gefran TPD32-EV-...-4B - Figure 6.6.2.1: S Shape Acceleration Ramp

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S shape t const Denestheacceleration/decelerationcurveforS-shapedramp.
S acc t const DenestheaccelerationcurveforS-shapedramp.
S dec t const DenesthedecelerationcurveforS-shapedramp.
ForRamp Shape =Linearrefertoprevioussection6.6.1forrampdescription.
ForRamp Shape =S-Shaped refertothedescriptionreportedhereafter.
Duringamotoracceleration,theSrampisdenedby3section.
Therstandthethird,namedTsinthefollowingpicture,areequal.Theirshapedependsonthejerksetinthe
parameterS acc t cons.Thesecondsection,namedTlin,isalinearrampexpressedasdeltaspeed/deltatime.
Thesameconsiderationcanbedoneforthemotordeceleration.
Figure 6.6.2.1: S shape acceleration ramp
Ramp Reference
S
0
Ts
Tlin
Ts
t
Example: calculation of the total ramp time
P21Acc. Delta speed =10rpm
P22Acc. Delta time =10s
P110Ramp ref=60rpm
P663S acc t const =6000ms
Acc Jerk= Acceleration Jerk [rpm/s^2 ]
Acc Jerk= 2*Acc. Delta speed/( S acc t const/1000)^2
Acc Jerk= 2*10/(6000/1000)^2 =0.56 [rpm/s^2 ]
Alin= Linear Acceleration [rpm/s]
Alin= Acc. Delta speed/Acc Delta time [rpm/s]
Alin= 10/10=1 [rpm/s]
T1= Theoretic time to end the S shape [s]
T1= Alin/Acc Jerk [s]
T1= 1/0.56=1.8 [s]
VT1= Speed reached at T1 [rpm]
VT1=1/2*Acc Jerk*T1^2 [rpm]
VT1=1/2*0.56*(1.8)^2=0.9 [rpm]
If
VT1<Ramp ref/2
Jerk time Ts=T1=1.8 [s]
Linear acceleration time= Tlin [s]
Tlin=((Ramp ref-(2*VT1)))/Alin [s]
Tlin=(60-( 2*0.9 ))/1.8=58.2 [s]
Total acceleration time=Ttacc=Tlin+(2*Ts) [s]
Ttacc=58.2+(2*1.8)=61.8 [s]