题目要求

公式推导和计算

![在这里插入图片描述](https://img-blog.csdnimg.cn/20210610210803488.jpg?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80NjM3NjE4OA==,size_16,color_FFFFFF,t_70#pic_center

计算流程图

pyhton代码

from abc import ABCMeta, abstractmethod
from mpl_toolkits import axisartist
import math
from matplotlib import pyplot as plt
import matplotlib.font_manager as font_manager
from matplotlib.pyplot import MultipleLocator
import numpy as npclass travel():__mata_class_=ABCMetadef __init__(self,**kwargs):self.h=kwargs.get("h")self.Phi=kwargs.get("Phi")@abstractmethoddef state_phi(self):passclass sin_travel(travel):def __init__(self,**kwargs):super().__init__(**kwargs)self.push_travel=kwargs.get("push_travel")def state_phi(self,phi):Phi=self.Phi*math.pi/180phi=phi*math.pi/180if (self.push_travel):return [self.h*(phi/Phi-math.sin(2*math.pi*phi/Phi)/(2*math.pi)),self.h*(1-math.cos(2*math.pi*phi/Phi))/Phi,self.h*2*math.pi*math.sin(2*math.pi*phi/Phi)/Phi**2]else:return [self.h*(1-phi/Phi+math.sin(2*math.pi*phi/Phi)/(2*math.pi)),-self.h*(1-math.cos(2*math.pi*phi/Phi))/Phi,-self.h*2*math.pi*math.sin(2*math.pi*phi/Phi)/Phi**2]class pause_travel(travel):def state_phi(self,phi):return [self.h,0,0]class cam():def __init__(self,Law_of_motion:list,**kwarg):self.travel=Law_of_motionself.e=kwarg.get("e")self.r_0=kwarg.get("r_0")self.r_r=kwarg.get("r_r")self.omega=kwarg.get("omega")if(self.r_0!=None and self.e!=None):self.s0=math.sqrt(self.r_0**2+self.e**2)#求位移类速度类加速度def get_motion_state_phi(self,phi)->list:i=0while(phi>self.travel[i].Phi):phi-=self.travel[i].Phii+=1return self.travel[i].state_phi(phi)def get_motion_state(self,phi)->list:def tf(i):i+=1 return i-1i=0return list(map(lambda x:x*self.omega**tf(i),self.get_motion_state_phi(phi)))def get_pressure_angle(self,phi):state_phi=self.get_motion_state_phi(phi)return math.atan(abs(state_phi[1]-self.e)/\(self.s0+state_phi[0]))*180/math.pidef get_theoretical_outline(self,phi)->tuple:t=self.s0+self.get_motion_state_phi(phi)[0]phi=phi*math.pi/180return (-t*math.sin(phi)-self.e*math.cos(phi),t*math.cos(phi)-self.e*math.sin(phi))def get_theoretical_outline_dphi(self,phi)->tuple:state=self.get_motion_state_phi(phi)t1=self.s0+state[0]t2=state[1]-self.ephi=phi*math.pi/180return (-t1*math.cos(phi)-t2*math.sin(phi),-t1*math.sin(phi)+t2*math.cos(phi))def get_theoretical_outline_ddphi(self,phi)->tuple:state=self.get_motion_state_phi(phi)phi=phi*math.pi/180t1=2*state[1]-self.et2=state[2]-self.s0-state[0]return (-t1*math.cos(phi)-t2*math.sin(phi),-t1*math.sin(phi)+t2*math.cos(phi))def get_rho(self,phi):(dx,dy)=self.get_theoretical_outline_dphi(phi)(ddx,ddy)=self.get_theoretical_outline_ddphi(phi)return math.sqrt(dx**2+dy**2)**3/(dx*ddy-dy*ddx)def