# 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) ${T}_{m}=\frac{d{W}_{m}}{d\theta }$
• 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)
• 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) ${F}_{x}=\frac{d{W}_{m}}{dx}$
• 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
• 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
• 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)
• 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)
• 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)
• 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.