2014 RecurDyn User conference - functionbay.co.krŽ‘션베이... · ADAMS Function과95% ... AKISPL Akima spline 간법을

2014 FunctionBay, Inc.12014 User Conference

Power User Expression

2014 RecurDyn User conference


Index

I. RecurDyn Expression

II. Expression

III.Expression

IV.Basic Expression 1. ,

2.

3. Joint

V. Advanced Expression 1.

2.

3. Expression

4.

5. Bouc-Wen Hysteresis

6.

7.

8.


v

2014 FunctionBay, Inc.

RecurDyn Expression


Expression ?

RecurDyn Expression

FE static solution MBD solution

Element

,

,

Expression MBD

Solution

VS


Expression ?

RecurDyn Expression


RecurDyn Expression

UI Fortran

Text Editing

Argument

Value Expression List

ADAMS Function 95%

RecurDyn Expression

Entity

List Editor


v


Expression


Expression

10 10,20,30,40

Time=1,2,3,4.

1.09443, 2.1757, 3.23084

Time=1,2,3,.

SolverExpression

double

(double), (double), (double)

Expression

10 10*Time 10*sin(2*pi*Time)


Argument

Body, Joint Marker

Argument

Expression

Expression

DX(1{,2}{,2})

Marker1

Marker2

Marker3

Marker2 Marker1 Marker3 X

DX,DY,DZ,AX,AY,AZ,VX,VY,VZ,WX,WY,WZ,ACCX,ACCY,ACCZ,WDTX,WDTY,WDTZ.

Ex) sin( DX(1,2,2) * 2 * pi ) * Time Solver ( )

If

(1)

(2)

(3)


Parametric Value

Parametric Value

Variable Equation

. VE Expression

Expression

PV

PV PV

VE Expression VE

VE varval(), VE


v


Expression


Expression

OPERATORSFORTRAN FUNCTIONS

SIMULATION CONSTANTS

DISPLACEMENT

VELOCITY

ACCELERATION

GENERIC FORCE

SPECIFIC FORCE

SYSTEM ELEMENT

ARITHMETIC IF

INTERPOLATION

GENERAL

Expression

+

-

*

/

**

< Is less than1.0=2.0, return the value 02.0>=1.0, return the value 1

Is not equal toAB, return the value 0( If |A-B|=IF Tolerance)

|| Logical OR&& Logical AND


Expression

OPERATORS

FORTRAN FUNCTIONSSIMULATION CONSTANTS

DISPLACEMENT

VELOCITY

ACCELERATION

GENERIC FORCE

SPECIFIC FORCE

SYSTEM ELEMENT

ARITHMETIC IF

INTERPOLATION

GENERAL

Expression

ABS

ACOS Arccosine

AINT

ANINT

ASIN Arcsine

ATAN Arctangent ex)atan(x/y)

ATAN2 Arctangent2 ex)atan2(x,y)

COS Cosine

COSH Hyperbolic cosine

DIM 0

EXP e

LOG Log e

LOG10 Log 10

MAX 2 3

MIN 2 3

MOD

SIGN x y sign(x,y)

SIN Sine

SINH Hyperbolic sine

SQRT

TAN Tangent

TANH Hyperbolic tangent


Expression

OPERATORS

FORTRAN FUNCTIONS

SIMULATION CONSTANTSDISPLACEMENT

VELOCITY

ACCELERATION

GENERIC FORCE

SPECIFIC FORCE

SYSTEM ELEMENT

ARITHMETIC IF

INTERPOLATION

GENERAL

Expression

TIME Solver Simulation Time

PI 3.1415926.

