超声珩齿新型变幅器动力学特性研究

为解决超声珩齿振动系统的设计问题,将齿轮简化为厚环盘,基于变截面变幅杆纵向振动波动方程和中厚圆环板弯曲振动位移方程,根据中间有孔圆锥型变幅杆与中厚圆环组成的新型超声珩齿变幅器的非谐振性和边界条件,推导出了系统谐振频率方程,利用数值计算分析了变幅器的几何参数对系统谐振频率的影响。通过有限元分析得出变幅器的谐振频率与理论计算结果基本一致。在此基础上,对设计的变幅器进行了动力学试验,测得的动力学参数与理论结果一致,其结果不仅证实了非谐振理论的正确性,而且为超声珩齿变幅器的设计和应用提供了理论依据。     

超声珩齿复合变幅器设计及其动力学研究

在超声珩齿加工中,由变幅杆和被加工齿轮组成的变幅器的设计是一项关键技术,探索新型变幅器显得非常重要。基于变截面复合变幅杆纵向振动波动方程和中厚圆环板弯曲振动位移方程,根据复合变幅杆与中厚圆环组成的超声珩齿复合变幅器的非谐振性和边界条件,推导了系统的谐振频率方程,利用数值计算对设计参数、谐振频率、变幅杆及圆环振幅分布等进行研究,同时分析了变幅器几何参数对系统谐振频率的影响。结果表明,有限元分析结果与理论计算结果和实验测试基本一致,系统谐振频率随复合变幅杆各段长度的增加而减小;当复合变幅杆大小端半径比和各段长度保持不变时,系统谐振频率随两端半径成比例地增加而增加;其他参数不变时随圆环厚径比地增加而增加,其结论不仅证实了非谐振理论的正确性,而且为超声珩齿变幅器的设计和应用提供了理论依据。     

纵向谐振变幅器的非谐振设计理论研究与验证

为了实现齿轮超声加工纵向谐振变幅器的设计,提出了纵向谐振变幅器的非谐振设计理论,将变幅器简化为由变幅杆、齿轮等效圆环、心轴、螺母等效圆柱四部分组成的理论分析模型,根据各部分的动力学方程、各结合面的力、位移耦合条件和两端面的边界条件,建立变幅器的频率方程,实现纵向谐振变幅器的设计。分别设计了变幅杆材料为45钢、齿轮材料为铸造锡青铜以及变幅杆材料为45钢、钛合金、硬铝合金、齿轮材料为45钢的纵向谐振变幅器,通过有限元软件ANSYS模态分析和谐振特性实验研究了变幅器的谐振特性,变幅器的谐振频率与理论设计频率的误差小于5%,在误差允许范围内,表明变幅器的非谐振设计理论对于设计齿轮超声加工纵向谐振变幅器具有很好的通用性,为齿轮超声加工振动系统的设计提供了理论基础。     

非谐振单元变幅器的设计及其动力学研究

在超声珩齿加工中,由变幅杆和被加工齿轮组成的变幅器的设计是一项关键技术,变幅器的动力学特性对齿轮的加工质量有很大影响。齿轮作为变幅杆的负载,一方面其尺寸和质量大,对变幅器谐振频率的影响不能忽略,另一方面,齿轮的尺寸是由使用要求决定的,不能被任意设计,因此现有的功率超声变幅杆的设计方法不能适用于这种情况。以Mindlin厚板理论为基础,将齿轮简化为一厚圆板,圆板外径等于齿轮分度圆直径,根据齿轮与变幅杆在连接面的耦合关系及各自的动力学方程,建立变幅杆和齿轮组合系统的动力学模型,在此基础上设计变幅器,并进行动力学特性的分析,分析结论为超声珩齿变幅杆的设计提供了理论依据。通过有限元分析验证了设计理论完全可行。     

