发动机悬置python仿真计算

代码可复制到https://hub.gke2.mybinder.org/user/lijil168-requirements-l6zexquh/tree运行
1、发动机悬置模态及解耦参考
2、发动机动力学激励计算参考
3、用数组和矩阵两种方式计算刚度矩阵，并对比结果，原文公式推导有点点错误。python用多维数组完成矩阵运算，很简洁而且可读性好。
4、思路：由发动机爆压计算倾覆力矩，建立状态空间动力学模型，进行模态及解耦率计算，最后进行仿真，得到发动机质心的状态，再换算到各个悬置点。
5、结果
- 5.1发动机激励计算结果
- 5.1悬置系统仿真结果
6、完整的仿真代码

代码可复制到https://hub.gke2.mybinder.org/user/lijil168-requirements-l6zexquh/tree运行

点击进入jupyter notebook

1、发动机悬置模态及解耦参考

http://www.doc88.com/p-6364178164728.html

2、发动机动力学激励计算参考

发动机动力学理论参考

3、用数组和矩阵两种方式计算刚度矩阵，并对比结果，原文公式推导有点点错误。python用多维数组完成矩阵运算，很简洁而且可读性好。

4、思路：由发动机爆压计算倾覆力矩，建立状态空间动力学模型，进行模态及解耦率计算，最后进行仿真，得到发动机质心的状态，再换算到各个悬置点。

5、结果

分别为质量矩阵、刚度矩阵、自然频率、模态振型矩阵（每列对应振型向量）、解耦率（每列对应模态阶次，行从上到下对应x,y,z,theta_x,theta_y,theta_z 6个自由度）、阻尼矩阵。

