Gear Elasticity
The Gear Elasticity subnode is automatically added to a Gear Pair, Worm and Wheel, or Rack and Pinion node when Include gear elasticity is selected under Gear Properties. In this node, you can enter the elastic properties of a gear pair, such as gear mesh stiffness, mesh damping, and contact ratio.
The contents of the Gear Elasticity settings adapt to the type of gear pair where it is used.
Sketch
This section shows a sketch of the contact point of gear pair in the gear tooth normal plane. The sketch highlights the line of action along which stiffness and damping are interpreted.
Mesh Stiffness
Select the mesh stiffness method Specify — Tooth stiffness of individual gears or Total stiffness of gear pair.
For Tooth stiffness of individual gears, enter the following:
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When the parent node is Gear Pair, enter Wheel tooth stiffness as function of mesh cycle, kt,wh, and Pinion tooth stiffness as function of mesh cycle, kt,pn. The default expressions are (0[N/m])*mbd.grp1.thm_wh and (0[N/m])*mbd.grp1.thm_pn, respectively. The exact naming of the variables depends on the tags of the nodes in the model tree.
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When the parent node is Worm and Wheel, enter Worm tooth stiffness as function of mesh cycle, kt,wm, and Wheel tooth stiffness as function of mesh cycle, kt,wh. The default expressions are (0[N/m])*mbd.grp1.thm_wm and (0[N/m])*mbd.grp1.thm_wh, respectively. The exact naming of the variables depends on the tags of the nodes in the model tree.
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When the parent node is Rack and Pinion, enter Rack tooth stiffness as function of mesh cycle, kt,rk, and Pinion tooth stiffness as function of mesh cycle, kt,pn. The default expressions are (0[N/m^2])*mbd.grp1.um_rk and (0[N/m])*mbd.grp1.thm_pn, respectively. The exact naming of the variables depends on the tags of the nodes in the model tree.
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Specify Contact ratio in mesh cycle — Constant or Varying.
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For Constant contact ratio, select Contact ratio — 1, 2, or 3.
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For Varying contact ratio, select Maximum contact ratio — 2, or 3. Also enter the Next tooth engagement position in mesh cycle, ζ. The value of ζ must vary between 1/2 and 1 when Maximum contact ratio is set to 2 and between 1/3 to 1/2 when Maximum contact ratio is set to 3.
For Total stiffness of gear pair, enter the following:
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In case the parent node is Gear Pair, select the Total stiffness as function of — Wheel mesh cycle, Wheel full revolution, Pinion mesh cycle, or Pinion full revolution.
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In case the parent node is Worm and Wheel, select the Total stiffness as function of — Worm mesh cycle, Worm full revolution, Wheel mesh cycle, or Wheel full revolution.
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In case the parent node is Rack and Pinion, select the Total stiffness as function of — Rack mesh cycle, Pinion mesh cycle, or Pinion full revolution.
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Enter Total stiffness, kg. The default expression of total stiffness depends on the selection in previous input; for example, it is (0[N/m])*mbd.grp1.thm_wh when Wheel mesh cycle is selected. The exact naming of the variable depends on the tags of the nodes in the model tree.
Mesh Damping
Enter Mesh damping, cg. The mesh damping can be specified as proportional to the mesh stiffness. The default expression is (0[s])*mbd.grp1.kg. The exact naming of the variable depends on the tags of the nodes in the model tree.
Theory for Gear Elasticity
Location in User Interface
This node is automatically added when Include gear elasticity is selected in the parent Gear Pair, Worm and Wheel, and Rack and Pinion nodes. It cannot be added or removed manually.