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Sun and planet gear

The sun and planet gear (also called the planet and sun gear) was a method of converting

reciprocating motion to rotary motion and was used in the first rotative beam engines. 

It was invented by the Scottish engineer  William Murdoch, an employee of  Boulton and Watt, 

 but was patented by James Watt in October 1781. It was invented to bypass the patent on the

crank , already held by James Pickard.[1]

 It played an important part in the development of devices for rotation in the Industrial Revolution.

[citation needed ] 

The Sun-Planet Worm Gear block represents a two-degree-of-freedom planetary gear built fromcarrier, sun and planet gears. By type, the sun and planet gears are crossed helical spur gears

arranged as a worm-gear transmission, in which the planet gear is a worm. Such transmissions

are used in the Torsen type 1 differential. When transmitting power, the sun gear can be

independently rotated by the worm (planet) gear, or by the carrier, or both.

You specify a fixed gear ratio, which is determined as the ratio of the worm angular velocity tothe sun gear angular velocity. You control the direction by setting the worm thread type, left-handed or right-handed. Rotation of the right-handed worm in positive direction causes the sun

gear to rotate in positive direction too. The positive directions of the sun gear and the carrier are

the same.

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Most automatic transmissions use epicyclic or planetary gears. They are constantly in mesh with

each other.

A basic planetary gearset has a sun gear, which meshes with planet gears, also called planet

 pinions.

The planet pinions, in sets of three or more, rotate on bearings, on hardened steel pins, on a

 planet carrier, which spaces the pinions equally around the sun gear. It also locates them so they

can mesh with an internally toothed ring gear.

This means the planet pinions are always in mesh with the sun gear and the ring gear.

In operation, their motion is described as either “Walking" or "Idling".

“Walking” means that if either the sun gear, or the ring gear, is held stationary, the alternative

driving member rotates the planet gears on their pins. This turns the planet carrier in the same

direction as the driving member.

Planet gears always turn in the same direction on their pins as planet carrier rotation, while they

walk around a stationary sun gear. They always turn in the opposite direction on their pins whilewalking inside a stationary ring gear.

"Idling" refers to the rotation of the planet gears on their pins whenever the planet carrier isstationary. Torque is transmitted from the sun gear to the ring gear, or from the ring gear to the

sun gear, via the planet gears and the stationary carrier.

In both cases the driven member is turned in the opposite direction to the driving member. To

 provide the ratios available from the gearset, one or more of the components must be held - or released. This is normally done by hydraulic servos, operated by transmission fluid under  pressure, acting on lined bands or clutches, or, by one-way clutches. They allow turning in one

direction, but act as a lock-up, or reaction member in the opposite direction.

In practice, a combination of these is normally used.

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Operation

The sun and planet gear  converted the vertical motion of a beam, driven by a steam engine, intocircular motion using a 'planet', a cogwheel fixed at the end of the connecting rod (connected to

the beam) of the engine. With the motion of the beam, this revolved around, and turned, the 'sun',

a second rotating cog fixed to the drive shaft, thus generating rotary motion. An interestingfeature of this arrangement, when compared to that of a simple crank, is that when both sun and

 planet have the same number of teeth, the drive shaft completes two revolutions for each double

stroke of the beam instead of one. The planet gear is fixed to the connecting rod and thus does

not rotate around its own axis.

 Note that the axle of the planet gear is tied to the axle of the sun gear by a link that freely rotates

around the axis of the sun gear and keeps the planet gear engaged with the sun gear but does notcontribute to the drive torque. This link appears, at first sight, to be similar to a crank but the

drive is not transmitted through it. Thus, it did not contravene the crank patent.

What is Sun and Planetary Gear or Epicyclic Gear?

The sun and planetary gear arrangement, sometimes also called as Epicyclic gear  train, is a gear train, where typically few smaller gears rotate and revolve by meshing around a bigger sun gear.

So, that’s how the name comes. 