DTOR Degree Radian

RTOD Radian Degree


Expression

OPERATORS

FORTRAN FUNCTIONS


DISPLACEMENTVELOCITY

ACCELERATION

GENERIC FORCE

SPECIFIC FORCE

SYSTEM ELEMENT

ARITHMETIC IF

INTERPOLATION

GENERAL

Expression

AX Marker x

AY Marker y

AZ Marker z

DM Marker

DX Marker x

DY Marker y

DZ Marker z

PHI Marker Euler Orientation 1

THETA Marker Euler Orientation 2

PSI Marker Euler Orientation 3

ROLL Marker Orientation x

PITCH Marker Orientation y

YAW Marker Orientation z


Expression

OPERATORS

FORTRAN FUNCTIONS


DISPLACEMENT

VELOCITY

ACCELERATION

GENERIC FORCE

SPECIFIC FORCE

SYSTEM ELEMENT

ARITHMETIC IF

INTERPOLATION

GENERAL

Expression

VM Marker

VR Marker

VX Marker x

VY Marker y

VZ Marker z

WM Marker

WX Marker x

WY Marker y

WZ Marker z


Expression

OPERATORS

FORTRAN FUNCTIONS


DISPLACEMENT

VELOCITY

ACCELERATION

GENERIC FORCE

SPECIFIC FORCE

SYSTEM ELEMENT

ARITHMETIC IF

INTERPOLATION

GENERAL

Expression

ACCM Marker

ACCX Marker x

ACCY Marker y

ACCZ Marker z

WDTM Marker

WDTX Marker x

WDTY Marker y

WDTZ Marker z


Expression

OPERATORS

FORTRAN FUNCTIONS


DISPLACEMENT

VELOCITY

ACCELERATION

GENERIC FORCE

SPECIFIC FORCE

SYSTEM ELEMENT

ARITHMETIC IF

INTERPOLATION

GENERAL

Expression

FM Marker

FX Marker x

FY Marker y

FZ Marker z

TM Marker

TX Marker x

TY Marker y

TZ Marker z


Expression

OPERATORS

FORTRAN FUNCTIONS


DISPLACEMENT

VELOCITY

ACCELERATION

GENERIC FORCE

SPECIFIC FORCE

SYSTEM ELEMENT

ARITHMETIC IF

INTERPOLATION

GENERAL

Expression

CONTACT Contact

MOTION Motion

JFRICTION Joint Friction

COUPLER Coupler

GEAR Gear

SHT3D_CF MTT3D Sheet

JOINT Joint

PTCV PTCV joint

CVCV CVCV Joint

AXIAL Axial Force

TFORCE Translational Force

RFORCE Rotational Force

SCREWFORCE Screw force

BEAM Beam

BUSH Bushing

SPRING Spring

MATRIXFORCE Matrix force


Expression

OPERATORS

FORTRAN FUNCTIONS


DISPLACEMENT

VELOCITY

ACCELERATION

GENERIC FORCE

SPECIFIC FORCE

SYSTEM ELEMENT

ARITHMETIC IF

INTERPOLATION

GENERAL

Expression

DIF

Differential Equation Entity Ex) DIF(DE1) I

DIF1

Differential Equation Entity Ex) DIF1(DE1) dI/dt

VARVAL

Variable Equation ExpressionEx) VARVAL(VE1) VE1

V RI dII V RI L

L dt

Motor Torque K I

- = = +

= ?

&

DE1: (V-R*I)/L VE1: DIF(DE1)


Expression

OPERATORS

FORTRAN FUNCTIONS


DISPLACEMENT

VELOCITY

ACCELERATION

GENERIC FORCE

SPECIFIC FORCE

SYSTEM ELEMENT

ARITHMETIC IF

INTERPOLATION

GENERAL

Expression

f2, when f1 IFT

= f3, when IFT f1 IFT

f4, when IFT f1

IFT(If Tolerance)

IF f1: f2, f3,

:

f4

0

0

IF(f1:f2,f3,f4)

f1 f2, f3, f4 f1 0 f2 f1 0 f3 f1 0 f3

f1 = -5,-3,2,0,-3

IF(f1,f2,f3,f4)

f2,f2,f4,f3,f2

f2=time

f3=sin(dx(1,2))

f4=0

Example


Expression

OPERATORS

FORTRAN FUNCTIONS


DISPLACEMENT

VELOCITY

ACCELERATION

GENERIC FORCE

SPECIFIC FORCE

SYSTEM ELEMENT

ARITHMETIC IF

INTERPOLATION

GENERAL

Expression

AKISPL

Akima spline Spline

CUBSPL

Cubic spline Motion Spline

LINSPL

Akima Cubic spline Akima 1 , Cubic 2 (Force Akima, Motion Cubic)


