石川法，啮合冲击载荷程序

clear; z1=19;z2=45;%两齿轮的齿数 m=1.75; b=m*z1*0.6; ha=m; c=0.25*m; d1=m*z1;d2=m*z2; r1=m*z1/2;r2=m*z2/2;%分度圆半径 hf1=1.25*m; hf2=1.25*m; alpha=20*pi/180;%分度圆压力角 invalpha=tan(alpha)-alpha; db1=d1*cos(alpha); db2=d2*cos(alpha); rb1=db1/2; rb2=db2/2;%基圆半径 rf1=r1-hf1; rf2=r2-hf2;%齿根圆半径 da1=d1+2*ha; da2=d2+2*ha; ra1=da1/2; ra2=da2/2;%齿顶圆半径 alpha_a1=acos(rb1/ra1); alpha_a2=acos(rb2/ra2);%齿顶圆压力角 alpha_f1=acos(rb1/rf1); alpha_f2=acos(rb2/rf2);%齿根圆压力角 s=pi*m/2;%分度圆弧齿厚 e=s;%分度圆齿槽宽 sk1=ra1*(s/r1+2*((tan(alpha)-alpha)-(tan(alpha_a1)-alpha_a1))); sk2=ra2*(s/r2+2*((tan(alpha)-alpha)-(tan(alpha_a2)-alpha_a2)));%齿顶圆齿厚 PB1=r1*cos(alpha)*(tan(alpha_a1)-tan(alpha)); PB2=r2*cos(alpha)*(tan(alpha_a2)-tan(alpha)); B1B2=PB1+PB2; Pb=pi*m*cos(alpha);%基圆齿距 Epsilona=B1B2/Pb; N1B1=sqrt(ra1^2-rb1^2); N1B2=N1B1-B1B2; N2B2=sqrt(ra2^2-rb2^2); N2B1=N2B2-B1B2; rF2=sqrt(rb2^2+N2B1^2); rF1=sqrt(rb1^2+N1B2^2);%有效齿根圆半径 alpha_F1=acos(rb1/rF1); alpha_F2=acos(rb2/rF2); sf1=2*rF1*sin(pi/2/z1+invalpha-tan(alpha_F1)+alpha_F1); sf2=2*rF2*sin(pi/2/z2+invalpha-tan(alpha_F2)+alpha_F2); h1=sqrt(ra1^2-(sk1/2)^2)-sqrt(rf1^2-(sf1/2)^2); h2=sqrt(ra2^2-(sk2/2)^2)-sqrt(rf2^2-(sf2/2)^2); hr1=sqrt(rF1^2-(sf1/2)^2)-sqrt(rf1^2-(sf1/2)^2); hr2=sqrt(rF2^2-(sf2/2)^2)-sqrt(rf2^2-(sf2/2)^2); hi1=(h1*sf1-hr1*sk1)/(sf1-sk1); hi2=(h2*sf2-hr2*sk2)/(sf2-sk2); N2C=N2B1+Pb; B2C=B1B2-Pb;%双齿啮合区 CD=Pb-B2C;%单齿啮合区 N1C=N1B1-Pb; Fn=754;%外力 E=2e+008;%弹性模量 v=0.26;%泊松比 n=100; step=B2C/n;%B2C为双齿啮合区 nz1=3600;%齿轮1转速r/min Tz=60/z1/nz1;%循环的周期 t1=B2C/Pb*Tz; t2=CD/Pb*Tz; step2=t1/n; step4=t2/n; %双齿啮合区设一啮合为i点，一啮合点为j点。 for i=1:n x(i)=i*step; tt(i)=i*step2; xx(i)=Pb+i*step; N1Bi(i)=N1B2+i*step;%双齿啮合区i啮合点公式中具体参数的计算 O1Bi(i)=sqrt(N1Bi(i)*N1Bi(i)+rb1^2); ai1(i)=acos(rb1/O1Bi(i)); gamai1(i)=pi/2/z1+invalpha-tan(ai1(i))+ai1(i); miui1(i)=ai1(i)-gamai1(i); rxi1(i)=O1Bi(i); hxi1(i)=rxi1(i)*cos(gamai1(i))-sqrt(rf1^2-(sf1/2)^2); N2Bi(i)=N2B2-i*step; O2Bi(i)=sqrt(N2Bi(i)^2+rb2^2); ai2(i)=acos(rb2/O2Bi(i)); gamai2(i)=pi/2/z2+invalpha-tan(ai2(i))+ai2(i); miui2(i)=ai2(i)-gamai2(i); rxi2(i)=O2Bi(i); hxi2(i)=rxi2(i)*cos(gamai2(i))-sqrt(rf2^2-(sf2/2)^2); N1Bj(i)=N1Bi(i)+Pb;%双齿啮合区j啮合点公式中具体参数的计算 