Maxwell v15		6.3
	Eddy Current – Application Note

View the Results

1.Select Maxwell 2D > Results > Solution Data… and click on the Force tab. The force results are reported for a 1 meter depth of the model. The DC forces are shown below.

2.Now select Type:AC<Mag,Phase> This shows the magnitude of the force F(x)Mag is approximately 5e-6 (N) and the phase F(x)Phase is -2.0 radians or -120 degrees.

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Maxwell v15		6.3
	Eddy Current – Application Note

Create a Plot of Force vs. Time

The average, AC, and instantaneous components of the Lorentz force can be plotted vs. phase by creating named expressions in the calculator using the formulas at the beginning of the application note.

1.Determine the time-averaged component of Lorentz force:

•Click on Maxwell 2D > Fields > Calculator and then perform the following:

•Quantity > J

•Quantity > B > Complex > Conj > Cross

•Scalar X > Complex > Real

•Number > Scalar > 0.5 > OK

•Multiply

•Geometry > Volume > left > OK

•Integrate

•Add… Name: Force_DC

•Click OK

2.Determine the AC component of Lorentz force:

•Quantity > J

•Quantity > B > Cross

•Scalar X

•Function > Phase > OK

•Complex > AtPhase

•Number > Scalar > 0.5 > OK

•Multiply

•Geometry > Volume > left > OK

•Integrate

•Add… Name: Force_AC

•Click OK

3.Determine the instantaneous (DC + AC) component of Lorentz force. In the Named Expressions panel:

•In the Named Expressions window, select Force_DC and Copy to stack

•Select Force_AC and Copy to stack

•Add

•Add… Name: Force_inst

•Click OK and Done to close the calculator window.

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Maxwell v15		6.3
	Eddy Current – Application Note

4.Create a plot of Force vs. Phase. Now that the force quantities have been created, a plot of these named expressions can been created.

•Select Maxwell 2D > Results > Create Fields Report > Rectangular Plot

•Change the Primary Sweep: from the default Freq to Phase.

•Category: Calculator Expressions

•Quantity: Force_DC, Force_AC, Force_inst (hold down shift key to select all three at once)

•New Report > Close

•Right mouse click on the legend and select: Trace Characteristics > Add…

•Category: Math

•Function: max

•Add > Done

•Double left mouse click on the legend and change from the Attribute to the General tab.

•Check Use Scientific Notation and click on OK.

Note: The "max" values match the results from Solution Data > Force. I can also be observed that the forces fluctuate at 2 times the excitation frequency since there are two complete cycles over 360 degrees as shown below.

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Maxwell v15		6.3
	Eddy Current – Application Note

6.Finally, the instantaneous force on the left busbar can be calculated using an alternate method, the Maxwell Stress Tensor method. This method is different than both the Lorentz force and virtual force methods. The Maxwell Stress Tensor method is extremely sensitive to mesh. The force on an object can be determined by the following equation:

FMST = ∫(B n )H −0.5 (B H )n dV evaluated at phase (ωt = degrees)

Determine the instantaneous component of force at time wt=0 using the Maxwell Stress Tensor method in the calculator:

Quantity > B	Loads the B vector
Function > Phase > OK	Loads the function Phase
Complex > At Phase	Evaluates the B vector at phase = wt
Geometry > Line > left > OK This enters the edge of the left busbar
Unit Vector > Normal	To determine the unit normal vector for left busbar
Dot	To take B-dot-Unit Normal
Quantity > H	Loads the H vector
Function > Phase > OK	Loads the function Phase
Complex > At Phase	Evaluates the H vector at phase = wt
Multiply	This multiplies B and H
Quantity > B	Loads the B vector
Function > Phase > OK	Loads the function Phase
Complex > At Phase	Evaluates the B vector at phase = wt
Quantity > H	Loads the H vector
Function > Phase > OK	Loads the function Phase
Complex > At Phase	Evaluates the H vector at phase = wt
Dot	Computes B-dot-H
Number > Scalar > 0.5 > OK
Multiply	Multiplies the quantity by 0.5
Geometry > Line > left > OK Enters the edge of the left busbar
Unit Vector > Normal	To determine the unit normal vector for left busbar
Multiply	This multiplies the quantity times unit normal vector
Neg	This takes the negative
Add
Scal? > ScalarX	To extract the x-component of the quantity
Geometry > Line > left > OK Enters the edge of the left busbar
Integrate	To integrate the force density and obtain the force in newtons
Add…	Name: Force_MST

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Maxwell v15		6.3
	Eddy Current – Application Note

7.Create a plot of the Maxwell Stress Tensor Force vs. Phase.

•Select Maxwell 2D > Results > Create Fields Report > Rectangular Plot

•Change the Primary Sweep: from the default Freq to Phase.

•Category: Calculator Expressions

•Quantity: Force_inst, Force_MST

Note: The slight difference in these curves is due to mesh error in the stress tensor calculation.

This completes PART 1 of the exercise.

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