# Simplification of tooth profile of spiral bevel gear

In order to facilitate calculation, the involute tooth profile of spiral bevel gear is simplified into linear tooth profile according to the principle of equal area, as shown in the figure.

Make the tooth root thicknesses C1 and D1 of the small end and large end of the tooth profile of the simplified spiral bevel gear equal to the tooth thickness of the corresponding tooth root circle before simplification, while the tooth height of the spiral bevel gear remains unchanged, that is:

Where:

M — modulus of large end of spiral bevel gear tooth profile, mm;

Sc1 – tooth thickness at the root circle of the small end of the simplified front tooth shape of the spiral bevel gear, mm;

Sd1 -Simplified front tooth shape of spiral bevel gear, tooth thickness at tooth root circle of small end, mm;

Hc — tooth height of small end of simplified tooth profile of spiral bevel gear, mm;

Hd — Simplified tooth profile of spiral bevel gear, tooth height of large end, mm.

Then the simplified tooth profile area a’1 at the large end and a’2 at the small end of the spiral bevel gear are respectively:

According to the principle of equal area, that is, a’1 = A1 and a’2 = A2, the simplified tooth top thickness D2 at the large end and C2 at the small end are respectively:

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