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Users Manual for Program KC_PROP



Program for calculating the energy loss coefficient in a system consisting of springs and dampers.


The energy loss coefficient in a system is defined as: 

 η =    D  
      2 π U

 where: η = Energy loss coefficient
        D = Energy loss per cycle             0∫2π/ω Re F*·Re ε·*·dt
        U = Elastic energy at max. deflection 0∫εa Re F*·Re dε* 
        F*= The complex force
        ε*= The complex displacement

The energy loss coefficient is also defined as: 

 η = tan(δ)

 where: δ = Phase lag between force and displacement

The energy loss coefficient can also be written as: 

 η =   E"
       E'

 where: E' = Elastic stiffness 
        E" = Imaginary stiffness or out of phase component
        E* = Complex stiffness E'+ iE"

INPUT DATA


OPER_MODE
Command OPER_MODE controls the mode of operation of program kc_prop.
OPER_MODE can be given one of these two values:
calc_properties
OPER_MODE set to calc_properties implies that stiffnesses and damping coefficients for the springs and dampers in the model shall be calculated. As input data different main properties of the suspension must be given, which are different for different spring models, please look under command SPRING_MODEL for more information.
generate_curve
OPER_MODE set to generate_curve implies that a curve of the stiffness v.s. frequency will be generated. In this mode of operation all stiffnesses and damping coefficients must be defined.
Declared= Character*20    Default= 'calc_properties'

SPRING_MODEL
Command SPRING_MODEL controls the spring-damper model which shall be used.
In current release of program kc_prop, two spring-damper models are available:

k+(k-c)
A spring-damper model where the components are attached to each other according to the following figure:
misc_kkc.gif
If OPER_MODE= generate_curve the following input data values must be defined:
KP = Parallel stiffness
KS = Serial stiffness
C = Viscous damping coefficient

If OPER_MODE= calc_properties the following input data values must be defined:
FREQ_T = Cut-off frequency where the stiffness shifts from static to dynamic stiffness. FREQ_T is also the frequency where η reaches its maximum value.
KMID = Stiffness at frequency FREQ_T.
ETA_T = The energy loss coefficient η at frequency FREQ_T.


k+(k-(k+c))
A spring-damper model where the components are attached to each other according to the following figure:
misc_kkkc.gif
If OPER_MODE= generate_curve the following input data values must be defined:
KP = Parallel stiffness
KS = Serial stiffness
KC = Damper stiffness
C = Viscous damping coefficient

If OPER_MODE= calc_properties the following input data values must be defined:
FREQ_T = Cut-off frequency where the stiffness shifts from static to dynamic stiffness. FREQ_T is also the frequency where η reaches its maximum value.
KP = Parallel stiffness.
KDYN = Dynamic stiffness at a very high frequencies.
ETA_T = The energy loss coefficient η at frequency FREQ_T.
Declared= Character*20    Default= 'k+(k-c)'

FREQ_T
Transition frequency.
FREQ_T can have different meanings in different spring-damper-models, for more information please look under command SPRING_MODEL.
Declared= Real*4    Default= -999.

FSTART
Starting frequency.
Frequency which starts the generation of results when OPER_MODE is equal to generate_curve.
Declared= Real*4    Default= 0.

FSTEP
Frequency increment.
Increment between points in the generated frequency curve. when OPER_MODE is equal to generate_curve.
Declared= Real*4    Default= 0.1

FSTOP
Stop frequency.
Frequency which ends the generation of results when OPER_MODE is equal to generate_curve.
Declared= Real*4    Default= 40.

ETA_T
The energy loss coefficient η at FREQ_T.
ETA_T can have different meanings in different spring-damper-models, for more information please look under command SPRING_MODEL.
Declared= Real*4    Default= -999.

C
Damping coefficient in damper.
C can have different meanings in different spring-damper-models, for more information please look under command SPRING_MODEL.
Declared= Real*4    Default= -999.

KMID
Absolute value of the stiffness at FREQ_T.
KMID can have different meanings in different spring-damper-models, for more information please look under command SPRING_MODEL.
Declared= Real*4    Default= -999.

KDYN
Dynamic stiffness at high frequencies.
KDYN can have different meanings in different spring-damper-models, for more information please look under command SPRING_MODEL.
Declared= Real*4    Default= -999.

