NATIONAL
INSTITUTE OF INDUSTRIAL ENGINEERING
SIMPLE
WORD RULES FOR THE DETERMINATION
OF GEAR FORCE DIRECTIONS
SUBMITTED BY
B.SANKAR
ROLL NO 87
PGDIE 42
INTRODUCTION :
Gears are basically used for transmitting the motion
from one shaft to another shaft .There are two forces are acting the shafts
those are axial force and radial force .Static equilibrium used for determining
the bearing reactions.
The transmitted
force, Ft, acts tangent to the pitch circle of a gear and is
sometimes called
the tangential force. The radial force, Frad is a separating force that
acts radially inward toward the gear centre. The radial force tries to
push the two gears apart, but equal and opposite forces exerted by the separation of the gears. Axial
forces, Fa, are gear forces
which ad parallel to the shaft, and
are opposed by thrust.
Spur and helical gears are used to combine two shafts that are parallel to each other. Spur
gears are the most common gears,
and due to their straight cut teeth will transfer no axial force, and thus will not require shaft thrust bearings. Helical
gears are quieter and can be run at higher speeds than spur gears, but will require thrust
bearings to counteract the axial force due to the angle tilted teeth
make with the shaft center.
Bevel gears are used to com&
two shafts, at right angles to each
other that would intersect if extended beyond the gears. Worm gears are used to provide
right-angle connection of two non intersecting shafts. Use of bevel or worm gears will result in transmitted,
radial and axial gear forces. Machine design or machine elements courses
presented at a level.
Appropriate for junior students
in the Mechanical Engineering Technology
or Mechanical Engineering departments. Since lecture material typically includes methods to determine the magnitudes
of the gear forces, the material presented here is for determination of only
the gear force directions. Methods
for the calculation of gear
force magnitudes can be found in a number.
SPUR
GEARS :
Gear A is the driving gear and
gear B is the driven gear. The transmitted force, Ft, tangent to the pitch
circles at the pitch point. The transmitted force is one component of the total
gear force, F. The other component of the total gear force is the radial, or
separating force, Fr.
The directions of the transmitted and radial forces will vary
depending on whether the gear is a driving gear or a driven gear.
The directions of the gear forces can be determined using the following
word rules
GEAR
FORCE DIRECTIONS:
Ft, Transmitted Force:
Driving gear - Opposed to the direction of motion and applied at the
pitch point.
Driven gear - In the direction of motion and applied at the pitch point.
Fr Radial Force: Driving or
driven gears directed radially inward to the gear centre and applied at the
pitch point.
The proper force directions of the transmitted and
radial forces for applying the word rules,
the Ft, for driving gear A is shown
acting to the left, opposite to
the direction of motion, at the
pitch point.
The radial force, Fn is applied at the
pitch point adding vertically downward, which corresponds to radially inward toward the gear centre For the driven gear B, the transmitted force, Ft,
is shown applied at the pitch point and acting to the right, in the direction of motion.
The radial force for driven gear B ads
vertically up, or radially inward to the gear center.3 Based on the word rule
established directions, the gear forces for gear A are drawn acting at the pitch point, which is at the pitch circle radius.
It should be noted that if the gear
were part of a gear train, a driven gear may also drive another gear, and would then be subjected to both
driving and driven gear force
direction word rules.
BEVEL GEARS:
For the determination of bevel
gear forces, it can be assumed I hat these forces ad through the face
midpoint, rather than through pitch
point at the outside face. Since the transmitted
torque will the same anywhere on the gear
face, using the face midpoint
will result in a conservative design since the gear force is slightly larger than the force used in a strength or
wear analysis of the gear.
GEAR
FORCE DIRECTIONS:
Ft, Transmitted Force Driving
gear:
Opposed to the direction of motion and applied
at the face midpoint. Driven gear - In the direction of motion and applied at the
fare midpoint
The transmitted force,Ft: acts at the face midpoint vertically
up in the direction of motion.
