# Create vibration spectrum in the form of a waterfall plot for differential rolling element bearing

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Kyle McLaughlin on 10 Nov 2020
Hello,
I am being asked to create a vibration spectrum plot in the form of a waterfall plot as measured by a wireless accelerometer attached to the face of the outer race for a differential rolling element bearing based on an rpm vs time graph (defined below). My homework assignment previously asked that I calculate the bearing characteristic frequecies of Fundamental Train Frequency, Ball Spin Frequency, Ball Pass Frequency w/ respect to outer ring, and BPF w/ respect to inner ring, which was simple just plug and chug. My question now is how to use these frequencies to create a vibration spectrum using a waterfall plot.
time = linspace(0,43,43); %process time
thetaA = 0; %bearing contact angle
D = 180; %pitch diameter
d = 10; %ball diameter
n = 11; %number of balls in bearing
Nir = [linspace(0,11000,12) 11200 10000 8000 linspace(7600,7600,14) 8000 9000 10600 linspace(10000,0,11)]; %inner ring rpm
Nor = [linspace(0,4000,13) 3600 2660 linspace(2646,2646,14) 2660 3200 linspace(3800,0,12)] ; %outter ring rpm
%characteristic frequencies for theta = 0 deg
FTF_A = (1/120)*(Nor*(1+(d/D)*cos(thetaA))+Nir*(1-(d/D)*cos(thetaA))); %Fund Train Freq
BSF_A = (D/(120*d))*(1-(d/D)*cos(thetaA))*(1+(d/D)*cos(thetaA))*(abs(Nor+Nir)); % Ball Spin Freq
BPFI_A = (n/120)*(1+(d/D)*cos(thetaA))*(abs(Nor+Nir)); % BPF inner
BPFO_A = (n/120)*(1-(d/D)*cos(thetaA))*(abs(Nor+Nir)); % BPF outter
%plots the given info from the hw assignment: this is the rpm vs time graph
figure(3)
plot(time,Nir,'g',time,Nor,'b')
title('Bearing Operational Conditions')
xlabel('Time (min)')
ylabel('Rotational Speed (rpm)')
legend('Inner Race', 'Outer Race')
grid on

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