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	Computation entity
Torque on a mechanical set (virtual works)	$T_{m} = \frac{d W_{m}}{d θ}$ dWm: variation of the magnetic energy dθ: virtual displacement of the nodes around an axis	On a mechanical set
Torque ripple on a mechanical set (virtual works)	$∆ T = (\frac{T_{m a x} - T_{m i n}}{T_{m e a n}}) * 100$ Tmax: Maximum value of the torque Tmin: Minimum value of the torque Tmean: Mean value of the torque	On a mechanical set
Force on a face region (virtual works)	$F_{x} = \frac{d W_{m}}{d x}$ dWm: variation of the magnetic energy dx: virtual displacement of the nodes along an axis	On a face region
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
Flux flowing through lines	$φ = L (A_{z} (n_{1}) - A_{z} (n_{2}))$ 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
Volume of 2D faces		On faces
Force computed on a path (Maxwell tensor)	$F m = L \int \frac{B_{n}^{2} - B_{t}^{2}}{μ_{0}} d l$ 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 on a path (Maxwell tensor)	$T m = L p R \int \frac{B_{n} B_{t}}{μ_{0}} d l$ 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's tensors, this method requires also a path in the airgap of a rotating machine, this path is automatically computed by Flux.
Torque ripple computed on a path (Maxwell tensor)	$∆ T = (\frac{T_{m a x} - T_{m i n}}{T_{m e a n}}) * 100$ Tmax: Maximum value of the torque Tmin: Minimum value of the torque Tmean: Mean value of the torque	Based on the torque computation explained above, this method requires also a path in the airgap of a rotating machine, this path is automatically computed by Flux.