Modeling of mechanical gears with losses
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Library Blocks Gears They take into account friction losses and allow us to describe real (non-ideal) gears.
In such a pair (1,2), the angular velocity, tooth radii, limitations, and gear ratio are they remain the same as in the ideal model. But the transmitted torque and power are reduced due to:
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Coulomb friction between the teeth of the gears (1 and 2). It is taken into account through the efficiency coefficient . It is usually approximated as constant.
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Viscous friction in shafts and bearings, which is determined by the coefficient .
Constant EFFICIENCY
In a simple model, efficiency it is considered constant and does not depend on the load.
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Friction losses with a coefficient of they are fully manifested only when the power is above the threshold . A smoothing function is used below this value.
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If no power is transmitted, Engee takes into account the moment of friction.
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For gears with a carrier — this is the usual efficiency when the carrier is stationary.
For different efficiencies with forward and reverse power flow:
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, where — efficiency of transmission from the driven to the base shaft.
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, where — efficiency of transmission from the base to the driven shaft.
The moment of friction is calculated by the formula:
where:
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— the transmitted moment,
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— transmitted power,
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— threshold power, after which total efficiency losses occur.
In some blocks, for example Simple Gear, The efficiency is the same for forward and reverse directions ( ). In blocks like Leadscrew instead of the moment of friction Using the power of loss .
Load-dependent efficiency
Ratio it may vary depending on the load, which makes the model more accurate (for more information, see Simple Gear).
Geometry-dependent efficiency
Dependence The geometry of the teeth also increases the accuracy of the model. An example is given in the description of the Leadscrew block.
Viscous friction
If the shaft is fixed in the gear through bearings, it experiences viscous friction. It is set by the coefficient . The moment of viscous friction on the shaft “a” is equal to , where — the angular velocity of the shaft relative to the mount (or holder, if any).