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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 =D2 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"

**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.

**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 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:

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.

**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

**END**- Marks the end of the 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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