get_partical_outline(self,phi)->tuple:t=math.sqrt(self.get_theoretical_outline_dphi(phi)[0]**2+\self.get_theoretical_outline_dphi(phi)[1]**2)t1=self.get_theoretical_outline_dphi(phi)[1]/tt2=self.get_theoretical_outline_dphi(phi)[0]/treturn (self.get_theoretical_outline(phi)[0]-self.r_r*t1,\self.get_theoretical_outline(phi)[1]+self.r_r*t2)def set_co_axis(ax:axisartist.Subplot,title="",xlabel="",ylabel="",pxl=(0,0),pyl=(0,0)):ax.axis[:].set_visible(False)ax.axis["x"] = ax.new_floating_axis(0,0)ax.axis["x"].set_axisline_style("->", size = 1.0)ax.axis["y"] = ax.new_floating_axis(1,0)ax.axis["y"].set_axisline_style("-|>", size = 1.0)ax.axis["x"].set_axis_direction("top")ax.axis["y"].set_axis_direction("right")ax.set_xticks([ 0, np.pi/2, np.pi, 3*np.pi/2, 2*np.pi])ax.set_xticklabels([ "", 'π/2', 'π', '3π/2', '2π' ])ax.text(pxl[0],pxl[1],xlabel,ha="center",va="center")ax.text(pyl[0],pyl[1],ylabel,ha="center",va="center")ax.set_title(title)if (__name__=="__main__"):h=55Phi_0_1=115Phi_0_2=135Phi_s_1=80Phi_s_2=30alpha_1=30alpha_2=70omega=1Law_of_motion=[sin_travel(h=h,Phi=Phi_0_1,push_travel=True),pause_travel(h=h,Phi=Phi_s_1),sin_travel(h=h,Phi=Phi_0_2,push_travel=False),pause_travel(h=0,Phi=Phi_s_2)]Cam=cam(Law_of_motion,omega=1)mo_data=[[],[],[]]mo_dphi_data=[[],[],[]]for i in range(0,360):mo_dphi_data=list(map(lambda x,y:x+[y],mo_dphi_data,Cam.get_motion_state_phi(i)))mo_data=list(map(lambda x,y:x+[y],mo_data,Cam.get_motion_state(i)))y1=mo_dphi_data[0][i]-math.tan((90-alpha_1)*math.pi/180)*mo_dphi_data[1][i]y2=mo_dphi_data[0][i]-math.tan((90+alpha_2)*math.pi/180)*mo_dphi_data[1][i]if (i==0):py1,py2,f1,f2=y1,y2,0,0else:if(f1!=-1):if(f1==1 and py1<y1):f1,s_1,x_1=-1,mo_dphi_data[0][i-1],mo_dphi_data[1][i-1]elif(f1==0 and y1<py1):f1=1py1=y1if(f2!=-1):if(f2==1 and py2<y2):f2,s_2,x_2=-1,mo_dphi_data[0][i-1],mo_dphi_data[1][i-1]elif(f2==0 and y2<py2):f2=1py2=y2            fig1=plt.figure(figsize=(10,10),dpi=80)phi_x=np.linspace(0,2*math.pi,360)s_phi=axisartist.Subplot(fig1,3,1,1)v_phi=axisartist.Subplot(fig1,3,1,2)a_phi=axisartist.Subplot(fig1,3,1,3)s_phi.plot(phi_x,mo_data[0])v_phi.plot(phi_x,mo_data[1])a_phi.plot(phi_x,mo_data[2])set_co_axis(s_phi,"s(φ)","φ","s",(2.15*math.pi,3),(0.1,60))set_co_axis(v_phi,"v(φ)","φ","v",(2.15*math.pi,3),(0.1,65))set_co_axis(a_phi,"a(φ)","φ","a",(2.15*math.pi,3),(0.1,100))fig1.add_axes(s_phi)fig1.add_axes(v_phi)fig1.add_axes(a_phi)X_Phi=[0,Phi_0_1,Phi_0_1+Phi_s_1,Phi_0_1+Phi_s_1+Phi_0_2,360]for i in range(0,4):a_phi.arrow((X_Phi[i+1]+X_Phi[i])*math.pi/360, -100, (X_Phi[i+1]-X_Phi[i])*math.pi/360, 0,width=0.01,length_includes_head=True, head_width=3,head_length=0.1,fc='r',color='b',ec='b')a_phi.arrow((X_Phi[i+1]+X_Phi[i])*math.pi/360, -100, -(X_Phi[i+1]-X_Phi[i])*math.pi/360, 0,width=0.01,length_includes_head=True, head_width=3,head_length=0.1,fc='r',color='b',ec='b') for X in [Phi_0_1,Phi_0_1+Phi_s_1,Phi_0_1+Phi_s_1+Phi_0_2,360]:a_phi.plot([X*math.pi/180,X*math.pi/180],[-105,0],c="black",linewidth=1)a_phi.text((X_Phi[0]+X_Phi[1])*math.pi/360,-108,r"$Φ_0$",ha='center',va='center')a_phi.text((X_Phi[2]+X_Phi[1])*math.pi/360,-108,r"$Φ_s$",ha='center',va='center')a_phi.text((X_Phi[2]+X_Phi[3])*math.pi/360,-108,r"${Φ_0}^{'}$",ha='center',va='center')a_phi.text((X_Phi[3]+X_Phi[4])*math.pi/360,-108,r"${Φ_s}^{'}$",ha='center',va='center')fig2=plt.figure(figsize=(10,10),dpi=80)ds_dphi_s=axisartist.Subplot(fig2,1,1,1)set_co_axis(ds_dphi_s,"","ds/dφ","s",(67,3),(3,65))ds_dphi_s.set_xticks(np.linspace(-40,60,11))ds_dphi_s.set_yticks(np.linspace(-100,60,17))x1=np.linspace(0,60,600)x2=np.linspace(-50,50,1000)x3=x1s1=math.tan((90-alpha_1)*math.pi/180)*(x1-x_1)+s_1s2=math.tan((90+alpha_2)*math.pi/180)*(x2-x_2)+s_2s3=-math.tan((90-alpha_1)*math.pi/180)*x3ds_dphi_s.plot(mo_dphi_data[1],mo_dphi_data[0])ds_dphi_s.plot(x1,s1)ds_dphi_s.plot(x2,s2)ds_dphi_s.plot(x3,s3)ds_dphi_s.text(67,3,"ds/dφ",ha="center",va="center")ds_dphi_s.text(3,65,"s",ha="center",va="center")e=-(s_1-math.tan((90-alpha_1)*math.pi/180)*x_1)/(2*math.tan((90-alpha_1)*math.pi/180))s_0=(s_1-math.tan((90-alpha_1)*math.pi/180)*x_1)/2ds_dphi_s.plot(e,s_0,marker='o')ds_dphi_s.annotate("(%.2f,%.2f)" % (e,s_0), xy=(e,s_0),xytext=(5,0),textcoords='offset points')ds_dphi_s.set_aspect(1)ds_dphi_s.grid()fig2.add_axes(ds_dphi_s)Cam.e,Cam.s0,Cam.r_0=e,-s_0,math.sqrt(e**2+s_0**2)alpha_data=[]rho_data=[]for i in range(0,360):alpha_data.append(Cam.get_pressure_angle(i))rho_data.append(Cam.get_rho(i))if(i==0 or (rho_data[i]>0 and rho_data[i]<rho_min)):rho_min=rho_data[i]fig3=plt.figure(figsize=(10,10),dpi=80)alpha_phi=axisartist.Subplot(fig3,2,1,1)rho_phi=axisartist.Subplot(fig3,2,1,2)set_co_axis(alpha_phi,R"e=%.2f $r_0$=%.2f"%(e,math.sqrt(e**2+s_0**2)),"φ","α",(2.15*math.pi,0.5),(0.1,53))set_co_axis(rho_phi,'ρ(φ)',"φ","ρ",(2.15*math.pi,0.5),(0.1,1200))alpha_phi.plot(phi_x,alpha_data)rho_phi.plot(phi_x,rho_data)fig3.add_axes(alpha_phi)fig3.add_axes(rho_phi)Cam.r_r=rho_min*0.4x_data=[]y_data=[]px_data=[]py_data=[]for i in range(0,360):x_data.append(Cam.get_theoretical_outline(i)[0])y_data.append(Cam.get_theoretical_outline(i)[1])px_data.append(Cam.get_partical_outline(i)[0])py_data.append(Cam.get_partical_outline(i)[1])fig4=plt.figure(figsize=(10,10),dpi=80)x_y=plt.subplot(1,1,1)x_y.set_aspect(1)x_y.grid()x_y.xaxis.set_major_locator(MultipleLocator(10))x_y.yaxis.set_major_locator(MultipleLocator(10))l1,=x_y.plot(x_data,y_data,label="理论廓线",linestyle='--')l2,=x_y.plot(px_data,py_data,label='实际廓线')x_y.set_title(r'${ρ}_{min}=$'+'%.2f\n'%(rho_min)+r'${r}_{r}={ρ}_{min}*0.4=$'+'%.2f\n'%(rho_min*0.4))font=font_manager.FontProperties(fname='C:\Windows\Fonts\simsun.ttc')fig4.legend(handles=[l1,l2],labels=['理论廓线','实际廓线'],loc=[0.15,0.72],prop=font)fig4.add_axes(x_y)plt.show()

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