Program 60-1162Compound Epicyclic Gear Design (Parallel Axis)

Introduction The compound epicyclic gear unit consists of a central external gear (sun gear) meshed with one or more external gears (sun planet gears). The sun planet gears are part of a two-gear cluster on the same shaft or axis. The second gear is the ring planet gear. The ring planet gears are then meshed with an internal gear (ring gear) which encloses the system. The planet gears and planet gear support bearings are held in a carrier which rotates about the geometrical center of the unit.(The term epicyclic comes from the path of a point on a planet gear which traces out an epicycloid in space.) There are three basic types of compound epicyclic gear units. Planetary: When the ring gear is fixed or grounded and the sun and carrier are

input/output members the unit is called a planetary gear. Star: When the carrier is fixed and the sun and ring are input/output members

the unit is a star gear. The star gear is not an epicyclic gear as the planet gear centers do not rotate about the unit central axis but since the construction is basically the same it is included in the family. For high speed units the star gear is often used in cases where planetary gears are not practical because of the high centripetal acceleration loads on the planet gears.

Solar: When the sun is fixed and the carrier and ring are input/output members

the unit is a solar gear. The range of speed reduction ratios for which these units can be designed with reasonable proportions is as follows: Planetary Gear: 6:1 to 25:1 Star Gear: 5:1 to 24:1 Solar Gear: 1.05:1 to 2.2:1 Below these ranges the planet gears become quite small and it becomes difficult to design the gears and planet bearings for reasonable life. Above these ranges the sun gear becomes small and the number of planets that can be used without interference is limited. This, again, makes the design of the bearings difficult. If more than one planet gear is used, the number of planets that will assemble between the sun and ring is limited by the numbers of teeth in the gears and by the possibility of interference between the tips of the planet gear teeth. For a number of

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identical planets to assemble equally spaced around the center, the following relationship between the tooth numbers in the gears must be met: [(NringNpl-sun )+(NsunNpl-ring)]/np =integer where: Nring = Number of teeth in ring gear

Npl-sun = Number of teeth in sun gear planet Nsun = Number of teeth in sun gear

Npl-ring = Number of teeth in ring gear planet np = Number of planet gears The distance between the planet gear centers in the carrier must, of course, be greater than the outside diameter of the planet gears or tooth tip interference will result (assuming the planet gears are in the same plane). It is not necessary that the planets be equally spaced. However, to make assembly possible, they must be spaced at multiples of the least mesh angle.

ep/ = integer

= 360 / [(NringNpl-sun )+(NsunNpl-ring)]

where: ep = Angle between adjacent planet gears, deg

= Least mesh angle, deg

It is not necessary (or even desirable) that PDring = PDsun+PDpl-sun+PDpl-ring (where PD = Teeth/(TransPitch)). If this relationship is met, the center distance is standard and the operating pressure angles at the sun/planet external mesh, ext, and the planet/ring internal mesh, int,will be equal to the nominal pressure angle of the systems. A higher operating pressure angle at the external mesh, ext, will often increase the strength of the gear set while not affecting the operating characteristics of the mesh adversely. (If the ring gear rim thickness is 2 tooth depths or more, a highint will tend to reduce the bending stress. If the ring gear rim thickness is 1.5 tooth depths or less, a low int will tend to reduce the bending stress.) Epicyclic units are often used as differentials. UTS model 60-1162 is restricted to systems where one element is fixed, and it does not consider use as a differential. UTS models 60-1163 and 60-1164 treat simple and compound epicyclic units used as differentials.

60-1162Compound Epicyclic Gear Design (Parallel Axis)

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Examples If you are using model 60-1162 for the first time you may wish to run the following example. Assume we wish to design a spur gear compound planetary set with about 15.5 to 1 reduction ratio with a ring gear diameter of about 12 inches. Assume also that the smallest number of teeth we wish to use is 20 for the sun gear and 28 for the internal mesh planetary gears. (The number of teeth would be selected based upon material and duty cycle. See UTS model 60-180.) Open a new analysis in 60-1162. Enter 20 in the input column for Sun Gear Teeth, 28 for Ring Planet Teeth and 15.5 for Planetary Gear ratio. Figure 1 shows the data input form with this data. Report 1 shows the solution. Fig. 1

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Report 1

Model Title : Program 60-1162 Unit System: US

MESSAGE FIELD

ERROR MESSAGE, internal mesh

ERROR MESSAGE, external mesh

ERROR MESSAGE, mesh - general

Prime factors greater than 100

NUMBER OF TEETH

Ring Gear Teeth

Ring Planet Teeth (Internal mesh) 28

Sun Planet Teeth (External mesh)

