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The substructure file wr_coupl_ne1.ins



The model of the track in substructure file wr_coupl_ne1.ins is built up according to the following figure:

analyse_wr_coupl_ne1.gif

The track consists of two masses trc(track) and grd(ground). Mass grd have no degrees of freedom, the mass only follows the designed track curvature. Mass trc can have degrees of freedom, in lateral-, vertical- and roll- direction of motion. The normal case is to have constrains to mass trc in all directions except in the lateral direction. The constraints are set in substructure file wr_coupl_ne1.ins. If the user wishes to have other constraints he/she must make a local copy of the wr_coupl_ne1.ins-file, and edit the constraints which are in the beginning of the file.

If constraints are removed in vertical and roll direction the user must supply the model with vertical spring between trc and grd, otherwise the model will accelerate downward because of the earth gravitation.



The model consists of the following springs and dampers:
knwr, cnwr
Stiffness and damping between wheel and rail. The spring and the damper is always perpendicular to the contact surface. The stiffness in the spring and damping coefficient in the damper, shall be given in a memory field as a function of the contact angle. Recommended values for wooden and concrete sleeper track can be found in file knwr_n.runf.
If mass trc has vertical constraints as the figure above shows, the vertical flexibility in knwr must contain all flexibilities between the wheel and the fixed ground. The total vertical flexibility can consists of elasticity in contact point, flexibility in rail pad, elasticity in ballast.
The lateral flexibility consists of bending of the rail, deformation in the rail fasteners.
kytg, cytg
Stiffness and damping between trc and grd. The spring and the damper coefficient should refer to the lateral stiffness of the ballast. The stiffness and damping should be defined as a property defined in calc_coupl.html#p_*. Recommended values for wooden and concrete sleeper track can be found in file knwr_n.runf.



The substructure-file operates in the following way:
  1. Set constraints to the axle in pitch motion, and in all directions for the track except in lateral direction.
  2. Interpolate the track irregularities by cubic splines
  3. Calculate cp_$2r.eta and cp_$2l.eta as the lateral displacement between wheel and rail
  4. Interpolate the wheel-rail geometry functions linearly
  5. Calculate the deformations and normal forces in the contact points.
  6. Calculate creep and creep forces in the contact points.

The creep forces are in substructure-file wr_coupl_ne1.ins calculated in a lookup table. For a more detailed description in how to calculate creepage and creep forces, the interested reader can find more information in theory_creepage.html.



Input:


Geometrical variables which must be defined before this substructure file can be used

Vo = Nominal speed of the vehicle in m/s.
The speed can be positive or negative, but not equal to 0(zero).
     
ro_$2r = Nominal rolling radius, axle number $2, right side.
ro_$2 = If ro_$2r not can be found
ro_$1 = If ro_$2 not can be found
ro_ = If ro_$1 not can be found
ro = If ro_ not can be found
     
ro_$2l = Nominal rolling radius, axle number $2, left side.
ro_$2 = If ro_$2r not can be found
ro_$1 = If ro_$2 not can be found
ro_ = If ro_$1 not can be found
ro = If ro_ not can be found
     
Boh = Lateral distance between track center line and nominal rolling circle of right wheel
Bo = If Boh not can be found
bo = If Bo not can be found
0.75 = If bo not can be found
     
Bov = Lateral distance between track center line and nominal rolling circle of left wheel
Bo = If Bov not can be found
bo = If Bo not can be found
75 = If bo not can be found


Coefficient of friction between wheel and rail

cpt_$2r.mu = Friction coefficient between wheel and rail, tread right side.
cpt_$1.mu = If cpt_$2r.mu not can be found
mutr = If cpt_$1.mu not can be found
mu = If mutr not can be found
     
cpt_$2l.mu = Friction coefficient between wheel and rail, tread left side.
cpt_$1.mu = If cpt_$2l.mu not can be found
mutl = If cpt_$1.mu not can be found
mu = If mutl not can be found
     
cpf_$2r.mu = Friction coefficient between wheel and rail, flange right side.
cpf_$1.mu = If cpf_$2r.mu not can be found
mufr = If cpf_$1.mu not can be found
mu = If mufr not can be found
     
cpf_$2l.mu = Friction coefficient between wheel and rail, flange left side.
cpf_$1.mu = If cpf_$2l.mu not can be found
mufl = If cpf_$1.mu not can be found
mu = If mufl not can be found


