条件方程

The key to the formula derivation is solving an equation of conjugate-contact condition.

明确了盘形刀具齿形计算的关键是共轭接触条件方程的求解，从而进一步论述了圆弧齿轮盘形刀具共轭条件方程求解的新方法。

In this paper, we invert the condition equation into a complete nonlinear partial differential equation, and study some properties of the solution of this equation from a theoretical point.

本文把其条件方程转化为一个非线性偏微分方程，从理论角度探讨了一下此方程的解的一些性质。

Keywords: ADT, Algebraic specifications, Conditional equation, Correctness

如果能获得简明的条件描述，那么就容易写出条件方程。

The last time when the valves open and close the boundary condition equation and heating systems in the other boundary condition equations, one-dimensional unsteady flow equations of motion and the joint solution of continuity equation, we can find the non-dimensional opening when the valve changes, heating system to calculate changes in surface pressure.

上回阀启闭时的边界条件方程与供热系统中的其它边界条件方程、一维不定常流动的运动方程和连续方程联解，就可以求出当止回阀无量纲开度变化时，供热系统各计算截面压力的变化情况。

However the lower order traditional absorbing boundary conditions are only effective for the incident waves with smaller incident angles. A fourth-order absorbing boundary condition equation based on Higden's ABC is deduced in this thesis, and a new algorithm is presented to automatically select the Higden's parameters.

本文基于Higdon提出的吸收边界条件方法，推导出四阶吸收边界条件方程，并提出了一种新的吸收边界条件角度参数的自动选择方法，使该吸收边界条件能够吸收全角度(0～90度)入射波。

A fourth-order absorbing boundary condition equation based on Higdon's ABC is deduced in this paper, and a new optimal algorithm is presented to automatically select the parameters of Higdon's ABC.

本文基于Higdon提出的渐进吸收边界条件方法，推导出四阶吸收边界条件方程，并提出了一种新的吸收边界条件角度参数的优化选择方法。

In this topic, the dynamic analysis methods for piezoelectric vibrator are studied systematically based on the theoretical model, FEM numerical experimentation and FEM governing equation for given compound-mode vibrator, and some valuable conclusions are obtained. The main work accomplished is summarized as follows: 1.Elaborate the main modeling methods for piezoelectric vibrator and the significance and necessity to study the dynamic characteristics of piezoelectric vibrator which emphasize the urgency of this paper. 2.Take the bending deformation induced by piezoelectric ceramic as example, the energy transfer mechanism of electric energy to mechanical energy are analyzed; the motion and force transfer mechanism are analyzed for the longitudinal-bending vibrator. 3.Based on mode assumption and Hamilton principle, the coupling model of piezoelectric vibrator of linear USM is built; moreover, the equivalent circuit model is obtained and a coupling equation represents the relation between electric parameters and mechanical parameters is derived which provides foundation to match the vibrator and driving circuit. 4.Combine the constitutive equation of piezoelectric ceramic with elastic-dynamical equation, geometric equation in force field and the Maxwell equation in electric field and the corresponding boundary condition equation, the FEM control equation for piezoelectric vibrator of USM to solve dynamic electro-mechanical coupling field is established by employing the principle of virtual displacement. The equation lays the foundation to study the non-linear constitutive equation of piezoelectric ceramic driven by high-power. 5.Define the dynamic indexes of characteristic of vibrator and carry out variable parameters simulation by calculating the model parameters and the electric characteristics of vibrator are simulated according to the equivalent circuit model. By numerical experimentation, the working mode of vibration of vibrator and the shock excitation results of the working frequency band which provides the mode frequency to realize bimodal are analyzed. Detailed calculation of the electro-mechanical coupling field parameters is made by programming the FEM control equation.