5.1发动机激励计算结果

5.1悬置系统仿真结果

6、完整的仿真代码

# _*_ coding:UTF-8 _*_
import numpy as np
from numpy import sin
from numpy import cos
from numpy import arcsin as asin
from numpy import sqrt
from numpy import tan
from matplotlib.pyplot import*
from scipy import interpolatedef M_sys(m,Ixx,Ixy,Ixz,Iyy,Iyz,Izz):return np.array([[m,0,0,0,0,0],\[0,m,0,0,0,0],\[0,0,m,0,0,0],\[0,0,0,Ixx,-Ixy,-Ixz],\[0,0,0,-Ixy,Iyy,-Iyz],\[0,0,0,-Ixz,-Iyz,Izz]])
def K_element_i(k_pi,k_qi,k_ri,theta_pi,phi_pi,psi_pi,theta_qi,phi_qi,psi_qi,theta_ri,phi_ri,psi_ri):#k_pi:第i个悬置的p向刚度；#theta_pi：p轴与系统x轴的夹角；#phi_pi：p轴与系统y轴的夹角；#psi_pi:p轴与系统z轴的夹角；K_xxi=k_pi*cos(theta_pi)**2+k_qi*cos(theta_qi)**2+k_ri*cos(theta_ri)**2K_yyi=k_pi*cos(phi_pi)**2+k_qi*cos(phi_qi)**2+k_ri*cos(phi_ri)**2K_zzi=k_pi*cos(psi_pi)**2+k_qi*cos(psi_qi)**2+k_ri*cos(psi_ri)**2K_xyi=k_pi*cos(theta_pi)*cos(phi_pi)+k_qi*cos(theta_qi)*cos(phi_qi)+k_ri*cos(theta_ri)*cos(phi_ri)K_xzi=k_pi*cos(theta_pi)*cos(psi_pi)+k_qi*cos(theta_qi)*cos(psi_qi)+k_ri*cos(theta_ri)*cos(psi_ri)K_yzi=k_pi*cos(psi_pi)*cos(phi_pi)+k_qi*cos(psi_qi)*cos(phi_qi)+k_ri*cos(psi_ri)*cos(phi_ri)return [K_xxi,K_xyi,K_xzi,K_yyi,K_yzi,K_zzi]def K_sys(K_xxi,K_xyi,K_xzi,K_yyi,K_yzi,K_zzi,Ai,Bi,Ci):Ai=np.array(Ai)Bi=np.array(Bi)Ci=np.array(Ci)K_xx=sum(K_xxi)K_xy=sum(K_xyi)K_xz=sum(K_xzi)K_yy=sum(K_yyi)K_yz=sum(K_yzi)K_zz=sum(K_zzi)K_alpha_alpha=sum(K_yyi*Ci**2)+sum(K_zzi*Bi**2)-2*sum(K_yzi*Bi*Ci) ###K_beta_beta=sum(K_xxi*Ci**2)+sum(K_zzi*Ai**2)-2*sum(K_xzi*Ai*Ci)K_gamma_gamma=sum(K_xxi*Bi**2)+sum(K_yyi*Ai**2)-2*sum(K_xyi*Ai*Bi)   ####原公式有误！！！K_alpha_beta=sum(K_xzi*Bi*Ci)+sum(K_yz*Ai*Ci)-sum(K_zzi*Ai*Bi)-sum(K_xyi*Ci**2)K_beta_gamma=sum(K_xyi*Ai*Ci)+sum(K_xz*Ai*Bi)-sum(K_xxi*Ci*Bi)-sum(K_yzi*Ai**2) ###K_alpha_gamma=sum(K_xyi*Ci*Bi)+sum(K_yz*Ai*Bi)-sum(K_yyi*Ci*Ai)-sum(K_xzi*Bi**2)K_x_alpha=sum(K_xzi*Bi)-sum(K_xyi*Ci)K_x_beta=sum(K_xxi*Ci)-sum(K_xzi*Ai)K_x_gamma=sum(K_xyi*Ai)-sum(K_xxi*Bi)K_y_alpha=sum(K_yzi*Bi)-sum(K_yyi*Ci)K_y_beta=sum(K_xyi*Ci)-sum(K_yzi*Ai)K_y_gamma=sum(K_yyi*Ai)-sum(K_xyi*Bi) K_z_alpha=sum(K_zzi*Bi)-sum(K_yzi*Ci)K_z_beta=sum(K_xzi*Ci)-sum(K_zzi*Ai)K_z_gamma=sum(K_yzi*Ai)-sum(K_xzi*Bi) K=np.array([[K_xx,K_xy,K_xz,K_x_alpha,K_x_beta,K_x_gamma],\[K_xy,K_yy,K_yz,K_y_alpha,K_y_beta,K_y_gamma],\[K_xz,K_yz,K_zz,K_z_alpha,K_z_beta,K_z_gamma],\[K_x_alpha,K_y_alpha,K_z_alpha,K_alpha_alpha,K_alpha_beta,K_alpha_gamma],\[K_x_beta,K_y_beta,K_z_beta,K_alpha_beta,K_beta_beta,K_beta_gamma],\[K_x_gamma,K_y_gamma,K_z_gamma,K_alpha_gamma,K_beta_gamma,K_gamma_gamma]])return Kdef K_sys_byMatrix(k_pi,k_qi,k_ri,theta_pi,phi_pi,psi_pi,theta_qi,phi_qi,psi_qi,theta_ri,phi_ri,psi_ri,Ai,Bi,Ci):#参数均采用数组格式n=np.size(Ai)ki=np.zeros((n,3,3))Ti=np.zeros_like(ki)BBi=np.zeros((n,3,6))Ki=np.zeros((n,6,6))K=np.zeros((6,6))for i in