Details of the Sun and Planetary Gear Arrangement 

  Various arrangements of the sun and planetary gear are possible and used across the industry.

And the complexity increases with the addition of the numbers of planetary gears.

  For the purpose of the discussion, we will use the following simple Epicyclic gear arrangement:

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  As you can see from the above picture, the planet gears are connected by a rigid arm in such a

way that the rotation axis of the combined planet gears and that of the sun gear lies at the sameline.

  As the sun gear rotates, the meshed planet gears also rotates in the opposite direction and as

the planet gears rotates it causes rotation to the arm connecting the planet gears.

  The beauty of this kind of gear arrangement is that you will have multiple options for giving

input torque and getting output to and from the gear box. How?

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  Look at the cross section drawing of the gear above. The axis-1 and axis-3 are the axis of the

planetary gears. Axis of the arm is marked as axis-2 and the axis of the sun gear is marked as

axis-4. 

  You can use the axis-4 as input and axis-2 as output for transmitting the powers. One of the

benefits you will get here is both the input as well as the output axis fall in the same line. So

whenever you need to transmit power and require reduction as well then you can think of using

this configuration.

  Similarly, depending upon your power transmission requirement you can think of using any

other axis combinations as your input and output axis.

Applications of Sun Planet Gear Arrangement 

  The sun and planetary gear is used in most of the automatic transmission system. In automatic

transmission compound sun and planetary gear is used.

  These kinds of gear also find application for converting reciprocal motion to the rotary motion in

steam engine. 

  Another application of the sun and planetary gear is electric screw driver. You need to achieve a

moderate reduction ratio in a limited space.

  This kind of gear trains can provide solution for wide range of  transmission problem if you can

customize and understand the system suitably.

Conclusion

The sun and planet gear arrangement is a non linear or Epicyclic gear train. As the namesuggests, the construction of this type of gear train is similar to that of our solar system.

Most of the automatic transmissions use this kind of gear train. Though we use the basic gearing

law for calculating the gear ratio for the sun and planet gear arrangement as well but slightly

different way.

The error in cutting teeth may cause

vibrations and noise during operation 

2. The error in cutting teeth may cause vibrations and noise during operation.

1 2 . 3 . Advantages and Disadvantages of Gear Drive

The following are the advantages and disadvantages of the gear drive as compared to belt,

rope and chain drives :

Advantages

1. It transmits exact velocity ratio.

2. It may be used to transmit large power.

3. It has high efficiency.

. It has reliable service.5. It has compact layout.

Disadvantages

1. The manufacture of gears require special tools and equipment.

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Sun-Planet Worm Gear Model

Model Variables

RWG  Gear, or transmission, ratio determined as the ratio of the worm angular velocity to the gear

angular velocity.

The ratio is positive for the right-hand worm and negative for the left-hand worm. 

ωS  Angular velocity of the sun gear 

ωP  Planet (that is, worm) angular velocity 

ωC  Carrier angular velocity 

ωSC  Angular velocity of the sun with respect to the carrier 

α  Normal pressure angle 

 λ  Worm lead angle 

L  Worm lead 

d   Worm pitch diameter 

τ S  Torque applied to the sun shaft 

τ P  Torque applied to the planet shaft 

τ C  Torque applied to the carrier shaft 

τ loss  Torque loss due to meshing friction. The loss depends on the device efficiency and the power flow

direction.

To avoid abrupt change of the friction torque at ωS = 0, the friction torque is introduced via the

hyperbolic function. 

τ instfr  Instantaneous value of the friction torque added to the model to simulate friction losses 

τ fr  Steady-state value of the friction torque 

k   Friction coefficient 

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ηWG  Efficiency for worm-gear power transfer 

ηGW  Efficiency for gear-worm power transfer 

ωth  Absolute angular velocity threshold

 μSC  Sun-carrier viscous friction coefficient 

 μWC  Worm-carrier viscous friction coefficient 

 Advantages and disadvantages

Advantages of planetary gears over parallel axis gears include high power density, large

reduction in a small volume, multiple kinematic combinations, pure torsional reactions, and

coaxial shafting. Disadvantages include high bearing loads,constant lubrication requirements,inaccessibility, and design complexity.