Sun Gear Teeth 20

RATIOS

Planetary Gear (Forward rotation) 15.5000

Star Gear (Reverse rotation)

Solar Gear (Forward rotation)

Planet/Sun Ratio

Ring/Planet Ratio

EXTERNAL MESH (SUN/PLANET)

Normal Pitch 1.000000 1/in

Normal Pressure Angle 20.000000 deg

Nominal helix Angle 0.000000 deg

60-1162Compound Epicyclic Gear Design (Parallel Axis)

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Model Title : Program 60-1162 Unit System: US Transverse Pitch 1.0000 1/in

Transverse Press Angle 20.0000 deg

Normal Module 25.4 mm'

Transverse Module 25.4 mm'

Opr Pitch Dia, planet in

Opr Pitch Dia, sun gear in INTERNAL MESH (RING/PLANET)

Normal Pitch 1.000000 1/in

Normal Pressure Angle 20.000000 deg

Nominal helix Angle 0.000000 deg

Transverse Pitch 1.0000 1/in

Transverse Press Angle 20.0000 deg

Normal Module 25.4 mm'

Transverse Module 25.4 mm'

Opr Pitch Dia, ring gear in

Opr Pitch Dia, planet in

The model has set the normal diametral pitch to 1, the normal pressure angle to 20 degrees and the helix angle to 0 degrees since no values were input. A solution for the numbers of teeth in the ring gear and sun planet gears requires an iterative solution, since the equations solved in this direction cannot be solved directly. We also need to temporarily fix an operating pitch diameter to provide enough input for the solution. For now we will set the operating pitch diameter of the sun to the standard pitch diameter.

To do this we must work directly in the TK Solver Variable Sheet. Toggle to this, move the mouse pointer to the input column for Opr Pitch Dia, sun gear and type ns/pt_s. When you press the enter key you should have 20 in the input column. We will make a guess of 100 teeth for the ring gear. Type 100 in the input column for this variable. Move the mouse pointer to the status column and type G, or double-click the Status cell and pick Guess from the drop-down list that appears. This will

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tell TK to start an iteration with a first guess of 100. Your screen should be like Sheet 1. Sheet 1

60-1162 COMPOUND EPICYCLIC (Ver 6.01)

Use Tools, GwzUnits to Change Units

m_i ERROR MESSAGE, internal meshm_x ERROR MESSAGE, external meshm_g ERROR MESSAGE, mesh - generalm_p Prime factors greater than 100

NUMBER OF TEETH:G 100 nr Ring Gear Teeth28 np_r Ring Planet Teeth (Internal mesh)

np_s Sun Planet Teeth (External mesh)20 ns Sun GearTeeth

RATIOS:15.5 pl_mg Planetary Gear (Forward rotation)

st_mg StarGear (Reverse rotation)sl_mg SolarGear (Forward rotation)mx Planet/Sun Ratiomi Ring/Planet Ratio

opr_cd in Operating Center Distancestd_cds in "Standard" CD - External meshstd_cdr in "Standard" CD - Internal meshtpa_x deg Opr Press Angle - External meshtpa_i deg Opr Press Angle - Internal mesh

RATIO RANGE: (Speed Reduction Gears)ms_pl Planetary Range (Normal = 6 to 25)

In: Sun Fixed: Ring Out: Carrierms_st Star Range (Normal = 5 to 24)

In: Sun Fixed: Carrier Out: Ringms_sl Solar Range (Normal = 1.05 to 2.2)

In: Ring Fixed: Sun Out: Carrier

PLANETSPACING:lma deg Least mesh angle (IDENTICAL planets

must be spaced at increments ofthe least mesh angle for assembly)

NUMBER OF EQUALLY SPACED PLANETSp1 (These are the 1st 4 up to 50 thatp2 will assemble without interference -p3 planets will assemble equally ifp4 (ring*sun planet)+(sun*ring planet)

divided by planets is an integer

EXTERNAL MESH (Sun/Planet):pn_s 1 1/in Normal Pitchnpa_s 20 deg Normal Pressure Angleha_s 0 deg Nominal helix Anglept_s 1 1/in Transverse Pitchtpa_s 20 deg Transverse Press Angle

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mod_n_s 25.4 mm Normal Modulemod_t_s 25.4 mm Transverse Moduleopr_pdp in Opr Pitch Dia, planet

20 opr_pds in Opr Pitch Dia, sun gear

Solve and you should have Report 2. Report 2

Model Title : Program 60-1162 Unit System: US

MESSAGE FIELD

ERROR MESSAGE, internal mesh none

ERROR MESSAGE, external mesh none

ERROR MESSAGE, mesh - general non_integer_teeth

Prime factors greater than 100 unknown NUMBER OF TEETH

Ring Gear T