NUMERICAL CODE FOR DESIGN OF SPUR GEAR IN MATLAB

Numerical Code for design of spur gear in Matlab.

zp=input('no of teeth on pinion=');

zg=input('no of teeth on gear=');

p=input('enter the value of power transmitted=');

np=input('enter the rpm of pinion=');

cs=input('enter the value of service factor=');

sutp=input('ultimate tensile strength of pinion=');

sutg=input('ultimate tensile strength of gear=');

fs=input('enter the factor of safety=');

yp=0.484-(2.85/zp);

yg=0.484-(2.85/zg);

sigbp=sutp*(1/3);

sigbg=sutg*(1/3);

ng=zp/zg*np;

if (sigbp*yp)<(sigbg*yg)

    n=np;z=zp;sut=sutp;

    sigb=sigbp;

    y=yp;

    disp('Pinion is weak. Designing acc. to pinion');

else

    n=ng;z=zg;sut=sutg;

    sigb=sigbg;

 y=yg;

    disp('Gear is weak. Designing acc. to gear');

end

v=5;

cv=3/(3+v);

Mt=(60000000*p)/(2*pi*n);

m=1;

sb=0;

peffa=0;

while(sb<=peffa)

dg=m*zg;

dp=m*zp;

pt=(2*Mt)/dg;

vact=(pi*dg*ng)/60000;

if (vact>20)

    cv=5.6/(5.6+(vact^0.5));

elseif (vact<10)

    cv=3/(3+vact);

else

    cv=6/(6+vact);

end

peffa=(cs*pt)/cv;

b=10*m;

sb=m*b*sigb*y;

if (sb>peffa)

    disp('module=');

    disp(m);

    disp('design is safe');

else

    m=m+1;

end

end

ha=m;

hf=1.25*m;

c=0.25*m;

th=1.5708*m;

fr=0.4*m;

disp('standard properties of designed gear');

disp('adendum=');

disp(ha);

disp('dedendum=');

disp(hf);

disp('tooth thickness=');

disp(th);

disp('clearance=');

disp(c);

disp('fillet radius=');

disp(fr);

n=z;            %Number of teeth

pd=10/m;            %Diametral pitch

phi_d=input('enter the pressure angle=');   %Pressure angle in degrees .

r_fillet=fr/10;     %Radius of the fillet of a tooth.

%Initializes all matrices.

xp=zeros(10,1);yp=zeros(10,1);

xo=zeros(10,1);yo=zeros(10,1);

xr=zeros(2,1);yr=zeros(2,1);

xro=zeros(5,1);yro=zeros(5,1);

xf=zeros(5,1);yf=zeros(5,1);

theta=zeros(10,1);

f=zeros(2,32);

M=[];c=[];e=[];g=[];h=[];

d=n/pd;             %Pitch diameter

phi=phi_d*pi/180;   %Pressure angle in radians

db=d*cos(phi);      %Diameter of the base circle

do=d+2/pd;          %Diameter of the addendum (outside) circle

tt=pi/(2*pd);       %Tooth thickness at the pitch circle

dr=d-2*1.25/pd; %Diameter of dedendum(root) circle

%Calculates the coordinates of the involute profile.

n1=10;

tp=pi*d/(2*n);

for i=1:n1;

    r=do/2-(do-db)*(i-1)/(2*(n1-1));

    pha=acos(db/(2*r));

    t=2*r*(tp/d+(tan(phi)-phi)-(tan(pha)-pha)); %Tooth tickness at an angle phi

                                                                %Involute equation from Shigley's book.

    theta(i)=t/(2*r);

    %Coordinate transformation from polar coordinates to Cartesian coordinates

   xp(i)=r*sin(theta(i));      

   yp(i)=r*cos(theta(i));

end

xp=xp';yp=yp';

%Calculates the addendum arc.

n2=10;

for i=1:n2;

    theta_o=theta(1)*(i-1)/(n2-1);

    xo(i)=(do/2)*sin(theta_o);

    yo(i)=(do/2)*cos(theta_o);

end

xo=xo';yo=yo';

%Calculates the non-involute portion of the curve which is between the base circle and

