Calculate Characteristic Frequencies and Orders

Faults on the inner race, outer race, or rolling elements of a rolling-element bearing exhibit peaks of characteristic frequencies or orders in the power spectrum of the envelope signal of the vibration signal. You can calculate the characteristic frequencies or orders of a rolling-element bearing and compare them with the peaks in the power spectrum of the envelope signal to identify the source of the bearing faults.

The following illustration shows the structure and the geometric parameters of a typical rolling-element bearing:

Figure 58. Typical Rolling-Element Bearing's Structure and Geometric Parameters

1378

Dball is the bearing ball diameter, Dpitch is the pitch diameter, and Φ is the contact angle between the ball and the race.

You can use the following equations to calculate the characteristic frequencies of the bearing:

Table 8. Equations for Calculating Characteristic Bearing Frequencies
Characteristic Bearing Frequency Equation
Fundamental train frequency, fFTF
f F T F = f s 2 [ 1 − D b a l l D p i t c h cos ϕ ]
Ball spin frequency, fBS
f B S = f s 2 D p i t c h D b a l l [ 1 − ( D b a l l D p i t c h ) 2 cos 2 ( ϕ ) ]
Outer race frequency, fOR
f O R = N f F T F
Inner race frequency, fIR
f I R = N ( f s − f F T F )

where fs is the rotational frequency of the shaft in revolutions per second, and N is the number of rollers or balls.

You can use the following equations to calculate the characteristic orders of the bearing:

Table 9. Equations for Calculating Characteristic Orders
Characteristic Order Equation
Fundamental train order, oFTF
o F T F = 1 2 [ 1 − D b a l l D p i t c h cos ⁡ ϕ ]
Ball spin order, oBS
o B S = 1 2 D b a l l D p i t c h [ 1 − ( D b a l l D p i t c h ) 2 cos 2 ϕ ]
Outer race order, oOR
o O R = N o F T F
Inner race order, oIR
O I R = N ( 1 − o F T F )

As shown in the table above, the characteristic orders are functions of the geometric parameters of the bearing and therefore are constant values.

The equations for calculating the characteristic frequencies and orders assume no slippage of the rollers or balls when the bearing is running. In real-world applications, however, the actual characteristic frequencies or orders might differ slightly from the calculated frequencies or orders because of slippage.