Angular Acceleration Linear Accelerometers

Engineers performing multi-axis testing often seek to calculate the angular acceleration of rotational motion. VibrationVIEW can be configured to automatically calculate the angular acceleration between two linear accelerometers while a test is running.

Question

How do you calculate the angular acceleration between two points?

Answer

VibrationVIEW can calculate the angular acceleration between two accelerometers in real time using the difference between the two channels. The process is outlined below.

Theory

The formula for angular acceleration between two points is as follows:

(1)  

Where alpha (α) is the resultant angular acceleration in radians/second², A₁ is the linear acceleration of the first accelerometer (meters/second²), A₂ is the linear acceleration of the second accelerometer, and D₁₂ is the distance between the two accelerometers in meters. A negative sign is placed in front of A₂ as a correction because the A₂ accelerometer is oriented in the same direction as A₁.

Figure 1 displays a truck axle with two linear accelerometers mounted to the axle to measure angular acceleration. The proceeding diagram shows how the angle, α, is calculated when the axle rotates counter-clockwise.

Figure 1. Angular acceleration calculation for a truck axle.

The body connecting the two accelerometers is assumed to be rigid. If there is a significant amount of flex between the two points, this method of determining angular acceleration is not valid.

Application 

To calculate angular acceleration in VibrationVIEW:

1. Select Configuration > Inputs

• • Enter Ch3-Ch2 as the label for Channel 4
  • Select the Conditioner checkbox for Ch4; a “Conditioner Sensitivity” field will appear to the right of the checkbox

Note: If you are using version 2026 or newer and the Conditioner column is unavailable, switch to the “Full Columns” layout option at the bottom right of the configuration dialog. If you are using an earlier version, select the Advanced Settings button.

• • In the Conditioner Sensitivity field, enter the distance between Ch2 and Ch3
  • Set the conditioner unit to distance/radians; the distance unit should align with the distance entered into the sensitivity field (meters in this example)
  • Select OK; Ch4 is now an angular acceleration measurement between Ch2 and Ch3

Figure 2. Calculation configuration in VibrationVIEW inputs.

2. To view a graph of angular acceleration, velocity, and displacement in the Sine test mode:

• • Select New Graph
  • Select Acceleration vs. Freq. to make an angular acceleration graph
  • Select Velocity vs. Freq. to make an angular velocity graph
  • Select Displacement vs. Freq. to make an angular displacement graph

Note: To plot angular units on the graphs’ axes, only select Ch4 (Ch3-Ch2).

Figure 3. Angular acceleration, angular velocity, and phase graphs.

Additional Considerations

You can configure control using the angular acceleration by selecting Ch4 as a control or reference channel.

The test setup must use the same accelerometers, including manufacturer and model, for channel pairs. Even small differences in the response between different accelerometers will likely lead to unusable results.

For best results, accelerometer pairs should be calibrated to each other. To do so, mount both accelerometers side by side on a shaker head. Run a system check test at 100 Hz and 1 G. Observe the difference between the accelerometers on a spectrum plot. Figure 4 shows an exaggerated example of a difference between Ch3 and Ch2.

Figure 4. Accelerometer calibration between channel pairs.

If the difference is measurable, slightly adjust the sensitivity of one accelerometer to see if it decreases the difference. Repeat this process until you can no longer decrease the difference.