range(n):ki[i]=np.array([[k_pi[i],0,0],\[0,k_qi[i],0],\[0,0,k_ri[i]]])Ti[i]=np.array([[cos(theta_pi[i]),cos(phi_pi[i]),cos(psi_pi[i])],\[cos(theta_qi[i]),cos(phi_qi[i]),cos(psi_qi[i])],\[cos(theta_ri[i]),cos(phi_ri[i]),cos(psi_ri[i])]])BBi[i]=np.array([[1,0,0,0,Ci[i],-Bi[i]],\[0,1,0,-Ci[i],0,Ai[i]],\[0,0,1,Bi[i],-Ai[i],0]])Ki[i]=BBi[i].T@Ti[i].T@ki[i]@Ti[i]@BBi[i]K=np.sum(Ki,axis=0)return Kdef Energy_DistributionJ(M,Value,Vector_Matrix):#3维能量分布：（阶次、Dof、Dof)n=M.shape[0]KE_klj=np.zeros((n,n,n))    for j in range(n):Value_j=Value[j] #0维数组：特征值 频率的平方Vector_r=Vector_Matrix[:,j] #一维数组：行向量Vector_c=Vector_r.reshape(n,1) #改成二维数组：列向量KE_klj[j]=0.5*Value_j*M*Vector_c*Vector_rreturn KE_kljdef Energy_percent(KE_klj): n=KE_klj.shape[0]#KE_klj 3维能量分布：（阶次、Dof、Dof=页、行、列）#将每行Dof的能量合并缩维，得到（各Dof总能量占比,阶）：Energy_perDof=np.sum(KE_klj,2)  #按行合并，第3维压缩掉，成2维数组：矩阵（阶次、各Dof能量）Energy_AllDof_r=np.sum(Energy_perDof,1) #按行合并，第2维压缩掉，成一维数组：行向量[1阶总能量、2阶总能量、...]Energy_AllDof_c=Energy_AllDof_r.reshape(n,1) #改成二维数组：列向量[[1阶总能量],[2阶总能量]、...]Energy_percent=100.0*Energy_perDof/Energy_AllDof_c #2维数组：矩阵（阶次、各Dof能量占比）Energy_percent=Energy_percent.T ########二维数组转置，得到矩阵（各Dof总能量占比,阶）return Energy_percentdef PointSensor(Yxyzi,x_p,y_p,z_p):#将刚体质心加速度Yxyzi根据传感器的的坐标转换到Pxyzi：TransMatrix=np.array([[1,0,0,0,z_p,y_p],\[0,1,0,z_p,0,x_p],\[0,0,1,y_p,x_p,0]])Pxyzi=Yxyzi@TransMatrix.Treturn Pxyzidef EngineSim(mPiston,mConnectingRod,l,lB,R,Ap,IC,offside_cylinder,pr,crank_angle,omega):#mPiston=430/1000;               #kg#mConnectingRod=440/1000;        #kg#l=140/1000;                 #m,Connecting rod pin-pin length#lB=37/1000;             #m,Connecting rod pin B-CG lengh#R=49/1000;                  #m,Crank radius#Ap=5800;               #mm2,Pistion area#IC=0.0015;                  #kg.m2,Connecting rod inertia#offside_cylinder=0/1000   #气缸与曲轴偏置距  add by lijilin 2020.12.23 #num_cylinders=6#-------Pressure in combustion chamber-------#pr=[18,32,32.5,32,20,15,10,8,6,5,3,1.2,0.6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1.0,2.0,4,9,15,18];#crank_angle=[0,20,23,26,50,60,70,80,100,110,150,190,200,220,230,250,280,300,330,360,380,400,440,460,480,500,540,600,630,660,690,710,720]; #omega=3000; #rpm speed of enginepi=np.pipr=np.array(pr)n=np.size(pr)pr.resize(n,1)crank_angle=np.array(crank_angle)crank_angle.resize(n,1)omeg=omega*pi/30;Rl=R/l;       #define ratio R over llA=l-lB;ang=crank_angle*pi/180;sa=sin(ang);ca=cos(ang);s2a=sin(2*ang);c2a=cos(2*ang);#beta=asin((Rl*sa));beta=asin((R*sa-offside_cylinder)/l)  #####update by lijilin 2020.12.23ka=ca+Rl*c2a/cos(beta)+Rl**3*s2a**2/cos(beta)**3/4;#//Piston acceleration:aP=R*ka*omeg**2;#//onnecting rod angular acceleration:alpha_c=Rl*omeg**2*sa/cos(beta);#//Connecting rod GC acceleration:k3=lA*sa/l;k4=ca+Rl*c2a*lB/cos(beta)/l;agx=-R*omeg**2*k3;agy=-R*omeg**2*k4;ag=sqrt(agx**2+agy**2);#//Piston