机车动力滑台铣平面时,当切削力Fi(t)变化时,滑台可能产生振动,从而降低被加工工件的切削表面质量。可将动力滑台连同铣刀抽象成如图所示的质量-弹簧-阻尼系统的力学模型。其中m为受控质量,k1,k2分别为铣刀系统,x0(t)为输出位移。试建立数学模型。РfРmРFi(t)Рk1Рk2Рx0(t)Р图2-31 题2-17图Рx1(t)Р解:微分方程为:Р?拉氏变换得:Р?传递函数为:РJ1РJ2Рθ0(t)Рk2РfРa)Рk1Рθ1(t)Р+Р-Рθi(s)Рk1РT1(s)Р+Р-Р+Р-Рk2Рθ0(s)РT2(s)Рb)Р图2-39 题2-25图Р2-25.试求图2-39a所示机械系统的传递函数,画出其函数框图,与图2-39b进行比较。Р解1:微分方程为:Р?拉氏变换得:Р?传递函数为:Р解2:画出框图如图所示,通过框图简化可得传递函数为:РJ1РJ2Рθ0(t)Рk2РfРk1Рθi(t)Р+Р-Рθi(s)Рk1РT1(s)Р+Р-Р+Р-Рk2Рθ0(s)РT2(s)Рθ1(t)Р+Р-Р+Р-Рk1РT1(s)Р+Р-Р+Р-Рk2Рθ0(s)РT2(s)Рθi(s)Р+Р-Рk1РT1(s)Р+Р-Р+Р-Рk2Рθ0(s)РT2(s)Рθi(s)Р+Р-Рk1РT1(s)Р+Р-Рθ0(s)РT2(s)Рθi(s)Р+Р-Рk1РT1(s)Р+Р-РT2(s)Рθi(s)Рθ0(s)Р+Р-РT2(s)Рθi(s)Рθ0(s)Рθi(s)Рθ0(s)Рθi(s)Р2-28.化简图2-42所示各系统框图求传递函数。Рc). РG1Р+Р+РXiРH1Р+Р-РX0РG2Р+Р-РG3РH2РG4Р-Рc)Р图2-42 题2-28图РG1Р+Р+РXiР+Р-РX0Р+РH2РG4Р-РG1Р+Р+РXiР+Р-РX0РG4РXiР+Р-РX0РG4РXiРX0
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