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]Lecture22-Rotational Mechanical system 转动机械系统建模

1E369-尿就操型、分桥与拉侧 变量 0:角位移[rad] 0=@ a:角速度[rad/sec】 0=0=a a:角加速度[rad/sec] 2.2救动机械尿统瑰棋 x:力矩[Nm] p=r…o=r…0=w p:功率恤/sc] w:功[恤、J刀 w6)=w6)+pd=w6)+r:0t Schoel of Mechanical Engineering 睡E369-4 ecture2.2 School of Mechanical Engineering Shanghai Jiao Tong University Fall 2015 Shanghai Jiao Tong University 理想元件-弹簧/阻尼器 理想元件--一-转动惯量(Moment of inertia) ∫=K(x-x) t=K(02-8) 777777777777777 M=∑f=f-6-6 % 拉射 a=B-)=By-) r-B8-)=Boa2-) Ji=∑x School of Mechanical Engineering ME369-leeture 2.2 School of Mechanical Engineering ME369-ecture 2.2 Shanshai Jias Teng Unirsraity Fall 2015 Shanghai Fss Toma University Fall 2015 1

1 BE315-Lecture 2.2 Fall 2011 ME369-lecture 2.2 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University ME369- 系统模型、分析与控制 2.2 转动机械系统建模 BE315-Lecture 2.2 Fall 2011 ME369-lecture 2.2 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 变量               p w  1 1 0 0 10 0 () () () ( )          t t t t w t w t pdt w t dt θ: 角位移 [rad] ω: 角速度 [rad/sec] α: 角加速度[rad/sec2] τ: 力矩 [Nm] p: 功率 [Nm/sec] w: 功 [Nm、J] BE315-Lecture 2.2 Fall 2011 ME369-lecture 2.2 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 理想元件----弹簧/阻尼器 2 1   K( )   2 1 ( ) sf  Kx x  21 21 ( )( ) Df  Bx x Bv v     21 2 1     B B ( )( )     BE315-Lecture 2.2 Fall 2011 ME369-lecture 2.2 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 理想元件----------转动惯量（Moment of inertia) i 123 i Mx   ffff  i i J   

理想元件----.平行轴(Parallel Axis)转动惯量 各种相关定律 -欧拉定律(Euler Law) oj=i-y. -牛顿第3定律(Newton's Third Law) J=Jo+Mr2 -作用力与反作用力(Action&Reaction Forces) 位移定理 School of Mechanical Engineering 睡E369-4 eeture2.2 School of Meeheieal Engineering ME369-ecture 2.2 Shanghai Jiao Tong University Fall 2015 Shanghai Jiao Tong University Fall 2015 建模步骤 例1门 [们理解功能，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]准导数字模型，如微分方程(df.Eq.) 一确定参考点和正方向 -为每个基本元件画自由物体受力图(Ffee-Body-Diagram,FBD) 一列出以基本元件为内部变量的方程 动力学(K灯etics)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化成标谁形式，得到运动方程(Equation of Motion,EO Schoel of Mechanical Engineering ME369-leeture 2.2 School of Mechanical Engineering ME369-ecture 2.2 Shacshai Jias Tena Unirsrsity Fall 2015 Shanghai Fsg Tora University Fall 2015 2

2 BE315-Lecture 2.2 Fall 2011 ME369-lecture 2.2 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 理想元件---------平行轴（Parallel Axis）转动惯量 2 0 J   J Mr BE315-Lecture 2.2 Fall 2011 ME369-lecture 2.2 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 各种相关定律 -欧拉定律（Euler Law ） ( ) ex i d J J dt        -牛顿第3定律（Newton’s Third Law） --作用力与反作用力（Action & Reaction Forces） -位移定理 BE315-Lecture 2.2 Fall 2011 ME369-lecture 2.2 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 2.2 Fall 2011 ME369-lecture 2.2 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [例1]

[例2]齿轮系 [例3] 图示齿轮系中各齿轮的转动圆量分别为hhdh,请列出以日，为输出变量的运动方程. School of Mechanical Engineering 睡E369-4 ecture2.2 School of Mechanical Engineering ME369-ecture 2.2 Shanghai Jiao Tong University Fall 2015 Shanghai Jiao Tong University Fall 2015 [例4无滑动的滚动(Rolling w/o slipping) [例4]续-瞬心法 School of Mechanical Engineering ME369-leeture 2.2 School of Mechanical Engineering ME369-ecture 2.2 Shanshai Jias Tena Unbrsraity Fall 2015 Shanghai Fss Toma University Fall 2015 3

3 BE315-Lecture 2.2 Fall 2011 ME369-lecture 2.2 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [例2]齿轮系 BE315-Lecture 2.2 Fall 2011 ME369-lecture 2.2 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [例3] 图示齿轮系中各齿轮的转动惯量分别为 j1,j2 and j3 ，请 列出以θ3为输出变量的运动方程。 BE315-Lecture 2.2 Fall 2011 ME369-lecture 2.2 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [例4]无滑动的滚动（Rolling w/o slipping) BE315-Lecture 2.2 Fall 2011 ME369-lecture 2.2 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [例4]续---瞬心法

[例5)无滑动小车 【例6 图示小车的车体质量M,四个相同车轮质量m半径R,给出以x为输出变量的运动方程 建立以x为输出变量的运动方程 School of Mechanical Engineering 睡E369-4 ecture2.2 School of Mechanical Engineering ME369-ecture 2.2 Shanghai Jiao Tong University Fall 2015 Shanghai Jiao Tong University Fall 2015 [讨论1 [讨论1]续一线性化 0 School of Mechanical Engineering ME369-leeture 2.2 School of Mechanical Engineering ME369-ecture 2.2 Shanshai Jias Tena Unbrsraity Fall 2015 Shanghai Fss Toma University Fall 2015 4

4 BE315-Lecture 2.2 Fall 2011 ME369-lecture 2.2 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University Example (6) -continue [例5]无滑动小车 图示小车的车体质量 M ，四个相同车轮质量m 半径 R， 给出以x为输出变量的运动方程 BE315-Lecture 2.2 Fall 2011 ME369-lecture 2.2 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [例6] 建立以x为输出变量的运动方程 BE315-Lecture 2.2 Fall 2011 ME369-lecture 2.2 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [讨论1] BE315-Lecture 2.2 Fall 2011 ME369-lecture 2.2 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [讨论1]续—线性化

[讨论2] 【例7刀 店轮店条系统，通过齿轮上施如力矩控制暖量块A的位置 ° B A☐ School of Mechanical Engineering 睡E369-4 ecture2.2 School of Mechanical Engineering ME369-ecture 2.2 Shanghai Jiao Tong University Fall 2015 Shanghai Jiao Tong University Fall 2015 [例7续 School of Mechanical Engineering ME369-leeture 2.2 Shanshai Jias Tena Unbrsraity Fall 2015 5

5 BE315-Lecture 2.2 Fall 2011 ME369-lecture 2.2 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [讨论2] BE315-Lecture 2.2 Fall 2011 ME369-lecture 2.2 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [例7] 齿轮齿条系统，通过齿轮上施加力矩控制质量块A的位置 BE315-Lecture 2.2 Fall 2011 ME369-lecture 2.2 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [例7]续