Spur Gear
Use the Spur Gear node to model a spur gear 2D and 3D. The gear is assumed to be rigid. Select one or more domains to make them a part of the gear.
A spur gear can be connected to the following gear types:
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Another Spur Gear, or a Helical Gear through the Gear Pair node.
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A Worm Gear through the Worm and Wheel node.
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A Spur Rack, or a Helical Rack through the Rack and Pinion node.
Any two gears or rack can be connected to each other only if they satisfy the Gear Pair Compatibility Criteria.
The gear has the following subnodes to constraint the displacement and rotation, to apply forces and moments, and to add mass and moment of inertia:
These subnodes are described in the Structural Mechanics Module User’s Guide:
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Fixed Constraint (Rigid Material)
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Prescribed Displacement/Rotation
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Applied Force (Rigid Material)
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Applied Moment (Rigid Material)
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Mass and Moment of Inertia (Rigid Material)
Sketch
This section shows a sketch of a spur gear. Some of the inputs are also highlighted in the sketch.
Gear Properties
Specify the properties of a spur gear in this section.
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Select the Gear mesh — External or Internal.
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Enter Number of teeth n.
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Enter Pitch diameter dp.
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Enter Pressure angle α.
Gear Axis
The gear axis is defined as the axis of rotation of the gear. The gear axis is defined as the axis of rotation of the gear. To define the axis, choose Specify direction or Select a parallel edge.
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For Specify direction, enter a value or expression for eg. The default is (0, 0, 1). The direction is specified in the selected coordinate system.
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For Select a parallel edge, an edge can be selected on the Gear Axis subnode, which is added automatically. The vector from the first to last end of the edge is used to define the gear axis. Any edge in the model can be used. Select the Reverse direction check box to reverse the direction of the gear axis.
This section is only present in 3D. In 2D, the gear axis is assumed to be the out-of-plane direction.
Density
The default Density ρ is taken From material. In this case, the material assignment for the domain supplies the mass density. For User defined enter another value or expression.
The density is needed for dynamic analysis. It is also used when computing mass forces for gravitational or rotating frame loads, and when computing mass properties (Computing Mass Properties).
Center of Rotation
Select a Center of Rotation — Center of mass, Centroid of selected entities, or User defined. The center of rotation is the point about which the rotation of the gear is interpreted.
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For Center of mass, the center of rotation is taken as the center of mass of the gear.
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For Centroid of selected entities select an Entity level — Boundary, Edge, or Point. The available choices depend on geometrical dimension. The center of rotation is located at the centroid of the selected entities, which do not need to be related to rigid domain itself. As a special case, you can select a single point and thus use that point as center of rotation.
When chosen, a default Center of Rotation: Boundary, Center of Rotation: Edge, or Center of Rotation: Point subnode is automatically added.
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For User defined, enter the Global coordinates of center of rotation, Xc, in the table.
Select the Offset check box to add an optional offset vector to the definition of the center of rotation. Enter values for the offset vector Xoffset.
The center of rotation used is the sum of the vector obtained from any of the input methods and the offset vector.
Initial Values
Select From physics interface node or Locally defined.
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When From physics interface node is selected, initial values for rigid body displacement, rotation, and velocities are inherited from the physics interface level.
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When Locally defined is selected, an Initial Values subnode is automatically added, in which you can initialize the rigid domain degrees of freedom.
Select a Consistent initialization — Default or Force initial values to enforce that the exact values given in this node should be maintained through the consistent initialization process. The default when the given initial values are inconsistent is to make them adapt to each other by adjusting all initial values. For Force initial values click to select the applicable check box or boxes — Translation along first axis, Translation along second axis, Translation along third axis, and Total rotation. Only the selected degrees of freedom have the initial values fixed during the consistent initialization process.
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The optional subnode is described in Initial Values (Rigid Material).
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For details about the input expressions at the physics interface level, see Initial Values.
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See Rigid Material in the Structural Mechanics Module User’s Guide for more information.
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For details about the initialization process, see Initialization in Time-Dependent Studies.
Formulation
Some contributions from a gear will, under geometric nonlinearity, result in a nonsymmetric local stiffness matrix. If all other aspects of the model are such that the global stiffness matrix would be symmetric, then such a nonsymmetric contribution may have a heavy impact on the total solution time and memory usage. In such cases, it is often more efficient to use an approximative local stiffness matrix that is symmetric.
Select Use symmetric formulation for geometric nonlinearity to force all matrix contributions from the gear and its subnodes to be symmetric.
Using an approximative stiffness matrix will in general require more iterations. However, since the computational cost per iteration will be cut by at least a factor of two if a symmetric matrix can be used, it is usually more efficient to ignore a weak nonsymmetry.
In particular, if the rotation of the gear per time step or parameter increment is small, there will in general be no increase in the number of iterations if this option is used.
When the global stiffness matrix is nonsymmetric for other reasons, then there is nothing to be gained from symmetrizing the contribution from the gear.
Constraint Settings
On the boundaries where the gear is coupled to a flexible material, all nodes on such a boundary are constrained to move as a rigid body. As a default these constraints are implemented as pointwise constraints. If you want to use a weak constraint formulation, select Use weak constraints for rigid-flexible connection.
See also Spur Gear Theory.
Location in User Interface
Context Menus
Multibody Dynamics>Gears>Spur Gear
Ribbon
Physics tab with Multibody Dynamics selected:
Domains>Gears>Spur Gear