From Manual of Gear Design: Spur and Internal Gears, Volume II
Internal Differential Drives
DIFFERENTIAL GEAR TRAINS MAKE POSSIBLE THE GREATEST SPEED REDUCTION IN THE MINIMUM SPACE. THEY ARE OF GREAT VALUE WHERE A LARGE REDUCTION OF MOTION IS REQUIRED, BUT THEY ARE SELDOM PRACTICAL WHEN ANY APPRECIABLE AMOUNT OF POWER IS TO BE TRANSMITTED BECAUSE OF THE EXCESSIVELY HIGH TOOTH LOADS AND HIGH VELOCITIES OF TOOTH ENGAGEMNT WHICH RESULT FROM THIS CONSTRUCTION.
WHEN,
N 1 = NUMBER OF TEETH IN FIXED INTERNAL GEAR
N 2 = NUMBER OF TEETH IN DRIVEN INTERNAL GEAR
N 3 = NUMBER OF TEETH IN PINION MESHING WITH N 1
N 4 = NUMBER OF TEETH IN PINION MESHING WITH N 2
n = NUMBER OF REVOLUTIONS PER MINUTE OF DRIVING SHAFT
n' = NUMBER OF REVOLUTIONS PER MINUTE OF DRIVEN SHAFT
WHEN THE VALUE OF THE REDUCTION RATIO IS PLUS THE DRIVEN MEMBER WILL TURN IN THE SAME DIRECTION AS THE DRIVING MEMBER. WHEN THE VALUE IS MINUS, THE DRIVEN MEMBER WILL TURN IN THE OPPOSITE DIRECTION TO THE DRIVING MEMBER.
WHEN,
A = RADIUS OF ARM OR ECCENTRICTY OF STUD CARRYING PINIONS, INCHES.
V = VELOCITY OF CENTER OF PINIONS, FT. PER. MIN.
V 1 = PITCH LINE VELOCITY OF TOOTH ENGAGEMENT ON FIXED INTERNAL GEAR (N 1), FT. PER MIN.
V 2 = PITCH LINE VELOCITY OF TOOTH ENGAGEMENT ON DRIVEN INTERNAL GEAR(N 2) FT. PER MIN.
| WHEN, | T = DRIVING TORQUE IN INCH POUNDS. |
| HP = NUMBER OF HORSEPOWER, TRANSMITTED LOAD. | |
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Gears are rotating mechanical devices employing 'teeth' in order to transmit torque between separate axes. Two or more cooperating gears are called a transmission and can produce a mechanical advantage by changing speed, torque or rotation direction.
Spur gears are the simplest type of gear. Transmitting power between parallel axes, the teeth project radially on the disc.
Worms and worm gears are gear sets that offer high gear reduction and torque multiplication with a small footprint. A worm drive is a cylindrical gear with a shallow spiral thread that engages the worm gear in a non-intersecting, perpendicular axes configuration.
Topics of Interest
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