Reduction in dry creepage due to a contaminated contact surface

mulfact_nux_tread = Longitudinal creepage reduction factor on tread
mulfact_nux = If mulfact_nux_tread not can be found
1.0 = If mulfact_nux not can be found
mulfact_nuy_tread = Lateral creepage reduction factor on tread
mulfact_nuy = If mulfact_nuy_tread not can be found
1.0 = If mulfact_nuy not can be found
mulfact_spin_tread = Spin creepage reduction factor on tread
mulfact_spin = If mulfact_spin_tread not can be found
1.0 = If mulfact_spin not can be found
mulfact_nux_flange = Longitudinal creepage reduction factor on flange
mulfact_nux = If mulfact_nux_flange not can be found
1.0 = If mulfact_nux not can be found
mulfact_nuy_flange = Lateral creepage reduction factor on flange
mulfact_nuy = If mulfact_nuy_flange not can be found
1.0 = If mulfact_nuy not can be found
mulfact_spin_flange = Spin creepage reduction factor on flange
mulfact_spin = If mulfact_spin_flange not can be found
1.0 = If mulfact_spin not can be found


Stiffness and damping in surface between rail and wheel

knwr_$2r = Stiffness perpendicular to the contact surface on tread of right wheel, defined in e.g. "func intpl_r".
Ex: func intpl_r knwr$2r
       -1.57  <Horizontal stiffness>
        0.        <Vertical stiffness>
         1.57  <Horizontal stiffness>
knwr_$1 = If knwr_$2r not can be found
knwr_ = If knwr_$1 not can be found
     
knwr.F0_$2r = Pre-stress force in spring knwr$2r above.
knwr.F0_$1 = If knwr.F0_$2r not can be found
knwr.F0_ = If knwr.F0_$1 not can be found
0 (zero) = If knwr.F0_ not can be found
     
cnwr_$2r = Damping perpendicular to the contact surface on tread of right wheel, defined in e.g. "func intpl_r".
cnwr_$1 = If cnwr_$2r not can be found
cnwr_ = If cnwr_$1 not can be found
     
knfr_$2r = Stiffness perpendicular to the contact surface on flange of right wheel, defined in e.g. "func intpl_r".
knfr_$1 = If knfr_$2r not can be found
knfr_ = If knfr_$1 not can be found
     
knfr.F0_$2r = Pre-stress force in spring knfr$2r above
knfr.F0_$1 = If knfr.F0_$2r not can be found
knfr.F0_ = If knfr.F0_$1 not can be found
0 (zero) = If knfr.F0_ not can be found
     
cnfr_$2r = Damping perpendicular to the contact surface on flange of right wheel, defined in e.g. "func intpl_r".
cnfr_$1 = If cnfr_$2r not can be found
cnfr_ = If cnfr_$1 not can be found

Individual stiffnesses and damping coefficients can also be given for the left wheels, simply substitute "r" with an "l". Ex: knwr_$2r, knwr.F0_$2r, cnwr_$2r,,, etc.



Track data variables

gauge_average = Average gauge of the track defined in the data field spv_trac
gauge_dev_v$1 = Deviation in gauge for vehicle number $1
A positive value entails a wider gauge
A negative value entails a narrower gauge
gauge_dev = If gauge_dev_v$1 not can be found
YMtrac = Multiplying factor for lateral irregularities
ZMtrac = Multiplying factor for vertical irregularities
CMtrac = Multiplying factor for cant irregularities
GMtrac = Multiplying factor for gauge irregularities
lsa_$2.pn = Position along the track of the linear local coordinate system lsa_$2
axl_$2.? = Variables containing the motions of the axle (wheelset)
trc_$2.? = Variables containing the motions of the track


Track irregularities will be interpolated from data fields with the following names:

lat_trac = Lateral irregularities (positive direction = right)
vert_trac = Vertical irregularities (positive direction = down)
fi_trac = Cant irregularities (positive direction = positive rotation round the x-axle)
spv_trac = Gauge irregularities (positive direction = wide gauge)


Wheel-rail geometry functions

Wheel-rail geometry functions describing the tread of the right wheel and rail shall be defined by command `func intpl_r` and must have one of the following names:
cpt_$2r.drfn = Change in rolling radius, tread, right wheel
cpt_$2.drfn = If cpt_$2r.drfn not can be found
cpt_$1r.drfn = If cpt_$2.drfn not can be found
cpt_$1.drfn = If cpt_$1r.drfn not can be found
cpt_r.drfn = If cpt_$1.drfn not can be found
cpt_.drfn = If cpt_r.drfn not can be found
     
cpt_$2r.gamfn = Angle of contact surface, tread, right wheel
cpt_$2.gamfn = If cpt_$2r.gamfn not can be found
cpt_$1r.gamfn = If cpt_$2.gamfn not can be found
cpt_$1.gamfn = If cpt_$1r.gamfn not can be found
cpt_r.gamfn = If cpt_$1.gamfn not can be found
cpt_.gamfn = If cpt_r.gamfn not can be found
     
