ENGINEERING RESEARCH PAPER SUMMARY ON DETERMINATION OF GEAR FORCE DIRECTIONS

           

        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