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

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Generating corner points of one tooth of basic rack

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Generating corner points of all teeth of basic rack

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> 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`);

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