O1Bj(i)=sqrt(N1Bj(i)^2+rb1^2); aj1(i)=acos(rb1/O1Bj(i)); gamaj1(i)=pi/2/z1+tan(alpha)-alpha-tan(aj1(i))+aj1(i); miuj1(i)=aj1(i)-gamaj1(i); rxj1(i)=O1Bj(i); hxj1(i)=rxj1(i)*cos(gamaj1(i))-sqrt(rf1^2-(sf1/2)^2); N2Bj(i)=N2Bi(i)-Pb; O2Bj(i)=sqrt(N2Bj(i)^2+rb2^2); aj2(i)=acos(rb2/O2Bj(i)); gamaj2(i)=pi/2/z2+tan(alpha)-alpha-tan(aj2(i))+aj2(i); miuj2(i)=aj2(i)-gamaj2(i); rxj2(i)=O2Bj(i); hxj2(i)=rxj2(i)*cos(gamaj2(i))-sqrt(rf2^2-(sf2/2)^2); sigmabri1(i)=12*Fn*cos(miui1(i))^2*(hxi1(i)*hr1*(hxi1(i)-hr1)+hxi1(i)^3/3)/b/E/sf1^3; sigmabri2(i)=12*Fn*cos(miui2(i))^2*(hxi2(i)*hr2*(hxi2(i)-hr2)+hxi2(i)^3/3)/b/E/sf2^3; sigmabti1(i)=6*Fn*cos(miui1(i))^2*((hi1-hxi1(i))/(hi1-hr1)*(4-(hi1-hxi1(i))/(hi1-hr1))-2*log((hi1-hxi1(i))/(hi1-hr1))-3)*(hi1-hr1)^3/b/E/sf1^3; sigmabti2(i)=6*Fn*cos(miui2(i))^2*((hi2-hxi2(i))/(hi2-hr2)*(4-(hi2-hxi2(i))/(hi2-hr2))-2*log((hi2-hxi2(i))/(hi2-hr2))-3)*(hi2-hr2)^3/b/E/sf2^3; sigmasi1(i)=2*(1+v)*Fn*cos(miui1(i))^2*(hr1+(hi1-hr1)*log((hi1-hr1)/(hi1-hxi1(i))))/b/E/sf1; sigmasi2(i)=2*(1+v)*Fn*cos(miui2(i))^2*(hr2+(hi2-hr2)*log((hi2-hr2)/(hi2-hxi2(i))))/b/E/sf2; sigmagi1(i)=24*Fn*hxi1(i)*cos(miui1(i))^2/pi/b/E/sf1^2; sigmagi2(i)=24*Fn*hxi2(i)*cos(miui2(i))^2/pi/b/E/sf2^2; sigmap=4*Fn*(1-v^2)/pi/b/E; sigmabrj1(i)=12*Fn*cos(miuj1(i))^2*(hxj1(i)*hr1*(hxj1(i)-hr1)+hxj1(i)^3/3)/b/E/sf1^3; sigmabrj2(i)=12*Fn*cos(miuj2(i))^2*(hxj2(i)*hr2*(hxj2(i)-hr2)+hxj2(i)^3/3)/b/E/sf2^3; sigmabtj1(i)=6*Fn*cos(miuj1(i))^2*((hi1-hxj1(i))/(hi1-hr1)*(4-(hi1-hxj1(i))/(hi1-hr1))-2*log((hi1-hxj1(i))/(hi1-hr1))-3)*(hi1-hr1)^3/b/E/sf1^3; sigmabtj2(i)=6*Fn*cos(miuj2(i))^2*((hi2-hxj2(i))/(hi2-hr2)*(4-(hi2-hxj2(i))/(hi2-hr2))-2*log((hi2-hxj2(i))/(hi2-hr2))-3)*(hi2-hr2)^3/b/E/sf2^3; sigmasj1(i)=2*(1+v)*Fn*cos(miuj1(i))^2*(hr1+(hi1-hr1)*log((hi1-hr1)/(hi1-hxj1(i))))/b/E/sf1; sigmasj2(i)=2*(1+v)*Fn*cos(miuj2(i))^2*(hr2+(hi2-hr2)*log((hi2-hr2)/(hi2-hxj2(i))))/b/E/sf2; sigmagj1(i)=24*Fn*hxj1(i)*cos(miuj1(i))^2/pi/b/E/sf1^2; sigmagj2(i)=24*Fn*hxj2(i)*cos(miuj2(i))^2/pi/b/E/sf2^2; ki1(i)=Fn/(sigmabri1(i)+sigmabri2(i)+sigmabti1(i)+sigmabti2(i)+sigmasi1(i)+sigmasi2(i)+sigmagi1(i)+sigmagi2(i)+sigmap);%双齿啮合时i点刚度 kj(i)=Fn/(sigmabrj1(i)+sigmabrj2(i)+sigmabtj1(i)+sigmabtj2(i)+sigmasj1(i)+sigmasj2(i)+sigmagj1(i)+sigmagj2(i)+sigmap);%双齿啮合时j点刚度 k(i)=ki1(i)+kj(i); end step3=CD/n;%CD为单齿啮合区 for i=1:n