考虑齿顶修缘的斜齿轮传动振动响应分析

渐开线斜齿轮进行适当修形后,可以有效地改善其啮合性能,降低噪音和延长齿轮的使用寿命。利用建立未修缘以及含不同齿廓修缘量的斜齿轮有限元模型,通过轮齿承载接触分析得到不同修缘量斜齿轮的静态传递误差和啮合刚度;在考虑齿顶修缘影响的基础上,建立了具有12个自由度的平行轴系斜齿轮转子系统动力学模型,将得到的时变啮合刚度应用于系统动力学模型中,研究不同修缘量对斜齿轮传动振动响应的影响规律。研究结果表明：在一定范围内,随着修缘量的增加,斜齿轮系统的径向振动和啮合力幅值明显降低,但当修缘量达到21 μm后其幅值有增大趋势。研究结果对确定斜齿轮的最优修形量和分析修形斜齿轮的振动特性具有重要意义。     

Envelope to a two-parameter family of point vectors method for surface swept by wheel during 5-axis gear form grinding

The wheel generating curve for gear grinding is always a composited curve which is composed of lines and arcs,and the calculation of the envelope surface is more complex than conventional rotary cutter. A method of envelope to a two-parametric family of point vectors is proposed,which defines the point and its normal vector on the wheel generating curve as a point vector. Each point vector corresponds to a virtual ball uniquely. The rotation of point vector forms latitude circle and the valid envelopment movement forms sectional circle. The intersection of latitude circle and sectional circle is grazing point. The analytical calculation model is established,in which the grazing point is determined by the geometry parameters of virtual ball and the velocity of virtual ball center,and the geometry parameters of virtual ball can be directly calculated from point vector. The kinematic geometry of 5-axis form gear grinder is analyzed. The coordinate transformation between fixed frame and moving frame is conducted,and the velocity of virtual ball center based on NC codes is obtained. An example is presented to demonstrate the effectiveness of the method which can be used for 5-axis gear grinding geometry simulation,accuracy evaluation and optimization of the wheel path.     

Worm wheel grinding method of convex pitch line non-circular gear

To overcome the precision machining difficulty of non-circular gear, a convex pitch curve of non-circular gear and worm grinding method is presented. Firstly, worm wheel is reduced to rack cutter and a rack machining convex pitch curves of non-circular gears sport model is set up. Then based on the structure of CNC worm wheel grinding machine tools and machining principle, electronic gear box of machine tools is designed and active and following axes are planned. At the mean time, the synchronous coefficient of machine tools between synchronization is deduced by machining principle of equal arc-length, and interaction models of grinding are established. At last, the worm wheel manual presetting cutter methods with non-circular gear are given and worm grinding wheel mounting angle, axial position and axial location parameter can be adjusted along the gear.     

Meshing performance analysis of planar internal gear enveloping crown worm driving

A new worm driving,i.e. planar internal gear enveloping crown worm driving,is presented. Its mathematical model of meshing functions and teeth surface equations are established basing on the theory of differential geometry and gear mesh. Various types of the driving,the macroscopic meshing performance and the microcosmic meshing performance are analyzed. The results show that the inclination angle of generating plane determines the distribution of contact lines,the planar internal gear primary-enveloping crown worm driving has ideal lubrication property,and the planar internal gear second-enveloping crown worm driving has high loading capacity. The studies are practicably instructive for developing new worm driving with high loading capacity,ideal lubrication and small volume.     

Tooth contact analysis of helical beveloid gear with parallel axis

The study object of this paper is helical beveloid gears with parallel axis. Based on the gear Mshing Principles and the tooth-surface equations of pinion and gear,the mathematical model of tooth contact is developed under standard installation and installations with center distance error,axis error and multiple error respectively. The MATLAB solver is used to obtain the contact trace and the transmission error under different installing conditions and the comparative analysis is made. The results indicate that this gear drive is sensitive to axis installation errors,it forms the edge contact and cause the periodic transmission error. It can provide the foundation for designs and analysis of this gear transmission.     

Mothematical Model for Planing of Precise and Hardened Gear

In this paper, the mathematical model for gear planing of precise and hardened gear is established. The computational charts and results for the tooth edge height,cutter edge contact length and cutter area are given out to improve the present planing technique.     

