Gears

Coupled simple and complex motions

Gear sets serve to transfer rotational motion and torque at a known ratio from one driveline axis to another. Simscape™ Driveline™ contains angular gears for transferring rotational motion and torque and linear gears, for transferring translational motion and force. Determine how heat generation affects the efficiency and temperature of driveline components using thermal variants of gear blocks.

Simscape Blocks

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Gear Assemblies

Compound Planetary Gear	Planetary gear train with stepped planet gear set
Cycloidal Drive	High-ratio speed reducer based on cycloidal disc motion
Differential	Gear mechanism that allows driven shafts to spin at different speeds
Double-Pinion Planetary Gear	Planetary gear train with two meshed planet gear sets
Harmonic Drive	High-ratio speed reducer based on elastic deformation of an elliptical gear
Limited-Slip Differential	Reduce velocity difference between two connected shafts
Planetary Gear	Gear train with sun, planet, and ring gears
Ravigneaux Gear	Planetary gear with two sun gears and two planet gear sets
Simple Gear	Simple gear of base and follower wheels with adjustable gear ratio, friction losses, and triggered faults
Simple Gear with Variable Efficiency	Gear set with parallel-axis rotation and variable meshing efficiency
Worm Gear	Worm gear with adjustable gear ratio and friction losses

Planetary Gear Subcomponents

Planet-Planet	Planetary gear set of carrier, inner planet, and outer planet wheels with adjustable gear ratio and friction losses
Ring-Planet	Planetary gear set of carrier, planet, and ring wheels with adjustable gear ratio and friction losses
Sun-Planet	Planetary gear set of carrier, planet, and sun wheels with adjustable gear ratio and friction losses
Sun-Planet Bevel	Planetary gear set of carrier and beveled planet and sun wheels with adjustable gear ratio, assembly orientation, and friction losses
Sun-Planet Worm Gear	Planetary gear set of carrier, worm planet, and sun wheels with adjustable gear ratio, worm thread type, and friction losses

Translational Mechanisms

Leadscrew	Leadscrew gear set of threaded rotating screw and translating nut, with adjustable thread and friction losses
Rack & Pinion	Rack and pinion gear coupling translational and rotational motion, with adjustable pinion radius and friction losses

Topics

Couple Two Spinning Inertias with a Simple Gear
Use gears to couple inertias that are spinning at the same or at different velocities.
Couple Two Spinning Inertias with a Variable Ratio Transmission
Model a transmission that has a variable gear ratio.
Couple Three Spinning Inertias with a Planetary Gear
Model a simple planetary gear and a planetary gear with a locked carrier.
Custom Planetary Gear Model
Model a coupled planetary gear train.
Model Gears with Losses
Model frictional losses in gear couplings.
Constant and Load-Dependent Gear Efficiencies
Model power loss due to nonideal gear meshing.
Couple Rotational Motion with Gears
Learn about the rules for coupling gears.
Rotational-Translational Couplings
Couple rotational and translational dynamics.
Model Thermal Losses in Driveline Components
Evaluate the effects of thermal losses on device temperature and performance.

Featured Examples

Custom Planetary Gear

Illustrates how you can build your own custom planetary gear components from the Simscape™ Driveline™ Planetary Subcomponents library. The example is based on Example 10.7 published in K.J. Waldron, G.L. Kinzel "Kinematics, Dynamics, and Design of Machinery", 1999. It consists of a coupled planetary train built from simple and compound planetary trains with a common carrier and bevel gears. The simple train fundamental train ratio is -N_4/N_2 * N_7/N_4 = -N_7/N_2. It connects shafts S2 and S7. The compound planetary train fundamental ratio is -N_4/N_2 * N_6/N_5 and it connects shafts S2 and S6. When the input shaft of the train is rotated at 100 rpm, the model shows the output shaft rotates at 1.4456 rpm as given in the reference.

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Epicyclic Gear Efficiency Measurement

An epicyclic gear drive with overall ratio of 256:1 and verifies its transmission efficiency given the individual gear meshing efficiencies. The example is based on Tuplin, W.A. "Designing Compound Epicyclic Gear Trains for Maximum Speed at High Velocity Ratios", Machine Design, April 4, 1957. The drive is built of two ring-planet elements as shown in the gearbox schematic. The example confirms the transmission efficiency value of 0.22 as predicted by the analytical analysis presented in the paper.

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Gear with Backlash

Model a gear with backlash using the Simple Gear block with two different backlash models: a spring-damper model and a coefficient of restitution model. The backlash is set to 1 mm, which is equivalent to 0.032 degrees rotation of the input gear that has a radius of 100 mm or 0.016 degrees rotation of the output gear that has a radius of 200 mm. Parameters in the two backlash models are adjusted so that there are a few oscillations when the torque is applied, and the models have similar behavior.

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Gearbox Efficiency Measurement

A test for measuring gear box efficiency. The input shaft is driven at a fixed speed and a variable torque is applied to the output shaft. Power is measured on both the input and output shafts, and efficiency is calculated as the ratio of output to input power. The simulation results match the parameters specified for the efficiency of the gear.

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Simple Gear

A simple gear coupling two inertias (shafts). The gear ratio between the follower (F) and base (B) is 2:1. Thus the angular velocity of the follower shaft is half the angular velocity of the base shaft. The follower shaft torque is twice the base shaft torque.

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Variable Ratio Gear

A variable ratio gear coupling two inertias (shafts). The gear ratio between the follower (F) and the base (B) is steadily increased from 1:1 to 2:1. The ratio of the follower to base angular speed decreases with gear ratio, and conversely the ratio of the follower to base torque increases with gear ratio. The variable gear is implemented using the Variable Ratio Transmission block which includes compliance. Appropriate stiffness and damping values for the compliance will depend upon the levels of torque transmitted by the variable gear. If the compliance damping is unrealistically low, the system can develop high frequency oscillations that require small simulation time steps.

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