length of path of contact

LENGTH OF PATH OF CONTACT

• Fig.4.23 shows two involute gears i.e., pinion and wheel in mesh.

• When the pinion (driver) rotates in clockwise direction, the contact between a pair of teeth begins at point K and ends at point L. Therefore the length of path of contact is KL.

• Point K is located on the flank near the base circle of pinion or the outer end of the tooth face on the wheel. Similarly, point L is on the flank near the base circle of pinion. MN is the common tangent...

• The point K is the intersection of the addendum circle of wheel and the common tangent. The point L is the intersection of the addendum circle of pinion and the common tangent.

• The lengths KP and PL are known as the path of approach and path of recess respectively. The total length KL is called the path of contact.

Let

r = O1 P = Pitch circle radius of pinion,

R = O2P = Pitch circle radius of wheel,

rA = O1 L = Addendum circle radius of pinion, and

RA = O2K = Addendum circle radius of wheel.

From Fig.4.23, the radius of the base circle of pinion is given by

O1M = O1P cos ϕ = r cos ϕ

and radius of the base circle of wheel,

O2N = O2P cos ϕ = R cos ϕ

From right angled triangle O2KN,

⸫ Length of path of approach is given by

Similarly from right angled triangle O1ML,

⸫ Length of path of recess is given by

Then, length of the path of contact is given by

Substituting the values of KP and PL from equations (4.8) and (4.9), we get