Relative displacement analysis of Spur Planetary Gear

As shown in the figure, the relative position relationship of each gear is in the meshing state.

(1) Projection of relative displacement between sun gear and planetary gear along the direction of meshing line

The direction of the sun gear pointing to the planetary gear is set as the positive direction of the meshing line, and the displacement of the two gears is projected to the direction of the meshing line

Where:

Xs, ys — the linear displacement of the sun wheel;

Xn, yn — linear displacement of planetary gear;

α – pressure angle of involute gear;

ψ SPN = π / 2 – α S + ψ n, α s is the meshing angle between sun gear and planetary gear.

(2) Projection of relative displacement between planetary gear and inner gear ring along the direction of meshing line

If the direction of the planetary gear pointing to the inner gear ring is set as the positive direction of the meshing line, and the displacement of the two gears is projected to the direction of the meshing line, the relative displacement between the two gears can be obtained as follows:

Where:

XR, yr — linear displacement of inner gear ring;

ψ SPN = π / 2 – α R + ψ n, α R is the meshing angle of the meshing pair between the inner gear ring and the planetary gear.

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