上海交通大学：《系统模型、分析与控制 Modeling、Analysis and Control》课程教学资源[02]Lecture21-Translational Mechanical system 平动机械系统建模

1E369-系横烈、分桥与控射 变量 x:位移[ i=v 2.1平功机被系峡瑰棋 v:速度[m/sec] i=i=a a:加速度[m/aec] :力NM p=f.v=f.i=w p:功率恤/aec] )=()+pdi)f.dt w:功恤、J刀 Schoel of Mechanical Engineering ME369-leeture 2.1 School of Mechanical Engineering Shanghai Jiao Tong University Fall 2015 Shanghai Jiao Tong University 模型元件 理想元件弹簧 惯性(Inertia)一质量(mass) x0 f()=m二 0=m dt dr2 刚度(Stiffness)-弹簧(spring) 最存动能Store Kinetic Energy) 人0=0-21=Kx) xn →0 厂=K(3-x) *r0 +0 =K)-g0a=K广0h W 奉擦Friction)一阻尼器Damper) E,I f0)=)-,(=B) -x(0) 露 =0_恋马1=B0 d 托後(Dissipate Energy Massless No Damping Linear Schoel of Mechanical Engineering ME369-leeture 2.1 School of Mechanical Engineering ME369-ecture 2.1 Shanshai lias Tong Unbrsraity Fall 2015 Shanghai Fsg Tona University Fall 2015 1

1 BE315-Lecture 2.1 Fall 2011 ME369-lecture 2.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University ME 369– 系统模型、分析与控制 2.1 平动机械系统建模 BE315-Lecture 2.1 Fall 2011 ME369-lecture 2.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 变量 x   v vxa     p  fv fx w    1 1 0 0 10 0 () () () ( )      t t t t w t w t pdt w t f x dt x: 位移 [m] v: 速度 [m/sec] a: 加速度 [m/sec2] f: 力 [N] p: 功率 [Nm/sec] w: 功 [Nm、J] BE315-Lecture 2.1 Fall 2011 ME369-lecture 2.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 模型元件 惯性(Inertia) --质量(mass) 刚度(Stiffness)--弹簧(spring) 摩擦(Friction)--阻尼器(Damper) 2 2 () () ( ) m dv t d x t ft m m dt dt   1 2 1 2 ( ) [ ( ) ( )] ( ) [ ( ) ( )] ( ) k t t f t K x t x t Kx t K v t v t dt K v t dt          1 2 1 2 ( ) [ ( ) ( )] ( ) () () ( ) [ ] Bf t B v t v t Bv t dx t dx t dx t B B dt dt dt      耗能（Dissipate Energy） 储存势能(Store Potential Energy) 储存动能(Store Kinetic Energy) BE315-Lecture 2.1 Fall 2011 ME369-lecture 2.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 理想元件-----------弹簧 2 1 ( ) sf  Kx x  Massless / No Damping / Linear K

理想元件--一阻尼器 元件连接一弹簧串并联(in Series/Parallel) D时tane Pneumatic door closer Cuter eylindet lnner clider 气动闭门器 用l Shock absorber ("oleo strut") 吸振器(“黄油支柱”) Schoel of Mechanical Engineering 睡E369-4 ecture2,1 School of Mechanical Engineering ME369-ecture 2.1 Shanghai Jiao Tong University Fall 2015 Shanghai Jiao Tong University Fall 2015 元件连接一阻尼器串并联(in Series/Parallel) 各种相关定律 申联 牛顿第2定律(Newton's Second Law) =6-k 牛顿第3定律(Newton's Third Law) -作用力与反作用力(Action&Reaction Forces) 并联 位移定律(Displacement Law) 子一x 77777777777777 School of Mechanical Engineering ME369-leeture 2.1 School of Meehaeieal Engineering ME369-ecture 2.1 Shanshai Jias Tena Unbrsraity Fall 2015 Shanghai Fsg Tora University Fall 2015 2

