螺旋齿轮传动设计计算

%螺旋齿轮传动设计计算%已知条件：齿数、法面压力角、法面模数、齿顶高系数、顶隙系数、轴交角z1=17;z2=50;alpha_n=20;m_n=2;ha=1;C=0.25;Sigma=60;hd=pi/180;%计算齿轮的分度圆柱压力角、基圆柱和节圆柱螺旋角、法面和端面节圆压力角beta_1=0.5*(Sigma-1);beta_2=beta_1;fprintf('两齿轮螺旋角beta_1=%3.4f°\n',beta_1);alpha_t1=atan(tan(alpha_n*hd)/cos(beta_1*hd));alpha_t2=alpha_t1;fprintf('两齿轮分度圆柱螺旋角alpha_t1=%3.4f°\n',alpha_t1/hd);beta_b1=atan(tan(beta_1*hd)*cos(alpha_t1));beta_b2=beta_b1;fprintf('两齿轮基圆柱螺旋角beta_b1=%3.4f°\n',beta_b1/hd);k=sin(beta_b1)/sin(beta_b1);beta_1p=atan(k*sin(Sigma*hd)/(1+k*cos(Sigma*hd)));beta_2p=beta_1p;fprintf('两齿轮节圆柱螺旋角beta_1p=%3.4f°\n',beta_1p/hd);alpha_np=acos(sin(beta_b1)/sin(beta_1p));fprintf('两齿轮法面节圆压力角alpha_np=%3.4f°\n',alpha_np/hd);alpha_t1p=acos(tan(beta_b1)/tan(beta_1p));alpha_t2p=alpha_t1p;fprintf('两齿轮端面节圆压力角alpha_t1p=%3.4f°\n',alpha_t1p/hd);%确定两齿轮的变位系数inv_t1p=tan(alpha_t1p)-alpha_t1p;inv_t1=tan(alpha_t1)-alpha_t1;inv_t2p=tan(alpha_t2p)-alpha_t2p;inv_t2=tan(alpha_t2)-alpha_t2;xc=(z1*(inv_t1p-inv_t1)+z2*(inv_t2p-inv_t2))/(2*tan(alpha_n*hd))x_n1=input('选择小齿轮法面变位系数x_n1=');x_n2=xc-x_n1;fprintf('大齿轮法面变位系数x_n2=%3.4f\n',x_n2);%计算齿轮的几何尺寸m_np=m_n*cos(alpha_n*hd)/cos(alpha_np);fprintf('公共齿条的法面模数m_np=%3.4fmm\n',m_np);r_1p=m_np*z1/(2*cos(beta_1*hd));r_2p=m_np*z2/(2*cos(beta_2*hd));fprintf('小齿轮节圆柱半径r_1p=%3.4fmm\n',r_1p);fprintf('大齿轮节圆柱半径r_2p=%3.4fmm\n',r_2p);a=(r_1p+r_2p);fprintf('两齿轮最小中心距a=%3.4fmm\n',a);r_1=m_n*z1/(2*cos(beta_1*hd));r_2=m_n*z2/(2*cos(beta_2*hd));fprintf('小齿轮分度圆半径r_1=%3.4fmm\n',r_1);fprintf('大齿轮分度圆半径r_2=%3.4fmm\n',r_2);r_b1=r_1*cos(alpha_t1);r_b2=r_2*cos(alpha_t2);fprintf('小齿轮基圆柱半径r_b1=%3.4fmm\n',r_b1);fprintf('大齿轮基圆柱半径r_b2=%3.4fmm\n',r_b2);r_f1=r_1-m_n*(ha+C-x_n1);r_f2=r_2-m_n*(ha+C-x_n2);fprintf('小齿轮齿根圆柱半径r_f1=%3.4fmm\n',r_f1);fprintf('大齿轮齿根圆柱半径r_f2=%3.4fmm\n',r_f2);r_a1=a-r_f2-0.25*m_n;%为保证合理顶隙0.25*mn，根据中心距计算齿轮齿顶圆柱半径r_a2=a-r_f1-0.25*m_n;fprintf('小齿轮齿顶圆柱半径r_a1=%3.4fmm\n',r_a1);fprintf('大齿轮齿顶圆柱半径r_a2=%3.4fmm\n',r_a2);%校验齿轮传动的重合度B1=sqrt(r_a1^2-r_b1^2)/cos(beta_b1)+sqrt(r_a2^2-r_b2^2)/cos(beta_b2);B2=(a-r_b1*cos(alpha_t1p)-r_b2*cos(alpha_t2p))/sin(alpha_np);B1B2=B1-B2;fprintf('齿轮传动实际啮合线长度B1B2=%3.4fmm\n',B1B2);b_a1=B1B2*sin(beta_b1);b_a2=B1B2*sin(beta_b2);fprintf('小齿轮有效宽度b_a1=%3.4fmm\n',b_a1);fprintf('大齿轮有效宽度b_a2=%3.4fmm\n',b_a2);epsilon=B1B2/(pi*m_n*cos(alpha_n*hd));fprintf('齿轮传动重合度epsilon=%3.4f\n',epsilon);计算结果：两齿轮螺旋角beta_1=29.5000°两齿轮分度圆柱螺旋角alpha_t1=22.6940°两齿轮基圆柱螺旋角beta_b1=27.5632°两齿轮节圆柱螺旋角beta_1p=30.0000°两齿轮法面节圆压力角alpha_np=22.2632°两齿轮端面节圆压力角alpha_t1p=25.3006°xc=0.8312选择小齿轮法面变位系数x_n1=0.40大齿轮法面变位系数x_n2=0.4312公共齿条的法面模数m_np=2.0308mm小齿轮节圆柱半径r_1p=19.8328mm大齿轮节圆柱半径r_2p=58.3317mm两齿轮最小中心距a=78.1644mm小齿轮分度圆半径r_1=19.5322mm大齿轮分度圆半径r_2=57.4478mm小齿轮基圆柱半径r_b1=18.0200mm大齿轮基圆柱半径r_b2=53.0001mm小齿轮齿根圆柱半径r_f1=17.8322mm大齿轮齿根圆柱半径r_f2=55.8102mm小齿轮齿顶圆柱半径r_a1=21.8543mm大齿轮齿顶