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

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:

- Set constraints to the axle in pitch motion, and in all directions for the track except in lateral direction.
- Interpolate the track irregularities by cubic splines
- Calculate cp_$2r.eta and cp_$2l.eta as the lateral displacement between wheel and rail
- Interpolate the wheel-rail geometry functions linearly
- Calculate the deformations and normal forces in the contact points.
- 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.

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 |

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 |

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 |

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.

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 |

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) |

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".

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_*.