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2014 FunctionBay, Inc.12014 User Conference
Power User Expression
2014 RecurDyn User conference
2014 FunctionBay, Inc.22014 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.
2014 FunctionBay, Inc.32014 User Conference
v
2014 FunctionBay, Inc.
RecurDyn Expression
2014 FunctionBay, Inc.42014 User Conference
Expression ?
RecurDyn Expression
FE static solution MBD solution
Element
,
,
Expression MBD
Solution
VS
2014 FunctionBay, Inc.52014 User Conference
Expression ?
RecurDyn Expression
2014 FunctionBay, Inc.62014 User Conference
RecurDyn Expression
UI Fortran
Text Editing
Argument
Value Expression List
ADAMS Function 95%
RecurDyn Expression
Entity
List Editor
2014 FunctionBay, Inc.72014 User Conference
v
2014 FunctionBay, Inc.
Expression
2014 FunctionBay, Inc.82014 User Conference
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)
2014 FunctionBay, Inc.92014 User Conference
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)
2014 FunctionBay, Inc.102014 User Conference
Parametric Value
Parametric Value
Variable Equation
. VE Expression
Expression
PV
PV PV
VE Expression VE
VE varval(), VE
2014 FunctionBay, Inc.112014 User Conference
v
2014 FunctionBay, Inc.
Expression
2014 FunctionBay, Inc.122014 User Conference
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
2014 FunctionBay, Inc.132014 User Conference
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
2014 FunctionBay, Inc.142014 User Conference
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
2014 FunctionBay, Inc.152014 User Conference
Expression
OPERATORS
FORTRAN FUNCTIONS
SIMULATION CONSTANTS
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
2014 FunctionBay, Inc.162014 User Conference
Expression
OPERATORS
FORTRAN FUNCTIONS
SIMULATION CONSTANTS
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
2014 FunctionBay, Inc.172014 User Conference
Expression
OPERATORS
FORTRAN FUNCTIONS
SIMULATION CONSTANTS
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
2014 FunctionBay, Inc.182014 User Conference
Expression
OPERATORS
FORTRAN FUNCTIONS
SIMULATION CONSTANTS
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
2014 FunctionBay, Inc.192014 User Conference
Expression
OPERATORS
FORTRAN FUNCTIONS
SIMULATION CONSTANTS
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
2014 FunctionBay, Inc.202014 User Conference
Expression
OPERATORS
FORTRAN FUNCTIONS
SIMULATION CONSTANTS
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)
2014 FunctionBay, Inc.212014 User Conference
Expression
OPERATORS
FORTRAN FUNCTIONS
SIMULATION CONSTANTS
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
2014 FunctionBay, Inc.222014 User Conference
Expression
OPERATORS
FORTRAN FUNCTIONS
SIMULATION CONSTANTS
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)
2014 FunctionBay, Inc.232014 User Conference
Expression
OPERATORS
FORTRAN FUNCTIONS
SIMULATION CONSTANTS
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
2014 FunctionBay, Inc.242014 User Conference
v
2014 FunctionBay, Inc.
Basic Expression
2014 FunctionBay, Inc.252014 User Conference
,
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
2014 FunctionBay, Inc.262014 User Conference
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
2014 FunctionBay, Inc.272014 User Conference
?
y .
BALL.CM
OBSERVER.REF
PLANET.REF
Marker
ACCY(BALL.CM, Ground.REF )
Marker
ROCKET.CM
X
Y
ACCY(BALL.CM, ROCKET.CM )
Marker
2014 FunctionBay, Inc.282014 User Conference
?
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
2014 FunctionBay, Inc.292014 User Conference
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
2014 FunctionBay, Inc.302014 User Conference
v
2014 FunctionBay, Inc.
Advanced Expression
2014 FunctionBay, Inc.312014 User Conference
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
2014 FunctionBay, Inc.322014 User Conference
Step
-(STEP( VX(1,2,1),0, 0, 1, PV_forward_friction )+STEP( VX(1,2,1),-1,-PV_backward_friction, 0,0 ) )
2014 FunctionBay, Inc.332014 User Conference
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
2014 FunctionBay, Inc.342014 User Conference
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
2014 FunctionBay, Inc.352014 User Conference
(-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_velocity,
PV_contact_static_friction)
)
+IF(PV_contact_static_velocity-abs(VX(2)):
step( abs(VX(2)) ,
PV_contact_static_velocity,
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
2014 FunctionBay, Inc.362014 User Conference
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
2014 FunctionBay, Inc.372014 User Conference
+
-
+ -
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:
2014 FunctionBay, Inc.382014 User Conference
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
2014 FunctionBay, Inc.392014 User Conference
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 )
2014 FunctionBay, Inc.402014 User Conference
Expression
Expression
2014 FunctionBay, Inc.412014 User Conference
Expression
Variable Equation Differential Equation
RecurDyn UI Expression ,
MBD Expert means Expression Expert
2014 FunctionBay, Inc.422014 User Conference
228 15 1 2 5
Tel. 031-622-3696, Fax. 031-622-3704
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