Example29 Examine the Coriolis Force

General

A theoretical value and calculated value of the Coriolis force are compared.
The analysis is without piezoelectricity.

Analysis Condition

Item	Setting
Solver	Piezoelectric analysis [Galileo]
Analysis Space	3D
Analysis Type	Harmonic Analysis
Unit	mm
Variables to Constrain	Select Electric Potential
Analysis Options	Select Acceleration Select Angular Velocity for the model: rotation Deselect Angular Velocity for the model: no_rotation

The Acceleration tab is set as shown below.

Tab	Setting Item	Setting
Acceleration	Acceleration	X=Z=0.0, Y=2.e5[m/s2]
Angular Velocity(*)	Angular Velocity	X=Y=0.0, Z=1000[rad/s]

(*)This setting is for the rotation model only.

Model

A spherical solid body is defined.

Body Attributes and Materials

Body Number/Type	Body Attribute Name	Material Name
0/Solid	Body_Attribute_001	008_Cu (*)

* Available from the material DB

Boundary Condition

None

Results

The deformation diagrams of the result fields are shown below.

The diagrams are drawn with an actual scale. See Displacement diagram for the scale setting.

The dotted lines are the trajectory of the sphere. They are added for easy viewing. They are not drawn by Femtet.

Fig 1. Contour diagram (displacement/magnitude) + displacement (actual scale)

First, let’s look at the model without rotation. The vibration in the Y direction is given by the acceleration of Y component.

It is confirmed in the lower diagram of Fig 1. The temporal change of the Y component of the displacement is shown in Fig 2.

The phases are on the horizontal axis. The phase of 360 [deg] represents one period.

Since analysis is executed with 1 [KHz], 360 [deg] is 1 [ms]. The displacement of the center of the spheric body is plotted on the graph.

From Fig 2, it can be read that the marker M02 of the maximum point of the no_rotation model is 5.066 [mm].

This matches with a theoretical value of 5.066 [mm] given by the formula in the appendix below.

Next, let’s look at the model with rotation. The displacement in the X direction is generated as well due to the Coriolis force.

As in the upper diagram of Fig 1, the trajectory is elliptical. The displacement amplitude can be read from the markers in Fig 2 (Y component) and Fig 3 (X component).

Y component: 5.637 [mm]

X component: 1.794 [mm]

They match with the theoretical values in the appendix below.