2 BE315-Lecture 2.1 Fall 2011 ME369-lecture 2.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University Shock absorber (“oleo strut”) 吸振器（“黄油支柱”） Pneumatic door closer 气动闭门器 理想元件-----------阻尼器 BE315-Lecture 2.1 Fall 2011 ME369-lecture 2.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 元件连接—弹簧串并联（ in Series/ Parallel） BE315-Lecture 2.1 Fall 2011 ME369-lecture 2.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 串联 并联 元件连接—阻尼器串并联（ in Series/ Parallel） BE315-Lecture 2.1 Fall 2011 ME369-lecture 2.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 各种相关定律 -牛顿第2定律（Newton’s Second Law） ( )     ex i d Mv Mx f dt -牛顿第3定律 （Newton’s Third Law ） --作用力与反作用力（Action & Reaction Forces ） -位移定律（Displacement Law）

建模步骤 [例1 [们理解功能，分析系统。确定输入、输入变量 手一x ②]采用基本元件画出简化图 M 3]准导数字模型，如微分方程(df.E4.) 一确定参考点和正方向 777777777 77777 -为每个基本元件画白由物体受力图(Free-Body-Diagram,FBD) 一列出以基本元件为内富变量的方程 动力学（灯netics)定律如Newton/Euler laws 运动学(Kinematics)定律 connection can't break [4取消中何变量，化简方程形式 [)化成标谁形式，得到运动方程(Equation of Motion,EO Schoel of Mechanical Engineering 睡E369-4 eeture2.,1 School of Mechanical Engineering ME369-ecture 2.1 Shanghai Jiao Tong University Fall 2015 Shanghai Jiao Tong University Fall 2015 T例2] 例31 School of Mechanical Engineering E3594 ecture2,1 School of Mechanical Engineering ME369-ecture 2.1 Shanshai Jias Tena Unbrsraity Fall 2015 Shanghai Fss Toma University Fall 2015 3

3 BE315-Lecture 2.1 Fall 2011 ME369-lecture 2.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 建模步骤 [1]理解功能，分析系统，确定输入、输入变量 [2] 采用基本元件画出简化图 [3]推导数字模型，如微分方程（diff. Eq.） --确定参考点和正方向 --为每个基本元件画自由物体受力图（Free-Body-Diagram ，FBD） --列出以基本元件为内部变量的方程 动力学（Kinetics）定律 如 Newton/Euler laws 运动学（Kinematics）定律 connection can’t break [4]取消中间变量， 化简方程形式 [5] 化成标准形式， 得到 运动方程（Equation of Motion, EOM) BE315-Lecture 2.1 Fall 2011 ME369-lecture 2.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [例1] BE315-Lecture 2.1 Fall 2011 ME369-lecture 2.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [例2] BE315-Lecture 2.1 Fall 2011 ME369-lecture 2.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [例3]

例41 静态平衡(static equilibrium) wW·-M m x v 9 School of Mechanical Engineering 睡E369-4 ecture2,1 School of Meehanieal Engineering ME369-ecture 2.1 Shanghai Jiao Tong University Fall 2015 Shanghai Jiao Tong University Fall 2015 T例5] 双质量块的1/4车辆模型(Quarter--car model with2mass) 滑轮(u)系统，设滑轮的横量可以您略不计，请治出运动方程(E0M) LL4411∠LLL/ 2 m 7717777777T School of Mechanical Engineering ME369-leeture 2.1 School of Mechanical Engineering ME369-ecture 2.1 Shanshai Jias Teng Unirsraity Fall 2015 Shanghai Fas Tona University Fall 2015 4

4 BE315-Lecture 2.1 Fall 2011 ME369-lecture 2.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [例4] BE315-Lecture 2.1 Fall 2011 ME369-lecture 2.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 静态平衡(static equilibrium) BE315-Lecture 2.1 Fall 2011 ME369-lecture 2.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [例5] 滑轮 (pulley)系统， 设滑轮的惯量可以忽略不计，请给出运动方程（EOM） BE315-Lecture 2.1 Fall 2011 ME369-lecture 2.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 双质量块的1/4 车辆模型(Quarter–car model with 2 mass)