Chapter 5
Calculating Rotational Speed
LabVIEW Order Analysis Toolset User Manual
5-2
ni.com
Figure 5-1.
Tachometer Signal and Rotation Angle
The arrival time
t
k
of the pulses
P
(
k
) in the tachometer signal correspond to
the cumulative rotation angle
θ
(
t
k
). The cumulative rotation angle function
θ
(
t
) increases by a fixed angle
θ
in the time interval between times
t
k
and
t
k+
1
. As shown in the following equation, you can present rotational speed
as the first derivative of
θ
(
k
).
While the time interval between pulses varies with the rotational speed,
the cumulative angle increment remains constant. Calculating the first
derivative of
θ
(
t
) usually involves step-by-step polynomial curve fitting,
which requires multiple computations in each iteration. Instead of
observing
θ
(
t
) directly, the LabVIEW Order Analysis Toolset observes
t
(
θ
),
which is the inverse function of
θ
(
t
), because calculating the first derivative
t1
t2
t3
t4
(a) Tachometer Pulse
θ
4
θ
3
θ
2
θ
1
∆θ
∆θ
∆θ
ϖ
3
t
t
t1
t2
t3
t4
(b) Rotation Angle vs. Time
ω
t
( )
d
θ
dt
------
=