xxx(i)=B2C+i*step3; ttt(i)=t1+i*step4; N1Bi(i)=N1C+i*step3; O1Bi(i)=sqrt(N1Bi(i)^2+rb1^2); ai1(i)=acos(rb1/O1Bi(i)); gamai1(i)=pi/2/z1+invalpha-tan(ai1(i))+ai1(i); miui1(i)=ai1(i)-gamai1(i); rxi1(i)=O1Bi(i); hxi1(i)=rxi1(i)*cos(gamai1(i))-sqrt(rf1^2-(sf1/2)^2); N2Bi(i)=N2C-i*step3; O2Bi(i)=sqrt(N2Bi(i)^2+rb2^2); ai2(i)=acos(rb2/O2Bi(i)); gamai2(i)=pi/2/z2+invalpha-tan(ai2(i))+ai2(i); miui2(i)=ai2(i)-gamai2(i); rxi2(i)=O2Bi(i); hxi2(i)=rxi2(i)*cos(gamai2(i))-sqrt(rf2^2-(sf2/2)^2); sigmabri1(i)=12*Fn*cos(miui1(i))^2*(hxi1(i)*hr1*(hxi1(i)-hr1)+hxi1(i)^3/3)/b/E/sf1^3; sigmabri2(i)=12*Fn*cos(miui2(i))^2*(hxi2(i)*hr2*(hxi2(i)-hr2)+hxi2(i)^3/3)/b/E/sf2^3; sigmabti1(i)=6*Fn*cos(miui1(i))^2*((hi1-hxi1(i))/(hi1-hr1)*(4-(hi1-hxi1(i))/(hi1-hr1))-2*log((hi1-hxi1(i))/(hi1-hr1))-3)*(hi1-hr1)^3/b/E/sf1^3; sigmabti2(i)=6*Fn*cos(miui2(i))^2*((hi2-hxi2(i))/(hi2-hr2)*(4-(hi2-hxi2(i))/(hi2-hr2))-2*log((hi2-hxi2(i))/(hi2-hr2))-3)*(hi2-hr2)^3/b/E/sf2^3; sigmasi1(i)=2*(1+v)*Fn*cos(miui1(i))^2*(hr1+(hi1-hr1)*log((hi1-hr1)/(hi1-hxi1(i))))/b/E/sf1; sigmasi2(i)=2*(1+v)*Fn*cos(miui2(i))^2*(hr2+(hi2-hr2)*log((hi2-hr2)/(hi2-hxi2(i))))/b/E/sf2; sigmagi1(i)=24*Fn*hxi1(i)*cos(miui1(i))^2/pi/b/E/sf1^2; sigmagi2(i)=24*Fn*hxi2(i)*cos(miui2(i))^2/pi/b/E/sf2^2; sigmap=4*Fn*(1-v^2)/pi/b/E; ki2(i)=Fn/(sigmabri1(i)+sigmabri2(i)+sigmabti1(i)+sigmabti2(i)+sigmasi1(i)+sigmasi2(i)+sigmagi1(i)+sigmagi2(i)+sigmap); end o1=polyfit(tt,k,3); o2=polyfit(ttt,ki2,3); o3=polyfit(tt,ki1,3); o4=polyfit(tt,kj,3); %plot(2,2,1);plot(x,k);hold on;plot(xxx,ki2);xlabel('啮合线位移/(mm)');ylabel('线性啮合刚度k'); %plot(tt,k); %hold on; %plot(ttt,ki2); %hold on; T=0.0008772; for i=0:1; A=polyfit(tt,k,2) for TT=0.000048:0.0000005:0.000512; K=-187835724775138*TT.*TT+80690343132.3420*TT+502073826.920299; S1=6.15*0.000001*sin(2*pi*60*19*(TT+i*T)); if K.*S1<0 P1=0; else P1=K.*S1; end plot(TT+i*T,P1,'r');xlabel('啮合时间/(s)');ylabel('激励/（N）'); hold on; end for A1=0.000512:0.0000005:0.0006004; A2=1898981472963.80*A1+1466425788.53; S2=6.15*0.000001*sin(2*pi*60*19*(A1+i*T)); if A2.*S2<0 P2=0; else P2=A2.*S2; end plot(A1+i*T,P2,'r'); hold on; end for TTT=0.0006004:0.0000005:0.0008344; B=polyfit(ttt,ki2,2); KI2=-472401734368030*TTT.*TTT+659557708465.797*TTT+100570316.788086; S3=6.15*0.000001*sin(2*pi*60*19*(TTT+i*T)); if KI2.*S3<0 P3=0; else P3=KI2.*S3; end plot(TTT+i*T,P3,'r'); hold on; end for A3=0.0008344:0.0000005:0.0009252; A4=2020991673127.75*A3-1364307306.1; S4=6.15*0.000001*sin(2*pi*60*19*(A3+i*T)); if A4.*S4<0 P4=0; else P4=