超声铣削螺旋锥齿轮变幅器装置的设计

将超声加工应用在螺旋锥齿轮的铣削加工中,得到具有表面微观纹路的齿轮,滑油储存在纹路间隙中,能够增加油膜厚度,减小齿轮摩擦力转矩、表面温度、磨损率,降低齿轮啮合噪声。基于细长杆的一维纵振理论,对阶梯形变幅杆与铣刀盘进行整体设计。由变幅器每段的位移函数、应力函数及边界条件,建立变幅器的频率方程。根据实际要求设计了1/2波长超声变幅器实例,并运用ANSYS对其进行了动力学分析和频率优化。有限元分析结果表明:变幅器的谐振频率与理论设计频率的误差为2.15%,在误差允许范围内,验证了变幅器频率方程的正确性。运用APDL语言优化设计对变幅器的频率进行优化,使优化后的结构频率更加接近目标频率。最后,变幅器的阻抗特性试验和装置的雾化试验结果证明装置能够产生谐振,该装置可以进一步应用于齿轮的铣削。     

超声珩齿弯曲振动变幅器的位移特性

超声振动可以有效地减小珩磨力,超声空化现象与切削液的共同作用可以对珩磨轮实现实时动态清洗,从而减小珩磨轮堵塞,提高加工效率,因此超声和珩齿的复合加工是一种应用前景良好的齿轮精加工方法.超声珩齿的加工对象--齿轮,直径大,厚度小,是一类特殊负载,且对振动系统的加工频率影响大,所以在超声振动系统设计时,必须将变幅杆和齿轮全面考虑建立动力学方程.为此,将齿轮简化为圆盘,加工过程中齿轮作只有圆节线的弯曲振动,采用圆锥型变幅杆,推导变幅杆和圆盘组成的变幅器的频率方程,并利用它设计了变幅器,对变幅器动力学参数的数值计算、有限元分析及试验测量结果一致.通过计算变幅器中变幅杆和圆盘各自独立的谐振频率,发现与变幅器的谐振频率误差较大,说明变幅器设计时必须同时考虑变幅杆和圆盘的相互作用,否则设计的变幅器谐振频率误差过大.     

超声滚压装置中变幅器的仿真设计

运用两种不同方法设计超声滚压装置中的变幅器,一种采用传统设计法将变幅杆和滚轮分别设计后组装成变幅器;另一种方法是将变幅杆和滚轮整体考虑设计为变幅器.推导出变幅器的频率方程,求出了变幅器设计参数的数值解.通过有限元软件Marc分析,发现传统设计的变幅器中滚轮的设计频率与变幅器的谐振频率误差较大;而整体设计的变幅器的设计频率误差较小.经参数调整后两种变幅器的设计频率都可调至谐振频率20 kHz.由于传统方法设计的变幅器未考虑滚轮作为负载对变幅杆的影响,在实际应用未能达到超声系统良好的共振效果;而整体设计变幅器中变幅杆及滚轮尺寸小,对变幅器的谐振频率影响较小,结构紧凑,抗弯刚度好,通过有限元分析验证了变幅器的整体设计理论完全可行,能够达到良好的共振效果.     

基于传递矩阵法的超声珩齿复合变幅器设计

基于Mindlin中厚板理论,利用传递矩阵法设计了圆环板与复合变幅杆组合而成的超声珩齿复合变幅器,推导了这一复合变幅器的弯曲振动频率方程,并对其振动特性进行研究。研究结果表明,超声珩齿复合变幅器频率随变幅杆各段长度的增大而减小,随圆环厚度的增大而增大,随圆环外径的增大而减小。     

大负载纵弯谐振超声磨削变幅器的设计与试验

基于Mindlin中厚板理论,针对超声磨削系统中的大负载砂轮进行了纵弯谐振变幅器的设计研究。将纵弯谐振变幅器分为变幅杆、基体环盘、磨料层环盘三个部分,分别建立各部分的位移与应力函数,利用边界条件建立纵弯谐振超声磨削变幅器的频率方程。根据频率方程设计了超声磨削变幅器,通过有限元分析和超声谐振试验对所设计的变幅器进行了试验研究。试验结果证明:超声磨削变幅器的谐振频率与设计频率基本一致,实际测得的砂轮振幅曲线与有限元仿真和理论计算取得的曲线的形态基本一致,验证了超声磨削纵弯谐振变幅器设计方法的正确性,为超声磨削系统的设计提供了理论依据。     

