National Instruments Order Analysis Toolset - Manual (Page 48)

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
θ4
θ3
θ2
θ1
∆θ
∆θ
∆θ
ϖ3
t
t
t1 t2 t3 t4
(b) Rotation Angle vs. Time
ω t ( )
d θ
dt
------ =