The figure is the area differential diagram of the large end of the tooth profile of spiral bevel gear. Let ⌒AB = s ρ， Then the area of the differential unit composed of ⌒ AB, ⌒ CD and involute tooth profiles AD and BC is:
Where
A – tooth profile area of spiral bevel gear, mm2;
ρ —— Radius of any circle, mm;
S ρ —— Tooth thickness at any circle, mm.
Tooth thickness s at any circle at the big end of spiral bevel gear tooth profile ρ For:
Where
S — tooth thickness of large end indexing circle, mm;
R — radius of large end indexing circle, mm;
α —— Large end indexing circle pressure angle;
αρ —— The pressure angle corresponding to any circle at the big end.
By substituting the formula and integrating it, it is obtained that the tooth profile area A1 of the large end of the tooth profile of the spiral bevel gear is:
Of which:
Where
RA — radius of tooth tip circle of big end, mm;
RF — radius of large end tooth root circle, mm;
Ha — top height of big end tooth, mm;
HF — tooth root height of big end, mm;
δ —— Pitch cone angle;
I12 — transmission ratio.