pressure force:Fp=pr*Ap/9.8;#//Piston inertia force:FIP=-mPiston*aP;#//Resultant piston force:FPt=Fp+FIP;#//Connection rod inertia forces(N):FIx=-mConnectingRod*agx;FIy=-mConnectingRod*agy;#//Conneting rod inertia torque(Nm):TIG=IC*alpha_c;#//Crank-pin bearing forces:Bx=(-FIP-Fp+lB*FIy/l)*tan(beta)-lA*FIx/l-TIG/l/cos(beta);By=Fp+FIP-FIy;#//Engine torque:Te=R*(By*sa-Bx*ca);#//气缸壁侧压力：Fw=-FIx-Bx;#倾覆力矩：T_w=-Fw*(R*ca+l*cos(beta))T_offside=-By*offside_cylinderT_all=T_w+T_offsidecrank_angle_i=np.linspace(0,719,720)#"nearest","zero"为阶梯插值#slinear 线性插值#"quadratic","cubic" 为2阶、3阶B样条曲线插值# ‘slinear’, ‘quadratic’ and ‘cubic’ refer to a spline interpolation of first, second or third order)func_interp=interpolate.interp1d(crank_angle[:,0],T_all[:,0],"cubic")T_all_i=func_interp(crank_angle_i).reshape(720,1)psi_shift=int(720/num_cylinders)T_shift=np.zeros((720,num_cylinders))T_shift[:,0]=T_all_i[:,0]for i in range(num_cylinders-1):i=i+1T_shift[:-psi_shift*i,i]=T_all_i[psi_shift*i:,0]T_shift[-psi_shift*i+1:,i]=T_all_i[:psi_shift*i-1,0]T_output=np.sum(T_shift,1)return [Fp,FIP,FPt,FIx,FIy,crank_angle,TIG,Bx,By,crank_angle,Te,crank_angle,Fw,T_w,T_offside,T_all,crank_angle_i,T_shift,T_output]###===============================================================================================================
#######################begin:计算发动机激励#################################
#-----input-----
mPiston=430/1000;               #kg
mConnectingRod=440/1000;        #kg
l=140/1000;                 #m,Connecting rod pin-pin length
lB=37/1000;             #m,Connecting rod pin B-CG lengh
R=49/1000;                  #m,Crank radius
Ap=5800;               #mm2,Pistion area
IC=0.0015;                  #kg.m2,Connecting rod inertia
offside_cylinder=0/1000   #气缸与曲轴偏置距  add by lijilin 2020.12.23
num_cylinders=6
omega=3000
#-------Pressure in combustion chamber--------
pr=[18,32,32.5,32,20,15,10,8,6,5,3,1.2,0.6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1.0,2.0,4,9,15,18];
crank_angle=[0,20,23,26,50,60,70,80,100,110,150,190,200,220,230,250,280,300,330,360,380,400,440,460,480,500,540,600,630,660,690,710,720];[Fp,FIP,FPt,FIx,FIy,crank_angle,TIG,Bx,By,crank_angle,Te,crank_angle,Fw,\T_w,T_offside,T_all,crank_angle_i,T_shift,T_output]=EngineSim(mPiston,mConnectingRod,l,lB,R,Ap,IC,offside_cylinder,pr,crank_angle,omega)#-----output------
figure(figsize=(20,20))
subplot(3,3,1)
plot(crank_angle,np.c_[Fp,FIP,FPt]);#活塞气压力 惯性力  合力
title('Piston pressure force Piston inertia force  Resultant piston force')
subplot(3,3,2)
plot(crank_angle,np.c_[FIx,FIy]);#连杆惯性力x   y
title('Connection rod inertia forces(N)x   y')
subplot(3,3,3)
plot(crank_angle,TIG);#惯性力矩
title('Conneting rod inertia torque(Nm)')
subplot(3,3,4)