[6][7] The planetary gearbox arrangement is an engineering

design that offers many advantages over traditional gearbox arrangements. One advantage is its

unique combination of both compactness and outstanding power transmission efficiencies. Atypical efficiency loss in a planetary gearbox arrangement is only 3% per stage. This type of 

efficiency ensures that a high proportion of the energy being input is transmitted through the

gearbox, rather than being wasted on mechanical losses inside the gearbox.

Another advantage of the planetary gearbox arrangement is load distribution. Because the load

 being transmitted is shared between multiple planets, torque capability is greatly increased. Themore planets in the system, the greater load ability and the higher the torque density.

The planetary gearbox arrangement also creates greater stability due to the even distribution of mass and increased rotational stiffness. In a stepped planet system the vibrations are significantly

greater than that of a non-compound gearbox. As torque is applied to a cog of one size and

transferred on by a cog of another size, the compound gear will experience lateral pull, causinguneven pressure onto the gear teeth, increasing friction and wear, and decreasing gear life. In

comparison, torque applied radially onto a non-compound gear will be transferred on radially by

the gear, without any lateral pressure onto the gear teeth.

Ideal Gear Constraints and Gear Ratio

Sun-planet worm gear imposes one kinematic constraint on the three connected axes:

ωS = ωP/ RWG + ωC .

The gear has two independent degrees of freedom. The gear pair is (1,2) = (S,P).

The torque transfer is:

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 RWGτ P + τ S  –  τ loss = 0 ,

τ C = –  τ S,

with τ loss = 0 in the ideal case.

Nonideal Gear Constraints

In a nonideal gear, the angular velocity and geometric constraints are unchanged. But thetransferred torque and power are reduced by:

  Coulomb friction between thread surfaces on W and G, characterized by friction

coefficient k or constant efficiencies [ηWG, ηGW]

  Viscous coupling of driveshafts with bearings, parametrized by viscous frictioncoefficients μSC and  μWC 

The torque transfer for nonideal gear has the general form:

τ S = –   RWG(τ P  –   μWCωP) + τ instfr  ,

τ instfr = τ fr ·tanh(4ωSC/ωth) +  μSCωSC .

The hyperbolic tangent regularizes the sign change in the friction torque when the sun gear 

velocity changes sign.

Geometric Surface Contact Friction

In the contact friction case, ηWG and ηGW are determined by:

  The worm-gear threading geometry, specified by lead angle  λ and normal pressure angle

α.

  The surface contact friction coefficient k .

ηWG = (cosα  –  k ·tan λ)/(cosα + k /tan λ) ,

ηGW = (cosα  –  k /tan λ)/(cosα + k ·tanα) .

Constant Efficiencies

In the constant efficiency case, you specify ηWG and ηGW, independently of geometric details.

Self-Locking and Negative Efficiency

If you set efficiency for the reverse power flow to a negative value, the train exhibits self-locking . Power can not be transmitted from sun gear to worm and from carrier to worm unless

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some torque is applied to the worm to release the train. In this case, the absolute value of the

efficiency specifies the ratio at which the train is released. The smaller the train lead angle, the

smaller the reverse efficiency.

Meshing Efficiency

The efficiencies η of meshing between worm and gear are fully active only if the absolute value

of the gear angular velocity is greater than the velocity tolerance.

If the velocity is less than the tolerance, the actual efficiency is automatically regularized to unity

at zero velocity.

Viscous Friction Force

The viscous friction coefficients of the worm-carrier and sun-carrier bearings control the viscousfriction torque experienced by the carrier from lubricated, nonideal gear threads. For details, see

the  Nonideal Gear Constraints section.