The required change of frequency Δw = 50Hz. The acceleration and jerk are converted from the parameter values as follows:
a
Max
= 100 / ramp rate = 20.0Hz/s
J
Max
= 100 / Maximum Rate Of Change Of Acceleration (02.007) = 32.3Hz/s
2
The linear ramp time T
Linear
= Δw x a
Max
= 50.0 / 20.0 = 2.5s
The frequency change for the acceleration to reach its limit w
B
= a
Max
2
/ 2J
Max
= 20.0
2
/ (2 x 32.3) = 6.19Hz
The required frequency change for Δw = 50Hz and this is greater than 2w
B
, i.e. Δw > 2 x 6.19Hz. Therefore the time for the ramp
T
SRamp2
= (Δw / a
Max
) + (a
Max
/ J
Max
) = (50.0 / 20.0) + (20.0 / 32.3) = 2.5 + 0.62 = 3.12s
Note that the default value of Maximum Rate Of Change Of Acceleration (02.007) has been chosen so that when it is combined with the default
acceleration rate, each of the S sections of the ramp is 20% of the overall time for the frequency change, i.e. 0.62/3.12 x 100% = 20%. This is the same
as if S Ramp Set-up Mode (02.041) = 2 and S Ramp Percentage (02.040) = 20%.
If the required change of frequency had been 5.0Hz, i.e. less than 2 x wB, then the alternative equation should be used:
T
SRamp1
= 2 √(Δw / J
Max
) = 2 √(5.0 / 32.3) = 0.78s
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