机械优化设计课程设计题目：齿轮减速器最优化设计班级：机械班成员2013年6月19日一．设计题目：二级斜齿圆柱减速器的最优化设计二．设计要求：要求减速器有最小的体积和最紧凑的结构三．原始数据：四．设计内容1.设计方案的拟定及说明2.电动机的选择及参数计算3.带轮的初选与计算4.计算圆柱斜齿轮的输入转矩、传动比、转速，然后建立数学模型编写matlab语言程序，运行程序包括geardesign. m 齿轮系统设计主程序Gearobjfun. m目标函数子程序Gearconstr. m 约束条件子程序Gearparameter.m许用应力计算子程序5.输出结果1.该减速器为二级斜齿圆柱减速器，低速级采用二级斜齿圆柱齿轮传动，选择三相交流异步电动机，v带传动2.确定电动机的容量:选择电动机的容量应保证电动机的额定功率大于等于工作机所需要的功率电动机参数t=60/40=1.5s v=s/t=6.0*10^-3m/s P=0.5FV=0.5*110*60*0.001=3.3kw1.η=η1* η32*η23*η4*η5其中齿轮传动η1=0.96滚动轴承η2=0.98齿轮传动η3=0.97联轴器η4=0.99卷筒η5=1.0η=0.96*0.98^3*0.97^2*0.99*1.00=0.84 P d=3.3\0.84=2.93kw三，确定电动机的转速已知压片机的转速40piece/min带传动的传动比i1=2~4 二级齿轮减速器的传动比i2=8~40，所以电动机的转动范围n=i1i2n=640~6400r/min可行方案如下确定电动机的转速具体数据如下计算减速器输入转矩T1，输入转速n，总传动比iiα=1420/40=35.5 初值i0=3计算i=iα/i0=35.5/3=10.52转速n=n m/i0=1420/3=473.33r/min输入转矩T d=9550*3.93/1420=26.43N.mT=T d*i0*η=26.43*3*0.96=72.12N.m输入转矩T1=76.12N.m，输入转速n1=473.33r/min,总传动比11.83建立二级减速器的数学模型，并用MATLAB 语言编制求解程序，如下3.程序如下：(1)%geardesign.m4.global rat;5.global kk;6.global tt1;7.global n0;8.global t;9.global hbs;10.global sigmahp;11.global sigmafp;12.kk=1.2;13.tt1=7.612e4;14.rat01=4;15.rat=11.83;16.n0=473.33;17.t=24000;18.hbs=[280,240,280,240];19.[sigmahp,sigmafp]=gearparameter(rat01);20.x0=[2,3,30,25,4,10,15,];21.options=optimset('Display','iter','TolFun',1e-8);22.lbnd=[2,2,20,20,3,8,8];23.ubnd=[4,4,40,40,5,16,16];24.[x,f,exitflag,output]=fmincon('gearobjfun',x0,[],[],[],[],lbnd,ubnd,'gearconstr',options)(2)%gearobjfun.mfunction f=gearobjfun(x)global rat;f=(x(1)*x(3)*(1+x(5)))/cos(x(6)*pi/180)+(x(2)*x(4)*(1+rat/x(5)))/ cos(x(7)*pi/180);(3)%约束条件子程序gearconstr.mfunction [c,ceq]=gearconstr(x)global rat;global tt1;global kk;global sigmahp;global sigmafp;beta(1)=x(6)*pi/180;beta(2)=x(7)*pi/180;epa(1)=(1.88-3.2*(x(5)+1)/x(3)/x(5))*cos(beta(1));epa(2)=(1.88-3.2*(rat+x(5))/x(4)/rat)*cos(beta(2));for i=1:2yep(i)=1.053/epa(i);zep(i)=sqrt(yep(i));zh(i)=2.9027-0.3702*exp(beta(i));endzv(1)=x(3)/(cos(beta(1)))^3;zv(2)=x(5)*zv(1);zv(3)=x(4)/(cos(beta(2)))^3;zv(4)=rat/x(5)*zv(3);for i=1:4yfa(i)=3.8193-0.3628*log(zv(i));%齿形系数ysa(i)=1.1233+0.146*log(zv(i));%应力校正系数endfor i=1:2epsbeta(i)=0.318*x(i+2)*tan(beta(i));ybeta(i)=1.0-epsbeta(i)*x(i+5)/120;if(ybeta(i)<0.75)ybeta(i)=0.75;endendc(1)=zh(1)*zep(1)*(cos(beta(1)))^2*sqrt((1+1/x(5))/(x(1)*x(3))^3) *sqrt(kk*tt1)-3.726e-3*sigmahp(2);c(2)=zh(2)*zep(2)*(cos(beta(2)))^2*sqrt((x(5)*(1+x(5)/rat))/(x(2) *x(4))^3)*sqrt(kk*tt1)-3.802e-3*sigmahp(4);c(3)=(cos(beta(1)))^2/x(3)^2/x(1)^3*yfa(1)*ysa(1)*yep(1)*ybeta(1) *kk*tt1-0.5*sigmafp(1);c(4)=(cos(beta(1)))^2/x(3)^2/x(1)^3*yfa(2)*ysa(2)*yep(1)*ybeta(1) *kk*tt1-0.5*sigmafp(2);c(5)=x(5)*(cos(beta(2)))^2/x(4)^2/x(2)^3*yfa(3)*ysa(3)*yep(2)*ybe