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Double-Pinion Planetary Gear

Planetary gear train with two meshed planet gear sets

Gears

Description

This block represents a planetary gear train with two meshed planet gear sets between the sun gear and the ring gear. A single carrier holds the two planet gear sets at different radii from the sun gear centerline, while allowing the individual gears to rotate with respect to each other. The gear model includes power losses due to friction between meshing gear teeth and viscous damping of the spinning gear shafts.

Structurally, the double-pinion planetary gear resembles a Ravigneaux gear without its second, large, sun gear. The inner planet gears mesh with the sun gear and the outer planet gears mesh with the ring gear. Because it contains two planet gear sets, the double-pinion planetary gear reverses the relative rotation directions of the ring and sun gears.

The teeth ratio of a meshed gear pair fixes the relative angular velocities of the two gears in that pair. The dialog box provides two parameters to set the ring-sun and outer planet-inner planet gear teeth ratios. A geometric constraint fixes the remaining teeth ratios—ring-outer planet and inner planet-sun. This geometric constraint requires that the ring gear radius equal the sum of the sun gear radius with the inner and outer planet gear diameters:

${r}_{r}={r}_{s}+2\cdot {r}_{pi}+2\cdot {r}_{po},$

where:

• rr is the ring gear radius

• rs is the sun gear radius

• rpi is the inner planet gear radius

• rpo is the outer planet gear radius

In terms of the ring-sun and outer planet-inner planet teeth ratios, the ring-outer planet teeth ratio is

$\frac{{r}_{r}}{{r}_{po}}=2\cdot \frac{\frac{{r}_{r}}{{r}_{s}}}{\left(\frac{{r}_{r}}{{r}_{s}}-1\right)}\cdot \frac{\left(\frac{{r}_{po}}{{r}_{pi}}+1\right)}{\frac{{r}_{po}}{{r}_{pi}}},$

The inner planet-sun teeth ratio is

$\frac{{r}_{pi}}{{r}_{s}}=\frac{\left(\frac{{r}_{r}}{{r}_{s}}-1\right)}{2\left(\frac{{r}_{po}}{{r}_{pi}}+1\right)},$

The Differential block is a composite component. It contains three underlying blocks—Ring-Planet, Planet-Planet, and Sun-Planet—connected as shown in the figure. Each block connects to a separate drive shaft through a rotational conserving port.

Dialog Box and Parameters

Main

Specify the teeth ratios for ring-sun and outer planet-inner planet gears.

Ring (R) to sun (S) teeth ratio (NR/NS)

Enter the teeth ratio between ring and sun gears. This ratio is the number of teeth in the ring gear divided by the number of teeth in the sun gear. The default value is 2.

Outer planet (Po) to inner planet (Pi) teeth ratio (NPo/NPi)

Enter the teeth ratio between outer planet and inner planet gears. This ratio is the number of teeth in the outer planet divided by the number of gear teeth in the inner planet. The default value is 1.

Meshing Losses

Specify the power losses due to friction between meshing gear teeth.

Friction model

Select how to implement friction losses between meshing gears. The table describes the friction models.

ModelDescription
No meshing losses — Suitable for HIL simulationIgnore friction losses. Treat gear meshing as ideal.
Constant efficiencyInclude friction losses. Torque transfer between gears depends on a constant efficiency factor.

Sun-planet, ring-planet, and planet-planet ordinary efficiencies

Enter a vector with the torque transfer efficiencies between sun-planet, ring-planet, and planet-planet gear pairs, in that order. The default vector is [0.98 0.98 0.98].

Sun-carrier, ring-carrier, and planet-carrier velocity thresholds

Enter a vector with the sun-carrier, ring-carrier, and planet-carrier absolute angular velocities above which the full efficiency loss applies. From the drop-down list, select a physical unit. The default vector is [0.01 0.01 0.01] rad/s.

Viscous Losses

Specify the power losses due to viscous damping of the gear carriers.

Sun-carrier, ring-carrier, and planet-carrier viscous friction coefficients

Enter a vector with the viscous friction coefficients that dampen sun-carrier, ring-carrier, and planet-carrier motion, in that order. From the drop-down list, select a physical unit. The default vector is [0 0 0] N*m/(rad/s).

Ports

PortDescription
CConserving rotational port that represents the planet gear carrier
SConserving rotational port that represents the sun gear
RConserving rotational port that represents the ring gear