sun–Earth–Moon and Spacecraft can be decoupled in two different three-body problems (Sun–Earth + Moon Restricted Three-Body Problems (RTBPs) and Earth–Moon ephemeris model). Then, the transfer trajectory segments in different model are computed, respectively, and patched by Poincaré sections. The full-flight trajectory including transfer trajectory from lunar orbit to Sun–Earth L2 region and target Lissajous orbit is obtained by the differential correction method. Finally, the visibility of TT&C system at the key time is analyzed. Actual execution of CE-2 extended mission shows that the trajectory design of CE-2 mission is feasible.     

Broad-search algorithms for the spacecraft trajectory design of Callisto–Ganymede–Io triple flyby sequences from 2024 to 2040, Part II: Lambert pathfinding and trajectory solutions

Triple-satellite-aided capture employs gravity-assist flybys of three of the Galilean moons of Jupiter in order to decrease the amount of ΔV$\mathrm{\Delta }V$ required to capture a spacecraft into Jupiter orbit. Similarly, triple flybys can be used within a Jupiter satellite tour to rapidly modify the orbital parameters of a Jovicentric orbit, or to increase the number of science flybys. In order to provide a nearly comprehensive search of the solution space of Callisto–Ganymede–Io triple flybys from 2024 to 2040, a third-order, Chebyshev's method variant of the p-iteration solution to Lambert's problem is paired with a second-order, Newton–Raphson method, time of flight iteration solution to the _V∞$V_{\infty }$-matching problem. The iterative solutions of these problems provide the orbital parameters of the Callisto–Ganymede transfer, the Ganymede flyby, and the Ganymede–Io transfer, but the characteristics of the Callisto and Io flybys are unconstrained, so they are permitted to vary in order to produce an even larger number of trajectory solutions. The vast amount of solution data is searched to find the best triple-satellite-aided capture window between 2024 and 2040.     

On Lambert’s problem and the elliptic time of flight equation: A simple semi-analytical inversion method

In the two-body model, time of flight between two positions can be expressed as a single-variable function and a variety of formulations exist. Lambert’s problem can be solved by inverting such a function. In this article, a method which inverts Lagrange’s flight time equation and supports the problematic 180°$180°$ transfer is proposed. This method relies on a Householder algorithm of variable order. However, unlike other iterative methods, it is semi-analytical in the sense that flight time functions are derived analytically to second order vs. first order finite differences. The author investigated the profile of Lagrange’s elliptic flight time equation and its derivatives with a special focus on their significance to the behaviour of the proposed method and the stated goal of guaranteed convergence. Possible numerical deficiencies were identified and dealt with. As a test, 28 scenarios of variable difficulty were designed to cover a wide variety of geometries. The context of this research being the orbit determination of artificial satellites and debris, the scenarios are representative of typical such objects in Low-Earth, Geostationary and Geostationary Transfer Orbits. An analysis of the computational impact of the quality of the initial guess vs. that of the order of the method was also done, providing clues for further research and optimisations (e.g. asteroids, long period comets, multi-revolution cases). The results indicate fast to very fast convergence in all test cases, they validate the numerical safeguards and also give a quantitative assessment of the importance of the initial guess.     

A robust semi-analytic method to solve the minimum ΔV two-impulse rendezvous problem

A novel semi-analytic approach is developed to determine the minimum $\mathrm{\Delta }V$ for a two-impulse rendezvous and validated both empirically and analytically. A previously published closed-form $\mathrm{\Delta }V$ estimate and the Lambert minimum energy transfer is used to establish upper and lower bounds of the minimum $\mathrm{\Delta }V$ transfer between two orbits. These bounds, in conjunction with the bisection method, operate on a nonlinear radical cost function to guarantee linear convergence. This approach has several real world applications including a low earth orbit (LEO) to highly elliptical orbit (HEO), and a HEO to retrograde geosynchronous orbit transfer. The minimum $\mathrm{\Delta }V$ estimates are better than those reported in the existing literature, while run times improved as much as two orders of magnitude over a fixed time Lambert solver. All singularity cases were addressed such that any orbital geometry, including Hohmann and radial elliptic transfers, converged to the global minimum $\mathrm{\Delta }V$. This approach will work for both coplanar and non-coplanar 3D geometries for any orbit type.     

周向弹簧力分布对圆周密封装置密封性能的影响

为了研究周向弹簧力分布形式对密封装置密封性能的影响,针对周向弹簧建立力学模型,分析周向弹簧力不均匀分布形式产生的原因,并对其不均匀分布的临界范围进行预测分析,建立泄漏预测模型对密封结构的密封性能进行研究。首先对密封装置主要结构进行受力分析,研究周向弹簧不均匀加载对密封结构变形的影响,再结合ANSYS软件对圆周密封装置主要部件进行结构-热耦合仿真计算,进而通过仿真分析验证理论分析的合理性。仿真结果表明：不均匀周向弹簧力产生的附加力矩使得密封环翘曲变形,主密封面径向接触间隙最大位置出现在密封环的接头区域;相比弹簧力分布均匀条件,当弹簧力分布形式的不均匀程度处于临界范围内时,接触间隙增加了24.52%,气体泄漏量增加了7.99%;当弹簧力分布形式的不均匀程度处于临界范围外时,接触间隙值呈倍数增加,气体泄漏量增加一个数量级。综上,周向弹簧力不均匀分布导致主密封面接触间隙值增加、密封结构气体泄漏量增加、密封装置密封性能下降。周向弹簧力的不均匀分布对密封装置的密封性能有较为严重的影响,在实际工程应用中应尽可能保证周向弹簧的不均匀分布程度处于临界范围内,避免由于弹簧卡滞使得密封结构密封性能下降。     

变转速旋翼直升机单发失效低速回避区分析

利用最优控制方法研究变转速旋翼直升机在遭遇单发失效时,旋翼转速对自转着陆低速回避区的影响。首先,以UH-60A直升机为样机,建立三维刚体飞行动力学模型,并分析低速范围内旋翼转速对直升机需用功率的影响。然后,在模型中加入单发失效后自转着陆阶段发动机输出功率以及旋翼转速变化方程,并利用直接多重打靶法将直升机单发失效后的自转着陆过程转换为非线性最优控制问题进行数值求解。最后,基于最小化回避区面积的思想,得到并分析直升机在不同旋翼转速下单发失效后的自转着陆低速回避区,以及回避区高悬停点、拐点和低悬停点对应的最优着陆轨迹和操纵过程。结果表明：随着旋翼转速的降低,直升机单发失效后的低速回避区首先会逐渐缩小,然后迅速增大。最小回避区对应的旋翼转速略高于最小需用功率对应的旋翼转速。适当降低旋翼转速不仅能有效降低直升机的需用功率,还有利于提高直升机单发失效后的自转着陆性能。