ta(2)*kk*tt1-0.5208*sigmafp(3);c(6)=x(5)*(cos(beta(2)))^2/x(4)^2/x(2)^3*yfa(4)*ysa(4)*yep(2)*ybe ta(2)*kk*tt1-0.5208*sigmafp(4);%非线性约束问题d1=x(1)*x(3)/cos(beta(1));d2=x(1)*x(3)*x(5)/cos(beta(1));d3=x(2)*x(4)/cos(beta(2));d4=x(2)*x(4)*rat*x(5)/cos(beta(2));a1=0.5*x(1)*x(3)*(1+x(5))/cos(beta(1));a2=0.5*x(2)*x(4)*(1+rat/x(5))/cos(beta(2));c(7)=d4-d2-20;c(8)=40+0.5*d2-a2;c(9)=d2-350;c(10)=d4-350;c(11)=50-d1;c(12)=abs(2*x(1)-round(2*x(1)))-0.001;c(13)=abs(2*x(2)-round(2*x(2)))-0.001;ceq=[];(4)%gearparameter.mfunction [sigmahp,sigmafp]=gearparameter(rat01)global n0;global rat;global kk;global t;global hbs;for i=1:4sigmah(i)=495+0.889*(hbs(i)-150);sigmaf(i)=170+0.3*(hbs(i)-150);endnr(1)=n0;nr(2)=nr(1)/rat01;nr(3)=nr(1)/rat01;nr(4)=n0/rat;for i=1:4nn(i)=60*nr(i)*t;if(nn(i)<1e+5) zn(i)=1.6;elseif(nn(i)<1e+7) zn(i)=2.75-0.1006*log(nn(i));else zn(i)=1.0;endif(nn(i)<1e+4) yn(i)=2.5;elseif(nn(i)<3*1e6) yn(i)=5.06-0.2728*log(nn(i));else yn(i)=1.0;endendfor i=1:4sigmahp(i)=sigmah(i)*zn(i)/1.1;sigmafp(i)=sigmaf(i)*yn(i)*1.48;end运行上述最优化设计程序，得到以下结果：Max Line search Directional First-orderIter F-count f(x) constraint steplength derivative optimality Procedure0 8 611.911 3410 Infeasible start point1 16 620.428 1068 1 5.9 169 infeasible2 24 663.819 680.6 1 6.9 163 Hessian modified; infeasible3 32 614.864 544.1 1 -14.4 142 Hessian modified; infeasible4 40 557.166 479 1 -29 135 infeasible5 48 512.611 441.2 1 -16.4 135 infeasible6 58 506.971 435.8 0.25 -3.32 135 infeasible7 69 504.897 433.5 0.125 -3.22 135infeasible8 81 503.994 432.7 0.0625 -3.2 135 infeasible9 103 503.995 432.7 -6.1e-005 -3.19 135 infeasible10 125 503.996 432.7 -6.1e-005 -3.19 135 infeasible11 134 497.358 474.5 0.5 -3.19 134 infeasible12 143 493.941 496.3 0.5 -3.24 134 infeasible13 152 492.149 508.2 0.5 -3.38 134 infeasible14 160 490.287 521.5 1 -3.5 134 infeasible15 168 490.245 523.3 1 -14.9 134 infeasible16 190 490.245 523.3 -6.1e-005 88.7 134 Hessian modified twice; infeasible17 212 490.245 523.3 -6.1e-005 88.7 134 Hessian modified twice; infeasible18 234 490.245 523.3 -6.1e-005 88.7 134 Hessian modified