Expression

OPERATORS

FORTRAN FUNCTIONS


DISPLACEMENT

VELOCITY

ACCELERATION

GENERIC FORCE

SPECIFIC FORCE

SYSTEM ELEMENT

ARITHMETIC IF

INTERPOLATION

GENERAL

Expression

BISTOP

CHEBY

FORCOS cosine

FORSIN sine

HAVSIN Sine

IMPACT

POLY

SHF Sine

STEP 4

STEP5 5

SWEEP Sine


v


Basic Expression


,

Impulse: Step 20 * ( step(time,1,0,1.1,1) - step(time,1.1,0,1.2,1) )

:Sin dim 10* (1-cos(360d*dim(time,1)*5))

Sweep sweep(time, 10, 1, 1, 5, 10, 1)

Spline :Interpolation 10*akispl(dim(time,1),0,Sp1,0)

10*cubspl(dim(time,1),0,Sp1,0)

10*linspl(dim(time,1),0,Sp1,0)

/2 1

/2

1 Spline Data


DX,DY,DZ DX(Body2.Marker1, Body1.Marker1 ,Ground.Marker1 )

Body1.Marker1

Body2.Marker1

Ground.Marker1

DX

DY

X

Y

DM

VX,VY,VZ VX(Body2.Marker1, Body1.Marker1 ,Ground.Marker1 )

Global

Body1.Marker1

Body2.Marker1

Ground.Marker1

X

Y

VX VY

VM

ACCX,ACCY,ACCZ ACCX(Body2.Marker1, Body2.Marker1 ,Ground.Marker1, Ground.Marker1)

Body1.Marker1

Body2.Marker1

Ground.Marker1

Y

X

ACCXACCY

ACCM


?

y .

BALL.CM

OBSERVER.REF

PLANET.REF

Marker

ACCY(BALL.CM, Ground.REF )

Marker

ROCKET.CM

X

Y

ACCY(BALL.CM, ROCKET.CM )

Marker


?

ACCY(BALL.CM, ROCKET.REF, PLANET.REF) ACCY(BALL.CM, ROCKET.REF, PLANET.REF, PLANET.REF)

ACCY(BALL.CM, OBSERVER.REF, OBSERVER.REF, OBSERVER.REF)

A A Global

AB B A Global

ABC B A C

ABCC B A C C

ABBB B


Joint

RecurDyn Joint Force Driving Force Global .

FE Body Local

Joint

Global

Joint

Joint

LCA.ref

FX(LCA.Marker1, Knuckle.Marker1, LCA.ref)

FY(LCA.Marker1, Knuckle.Marker1, LCA.ref)

FZ(LCA.Marker1, Knuckle.Marker1, LCA.ref)

Reference Marker


v


Advanced Expression


DC RPM

Power(%)RPM

To

rqu

e(N

m)

Power(Volt or Ampair)

Name Expression

Ex_motor_torque AKISPL(varval(VE_motor_rpm),0,Sp_NM_RPM,0)*1000

Ex_motor_rpm WZ(1,2,2)*60/(2*pi)

Expression

Name Expression

VE_motor_rpm Ex_motor_rpm

Varible Equation

Spline

Name Data

Sp_NM_RPM 2D curve data

Power On


Step

-(STEP( VX(1,2,1),0, 0, 1, PV_forward_friction )+STEP( VX(1,2,1),-1,-PV_backward_friction, 0,0 ) )


Expression

Force

Name Expression

Ex_Fy -PV_stiffness*DY(1,2)*step( DM(1,2),PV_eps,1,PV_eps*1.001,0)

PV_eps=0.03, PV_stiffness = 1000000

PV_eps 0

F=K

Expression


Geometry Contact Expression .