KSTAT
Static stiffness at low frequency.
KSTAT can have different meanings in different spring-damper-models, for more information please look under command SPRING_MODEL.
Declared= Real*4    Default= -999.

KP
Parallel stiffness.
KP can have different meanings in different spring-damper-models, for more information please look under command SPRING_MODEL.
Declared= Real*4    Default= -999.

KS
Serial stiffness.
KS can have different meanings in different spring-damper-models, for more information please look under command SPRING_MODEL.
Declared= Real*4    Default= -999.

KC
Damper stiffness.
KC can have different meanings in different spring-damper-models, for more information please look under command SPRING_MODEL.
Declared= Real*4    Default= -999.

UTFIL
Output data file containing the stiffness v.s. frequency.
The file is written in five columns, with the following contents:
Column 1 = The excitation frequency.
Column 2 = The real part of the stiffness E'
Column 3 = The imaginary part of the stiffness E"
Column 4 = The absolute value of the stiffness E*
Column 5 = The energy loss coefficient η
Declared= Character*256    Default= 'x.kc_propr'

END
Marks the end of the input data file.

blurulr2.gif

Example of an input data file

Following example: Master.misc_kc_propf can be used as a master file: 

#
#        Input data file for program KC_PROP
#

  UTFIL= result.kc_propr
#
# ----------------------------------------------------------------------
#
# OPER_MODE= calc_properties
# SPRING_MODEL= k+(k-(k+c))
# KP    = 1e6
# KDYN  = 2e6
# FREQ_T= 4
# ETA_T = 0.3
## ----------------------------------------------------------------------
#
# OPER_MODE= generate_curve
# SPRING_MODEL= k+(k-(k+c))
# C  = 100e3            # Damping coefficient in damper
# KC = 8e3              # Stiffness in parallel to C
# KS = 5e6              # Series stiffness of C and Kc
# KP = 1e6              # Stiffness in parallel
## ----------------------------------------------------------------------
#
# OPER_MODE= calc_properties
# SPRING_MODEL= k+(k-c)
# FREQ_T= 110           # Frequency when max. tan(d) is achieved
# ETA_T = 0.05          # max. tan(d)
# KMID  = 100e6         # Stiffness at frequency= freq_t
## ----------------------------------------------------------------------
#
  OPER_MODE= generate_curve
  SPRING_MODEL= k+(k-c)
  KP = 9.512492E+07     # Stiffness in parallel
  C  = 1.376327E+04     # Damping coefficient in damper
  KS = 1.000000E+07     # Series stiffness in damper
## ----------------------------------------------------------------------
#
# Control the generated frequency curve
#
  FSTART= 0. FSTEP= .1 FSTOP= 40.
## ----------------------------------------------------------------------

In order to plot the curve generated by program kc_prop following input data file can be used:
(When using the following input data file, no ident shall be given to the MPLOT program. Do not answer the ident-question or set ident="mplot_id") 

##
##     Input data file for program MPLOT
##

 iscren= 1

 create_curve FILE_VPAIR_FREE     freq     Kreal
 format='(a,a,x,x,x)'  result.kc_propr
 create_curve FILE_VPAIR_FREE     freq     Kimag
 format='(a,x,a,x,x)'  result.kc_propr
 create_curve FILE_VPAIR_FREE     freq     Kabs
 format='(a,x,x,a,x)'  result.kc_propr
 create_curve FILE_VPAIR_FREE     freq     eta
 format='(a,x,x,x,a)'  result.kc_propr

 Page  ----------------------------------------
  x_left= auto  x_right= auto  xint/cm= auto
  y_bot=  auto  y_top=   auto  yint/cm= auto
  diagram 11
   curve yvar= Kabs
  diagram 12
   curve yvar= eta
 EndPage

 Page  ----------------------------------------
  x_left= auto  x_right= auto  xint/cm= auto
  y_bot=  auto  y_top=   auto  yint/cm= auto
  diagram 11
   curve yvar= Kreal
   curve yvar= Kimag
   curve yvar= Kabs
 EndPage

 Page  ----------------------------------------
  x_left= auto  x_right= auto  xint/cm= auto
  y_bot=  auto  y_top=   auto  yint/cm= auto
  diagram 11
   curve yvar= eta
 EndPage

stop

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