twice; infeasible19 256 490.245 523.3 -6.1e-005 88.7 134 Hessian modified twice; infeasible20 278 490.245 523.3 -6.1e-005 88.7 134 Hessian modified twice; infeasible21 300 490.245 523.3 -6.1e-005 88.7 134 Hessian modified twice; infeasible22 322 490.245 523.3 -6.1e-005 88.7 134 Hessian modified twice; infeasible23 344 490.245 523.3 -6.1e-005 88.7 134 Hessian modified twice; infeasible24 366 490.245 523.3 -6.1e-005 88.7 134 Hessian modified twice; infeasible25 388 490.245 523.2 -6.1e-005 88.7 134 Hessian modified twice; infeasible26 410 490.245 523.2 -6.1e-005 88.7 134 Hessian modified twice; infeasible27 432 490.245 523.2 -6.1e-005 88.7 134 Hessian modified twice; infeasible28 454 490.245 523.2 -6.1e-005 88.7 134 Hessian modified twice; infeasible29 476 490.245 523.2 -6.1e-005 88.7 134Hessian modified twice; infeasible30 498 490.245 523.2 -6.1e-005 88.7 134 Hessian modified twice; infeasible31 520 490.245 523.2 -6.1e-005 88.7 134 Hessian modified twice; infeasible32 542 490.245 523.2 -6.1e-005 88.7 134 Hessian modified twice; infeasible33 564 490.245 523.2 -6.1e-005 88.7 134 Hessian modified twice; infeasible34 586 490.245 523.2 -6.1e-005 88.7 134 Hessian modified twice; infeasible35 608 490.245 523.2 -6.1e-005 88.7 134 Hessian modified twice; infeasible36 630 490.245 523.2 -6.1e-005 88.7 134 Hessian modified twice; infeasible37 652 490.245 523.2 -6.1e-005 88.7 134 Hessian modified twice; infeasible38 674 490.245 523.2 -6.1e-005 88.7 134 Hessian modified twice; infeasible39 696 490.245 523.2 -6.1e-005 88.7 134 Hessian modified twice; infeasible40 707 490.255 523.3 0.125 88.7 134 Hessian modified twice; infeasibleSolver stopped prematurely.fmincon stopped because it exceeded the function evaluation limit,options.MaxFunEvals = 700 (the default value).x =2.5225 1.2726 40.4671 19.2726 2.2726 7.3134 7.2726f =490.2449exitflag =output =iterations: 40funcCount: 707lssteplength: 0.1250stepsize: 1.1490e-004algorithm: 'medium-scale: SQP, Quasi-Newton, line-search'firstorderopt: 133.5199constrviolation: 523.2813message: 'Solver stopped prematurely.fmincon stopped because it exceeded the function evaluation limit,options.MaxFunEvals = 700 (the default value).'>>输出最优解如下：x =2.5225 1.2726 40.4671 19.2726 2.2726 7.3134 7.2726f =490.2449经过适当的圆整和标准化修正后的齿轮传动系统设计参数见表如下：经过进一步的分析，证明此设计结果正确合理，是满足设计要求并使中心距取5 的倍数系列值时的最佳方案.注意上述材料有几处错误以上资料仅供参考。