APPLICATION OF VECTOR ROTATING METHOD IN GRINDING INVOLUTE WORM WITH PLANE ENVELOPE METHOD

The grinding principle of plane envelope is demonstrated with the medium rack theory.The basic and general fixing patterns of grinding involute worms with plane envelope method are uniformed.The vector rotating method is originally applied to calculate precisely the grinding wheel fixing angles γ h and γ n under the general fixing pattern.It is proved with experiments that the method is feasible.

AN IMPROVED ROTATION VECTOR ATTITUDE ALGORITHM FOR LASER STRAP-DOWN INERTIAL NAVIGATION SYSTEM

The laser gyro is most su it able for building the strap down inertial navigation system (SINS), and its acc uracy of attitude algorithm can enormously affect that of the laser SINS. This p aper develops three improved algorithmal expressions for strap down attitude ut ilizing the angular increment output by the laser gyro from the last two and cur rent updating periods according to the number of gyro samples, and analyses the algorithm error in the classical coning motion. Compared with the conventional algorithms, simulational results show that this improved algorithm has higher precision. A new way to improve the rotation vector algorithms is provided.

Research on in-light alignment error model based on quaternion and rotation vector

Euler angle error model, rotation vector error model （RVE） and quaternion error model （QE） were qualitatively and quantitatively compared and an in-flight alignment filter algorithm was designed. This algorithm used extended Kalman filter （EKF） based on RVE and QE separately avoi- ding the accuracy problem of the Euler angle model and used Rauch-Tung-Striebel（RTS） smoothing method to refine the accuracy recuperating the coning error for simplified RVE. Simulation results show that RVE and QE are more adapt for nonlinear filter estimation than the Euler angle model. The filter algorithm designed has more advantages in convergence speed, accuracy and stability comparing with the algorithm based on the three models separately.

考虑摆线轮磨损的RV减速器传动精度可靠性分析与参数优化

针对RV (rotate vector)减速器在工作过程中存在的零件磨损导致传动精度下降的问题,建立了考虑摆线轮磨损的RV减速器传动精度动态可靠性模型,进行传动精度可靠性分析,并对关键零件的公差以及摆线轮的修形参数进行优化设计。以某重载RV减速器为研究对象,利用Archard磨损公式对摆线轮的磨损深度进行计算,分析轮齿齿廓磨损的分布情况,并基于数值仿真数据利用高斯过程回归模型预测磨损量;建立了含动态磨损的RV减速器传动精度可靠性模型,用蒙特卡洛法求解其动态可靠度;建立了以传动精度动态可靠度为约束条件,以加工成本最低、额定寿命周期内最大磨损量最小为优化目标的优化模型,采用多目标遗传算法求得最优解。结果表明;优化后摆线轮的磨损量略微增大,而减速器的加工成本明显降低;优化后减速器传动精度可靠度得到明显提高,在额定寿命6 000 h内的可靠度满足预期要求。研究结果可以为高精度RV减速器的设计提供参考。

OPTIMIZED STRAPDOWN CONING CORRECTION ALGORITHM

Traditional coning algorithms are based on the first-order coning correction reference model.Usually they reduce the algorithm error of coning axis(z)by increasing the sample numbers in one iteration interval.But the increase of sample numbers requires the faster output rates of sensors.Therefore,the algorithms are often limited in practical use.Moreover,the noncommutivity error of rotation usually exists on all three axes and the increase of sample numbers has little positive effect on reducing the algorithm errors of orthogonal axes(x,y).Considering the errors of orthogonal axes cannot be neglected in the high-precision applications,a coning algorithm with an additional second-order coning correction term is developed to further improve the performance of coning algorithm.Compared with the traditional algorithms,the new second-order coning algorithm can effectively reduce the algorithm error without increasing the sample numbers.Theoretical analyses validate that in a coning environment with low frequency,the new algorithm has the better performance than the traditional time-series and frequency-series coning algorithms,while in a maneuver environment the new algorithm has the same order accuracy as the traditional time-series and frequency-series algorithms.Finally,the practical feasibility of the new coning algorithm is demonstrated by digital simulations and practical turntable tests.

Non-Exchangeable Error Compensation for Strapdown Inertial Navigation System in High Dynamic Environment

Strapdown non-exchangeable error compensation technology in high dynamic environment is one of the key technologies of strapdown inertial navigation system.Mathematical platform is used in strapdown inertial navigation system instead of physical platform in traditional platform inertial navigation system,which improves reliability and reduces cost and volume of system.The maximum error source of attitude matrix solution is the non-exchangeable error of rotation due to the non-exchangeable of finite rotation of rigid bodies.The rotation non-exchangeable error reaches the maximum in coning motion,although it can be reduced by shortening the correction period and increasing the real-time calculation.The equivalent rotation vector method is used to modify the attitude to reduce the coning error in this paper.Simulation experiments show that the equivalent rotation vector method can effectively suppress the non-exchangeable error and improve the accuracy of attitude calculation.

Scaling of motion and governing equations for baroclinic large-scale motions in equatorial ocean

An obvious characteristic of the baroclinic large-scale motions in the equatorial ocean is that the meridional scale H of motion is far smaller than the zonal scale L. The scaling of motion carefully with this striking characteristic in this paper results in two conclusions, i. e., the Coriolis terms associated with the horizontal component of the rotation vector cannot be neglected in the governing equations; and the use of the absence of heating is not suitable to the equatorial region. In this paper the equatorial β-plane nondimensional governing equations with the small parametersδ_0 andδ_1 have been Obtained.