cpt_$2r.zfn = Wheel lift, tread, right wheel
cpt_$2.zfn = If cpt_$2r.zfn not can be found
cpt_$1r.zfn = If cpt_$2.zfn not can be found
cpt_$1.zfn = If cpt_$1r.zfn not can be found
cpt_r.zfn = If cpt_$1.zfn not can be found
cpt_.zfn = If cpt_r.zfn not can be found
     
cpt_$2r.rofn = Wheel-rail curvature difference, tread, right wheel
cpt_$2.rofn = If cpt_$2r.rofn not can be found
cpt_$1r.rofn = If cpt_$2.rofn not can be found
cpt_$1.rofn = If cpt_$1r.rofn not can be found
cpt_r.rofn = If cpt_$1.rofn not can be found
cpt_.rofn = If cpt_r.rofn not can be found
     
cpt_$2r.poswfn = Position of contact surface of wheel, tread, right wheel
cpt_$2.poswfn = If cpt_$2r.poswfn not can be found
cpt_$1r.poswfn = If cpt_$2.poswfn not can be found
cpt_$1.poswfn = If cpt_$1r.poswfn not can be found
cpt_r.poswfn = If cpt_$1.poswfn not can be found
cpt_.poswfn = If cpt_r.poswfn not can be found
0. = If cpt_.poswfn not can be found

Wheel-rail geometry functions describing the flange of the right wheel and rail are similar to those on right tread just simply replace "cpt" by "cpf".
Wheel-rail geometry functions describing the tread of the left wheel and rail are similar to those on right side just simply replace "r" by "l".



Output:

This substructure file will generate the following variables:

tral$2.y = Lateral track irregularities, track center line
tral$2r.y = Lateral track irregularities, right rail
tral$2l.y = Lateral track irregularities, left rail
tral$2r.z = Vertical track irregularities, right rail
tral$2l.z = Vertical track irregularities, left rail
tral$2r.vy = First order derivative of lateral track irregularities, right rail
tral$2l.vy = First order derivative of lateral track irregularities, left rail
tral$2r.vz = First order derivative of vertical track irregularities, right rail
tral$2l.vz = First order derivative of vertical track irregularities, left rail
tral$2.f = Track irregularities in roll direction
tral$2r.k = Pitch irregularities right rail
tral$2l.k = Pitch irregularities left rail
tral$2r.p = Yaw irregularities right rail
tral$2l.p = Yaw irregularities left rail
     
cp_$2r.eta = lateral distance between wheel and rail right wheel
cpt_$2r.ksi = Longitudinal position of the contact point, tread right wheel
cpt_$2r.dr = Change in wheel radius right wheel
cpt_$2r.gam = Angle of contact point right wheel
cpt_$2r.z = Wheel lift right wheel
cpt_$2r.irx = Longitudinal wheel-rail curvature difference, tread right wheel
cpt_$2r.iry = Lateral wheel-rail curvature difference, tread right wheel
cpt_$2r.bo = Lateral distance track center line to contact point, tread right wheel
     
cpt_$2r.a/b = The a/b-ratio of the contact ellipse, tread right wheel
cpt_$2r.c = Geom. average radius of the contact ellipse c=sqrt(a*b), tread right wheel
     
cpt_$2r.nux = Longitudinal creepage, tread, right wheel
cpt_$2r.nuy = Lateral creepage, tread, right wheel
cpt_$2r.spin = Spin creepage, tread, right wheel
cpt_$2r.nuxm = Dry long. creepage, after multiplication with mulfact above
cpt_$2r.nuym = Dry lat. creepage, after multiplication with mulfact above
cpt_$2r.spim = Dry spin creepage, after multiplication with mulfact above
     
cpt_$2r.Fn = Contact force, tread, right wheel
cpt_$2r.Fny = Creep force tangential to the contact surface, tread, right wheel
cpt_$2r.Fx = Longitudinal force, tread, right wheel
cpt_$2r.Fy = Lateral force, tread, right wheel
cpt_$2r.Fz = Vertical force, tread, right wheel

The same naming convention has also been used on the wheels on the left hand side of the vehicle. The names of the variables on the left side can be created by changing "_$2r" to "_$2l".

If the wheel-rail geometry functions contain a separate description of the flange (two-point contact), an equal amount of variables as for the tread will be generated. The names of the variables will be the same as for the tread, just the introduction cpt_* will be changed to cpf_*.