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Introduction to Accelerometer Applications

This application note provides an overview for using the CXL Series acceleration modules in a variety of measurement systems. It is divided into several sections: basic concepts, vibration analysis, inertial navigation, and tilt/angle sensing. The CXL Series accelerometers are a cost-effective way to make a wide variety of acceleration-based measurements.

The standard CXL series linear accelerometers provide a fully signal conditioned high-level analog output voltage proportional to acceleration. The sensing action of the accelerometer is described by:

Vout = Scale_Factor * Acceleration + Offset Voltage

Where the parameters are defined as follows:

The sensitive axis(es) are clearly labeled on the package of the device. Keep in mind that acceleration signals are often three dimensional and that the accelerometer only responds to the component of acceleration along the sensitive axis.

There are several fundamental source or modes of acceleration that are worth listing. An example of each type is given in the following list:

• Linear Acceleration – A car accelerating from a stop sign
• Rotational Acceleration – The acceleration of a pendulum as it swings
• Centrifugal Acceleration – The acceleration which causes clothes to cling to the side of a washing machine
• Gravitational Acceleration – The acceleration that causes all objects to fall to the earth at equal rates

Using a CXL series accelerometer and an understanding of the mechanics of the overall system allows the measurement and control of a wide variety of quantities.  These include:

• Acceleration, Angular Acceleration
• Velocity (see Inertial Navigation section)
• Position(see Inertial Navigation section)
• RPM or Angular Rate
• Frequency(see Vibration Analysis section)
• Angle (see Tilt / Angle Sensing section)
• Impulse and Impulse Energy
• Force

Measuring the frequency, strength (amplitude), and signature (spectrum) of vibrations is useful in many machine health and industrial monitoring applications. The HF accelerometers are capable of determining the above parameters over a wide frequency and displacement range.

Machinery vibration problems consume excessive power and impose additional wear on bearings, seals, couplings and foundations. Vibrations are typically caused by machinery misalignment and unbalance; these are detectable via analysis of the FFT of an acceleration signal. When left uncorrected machinery vibration results in degraded quality on the machined parts, shorter tool life, unpleasant noise, and increased maintenance cost. The establishment of a vibration monitoring program allows potential problems to be identified prior to equipment failure.

• Structural Vibration - analysis and identification of vibration sources and problems in structures
• Product Testing - vibration and shock testing to identify potential design problems
• Acceptance Testing - testing and analysis to ensure products comply with specified vibration tolerance limits
• Workplace Vibration - measurement and analysis of vibration from hand tools and other equipment

Inertial Navigation

In inertial navigation acceleration sensors are used for making distance measurements. Inertial measurements are frequently required in the tracking of planes, boats, and automobiles over long distances and long time constants. Inertial navigation is an extremely demanding application for sensors and many factors contribute to the performance of an inertial navigation system. Alignment, scale factor errors, and offset errors are crucial, because a constant error in these readings will result in a quadratically growing position error as given in the following equation

A simple 1 dimensional system is shown in the next Figure 1.  This configuration would be use for measuring the distance traveled by a projectile fired down on tube, or the quarter-mile time of an automobile on a straight track. The acceleration is integrated into a velocity signal and a position signal.

Figure 1. 1 Dimensional Position Measurement

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A more complex inertial measurment is that of a 6 degree of freedom system such as an airplane or spacecraft.  These systems are free to move in any direction.  Figure 2 shows the block diagram of such a system.  The diagram shows the basic steps involved in such a system. Crossbow offers a wide range of such inertial systems already put together.

The IMU, VG, and AHRS series products have been proven in many inertial navigation settings.  The GPS system provides periodic updates in order to prevent error build-up within the navigation solution. This feedback loop typically makes use of a control algoirthm such as a Kalman filter.  Also notice that the acceleration readings have to be transformed (rotated) to the Earth frame.  This rotation is necessary because the accelerations as measured by the sensor are referenced to the local (body) coordinate frame.  The distances the system reports are measured with respect to the Earth.

Figure 2. 6 DOF Inertial Measurement

In inertial measurement applications there are two principle questions - What accuracy is required? and how long does the system have to run without an external position reading? Table below provides rough answers to these questions for a 1 dimensionsal system such as the one in Figure 1. TG Series accelerometers are recommended for these performance demanding applications.

The measurement of position inertially is a very difficult task with a reasonable accuracy. The reason being that the bias/offset variation would result in large error build-ups over short period of time. You need to have a long term reference (such as GPS) to correct for these errors.

Tilt / Angle Sensing

Angle sensing is the measurement of angles with an acceleration-based sensor. In most cases, these measurements are made using the Earth's G field as a reference. The CXTA, CXTLA and CXTILT series tilt sensors use a micro-machined acceleration sensing element with a DC response to measure inclination relative to gravity. The voltage response of the CXTA is a sine function of the tilt angle. Accurately measuring tilt involves solving the equation shown in figure 3.

Figure 3. Tilt Measurement

For angles less than 200, you can approximate the sine function with a linear response. Then the relationship between angle and Vout is:

Angle = (Vout-Offset_Voltage)/Scale_Factor

These measurements are referred to as sourceless because they require no local reference and do not have to be physically connected to the shaft or joint creating angular movement. The Crossbow CXTILT02 sensor is designed specifically for these applications and an on-line data sheet is available under Tilt Sensors. The LF series analog output accelerometer can also be used in these applications.