plot(crank_angle,np.c_[Bx,By]);#曲柄销力x y
title('Crank-pin bearing forcesx y')
subplot(3,3,5)
plot(crank_angle,Te);#发动机力矩
title('Engine torque')
subplot(3,3,6)
plot(crank_angle,Fw);#气缸侧压
title('offside_Force')subplot(3,3,7)
plot(crank_angle,np.c_[T_w,T_offside,T_all])
title('offside_Torque_w z  all')subplot(3,3,8)
plot(crank_angle_i,T_shift[:,:])
title('offside_Torque all')subplot(3,3,9)
plot(crank_angle_i,T_output,label='$mean: %f$' %np.mean(T_output)) ####
title('offside_Torque_output  all')
legend()
#######################end:计算发动机激励#################################
##==================================================================================================================
#######################begin:计算动力总成悬置模态及解耦率#################################
[m,Ixx,Iyy,Izz,Ixy,Ixz,Iyz]=[153.2,8.2,3.79,7.79,0.83,0.22,1.08]
M_sys=M_sys(m,Ixx,Ixy,Ixz,Iyy,Iyz,Izz)
Ai=[0.01953,-0.00631,0.10237]
Bi=[-0.39667,0.51314,-0.01586]
Ci=[0.05429,0.19266,-0.24009]
theta_pi=[0,0,0]
theta_qi=[90*np.pi/180,90*np.pi/180,90*np.pi/180]
theta_ri=[90*np.pi/180,90*np.pi/180,90*np.pi/180]
phi_pi=[90*np.pi/180,90*np.pi/180,90*np.pi/180]
phi_qi=[0,0,0]
phi_ri=[90*np.pi/180,90*np.pi/180,90*np.pi/180]
psi_pi=[90*np.pi/180,90*np.pi/180,90*np.pi/180]
psi_qi=[90*np.pi/180,90*np.pi/180,90*np.pi/180]
psi_ri=[0,0,0]
k_pi=[196000,154000,210000]
k_qi=[49000,154000,28000]
k_ri=[154000,189000,28000]#[K_xxi,K_xyi,K_xzi,K_yyi,K_yzi,K_zzi]=K_element_i(k_pi,k_qi,k_ri,theta_pi,phi_pi,psi_pi,theta_qi,phi_qi,psi_qi,theta_ri,phi_ri,psi_ri)
#K=K_sys(K_xxi,K_xyi,K_xzi,K_yyi,K_yzi,K_zzi,Ai,Bi,Ci)
#print(K*(abs(K)>0.001))
K_sys=K_sys_byMatrix(k_pi,k_qi,k_ri,theta_pi,phi_pi,psi_pi,theta_qi,phi_qi,psi_qi,theta_ri,phi_ri,psi_ri,Ai,Bi,Ci)Value, Vector_Matrix = np.linalg.eig(np.linalg.inv(M_sys)@K_sys)
#np.set_printoptions(formatter={'float': '{: 0.3f}'.format})
np.set_printoptions(precision=3, suppress=True)
print(M_sys)
print(K_sys)
print(np.sqrt(Value)/2/np.pi)
print(Vector_Matrix)
#print(Vector_Matrix.T@M_sys@Vector_Matrix)
#print(Vector_Matrix.T@K_sys@Vector_Matrix)KE_klj=Energy_DistributionJ(M_sys,Value,Vector_Matrix)
print(Energy_percent(KE_klj))
#######################end:计算动力总成悬置模态及解耦率#################################
##==================================================================================================================
##############begin:建立状态空间方程并用发动机倾覆力矩激励进行仿真 state space function########################import matplotlib.pyplot as plt
from scipy.signal import lti, lsim
import pandas as pd#plt.rcParams['font.sans-serif']=['SimHei'] #用来正常显示中文标签
#plt.rcParams['axes.unicode_minus']=False #用来正常显示负号c_pi=[100,100,100]
c_qi=[100,100,100]
c_ri=[100,100,100]
C_sys=K_sys_byMatrix(c_pi,c_qi,c_ri,theta_pi,phi_pi,psi_pi,theta_qi,phi_qi,psi_qi,theta_ri,phi_ri,psi_ri,Ai,Bi,Ci)
