Gear Hobbing *
*Maple 6
By B. Laczik, Technical University of Budapest, Hungary, e-mail: laczik@goliat.eik.bme.hu
NOTE: This worksheet demonstrates the Geometric Simulation of Involute Gear Hobbing in Transverse Section
Geometric Simulation of Involute Gear Hobbing in Transverse Section
Basic geometric data of involute gear:
z - number of teeth of gear m - modulus in mm (modulus = Diametral Pitch/25.4) m||n - normal modulus in transverse section of manufactured gear x - addendum modification coefficient h||t - height factor of teeth between pitch and bottom circle h||k - height factor of teeth between pitch and addendum circle c - clearance factor of depths - pressure angle in grad - helix angle in grad, min and sec N - number of position of tool by process of hobbing animation s - number of teeth of tool - increment angle of position of tool
> restart; with(plots):
Warning, the name changecoords has been redefined
>
Generating corner points of one tooth of basic rack
Generating corner points of all teeth of basic rack
> for p from 4 to (4*s-5) do Q[p]:=Q[p-4]+m||n*Pi: Q[p+4]:=Q[p]+m||n*Pi: od:
> Q[4*s]:=Q[0]: polygonplot([seq([Re(Q[j]),Im(Q[j])], j=1..4*s)], style=line, axes=normal, scaling=constrained, title=`The basic rack`);
Simulation of hobbing process
> for k from 0 to 4*s do for j from 0 to N do beta||j:=delta*j+0.2: h[j,k]:=evalf(((Q[k]+R*beta||j)+I*(R+x*m||n)) *exp(I*beta||j)); H[j,k]:=[Re(h[j,k]),Im(h[j,k])]: od; od;
> polygonplot([seq(seq([H[j,k][1],H[j,k][2]], k=0..4*s),j=0..N)],scaling=constrained, style=line, title=`Involute Gear Hobbing`);