基于小波分析的快速成形过程数学模型  

MATHEMATICAL MODEL OF RAPID PROTOTYPING PROCESS BASED ON WAVELET ANALYSIS

作　　者：吴任东[1] 颜永年[1] 卢伟[1] 卢清萍[1] 

机构地区：[1]清华大学机械工程系,北京100084

出　　处：《机械工程学报》2004年第12期1-4,9,共5页Journal of Mechanical Engineering

基　　金：国家自然科学基金资助项目(50105008)。

摘　　要：采用信号处理的方法来考察快速成形技术,将其分层制造所产生的特有的结果--阶梯效应理解为把输入的原型表面轮廓曲线函数改造成为阶梯函数,因此可以将快速成形设备理解为滤波器组。分别采用傅里叶变换、窗口傅里叶变换和小波变换描述了快速成形的轮廓信息变化过程,认为只有小波变换可以兼具处理非平稳信号和构建出阶梯波的特点,因此最适合用于建立表征快速成形过程的数学模型。针对分层制造的特点,以单位方波作为尺度函数构建出能够反映阶梯波特性的小波基函数,即Haar小波函数,并利用其间断性的特点,建立了快速成形过程的数学模型,其作用就是将输入的零件轮廓波形通过基于Haar基函数的小波变换改造成为阶梯波。In the view of signal process, the outcome of slicing forming process-step effect can be considered as transferring inputted function of the prototype's contour to step function, and men rapid prototyping(RP) machine can be comprehended as a filter bank. Fourier analysis, Gabor analysis and wavelet analysis has been used to describe the transforming process of prototype's contour information. Since wavelet analysis can preferably dispose nonstationary time series and construct step waveform, it is the better way to design the mathematical model to describe the forming process of RP. The unit square wave has been used as scale function to construct wavelet primary function which can reflect the characteristics of step wave. The primary function is Haar function. By wavelet analysis the math model of RP processing has been designed, which can transfer the inputted signal to step wave.

关 键 词：快速成形 小波分析 傅里叶分析 数学模型 

分 类 号：TH165[机械工程—机械制造及自动化]