Thermal deformation error analysis and a novel compensation method for NC gear hobbing machine tools

To compensate the thermal deformation error of NC(numerical control) gear hobbing machine tools and improve the accuracy of gear machining,based on the clustering regression analysis theory, temperature measurement points are optimized to compensate thermal error. Accordingly a thermal model is set up by using least squares theory, and experimental result shows that the model is very accurate. A thermal error differential helix compensation scheme is proposed,which adopts direct compensation outside completely and can achieve real-time compensation for thermal error independently. Compared with other compensation methods,this one is unlimited to the openness of NC system and has a great popularity.     

Error analysis of worm grinding wheel precise dressing by diamond roller with straight profile

In worm grinding wheel dressing with diamond roller, using straight line instead of theoretical curve of roller will result in dressing error. Method of the precise dressing is studied, while the mathematical model is presented. Theoretical curve of diamond roller is calculated based on the space meshing theory and helicoid equation of worm grinding wheel. The fitting error between the theoretical curve and approximate straight line which is obtained by the theoretical curve is calculated. The dressing error on normal section of worm grinding wheel is analyzed. The case study of a kind of worm grinding wheel with single head shows that the dressing error increases with diameter decreasing of worm grinding wheel and diamond roller, while the variation of diamond roller’s diameter makes little contribution. The validity of worm grinding wheel dressing using straight line diamond roller is proved, and the algorithm can be used as guidance in practice.     

两级星型五分支传动静态均载分析

为分析两级星型五分支传动系统的均载问题,根据该系统构成功率流动闭环的特点,推导扭转角变形协调条件,结合力矩平衡条件,运用当量啮合误差理论,建立静态条件下的均载力学分析模型,求解得到均载系数,分析制造误差、安装误差、构件浮动对均载特性的影响。结果表明：太阳轮、内齿圈、星轮的误差单独影响均载特性时,内齿圈的误差影响最大,各构件制造误差影响的均载系数随时间做周期变化;太阳轮基于花键间隙浮动和内齿圈径向浮动,改善了均载特性,通过试验验证了理论分析的正确性。     

Dynamic characteristic analysis and optimization of high power-density steering gear

Steering gear is an important device on a ship,whose performance quality affects ship greatly.Aiming at high power-density steering gear which is composed of electro-hydraulic system and ball rotary-oscillating actuator,a mathematics model of the steering gear system is deduced.The system optimization design is carried out using optimization theory.Dynamic simulations of the pre and post optimized systems are made by MATLAB software to analyze dynamic characteristics.The analysis results show that the optimized steering gear can meet practical needs.     

Analysis of gear micropitting for megawatt-class wind turbine gearbox

Gear micropitting phenomenon is common in megawatt-class wind turbine gearbox because of the hard operating environment and complicated load case. More and more attention has been paid to it during recent years. Main factors influencing gear micropitting, such as surface roughness, modification coefficient, oil temperature, are discussed in this paper according to ISO/TR 15144—1:2010. Reasonable values for the factors are suggested and software for calculating micropitting is developed. Based on observation and discussion, measures for reducing gear micropitting risk in wind turbine gearbox design are proposed.     

山西地膜棉花高产优质综合农艺措施数学模型的研究

本文采用五因素五水平二次回归旋转设计的方法，研究了山西不同生态棉区皮棉产量与密度、氮、磷、钾施肥量及化控次数（用量）关系的数学模型。分析了不同因素的影响效应，明确了各栽培措施的主次。通过模拟进优待选了不同产量等级的优化农艺措施组合方案，为不同生态棉区制定棉花高产优质决策方案提供依据。     

A kinematic mathematical model of impulse electro flotation

After an analysis of the characteristics of impulse electro flotation wastewater treatment equipment, we discussed the factors affecting the efficiency of this technology. A simplified steel ball model was used in the construction of the free particle flotation removal model based on the kinematical theory of flocculation processes. Variation of the concentration of a free particle over time was stimulated. This mathematical model showed a significant role in the design of the flocculator parameter, and provided theoretical guidance on the choice of electric flotation parameters and the design of the electric flotation treatment equipment. The simulated results suggest that when the treatment time was between 20 and 25 minutes, the free particle removal rate could exceed 90%, a finding consistent with the experimental data.     

New Technology of Profile Grindng for Tow Teeth Difference Cyclodal Gear

Two teeth diffenence cyclodal gears are the key parts in cyclodal reducer. The plate abrasive wheel method which is widely used at home has very low precision and productivity. So it' s the common problem to be immediately solved. The profile grinding technology discussed in this paper has been proved by practical production to be an efficient and economical cycodal gear manufacturing method.     

