Worm gear with adjustable gear ratio and friction losses
Simscape / Driveline / GearsSimscape / Driveline / Gears
The block represents a rotational gear that constrains the two connected driveline axes, worm (W) and gear (G), to rotate together in a fixed ratio that you specify. You can choose whether the gear rotates in a positive or negative direction. Right-hand rotation is the positive direction. If the worm thread is right-hand, ω_{W} and ω_{G} have the same sign. If the worm thread is left-hand, ω_{W} and ω_{G} have opposite signs.
You can model the effects of heat flow and temperature change through an optional thermal conserving port. By default, the thermal port is hidden. To expose the thermal port, right-click the block in your model and, from the context menu, select Simscape > Block choices. Select a variant that includes a thermal port. Specify the associated thermal parameters for the component.
R_{WG} | Gear ratio |
ω_{W} | Worm angular velocity |
ω_{G} | Gear angular velocity |
α | Normal pressure angle |
λ | Worm lead angle |
L | Worm lead |
d | Worm pitch diameter |
τ_{G} | Gear torque |
τ_{W} | Torque on the worm |
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 ω_{G} = 0, the friction torque is introduced via the hyperbolic function. |
τ_{fr} | Steady-state value of the friction torque at ω_{G} → ∞. |
k | Friction coefficient |
η_{WG} | Torque transfer efficiency from worm to gear |
η_{GW} | Torque transfer efficiency from gear to worm |
p_{th} | Power threshold |
[μ_{W} μ_{G}] | Vector of viscous friction coefficients for the worm and gear |
Worm gear imposes one kinematic constraint on the two connected axes:
ω_{W} = R_{WG}ω_{G} .
The two degrees of freedom are reduced to one independent degree of freedom. The forward-transfer gear pair convention is (1,2) = (W,G).
The torque transfer is:
R_{WG}τ_{W} – τ_{G} – τ_{loss} = 0 ,
with τ_{loss} = 0 in the ideal case.
In the nonideal case, τ_{loss} ≠ 0. For general considerations on nonideal gear modeling, see Model Gears with Losses.
In the contact friction case, η_{WG} and η_{GW} are determined by:
The worm-gear threading geometry, specified by lead angle λ and normal pressure angle α.
The surface contact friction coefficient k.
η_{WG} = (cosα – k·tanλ)/(cosα + k/tanλ) ,
η_{GW} = (cosα – k/tanλ)/(cosα + k·tanλ) .
In the constant friction case, you specify η_{WG} and η_{GW}, independently of geometric details.
η_{GW} has two distinct regimes, depending on lead angle λ, separated by the self-locking point at which η_{GW} = 0 and cosα = k/tanλ.
In the overhauling regime, η_{GW} > 0, and the force acting on the nut can rotate the screw.
In the self-locking regime, η_{GW} < 0, and an external torque must be applied to the screw to release an otherwise locked mechanism. The more negative is η_{GW}, the larger the torque must be to release the mechanism.
η_{WG} is conventionally positive.
The efficiencies η of meshing between worm and gear are fully active only if the transmitted power is greater than the power threshold.
If the power is less than the threshold, the actual efficiency is automatically regularized to unity at zero velocity.
The viscous friction coefficient μ_{W} controls the viscous friction torque experienced by the worm from lubricated, nonideal gear threads and viscous bearing losses. The viscous friction torque on a worm driveline axis is –μ_{W}ω_{W}. ω_{W} is the angular velocity of the worm with respect to its mounting.
The viscous friction coefficient μ_{G} controls the viscous friction torque experienced by the gear, mainly from viscous bearing losses. The viscous friction torque on a gear driveline axis is –μ_{G}ω_{G}. ω_{G} is the angular velocity of the gear with respect to its mounting.
Gear inertia is assumed negligible.
Gears are treated as rigid components.
Coulomb friction slows down simulation. See Adjust Model Fidelity.
Port | Description |
---|---|
W | Rotational conserving port representing the worm component |
G | Rotational conserving port representing the gear component |
H | Thermal conserving port for thermal modeling |
Gear or transmission ratio
R_{WG} determined as the
ratio of the worm angular velocity to the gear angular velocity. The
default is 25
.
Choose the directional sense of gear rotation corresponding to
positive worm rotation. The default is Right-hand
. If
you select Left-hand
, rotation of the worm in the
generally-assigned positive direction results in the gear rotation in
negative direction.
Parameters for meshing losses vary with the block variant chosen—that with a thermal port for thermal modeling or that without a thermal port.
Vector of viscous friction coefficients
[μ_{W}
μ_{G}], for the worm and gear,
respectively. The default is [0 0]
.
From the drop-down list, choose units. The default is
newton-meters/(radians/second) (N*m/(rad/s)
).
Thermal energy required to change the component temperature
by a single degree. The greater the thermal mass, the more resistant
the component is to temperature change. The default value is 50
J/K.
Component temperature at the start of simulation. The initial
temperature alters the component efficiency according to an efficiency
vector that you specify, affecting the starting meshing or friction
losses. The default value is 300
K.
For optimal simulation performance, use the Meshing Losses > Friction model parameter default setting, No meshing losses - Suitable
for HIL simulation
.