本课题从理论模型、有限元数值试验、有限元控制模型等方面以复合振动模式振子为例对超声电机压电振子的动力学特性及其分析方法进行了全面系统地研究，得出了许多有价值的结论，主要概括如下： 1、阐述了目前针对超声电机压电振子的主要建模方法，对压电振子动态特性的研究意义和必要性进行了论述，突出了本文研究内容的迫切性； 2、以压电陶瓷诱发弹性体发生弯曲变形为例，分析了压电陶瓷通过诱发应变来实现机电能量转换的机理；对基于纵弯模式的压电振子的运动及动力传递机理进行了分析； 3、基于模态假定，利用分析动力学的Hamilton原理，建立了面向直线超声电机压电振子的机电耦合动力学模型，并据此建立了压电振子的等效电路模型，导出了电参量与动力学特性参量的耦合方程，为压电振子与驱动电路的匹配提供了依据； 4、从压电陶瓷的本构方程出发，综合力场的弹性动力学方程、几何方程、电场的麦克斯韦方程以及相应的边界条件方程，采用虚位移原理，建立了压电振子动态问题机电耦合场求解的有限元控制方程，为研究其大功率驱动下的非线性本构模型奠定了基础； 5、界定压电振子的动力学特性指标，对压电振子的机电耦合动力学模型参数进行计算及变参数仿真；依据等效电路模型，对压电振子的电学特性进行了仿真分析；通过有限元数值实验，对压电振子工作模态附近的模态振型及工作频率附近的频段进行了激振效果分析，找出了实现模态简并的激振频率；利用有限元控制方程，通过编程计算，对压电振子的力电耦合场参数进行了详细计算，得出了一些有价值的结论。

So, some research on plane steering six-bar linkage has been done in this project as follows: based on the condition equation of correct steering and the equations of two closed loop of steering mechanism, a set of three equations in three variables can be obtained after a variable is expurgated with the elimination method.

本课题对平面转向六杆机构进行了如下的研究：根据转向条件方程，与转向机构的两个闭环方程，采用消元法消去一个未知变量，得出了转向六杆机构关于输入角的目标函数方程；利用边界条件，得出一个包含三个变量、三个方程的方程组

The invention comprises a free-form surface prism with three optical surfaces, and a micro-image display; the free-form surface prism is made of plastic glass materials with the refractive index greater than 1; the three free-form optical surfaces are concave surfaces, which meet one of the three surface-type equations, and the location relationship of each surface meets three condition equations; the incident angle formed between the widest-field upper edge rays emitted by an LCD and the second free-form surface meets the total reflection conditions; and an image source element is an LCD of 0.61 or 0.59 inches.

本发明包含一个具有三个光学表面的自由曲面棱镜和一个微型图像显示器，自由曲面棱镜采用折射率大于1的塑料玻璃材料，自由曲面棱镜的三个自由曲面光学表面均为凹形面，它们应满足三个面型方程之一，并且各表面的位置关系应满足三个条件方程，由LCD发出的最大视场上边缘光线在第二自由曲面上的入射角应满足全反射条件，像源元件为0.61或0.59英寸的LCD。

Based on the instantaneous motion of the moving platforms, the uncertainty configuration conditions and simplified uncertainty configuration equations are obtained for the widely studied parallel manipulators, such as planar 3-DOF parallel manipulator, spherical 3-DOF parallel manipulator, 6-SPS triangular platform parallel manipulator, three-branch 6-DOF parallel manipulator, twotriangular-platform parallel manipulator, DELTA parallel manipulator, 5-DOF parallel manipulator, two-tetragonal-platform parallel manipulator, pentagonal platform parallel manipulator and Stewart platform parallel manipulator.

采用这一方法，根据国内外常用的并联机器人机构的形式，建立了平面3自由度并联机器人、球面3自由度并联机器人、三角平台并联机器人、三支链6自由度并联机器人、双三角平台并联机器人、DELTA并联机器人、5自由度并联机器人、双四角平台并联机器人、五角平台并联机器人和Stewart平台并联机器人的奇异位形条件方程，除了Stewart平台并联机器人外，这些条件方程均为低于6阶的行列式，机器人结构类型不同，其简化程度各不相同。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。