Massive Vector Particles Tunneling from the Neutral Rotating Anti-de Sitter Black Holes in Conformal Gravity

We investigate the massive vector particles' Hawking radiation from the neutral rotating Anti-de Sitter(AdS) black holes in conformal gravity by using the tunneling method.It is well known that the dynamics of massive vector particles are governed by the Proca field equation.Applying WKB approximation to the Proca equation,the tunneling probabilities and radiation spectrums of the emitted particles are derived.Hawking temperature of the neutral rotating AdS black holes in conformal gravity is recovered,which is consistent with the previous result in the literature.

Comparison of strapdown inertial navigation algorithm based on rotation vector and dual quaternion

For the navigation algorithm of the strapdown inertial navigation system, by comparing to the equations of the dual quaternion and quaternion, the superiority of the attitude algorithm based on dual quaternion over the ones based on rotation vector in accuracy is analyzed in the case of the rotation of navigation frame. By comparing the update algorithm of the gravitational velocity in dual quaternion solution with the compensation algorithm of the harmful acceleration in traditional velocity solution, the accuracy advantage of the gravitational velocity based on dual quaternion is addressed. In view of the idea of the attitude and velocity algorithm based on dual quaternion, an improved navigation algorithm is proposed, which is as much as the rotation vector algorithm in computational complexity. According to this method, the attitude quaternion does not require compensating as the navigation frame rotates. In order to verify the correctness of the theoretical analysis, simulations are carried out utilizing the software, and the simulation results show that the accuracy of the improved algorithm is approximately equal to the dual quaternion algorithm.

An adaptive beamforming algorithm based on direction vector rotation and joint iterative optimization

An adaptive beamforming algorithm named robust joint iterative optimizationdirection adaptive （RJIO-DA） is proposed for large-array scenarios. Based on the framework of minimum variance distortionless response （MVDR）, the proposed algorithm jointly updates a transforming matrix and a reduced-rank filter. Each column of the transforming matrix is treated as an independent direction vector and updates the weight values of each dimension within a subspace. In addition, the direction vector rotation improves the performance of the algorithm by reducing the uncertainties due to the direction error. Simulation results show that the RJIO-DA algorithm has lower complexity and faster convergence than other conventional reduced-rank algorithms.

Modeling and Optimal Design of 3 Degrees of Freedom Helmholtz Resonator in Hydraulic System

Three degrees of freedom （3-DOF） Helmholtz resonator which consists of three cylindrical necks and cavities connected in series （neck-cavity-neck-cavity-neck-cavity） is suitable to reduce flow pulsation in hydraulic system. A novel lumped parameter model （LPM） of 3-DOF Helmholtz resonator in hydraulic system is developed which considers the viscous friction loss of hy- draulic fluid in the necks. Applying the Newton＇s second law of motion to the equivalent mechanical model of the resonator, closed-form expression of transmission loss and resonance frequency is presented. Based on the LPM, an optimal design method which employs rotate vector optimization method （RVOM） is proposed. The purpose of the optimal design is to search the reso- nator＇s unknown parameters so that its resonance frequencies can coincide with the pump-induced flow pulsation harmonics respectively. The optimal design method is realized to design 3-DOF Helmholtz resonator for a certain type of aviation piston pump hydraulic system. The optimization result shows the feasibility of this method, and the simulation under optimum parame- ters reveals that the LPM can get the same precision as transfer matrix method （TMM）.

HETEROCLINIC BIFURCATIONS OF A PREY-PREDATOR FISHERY MODEL WITH IMPULSIVE HARVESTING

In this paper, we consider a prey-predator fishery model with Allee effect and state- dependent impulsive harvesting. First, we investigate the existence of order-1 heteroclinic cycle. Second, choosing p as a control parameter, we obtain the sufficient conditions for the existence and uniqueness of order-1 periodic solution of system （2.3） by using the geometry theory of semi-continuous dynamic systems. Finally, on the basis of the theory of rotated vector fields, heteroclinic bifurcation to perturbed system of system （2.3） is also studied. The methods used in this paper are novel to prove the existence of order-1 heteroclinic cycle and heteroclinic bifurcations.

HOMOCLINIC BIFURCATION IN SEMI-CONTINUOUS DYNAMIC SYSTEMS

In this paper, a class of homoclinic bifurcations in semi-continuous dynamic systems are investigated. On the basis of rotated vector fields theory, existence of order-1 periodic solution and the rotated vector fields of the semi-continuous dynamic system are discussed. Furthermore, homoclinic cycles and homoclinic bifurcations are described. Finally, an example is provided to show the validity of our theoretical results.

Topologically conjugate classifications of the translation actions on low-dimensional compact connected Lie groups

In this article, we focus on the left translation actions on noncommutative compact connected Lie groups with topological dimension 3 or 4, consisting of SU(2), U(2), SO(3), SO(3)×S^(1) and Spin ^(C)(3). We define the rotation vectors(numbers) of the left actions induced by the elements in the maximal tori of these groups, and utilize rotation vectors(numbers) to give the topologically conjugate classification of the left actions. Algebraic conjugacy and smooth conjugacy are also considered. As a by-product, we show that for any homeomorphism f : L(p,-1) × S^(1)→ L(p,-1) × S^(1), the induced isomorphism(π■f■i)_(*) maps each element in the fundamental group of L(p,-1) to itself or its inverse, where i : L(p,-1) → L(p,-1) × S^(1) is the natural inclusion and π : L(p,-1) × S^(1)→ L(p,-1) is the projection.

BIFURCATION DIAGRAMS OF QUADRATIC DIFFERENTIAL SYSTEMS HAVING ONE FOCUS AND ONE SADDLE

This paper gives bifurcation diagrams of system (2) below in the (α,λ) para meter plane.