Analysis and optimization of resistive cavitation property of annular groove within relief valve

RNG k ε turbulence model is adopted to simulate the cavitating flow of annular groove within relief valve,and the influence of structural parameters of annular groove on cavititaing flow field is analyzed. The analysis results show that performances of resistive cavitations increase with the rising of structural parameter θ when structural parameters R1and R2 are the optimal values. According to numerical simulation data of annular groove’s structural parameters,the surrogate models is obtained via the kriging calculated method,i.e. the objective function is the maximum gas volume fraction,the correlation function is the Guass function and constant regression model is applied to the likelihood function of surrogate models. The surrogate function is optimized by the improved PSO algorithm,and resistive caviatation property of the optimized structural parameters has higher efficiency compared with other ones.     

A mathematical description of the liquid flows inside blast furnaces

The knowledge of liquid flows in blast furnaces may play an important role in controlling the blast furnace process. Appropriate assumptions are given to represent the main characteristics of the liquid flow in blast furnaces, such as liquid streams being composed of unwetting liquid droplets, inertial force having little effect on the liquid flows, and mass exchange existing along the direction perpendicular to liquid flow. A mathematical model is built to predict the distribution of the liquid flow rate and the liquid flow range in packed beds. The scale of the numerical grid used to solve this model may not necessarily be reduced to the particle level. The predicted results of this model accord well with the observed data. This model is an alternative theory for the simulation of blast furnaces     

Dynamic optimization design of gear transmission system for wind turbine

The differential equation which governs the behavior of the gear transmission system of 1.5 MW wind turbine is established. The external excitation caused by wind speed fluctuation is discussed and the internal excitation due to time varying mesh stiffness and comprehensive error is also analyzed. The calculating formulations of the harmonic balance method of nonlinear dynamic equations are presented. Then, the multi objective dynamic optimization model is developed to minimize the value of vibration acceleration and the overall volume. The optimization of a practical example using mixed discrete combined programming is performed. The result shows that the proposed method of modeling and optimization design can effectively reduce the wind turbines gearbox vibration levels and weight.     

二维高炉区域BFC网格生成技术及其Matlab实现

利用数学模型对高炉冶炼过程进行模拟是高炉炼铁新工艺研发的有效方法,网格生成技术是数值模拟过程中重要的前处理过程,是高炉模拟计算的先决条件。生成网格的质量对高炉模型模拟的精度、效率以及收敛性具有重要影响,因此,建立优质的网格对高炉数学模型的求解具有重要意义。文中提出了一种适用于高炉数学模型的适体坐标系(BFC)网格的生成方法,从求解区域的划分、椭圆型方程的转换、椭圆型方程的离散及BFC网格生成步骤等方面进行了研究,并把死料区的边界作为BFC网格计算的边界条件,使数学模型的求解过程得以简化。采用带有源项的泊松方程作为变换方程,网格的正交性和疏密程度便于控制。该网格生成算法原理简单、易于编程、网格生成效率高,生成的网格能够满足数学模型求解的要求。     

An Accurate Method of the Analysis of Allowable Error for the Self-adjustable Mechanisms Without Overconstraint

Aiming at the problem of the feasibility of the supposed self adjusting displacement equation when using the present method in the analysis of allowable errors for self adjustable mechanism with the mathematic approach of rotating vector, the authors establish the self adjusting displacement equation in the cylindrical pair, and calculate the self adjusting displacement to draw out the curve of the displacement by programming. The above results show that the suppose mentioned previously is feasible. Base on the equation established, an accurate method is used to determinate the allowable error angles which can make the mechanism realize self adjustment presented. By analyzing the results of the example, the method presented is proved to be correct and effective.     

Effects of different constitutive models on the calculation of stress of diaphragm wall

Stress of diaphragm wall is analyzed by plane finite element method for high earth-rockfill dams built on deep soil foundation. The differences of stress are studied with two kinds of different constitutive models, i.e. elastic model and nonlinear elastic model, and meanwhile, the influences of the height of dam and diaphragm wall for this two constitutive models are also compared. The results show that, the variation laws of the stress of diaphragm wall are similar for both of the models. But, the stress computed by nonlinear elastic model is much smaller than elastic model does. Under the condition of low stress, the results are similar for the two models, but have big differences for high stress. In addition, for this two models, with the increasing of height of dam and diaphragm wall, the maximal values of the stress are increasing constantly, and relative error of the maximal value of the stress as well, which have the linear relation with the height of dam and diaphragm wall. So, for the conditions of high dams or deep soil foundations, nonlinear elastic model is the right one to use because of the high stress of diaphragm wall.