PV

PV_contact_stiffness 10000

PV_contact_damping 1

PV_contact_exponent 1

PV_contact_penetration 1

PV_contact_freelength 0.1

PV_contact_static_velocity 15

PV_contact_dynamic_velocity 20

PV_contact_static_friction 1

PV_contact_dynamic_friction 0.8

IMPACT(

DZ(2,3,3) -AKISPL(DX(2,3,3),0,1,0),

VZ(2,3),

PV_contact_freelength,

PV_contact_stiffness,

PV_contact_exponent,

PV_contact_damping,

PV_contact_penetration)

Marker spline

Expression

Arg1:Marker1

Arg2:Marker2


(-IF(PV_contact_static_velocity-abs(VX(2)):

0,

step(VX(2) ,

-PV_contact_static_velocity,

-PV_contact_static_friction,

PV_contact_static_velocity,

PV_contact_static_friction),

step( VX(2) ,

-PV_contact_static_velocity,

-PV_contact_static_friction,


PV_contact_static_friction)

)

+IF(PV_contact_static_velocity-abs(VX(2)):

step( abs(VX(2)) ,


PV_contact_static_friction,

PV_contact_dynamic_velocity,

PV_contact_dynamic_friction),

0,

0)*(-sign(1,VX(2)))

)

* IMPACT(

DZ(2,3,3) -AKISPL(DX(2,3,3),0,1,0),

VZ(2,3),

PV_contact_freelength,

PV_contact_stiffness,

PV_contact_exponent,

PV_contact_damping,

PV_contact_penetration)

Expression static

staticSetp 0

0

static

Setp

0

F-V


Bouc-Wen histeresis z

Bouc-Wen Hysteresis

-1

( ) (1- ) ( )

( ) ( ) ( ) ( ) ( ) ( )

i i

n n

F t ak u t a k z t

z t u t u t z t u t z t

z

Differential Equation

Name Data

Ex_zdot alpha*varval(VE_udot) -beta*abs(varval(VE_udot))*abs(DIF(zdot))**(n-1)*DIF(zdot) -gamma*varval(VE_udot)*abs(DIF(zdot))**n

Ex_udot VY(1,2,2)

Ex_force a*ki*varval(VE_udot)+(1-a)*ki*DIF(zdot)

PV alpha 2beta 1

n 2

gamma 1a 0.5

ki 2

Expression

Name Data

zdot Ex_zdot

Sweep Sine z

F-D


+

-

+ -

PV_axis_K*IF(WZ(1,2,2):

akispl( -(AZ(1,2)+180d) ,0,3,0 ),

-akispl( (AZ(1,2)+180d) ,0,3,0 ),

-akispl( (AZ(1,2)+180d) ,0,3,0 ) )

-PV_damping*WZ(1,2,2)

Spline

PV_axis_K:Stiffness:PV_damping:


Expression Rotational Force

Name Data

Ex_rcnt BISTOP(AZ(1,2),WZ(1,2),-pi/2,pi/2,10000000000,2.0,1,1d)

Expression

2

1

BISTOP( A,B,C,D,E,F,G,H)

A

B

C

D

E Contact Stiffness

F Exponent

G Damping

H Max penetration

BISTOP


Pre-tension Belt

1 1 1 2 2 1 1 2 2( ) ( )TF K r r PT C r r

2 1 1 2 2 1 1 2 2( ) ( )TF K r r PT C r r

IF(

(-(PV_K*(r1*AZ(1,2) - r2*AZ(3,4)) + PV_C*(r1*WZ(1,2,2) - r2*WZ(3,4,4))) - PV_PT ):

(-(PV_K*(r1*AZ(1,2) - r2*AZ(3,4)) + PV_C*(r1*WZ(1,2,2) - r2*WZ(3,4,4))) - PV_PT ),

0,

0)

IF(

((PV_K*(r1*AZ(1,2) - r2*AZ(3,4)) + PV_C*(r1*WZ(1,2,2) - r2*WZ(3,4,4))) - PV_PT):

((PV_K*(r1*AZ(1,2) - r2*AZ(3,4)) + PV_C*(r1*WZ(1,2,2) - r2*WZ(3,4,4))) - PV_PT),

0,

0)

1TF

2TF

Screw Force

(ground to driver)

Screw Force

(ground to coupler)

Argument:1 Rev Jnt.1 Action mkr2 Rev Jnt.1 Base mkr3 Rev Jnt.2 Action mkr4 Rev Jnt.2 Base mkr

Revolute joint 1 Revolute joint 2

, 0 ( 0 )


Expression

Expression


Expression

Variable Equation Differential Equation

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2014 RecurDyn User conference - functionbay.co.krŽ‘션베이... · ADAMS Function과95% ... AKISPL Akima spline 간법을