Responses

Introduction

In the data tree of Flux the node Solver > Optimization > Responses allows the user to define physical quantity that will be optimized during the optimization process engaged by Flux. The short list of the responses is given below:

Table 1. Table summarizing all the responses available in Flux
Physical quantity to optimize	Formula	Entity
Flux flowing through faces	$φ = \frac{L}{S} \int A_{z} d S$ L : Depth of the domain S : Area of the coil Az : Magnetic vector potential in Z direction	On a face belonging to a coil conductor region
Flux flowing through a line	$φ = L (A_{z} (n_{1}) - A_{z} (n_{2}))$ L : Depth of the domain Az : Magnetic vector potential in Z direction n1 and n2 the end nodes of the line where the flux is computed	On a line
Sum of the fluxes of selected coils	$φ = \sum_{i = 1}^{n} φ_{i} = L \sum_{i = 1}^{n} N_{S i} \int A_{z} d S$ n : Number of selected coils L : Depth of the domain Nsi : Winding function of the associated coil Az : Magnetic vector potential in Z direction	On one or several coil conductor components
Force computed with the integral of Pn on a path	$F m = L \int \frac{B_{n}^{2} - B_{t}^{2}}{μ_{0}} d l$ L : Depth of the domain Bn : Normal magnetic flux density Bt : Tangential magnetic flux density µ0 : Air magnetic permeability	Based on the Maxwell tensors approach, this method requires a path in a front of a piece of iron (plunger for an actuator, stator tooth ...) Attention: This method is valuable only along a path in a air or vaccum region.
Torque computed with the integral of Pt on a path	$T m = L p R \int \frac{B_{n} B_{t}}{μ_{0}} d l$ L : Depth of the domain p : Number of periodicities R : Radius of the path Bn : Normal magnetic flux density Bt : Tangential magnetic flux density µ0 : Air magnetic permeability	Based on the Maxwell tensors approach, this method requires a path in the airgap of a rotating machine, on the stator side as depicted in th following picture: Attention: This method is valuable only along a path in a air or vaccum region.
Volume of 2D faces		On faces