超声珩齿加工工件对谐振频率影响的研究

将超声珩齿加工变幅杆和被加工齿轮组成的超声振动系统简化为变幅器,基于圆锥形变幅杆和环盘(被加工齿轮)组成变幅器的频率方程,导出齿轮半径、厚度变化对谐振频率的影响,以及变幅杆的调整规律,并运用有限元分析的方法对设计结果进行了验证,从而为变幅杆及工作频率的设计选择提供了依据。     

超声珩齿指数型变幅器的动力学特性

超声振动可以有效地减小珩磨力,超声空化现象与切削液的共同作用对珩磨轮实现实时动态清洗,从而减小珩磨轮堵塞、提高加工效率,超声和珩齿进行复合加工是一种应用前景良好的齿轮精加工方法.超声珩齿的加工对象--齿轮,是一类特殊负载(直径大,厚度小),且对振动系统的加工频率影响大,在超声振动系统设计时,必须将变幅杆和齿轮组成变幅器进行全面考虑.鉴于此,根据应力耦合,将齿轮作为圆盘,采用指数型变幅杆,推导频率方程,对变幅杆的设计长度和变幅器振动频率进行数值分析,发现变幅杆的共振频率恰好是变幅器的失谐频率,变幅器的共振频率与变幅杆的固有频率也不相同,这能够为超声珩齿变幅器的设计提供理论依据.     

Vibration analysis of piezoelectric FGM sensors using an accurate method

In this study, free vibration analysis of moderately thick smart FG annular/circular plates with different boundary conditions is presented on the basis of the Mindlin plate theory. This structure comprised a host FG plate and two bonded piezoelectric layers. Piezoelectric layers are open circuit therefore this plate can be used as a sensor. According to power-law distribution of the volume fraction of the constituents, material properties vary continuously through the thickness of host plate while Poisson's ratio is set to be constant. Using Hamilton's principle and Maxwell electrostatic equation yields six complex coupled equations which are solved via an exact closed-form method. The accuracy of the frequencies is verified by the available literature, finite element method (FEM) and the Kirchhoff theory. The effects of plate parameters like boundary condition and gradient index are investigated and significance of coupling between in-plane and transverse displacements on the resonant frequency is proved.     

A novel approach for in-plane/out-of-plane frequency analysis of functionally graded circular/annular plates

An exact closed-form frequency equation is presented for free vibration analysis of circular and annular moderately thick FG plates based on the Mindlin's first-order shear deformation plate theory. The edges of plate may be restrained by different combinations of free, soft simply supported, hard simply supported or clamped boundary conditions. The material properties change continuously through the thickness of the plate, which can vary according to a power-law distribution of the volume fraction of the constituents, whereas Poisson's ratio is set to be constant. The equilibrium equations which govern the dynamic stability of plate and its natural boundary conditions are derived by the Hamilton's principle. Several comparison studies with analytical and numerical techniques reported in literature and the finite element analysis are carried out to establish the high accuracy and superiority of the presented method. Also, these comparisons prove the numerical accuracy of solutions to calculate the in-plane and out-of-plane modes. The influences of the material property, graded index, thickness to outer radius ratios and boundary conditions on the in-plane and out-of-plane frequency parameters are also studied for different functionally graded circular and annular plates.     

