Clocks, Automobiles and Gears

INTRODUCTION

Gears are one of the most important power transmission component. They transmit motion between two shafts or between a shaft and a slide (Rack and pinion). They transmit motion by direct contact. The surfaces of the two gears make tangential contact.

The law of gearing states the condition that has to be satisified if the consistent angular velocity ratio has to be maintained between two gears. "The common normal at the point of contact of two mating teeth has to pass through the pitch point" Pitch point is the point of contact of two pitch circles. This law can also be interpreted as tangency law of gearing. Since, two pitch circles as to meet at a point, they have to be tangent to one another to maintain constant angular velocity ratio.

where N is the Angular speed, r is the radius, T is the number of teeth

There are various types of gears depending on the shaft alignment and gear reduction required, suitable one could be chosen. Some of them are as follows:

1) Spur Gear

2) Helical gear

3) Spiral Gear

4) Bevel gear

5) Rack and Pinion / Worm and worm wheel

However, in most circumstances, a single gear pair might not be able to provide the desired reduction, hence array of gears are used. The different types of gear trains are as follows:

SIMPLE GEAR TRAIN: In this one, each shaft supports single gear

COMPOUND GEAR TRAIN : Except the first and the last one, each shaft can support one or two gears

REVERTED GEAR TRAIN: If the first and last gear lie on the same axis of the compound gear train, its referred as the reverted gear traain. They are used in clocks

PLANETARY GEAR TRAIN: It is commonly known as Epicyclic gear train. Axis of atleast one of the gears moves relative to the frame. Large speed reductions are possible with epicyclic gears, if the annular gear is fixed, more complex motion could be obtained. It is popularly used in Automobile transmission.

6 possible combinations could be obtained:

1) Annular gear is fixed, Sun gear is the input

2) Carrier is fixed, Sun gear is the input

3) Sun gear is fixed, Annular gear is the input

4) Carrier is fixed, Annular gear is the input

5) Sun gear is fixed, Carrier is the input

6) Annular gear is fixed, carrier is the input

SIMULATION

GEOMETRY: ANSI Metric standards are chosen in the toolbox, gears are constructed with the following inputs.

Module for all the gears = 2.5

Annular gear: Number of teeth = 46, Pitch diameter = 2.5*46 = 115mm

Sun Gear: Number of teeth = 14, Pitch diameter = 2.5*14 = 35mm

Planet gear : Pitch diameter = Annular gear Dp - Sun gear Dp = 115 - 35 = 40mm, T = 40*2.5=16

Four planetary gears are chosen

Face width = 20mm

Shaft Diameter or through hole for external gears is 20mm

Outside diameter of the annular gear is chosen to be 125mm.

The carrier is modelled as follows. It is intended to carry four planetary gears and transmit motion onwards.

MOTION BODY ANALYSIS SETTINGS
All the components are assembled, gear mates are suppressed.

Input speed is maintained at 200RPM for all the cases

Steel (dry) contact pair is established between all the components (Total of 21 pairs)

RESULTS

CASE 1: Sun gear-Input, Annular gear - Fixed, Carrier - Output

CASE 2: Annular gear-Input, Sun gear - Fixed, Carrier - Output

CASE 3: Sun gear-Input, Carrier - Fixed, Annular gear - Output

CASE 4: Annular gear-Input, Carrier - Fixed, Sun gear - Output

CASE 5: Carrier - Input, Sun gear - Fixed, Annular gear - Output

CASE 6: Carrier - Input, Annular gear - Fixed, Sun gear - Output

DISCUSSION ON RESULTS

CASES\Parameters	Angular velocity(deg/sec)	Angular speed (RPM)
Case 1	280	46.6
Case 2	380	63.3
Case 3	920	153.3
Case 4	3613	602
Case 5	1633	272.16
Case 6	5530	921.6

Case 1, 2 and 3 are speed reducers. Case 4,5,6 are speed enhancers. However, why are speed increasers not very common?

Because they affect Bearing life, Gear tooth loading, Lubrication and higher chances of thermal failure and thermal runaways

The animated video can be found in this link : https://www.youtube.com/watch?v=fMyXYepnoQI&feature=youtu.be

CASES\PARAMETERS	Speed Ratio	Train value
Case 1	4.29	0.233
Case 2	3.1595	0.3165
Case 3	1.3046	0.7665

Speed gain comes at the expense of the torque. Hence case 1 is more used when torque is required, climbing uphill for example. Case 3 is more suitable when the speed is required compared to torque and is used on straight roads.

Hence the epicyclic gear trains forms the primary component in Automatic transmission system in the automobiles. The hydraulics are used to bring about automatic locking and unlocking of the planetary gear system and provide torque mode or speed mode as the desired by the vehicle conditon