This document discusses various topics related to gears, including: 1. Center distance variation in gears can affect time-varying mesh stiffness and gear vibration. A new kinematic model is proposed to evaluate actual contact positions under varying center distances. 2. The minimum number of teeth for gears without undercutting is typically 17, though gears with fewer can be used if strength and contact ratio allow. 3. Contact ratio measures the average number of teeth in contact during engagement, and is typically 1.3-1.4 for machine tool components depending on the application's precision requirements. 4. Spur gears have straight, parallel teeth but produce high stresses and noise. Helical gears generate thrust but allow

1. TOPIC: CENTRE DISTANCE VARIATION,MINIMUM NUMBER OF
TEETH,CONTACT RATIO,SPUR,HELICAL GEARS AND PROBLEMS
ROLL NUMBERS : 63,66,72,79,81
Kinematics of machine

2. CENTER DISTANCE VARIATION IN GEARS
• Backlash is a play between tooth surfaces of paired gears in mesh.
Mating gears also have a clearance (play) vertical to tooth depth. This is
called Tip and Root Clearance (c), the distance between tooth root and the
tooth tip of mating gears.
• Gear centre distance variation is one of the most common defects of gear
transmission systems. The changes in the gear center distance as well as
other faults have a direct influence on the Time Varying Mesh Stiffness
(TVMS) which further modifies gear vibration behaviors. Accurately
estimating gear TVMS under fault conditions is crucial in gear vibration
dynamic simulation. Common methods used to evaluate TVMS are
generally based on the assumption that the gear pair is perfectly mounted
and that all mesh points are at their theoretical positions. This assumption
prevents these methods from modeling deviations in gear center distance.

3. • To address this shortcoming, this paper proposes a new gear mesh
kinematic model that can evaluate the actual contact positions of
tooth engagement with time varying gear mesh centre distance. With
the proposed kinematic model, the actual TVMS of both healthy and
cracked gear teeth are computed under conditions of perfect
mounting, constant gear center distance deviation, and also time-
varying gear center distance. Numerical simulations indicate that gear
center distance variation has a significant effect on gear TVMS.
Comparison between the effect of multiple faults and summed
individual effects on TVMS indicates that the TVMS modification due
to multiple-faults do not appear to combine in a linear manner. The
proposed model for actual TVMS enables gear system dynamic
models to be used to study the effects of assembly errors, gear run-
out errors, shaft bending, and bearing deformation on the vibration
behavior of gear transmission systems.

4. MINIMUM NO. OF TEETH
• the minimum number of teeth (z) is: For pressure angle 20 degrees,
the minimum number of teeth free of undercutting is 17. However,
gears with 16 teeth or less can be usable if their strength and contact
ratio pose any ill effect.
1. Start with a two-gear train. To be able to determine a gear ratio,
you must have at least two gears engaged with each other — this is
called a "gear train." ...
2. Count the number of teeth on the drive gear. ...
3. Count the number of teeth on the driven gear. ...
4. Divide one teeth count by the other.

5. To avoid interference without undercutting, the addendum circles of both the pinion and the gear
should intersect the common tangent AB to the base circles within the points of tangency A and B.
When the addenda are equal, obviously, then the interference will always occur first at number of
teeth on the pinion (for a given speed ratio) for this situation can be determined as now explained.
The addendum length a = O2A – O2P. From ΔO2AP, we can write, with α as the pressure angle,

6. CONTACT RATIO
• The contact ratio is defined as the ratio of the length of arc
of contact (from lowest point to the highest point at contact exit) to
the circular pitch. In other words ,contact ratio is the average number
of teeth in mesh during a contact cycle; its value usually can span
from 1.30–140.
• In a simple way, it can be defined as a measure of the average
number of teeth in contact during the period during which a tooth
comes and goes out of contact with the mating gear.
Transverse contact ratio, mp, εα The contact ratio in a transverse
plane. It is the ratio of the angle of action to the angular pitch.

7. • For machine tool components, addressing this question is more
related to the end-purpose of the gears involved, e.g. (1) are the gear
train be used for precision driving of a turret or linear worktable.
• If the gears involved are used in precision-positioning devices, the
contact ratio must be high, e.g. 1.30–1.40, as this guarantees a more
uniform motion (more teeth involved), more sliding action and a
greater load capacity at the expense of little efficiency if helical
gearing is involved. On the other side, if the gears are to be used for a
spindle transmission drive, the contact ratio can range below 1.35, as
the requirements for precision in rotation can be addressed more
through the bearing precision and their preload (use of spur or low
helix-angle helical pairs).

8. SPUR GEARS
• Spur gears are a type of cylindrical gear, with shafts that are parallel
and coplanar, and teeth that are straight and oriented parallel to the
shafts. They’re arguably the simplest and most common type of gear
– easy to manufacture and suitable for a wide range of applications.
• The teeth of a spur gear have an involute profile and mesh one tooth
at a time. The involute form means that spur gears only produce
radial forces (no axial forces), but the method of tooth meshing
causes high stress on the gear teeth and high noise production.
Because of this, spur gears are typically used for lower speed
applications, although they can be used at almost any speed.

9. HELICAL GEARS
• Helical is the most commonly used gear in transmissions. They also
generate large amounts of thrust and use bearings to help support
the thrust load. Helical gears can be used to adjust the rotation angle
by 90 deg. when mounted on perpendicular shafts.
• Helical or "dry fixed" gears offer a refinement over spur gears. The
leading edges of the teeth are not parallel to the axis of rotation, but
are set at an angle. Since the gear is curved, this angling makes the
tooth shape a segment of a helix. Helical gears can be meshed in
parallel or crossed orientations.

10. • Another advantage of helical gears over spur gears is in torque
capacity. Spur gears, by design, are weaker than helical gears because
loads are transmitted over fewer teeth. Helical gearing is machined
with angled teeth, then hardened and ground, which is complex but
necessary to achieve a high-efficiency gear mesh.

11. PROBLEMS