Closed-form vibration analysis of thick annular functionally graded plates with integrated piezoelectric layers

This paper employs an analytical method to analyze vibration of piezoelectric coupled thick annular functionally graded plates (FGPs) subjected to different combinations of soft simply supported, hard simply supported and clamped boundary conditions at the inner and outer edges of the annular plate on the basis of the Reddy's third-order shear deformation theory (TSDT). The properties of host plate are graded in the thickness direction according to a volume fraction power-law distribution. The distribution of electric potential along the thickness direction in the piezoelectric layer is assumed as a sinusoidal function so that the Maxwell static electricity equation is approximately satisfied. The differential equations of motion are solved analytically for various boundary conditions of the plate. In this study closed-form expressions for characteristic equations, displacement components of the plate and electric potential are derived for the first time in the literature. The present analysis is validated by comparing results with those in the literature and then natural frequencies of the piezoelectric coupled annular FG plate are presented in tabular and graphical forms for different thickness-radius ratios, inner-outer radius ratios, thickness of piezoelectric, material of piezoelectric, power index and boundary conditions.     

圆柱直齿齿轮简化模型的弯曲振动特性研究

在超声珩齿加工中,齿轮既是被加工零件,也是振动系统的主要部件,其动力学特性和固有频率对振动系统的设计和优化至关重要。针对含轮毂、辐板、轮缘的齿轮结构特点,将其简化为一阶梯变厚度圆环盘,应用经典薄板理论推导了模型横向弯曲振动的频率方程,求得了其固有频率,并将计算结果与ANSYS模态分析结果进行了对比。结果表明:该简化模型的频率分析较为合理,且理论计算可以获得较高精度。     

Free vibration analysis of arbitrary shaped thick plates by differential cubature method

In this paper, a new numerical solution technique, the differential cubature method, is applied to solve the free vibration problems of arbitrary shaped thick plates. The basic idea of the differential cubature method is to express a linear differential operation such as a continuous function or any order of partial derivative of a multivariable function, as a weighted linear sum of discrete function values chosen within the overall domain of a problem. By using the differential cubature procedure, the governing differential equations and boundary conditions are transformed into sets of linear homogeneous algebraic equations. This is an eigenvalue problem, of which the eigenvalues can be calculated numerically. The subspace iterative method is employed in search of the free vibration frequency parameters. Detailed formulations are presented, and the method is examined here for its suitability for solving the vibration problems of moderately thick plates governed by Mindlin shear deformation theory. The applicability, efficiency and simplicity of the method are demonstrated through solving some example plate vibration problems of different shapes. The numerical accuracy of the method is ascertained by comparing the vibration frequency solutions with those of existing literatures.     

齿轮结构振动固有特性研究

建立了齿轮的弹力体力学模型,按照厚壁板理论建立了弹性体振动微分方程,分析了齿轱本体弹性的振动固有特性,并与实验结果进行了对比分析。给齿轮本体的结构振动分析提供了一种研究方法,为齿轮噪声辐射特性的研究奠定了基础。     

Vibration from a shaft-bearing-plate system due to an axial excitation of helical gears

In this paper, a simplified model is studied to predict analytically the vibration from the helical gear system due to an axial excitation of helical gears. The simplified model describes gear, shaft, bearing, and housing. In order to obtain the axial force of helical gears, the mesh stiffness is calculated in the load deflection relation. The axial force is obtained from the solution of the equation of motion, using the mesh stiffness. It is used as a longitudinal excitation of the shaft, which in turn drives the gear housing through the bearing. In this study, the shaft is modeled as a rod, while the bearing is modeled as a parallel spring and damper only supporting longitudinal forces. The gear housing is modeled as a clamped circular plate with viscous damping. For the modeling of this system, transfer matrices for the rod and bearing are used, using a spectral method with four pole parameters. The model is validated by finite element analysis. Using the model, parameter studies are carried out. As a result, the linearized dynamic shaft force due to the gear excitation in the frequency domain was proposed. Out-of-plan displacement from the forced vibrating circular plate and the renewed mode normalization constant of the circular plate were also proposed. In order to control the axial vibration of the helical gear system, the plate was more important than the shaft and the bearing. Finally, the effect of the dominant design parameters for the gear system can be investigated by this model.