# Planetary gear torque relationship

### Planetary Gear Set Torque Equation | Physics Forums

torque method, planetary gear train, speed ratio, efficiency. 1. Introduction It is also based on the lever analogy of three-shaft planetary gear trains – simple and compound [8]. by the following relation (considering. A. SI ω ω. ≡.): ·. Page 1. Page 2. Page 3. Page 4. compatibility equations and the torque balance equations of relationship among the speed of each unit in planetary gear train. Dynamic.

### Epicyclic gearing - Wikipedia

Consequently, a marginally higher maximum vehicle speed is achieved. Consequently, in this case the maximum possible vehicle speed cannot be reached.

This surplus of engine power over the power utilised in overcoming road resistance is a measure of the relative acceleration ability for a particular transmission overall gear ratio setting.

Also the area in the loop made between the developed and opposing power curves for direct drive top gear is the largest and therefore the engine has greatest flexibility to respond to the changing driving conditions.

Although this provides tjie highest possible theoretical speed, but the amount of reserve power over the road resistance power is less, so that acceleration response is not rapid as with the direct drive top gear.

Fuel consumption is also less Fig.

## Planetary Gear Set Torque Equation

This, therefore, necessitates for more frequent down changes of the gears with the slightest fall-off in road speed. An additional disadvantage with excessive overdrives is that the minimum specific fuel consumption is theoretically shifted to the engine upper speed range, which is an impractical situation.

Effect of over and under gearing on vehicle performance. Thus, with a good choice of under gearing in top gear for motorway cruising conditions, benefits of prolonged engine life, reduced noise, better fuel economy and reduced driver fatigue are achieved.

### DANotes: Spur Gears: Epicyclic trains

Another major consideration is the unladen and laden operation of the vehicle, particularly if it is to haul heavy loads. Therefore, a compromise has to be made in arriving at an optimum top gear overdrive ratio. For obtaining overdrive gear ratio, the sun gear is held stationary Fig. The planet carrier becomes the driving member and the annular gear the driven one. Therefore, the input shaft drives the planet carrier and the output shaft is driven by the annular gear.

An overdrive simple epicyclic gear train has sun and annulus gears with 21 and 75 teeth respectively. If the input speed from the engine drives the planet carrier at rpm, determine, a the overdrive gear ratio, b the number of planet gear teeth, c the annulus ring and output shaft speed, and id the percentage of overdrive.

Algebraic Method of obtaining Gear Ratios for Epicyclic Gear Train Algebraic method of determining velocity ratios is most suitable in the case of simple and compound epicyclic gear trains. To apply this method to the simple gear train it is convenient to consider the velocity of gear relative to that of the arm or planet carrier as the arm can be imagined fixed.

It is only the algebra that becomes complex in these cases. This statement il entered in the first column of the Table 5. In other words multiply the each motion entered in the first low by x. These statements are entered in the second row of the table. Each element of an epicyclic gear is given y revolution and entered in the third row of the table. Finally the motion of each element of the gear train is added up and entered in the fourth row of the table.

On the other hand the element possesses two degrees of kinematic freedom, as any two of the three velocities may be arbitrarily chosen, the third being dictated by the single equation 2a.

From 2b the net external torque on the three-component element as a whole is: Energy is supplied to the element through any component whose torque and velocity senses are identical.

From 2 the total external power being fed into the three-component element is: In practice, a number of identical planets are employed for balance and shaft load minimisation.

Application of the element relations to a complete train is carried out as shown in the example which follows. More complex epicyclic trains may be analysed in a similar manner, but the technique is not of much assistance when the problem is one of gear train design - the interested designer is referred to the Bibliography. The first element comprises the external sun gear 1 and planet 2; the second comprises the planet 3 and internal ring gear 4. The planets 2 and 3 are compounded together on the common arm axles.

The train is analysed via equations 2 applied to the two elements in turn, together with the appropriate equations which set out the velocity and torque constraints across the interface between the two elements arm and arm.

Neither input nor output is defined here - indeed this terminology can be confusing with multiple degrees of freedom - so for example select gear 1 as input, gear 4 as output.

**Planetary gear set manipulation -Torque**