print(C_sys)M=M_sys
K=K_sys
C=C_sysn=6
G=np.r_[np.c_[C,M],np.c_[M,np.zeros((n,n))]] #G=[C,M;M,O]
H=np.r_[np.c_[K,np.zeros((n,n))],np.c_[np.zeros((n,n)),-M]] #H=[K,O;O,-M]
ssA=-np.linalg.inv(G)@H;
ssB=np.linalg.inv(G)@np.row_stack([np.eye(n),np.zeros((n,n))]); #G dX +H X =E u => dX="-G\H" X +"G\E" u
#ssB=[zeros(n),inv(M);inv(M),-inv(M)^2]*[eye(n);zeros(n)];
#ssC=[-M\K,-M\C];
ssC=np.column_stack([-np.linalg.inv(M)@K,-np.linalg.inv(M)@C])
ssD=np.linalg.inv(M); #设输出Y= d^2X=[-M\K,-M\C]*[X,dX]+[M]\Usys=lti(ssA,ssB,ssC,ssD);#------------从文件中读入发动机倾覆力矩激励数据：---------
#data = pd.read_csv('testdata.txt', header=None, )
#data.head(10)
#Fs=data.values[0]
#y=data.values[1:]
#t=np.linspace(0,1/Fs[0]*(np.size(y)-1), num=np.size(y))  #Fs[0]才是采样频率的值！！！#------------使用计算的发动机倾覆力矩激励数据：---------t=crank_angle_i/360/omega*60
y=T_outputy.resize(np.size(y))
y1=(y-np.mean(y)) ###########U=np.zeros((np.size(y),6))
U[:,3]=y1
X0=np.zeros((n*2)) #X0=zeros(2*n,1);%X0=[x1_0,...,dx1_0,...]
tout,Y,X=lsim(sys,U,t,X0);#-------计算悬置点的加速度：
Pxyzi1=PointSensor(Y,Ai[0],Bi[0],Ci[0])
Pxyzi2=PointSensor(Y,Ai[1],Bi[1],Ci[1])
Pxyzi3=PointSensor(Y,Ai[2],Bi[2],Ci[2])plt.figure(figsize=(20,20))
plt.subplot(3,3,1)
plt.plot(t,U) #######
plt.xlabel('Torque of engine(Nm)');
#grid on
plt.grid(alpha=0.3)
plt.subplot(3,3,2)
plt.plot(t,X)  ######
plt.xlabel('6 DOFs of position,speed of engine');
plt.subplot(3,3,3)for i in range(3):plt.plot(t,Y[:,i],label='$Dof:%s$' % ["x","y","z","theta_x","theta_y","theta_z"][i])
plt.xlabel('G acc. of speed/(mps^2)');
plt.legend()plt.subplot(3,3,4)
for i in [3,4,5]:plt.plot(t,Y[:,i],label='$Dof:%s;;rms: %f$' %(["x","y","z","theta_x","theta_y","theta_z"][i],np.std(Y[:,i])))
plt.xlabel('G acc. of ang.speed/(radps^2)');
plt.legend()plt.subplot(3,3,5)
for i in range(3):plt.plot(t,Pxyzi1[:,i],label='$Dof:%s;;rms: %f$' %(["x","y","z"][i],np.std(Pxyzi1[:,i])))
plt.xlabel('Mount1 acc. of speed/(mps^2)');
plt.legend()plt.subplot(3,3,6)
for i in range(3):plt.plot(t,Pxyzi2[:,i],label='$Dof:%s;;rms: %f$' %(["x","y","z"][i],np.std(Pxyzi2[:,i])))
plt.xlabel('Mount2 acc. of speed/(mps^2)');
plt.legend()plt.subplot(3,3,7)
for i in range(3):plt.plot(t,Pxyzi3[:,i],label='$Dof:%s;;rms: %f$' %(["x","y","z"][i],np.std(Pxyzi3[:,i])))
plt.xlabel('Mount3 acc. of speed/(mps^2)');
plt.legend()plt.show()

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发动机悬置python仿真计算

发动机悬置python仿真计算

代码可复制到https://hub.gke2.mybinder.org/user/lijil168-requirements-l6zexquh/tree运行

1、发动机悬置模态及解耦参考

2、发动机动力学激励计算参考

3、用数组和矩阵两种方式计算刚度矩阵，并对比结果，原文公式推导有点点错误。python用多维数组完成矩阵运算，很简洁而且可读性好。

4、思路：由发动机爆压计算倾覆力矩，建立状态空间动力学模型，进行模态及解耦率计算，最后进行仿真，得到发动机质心的状态，再换算到各个悬置点。

5、结果

5.1发动机激励计算结果

5.1悬置系统仿真结果

6、完整的仿真代码

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