The radial force, Fp:
acts to the right, toward the gear centre. The axial force, Fa, is also
The inside face to
the outside face. Since the shaft angle is 90 degrees, computation of the radial and axial force magnitudes
for gears A and B would show that the radial force for gear A is equal to the axial force for gear
B and that the radial force for gear B is equal to the axial force for gear A, so the forces on the face midpoint are in
equilibrium.
The gear forces for
driving gear A, appropriate directions found using the above word rules, for a
free body diagram of shaft 1, and would be used to Calculate the bearing reactions
B1 and B2 The gear equal to the face midpoint
radius. Since the axial force, Fa, acts parallel to shaft 1, bearing B2 must be
thrust bearing to keep the shaft in compression, as good
design practice dictate.
HELICAL
GEARS:
Helical gears are Similar to spur
gears since sets of both are
used to transfer power between parallel shafts.
However the teeth on a helical
gear are at an angle (helix angle) with the axial centre line of the gear.Consequently, the total
gear force applied at the pitch point will have an axial force component, along
with the transmitted and radial gear force components. The directions of the
gear forces for the drive gear of
drive gear A. The word rules for
gear force directions for
helical gears are as follows
GEAR
FORCE DIRECTIONS:
Ft, Transmitted Force:
Driving gear - Opposite to the direction of motion and applied at the
pitch point.
Driven gear - In the direction of motion and applied at the
pitch point.
Fp Radial Force: Driving or driven gears.
Directed radially inward to the gear centre and applied at the pitch
point.
Fa, Axial Force: driving or
driven gears
Gear at the pitch point and draw
either the top (bottom) or front (back) view to find direction. Draw in the transmitted force, Ft, with its arrowhead
touching the pitch point as determined
above; the axial force must be applied on
the same side of the gear tooth
with its arrow head touching the
transmitted force arrowhead. The line of action of the axial force
is
WORM
GEARS:
Worm gear sets are used to
transfer power between non intersecting
shafts which are at right
angles. The worm resembles a screw thread in appearance, and normally
has a much smaller
diameter than the worm gear, which
is actually a helical gear.
High gear ratios can be
achieved with worm gear but at the
expense of efficiency.
The teeth of the worm gear are shaped to provide maximum
contact between the worm and worm gear, and normal practice is to have the worm drive the worm
gear. The directions of
the gear for- can then be determined.
GEAR
FORCE DIRECTIONS:
Ft, Transmitted Force:
Driving gear - Opposed to the direction of motion and applied at the pitch point.
Driven gear
- In the direction of motion and
applied at the pitch point.
Fr Radial Force:
Worm or worm gear.
Directed radially
inward to the gear centre and applied at the pitch point.
Fa, Axial Force: Worm gear.
Gear at the
pitch point and draw either the view of the gear. Draw in the transmitted
force, Ft, with its arrowhead touching the
pitch point as determined above.
The axial force, Fa must be applied on the
same side of the gear tooth at the pitch point with its arrowhead
touching the transmitted force arrowhead The line of action of the axial force
is parallel to the shaft.
For a 90 degree shaft angle
between the worm and worm gear, the following relationships should be
noted
1. The transmitted force on the
worm is the axial force on the
worm gear.
2. The axial force on the
worm is the transmitted force on the worm
gear.
3. Forces on the same Line of
action are but opposite when going
from the worm to the worm gear.
Therefore, at the pitch point of the
meshed gears the transmitted force on the
worm will be of equal magnitude but opposite
direction the axial force on the worm gear. Likewise, the axial force on the worm will be of equal magnitude but opposite sense to the transmitted
force on the worm gear, and the
radial forces on each gear will have equal magnitude but opposite direction.
CONCLUSIONS:
Proper gear force directions are necessary to determine bearing reactions on shafts with mounted gears. Gear
force directions for transmitted, radial and axial gear forces can be easily determined by following
simple word rules. The word rules presented here have
been applied to spur, bevel, helical and worm with illustrations
to clarify their doubts
The gear force word rules can help eliminate problems and confusion typically encountered by mechanical engineering and technology students when drawing free body diagrams of shafts with mounted
gears.
RESOURCES:
Knimbus
online library: gears journals
