Here the study:
An external system (not drawn) give energy for rotate disks around themselves and around green axis. All disks have energy at start, at $t=0$ friction is ON and at $t=0$ external system is OFF (it don't add energy to disks). I think this energy must be conserved in this case.
2 Layers of red disks turn at $w_1$ clockwise around green axis (center of the image). All red disks are link together with green stems. All red disks turn at $w_2$ anticlockwise around their center of gravity for the first layer and at $w_2'$ anticlockwise around their center of gravity for the second layer. There is force F when disks touch another one. Red disk touch disk side by side but it is only at the 4 corners that disks touch layer1/layer2.
$R$ = Radius of first square layer (a side of inside square = 2R)
$r$ = radius of red disk
$F$ = basic force from friction
$t$ = time
$w_2' < w_2 $
$R = 6r $
$w_1 > w_2$
I compute work from torques:
There are 24 disks inside and 32 disks outside.
- Disks: +24+32+8 torques on red disks = $Frt( 48(w_1-w_2)+64(w_1-w_2')+8(w_1-w_2)+8(w_1-w_2')$
- Friction : $+ 24Fr(w_2+w_2)t + 32Fr(w_2'+w_2')t + 8Fr(w_2+w_2')t $
- Corners: -8 torques layer1 - 8 torque layer2 $= -8(R+2r)Fw_1t -8(R+2r)Fw_1t= -8(6r+2r)Fw_1t-64Frw_1t = -128Frw_1t$
The sum of works from torque = $128Frtw_1-56Frtw_2-72Frtw_2' +56Frtw_2+72Frtw_2' -128Frw_1t$
The sum = 0
All is fine !
All forces from friction for watch where there is contact
I hope I don't forgot one :)
Zoom of a corner
Disks can be like that:
And this give the possibility for composed friction :