% the dedendum circle. In this case, a straight line segment represents the non-involute 

% portion which is parallel to the y axis and connects to the fillet arc .

for i=1:2;

    theta0=asin((xp(1,n1)+r_fillet)/(dr/2));

    %Calculates theta0, the angle between the central line (y-axis) and the line from 

    % the origin to the last point of the involute curve.

    xr(i)=xp(1,10);

    yr(i)=yp(1,10)-(yp(1,10)-r_fillet-(dr/2)*cos(theta0))*i/2;

    %yr(2)=(dr/2)*cos(theta0)+r_fillet

end

xr=xr';yr=yr';

%Calculates the dedendum arc.

n3=5;

for i=1:n3;

   thetar=theta0+(pi/n-theta0)*(i-1)/(n3-1);   

   %(pi/n-theta0) is the angle subtended of the dededem arc.

   xro(i)=dr*sin(thetar)/2; %xro(1) is the beginning point of the arc.

    yro(i)=dr*cos(thetar)/2;

end

xro=xro';yro=yro';

%Calculates the coordinates of the fillet of a tooth.

%Draws one quarter of a circle from the last point of the non-involute part

%  of the curve to the first point of the dedenum arc.

n4=5;

for i=1:n4;

xf(i)=xro(1)-r_fillet*cos((i-1)*pi/(2*n4-2));

   yf(i)=yro(1)+r_fillet*(1-sin((i-1)*pi/(2*n4-2)));    %yf(5)=yro(1)-r_fillet*sin(4*pi/8)

end

xf=xf';yf=yf';

%Appends each piece of curve defined earlier to generate a one-half profile of a tooth.

c=[c,xo,xp,xr,xf,xro];

e=[e,yo,yp,yr,yf,yro];

g=[c',e'];

g=g';                       %One-half tooth profile

%Reflectes the involute curve about y axis to get the whole tooth.

ff=[-1 0;0 1]*g;        %Reflects the first half to generate the second half.

n5=n1+n2+n3+n4+2;

for i=1:n5;             %n4 points =n1(involute)+n2(addendum)+n4(fillet)

                        %           +2(noninvolute)+n3(dedendum)

   f(1,i)=ff(1,n5+1-i); %Reverses the order of the points on the second half so that 

    f(2,i)=ff(2,n5+1-i);    % it is easy to plot when joining the first half.

end

h=[h,f,g];              %The whole tooth profile.

%Rotates and appends one tooth to generate n teeth.

for i=1:n;

    kk=[cos(2*pi*(i-1)/n) sin(2*pi*(i-1)/n);-sin(2*pi*(i-1)/n) cos(2*pi*(i-1)/n)];

                    %Rotation matrix

mm=kk*h;        %Rotates.

    M=[M,mm];   %Appends.

end

M=[M,h(:,1)];   %Add the first point, so the curve returns to the original point.

%Plots involute curve and basic circle

p=zeros(3,2);

x=[-2,2;0,0];  %Defines lines to draw x-axis and y-axis.

circle=[]; invo=[];

%Draws base circle.

for a=2*pi:-0.01:0;

p(1,1)=db*cos(a)/2;

p(2,1)=db*sin(a)/2;

circle=[circle, p(:,1)];

end

a0=2*pi/n+(pi/pd/2+n/pd*(tan(phi)-phi))/d+pi/2;

%Draws the invoulte curve.

for a=a0:-0.01*pi:a0-3*pi/4;

p(1,1)=db*cos(a)/2;         %Starting point of the involute curve.

p(2,1)=db*sin(a)/2;

len=db*(a0-a)/2;                %Arc length

p(1,2)=p(1,1)-len*sin(a);   %End point of the involute curve.

p(2,2)=p(2,1)+len*cos(a);

invo=[invo, p(:,2)];

plot(M(1,:),M(2,:), x(1,:),x(2,:),'k', x(2,:),x(1,:),'k', circle(1,:),circle(2,:), p(1,:),p(2,:),'--', invo(1,:),invo(2,:))

axis('equal');

axis ([-15 15 -15 15]);

drawnow; %Completes pending drawing events and updates the figure window.

end

axis('equal');