Winder Center Driven

Symbol	Description	Units
F_Tension	Tension due to Hanging Load	N
m_HL	Mass of Hanging Load	kg
m_Load	Mass of Payload	kg
m_MHL	Material mass per length	kg/m
L_MHL	Length of material from Pulley to Handing Load	m
g	Acceleration due to gravity = 9.81	m/s²
a	Material acceleration	m/s²
J_P	Inertia of pulley	kg-m²
a_P	Acceleration of pully	rad/s²
r_P	Radius of pulley	m

Symbol	Description	Units
J_DM	Inertia of drive mechanism	kg-m²
T_DM	Torque of drive mechanism	Nm
a_DM	Acceleration of drive mechanism	rad/s²
h	Efficiency of drive mechanism	1
J_R	Inertia of roller	kg-m²
r_R	Radius of roller	m
r_RM	Radius of roller with material	m
r_MaxRM	Max radius of roller with material	m
J_FR	Inertia of feed roll	kg-m²
r_FR	Radius of feed roll	m
n_FR	Number of feed rolls
W_M	Width of material	m
r_M	Density of material	kg/m³
F_Thrust	Thrust force	N
F_v	Force vector	N
F_Tension	Web tension	N
d_M	Material thickness	m
d_MS	Material diameter for spooling	m
J_Load	Inertia of payload	kg-m²

The r_MaxRM input is the roller starting radius with material for Unwinding applications.
An Unwinding Spooling application starts at the r_MaxRM and the spool is assumed fully wrapped at this radius.
If d_M = 0, then the roller is always assumed to be full throughout the entire sequence. I.e. r_RM = r_MaxRM and the roller is assumed full of material.
r_MaxRM is not used for Winding applications unless d_M = 0
d_MSmust be > 0

Material direction depends on the configuration as Winder or Unwinder
Winder	Start of Sequence, the Roller is empty Positive velocity adds material to the Roller
Unwinder	Start of Sequence, the Roller is full Positive velocity removes material from the Roller