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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:

                                                         
  eta = D / (2*pi*U)                                     
                                                         
  where: eta = energy loss coefficient                   
         D   = energy loss per cycle                     
         U   = elastic energy at max. deflection         
                                                         

For a k-coupling in parallel with a c-coupling the energy loss coefficient will increase linearly according to:

                                                       
  eta = 2 * set * f / fo                               
                                                       
  where: set = fraction of critical damping            
         f   = excitation frequency                    
         fo  = eigen frequency for the system          
                                                       

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'

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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:

If OPER_MODE=generate_curve the user must define following values Kp, Ks and C. If OPER_MODE=calc_properties the user must define the following:

Freq_t	=	Transition frequency where the stiffness shifts from static to dynamic stiffness. And where the phase factor adopts it's maximum value.
Kmid	=	Transition stiffness at frequency Freq_t.
eta_t	=	The tangent of the phase factor 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:

If OPER_MODE=generate_curve the user must define following values Kp, Ks, Kc and C. If OPER_MODE=calc_properties the user must define the following:

Freq_t	=	Transition frequency where the stiffness shifts from static to dynamic stiffness. And where the phase factor adopts it's maximum value.
Kp	=	The parallel stiffness.
Kdyn	=	Dynamic stiffness at a very high excitation frequency.
eta_t	=	The tangent of the phase factor at frequency Freq_t.

Declared= Character*20   Default= 'k+(k-c)'

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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.

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FSTART

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

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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

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FSTOP

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

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ETA_T

The tangent of the phase factor 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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.
Column 3	=	The imaginary part of the stiffness.
Column 4	=	The absolute value of the stiffness.
Column 5	=	The tangent of the phase factor, which equals the quotient when the imaginary part of the stiffness is divided by the real part of the stiffness.

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END

Marks the end of the input data file.

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. Answer "no" or "mplot_id" on the ident-question)

 ##                                                      
 ##     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