Machine Drives ( Gear Drives ) (14) (Interference in Involute gear)

Machine Design

Gear Drive

Interference in Involute gear

Introduction:

The phenomenon when the tip of a tooth undercuts the root on its mating gear is known as interference.

Interference in involute gears

• MN is the common tangent to the base circles and KL is the path of contact between the two mating teeth.
• If the radius of the addendum circle of pinion is increased to O1N, the point of contact L will move from L to N. When this radius is further increased, the point of contact L will be on the inside of base circle of wheel and not on the involute profile of tooth on wheel.
• The tip of tooth on the pinion will then undercut the tooth on the wheel at the root and remove part of the involute profile of tooth on the wheel. This effect is known as interference and occurs when the teeth are being cut.
• In brief, the phenomenon when the tip of a tooth undercuts the root on its mating gear is known as interference. Similarly, if the radius of the addendum circle of the wheel increases beyond O2M, then the tip of tooth on wheel will cause interference with the tooth on pinion.
• The points M and N are called interference points. Obviously interference may be avoided if the path of contact does not extend beyond interference points.
• The limiting value of the radius of the addendum circle of the pinion is O1N and of the wheel is O2M.
• The interference may only be avoided, if the point of contact between the two teeth is always on the involute profiles of both the teeth. In other words, interference may only be prevented, if the addendum circles of the two mating gears cut the common tangent to the base circles between the points of tangency.

Note :
In order to avoid interference, the limiting value of the radius of the addendum circle of the pinion (O1 N) and of the wheel (O2 M), may be obtained as follows

Machine Drives ( Gear Drives ) (13) ( Comparision between involute and cycloidal gear)

Machine Design

Gear Drive

Introduction:

The involute gears are more commonly used as compared to cycloidal gears.

Advantages of involute gears

1. The most important advantage of the involute gears is that the centre distance for a pair of involute gears can be varied within limits without changing the velocity ratio. This is not true for cycloidal gears which requires exact centre distance to be maintained.

2. In involute gears, the pressure angle, from the start of the engagement of teeth to the end of the engagement, remains constant. It is necessary for smooth running and less wear of gears. But in cycloidal gears, the pressure angle is maximum at the beginning of engagement, reduces to zero at pitch point, starts increasing and again becomes maximum at the end of engagement. This results in less smooth running of gears.

3. The face and flank of involute teeth are generated by a single curve whereas in cycloidal gears, double curves (i.e. epicycloid and hypocycloid) are required for the face and flank respectively.
Thus the involute teeth are easy to manufacture than cycloidal teeth. In involute system, the basic rack has straight teeth and the same can be cut with simple tools.

Note : The only disadvantage of the involute teeth is that the interference occurs with pinions having smaller number of teeth. This may be avoided by altering the heights of addendum and dedendum of the mating teeth or the angle of obliquity of the teeth.

Advantages of cycloidal gears

Following are the advantages of cycloidal gears :

1. Since the cycloidal teeth have wider flanks, therefore the cycloidal gears are stronger than the involute gears for the same pitch. Due to this reason, the cycloidal teeth are preferred specially for cast teeth.

2. In cycloidal gears, the contact takes place between a convex flank and concave surface, whereas in involute gears, the convex surfaces are in contact. This condition results in less wear in
cycloidal gears as compared to involute gears. However the difference in wear is negligible.

3. In cycloidal gears, the interference does not occur at all. Though there are advantages of cycloidal gears but they are outweighed by the greater simplicity and flexibility of the involute gears.

Machine Design (Gear Drives) (12) (Involute Teeth)

Machine Design

Gear Drive

Involute Teeth

Introduction:

An involute of a circle is a plane curve generated by a point on a tangent, which rolls on the circle without slipping or by a point on a taut string which is unwrapped from a reel.
Construction of involute teeth

Let A be the starting point of the involute.
The base circle is divided into equal number of parts e.g. AP1, P1 P2, P2 P3 etc.The tangents at P1, P2, P3 etc., are drawn and the lenghts P1A1, P2A2, P3A3 equal to the arcs AP1, AP2 and AP3 are set off.
Joining the points A, A1, A2, A3 etc., we obtain the involute curve AR. At any instant A3, the tangent A3T to the involute is perpendicular to P3A3 and P3A3 is the normal to the involute.

In other words, normal at any point of an involute is a tangent to the circle. Now, let O1 and O2 be the fixed centres of the two base circles as shown in Fig.(b).
Let the corresponding involutes AB and A'B' be in contact at point Q. MQ and NQ are normals to the involute at Q and are tangents to base circles.

Since the normal for an involute at a given point is the tangent drawn from that point to the base circle, therefore the common normal MN at Q is also the common tangent to the two base circles.

The common normal MN intersects the line of centres O1O2 at the fixed point P (called pitch point). Therefore the involute teeth satisfy the fundamental condition of constant velocity ratio.

From similar triangles O2 NP and O1 MP,
which determines the ratio of the radii of the two base circles. The radii of the base circles is given by

O1M = O1 P cos φ, and O2N = O2 P cos φ

where φ is the pressure angle or the angle of obliquity.
Also the centre distance between the base circles

If the centre distance is changed, then the radii of pitch circles also changes. But their ratio remains unchanged, because it is equal to the ratio of the two radii of the base circles. The common normal, at the point of contact, still passes through the pitch point. As a result of this, the wheel continues to work correctly. However, the pressure angle increases with the increase in centre distance.