These instructions are also available in pdf format.
Gulf Coast Data Concepts incorporates a digital 3-axis MEMS accelerometer sensor in the X6-2 and X6-1A USB data loggers. The MEMS (micro electromechanical system) sensor uses a suspended silicon structure that is free to move on the substrate when acceleration is applied. The position of the silicon structure is monitored as it moves from its nominal position. The change in position is converted to a digital output that changes linearly with acceleration. Factory characteristics of the sensor maintain linearity within +/-2% (Full scale) and the 0-g offset within +/-100mg. The sensor is considerably precise at a very affordable price.
The digital sensor output is converted to g-force using the linear equations 1 and 2. These are idealized equations assuming there is no offset or scaling error. The equations are in the format of y=mx+b, where y is calculated g-force, m is the scaling factor (g/counts), x is the sensor output (counts), and b is the y-intercept (or offset). The blue line in Figure 1 illustrates the ideal output at high gain. The red line represents a typical output, which may have both an offset and slope error. Calibration of the accelerometer determines the correct scale (m) and offset (b) factors and makes the red line equal the blue line in Figure 1.
High Gain Equation 1
Low Gain Equation 2
Increasing the accuracy of the accelerometer sensor is achieved using a "Tumble" calibration method. This calibration method uses gravity as a reference acceleration. Placing each axis in and out of the gravity vector provides +1g, -1g, and 0 g reference points to establish a scale factor and an offset factor that fine tunes the linear relationship of the sensor. The following instructions outline the tools and process to perform a 6 point tumble test for a 3-axis accelerometer.
A flat level table must be used in order to properly align the accelerometer sensor (see Figure 2). Here, a 12" square piece of marble tile commonly used for flooring is cut into a triangle. Marble tile is typically machined and polished with a very smooth flat surface. Furthermore, the marble is very easy to drill mounting holes through. The triangular shape is used because the three points of the triangle define a stable table plane (no wobbling). At each corner is a thumb screw for leveling the table. A precise circular bubble level is placed on the table to check the table orientation.
The six positions of the tumble test must be orthogonal to each other. Placing the accelerometer on the inside of the cube allows each side to sit flat on the table without the interference of the accelerometer. A 4" square aluminum tube segment serves as the cube. Aluminum extrusions are very straight and square, especially in the stretched tempers, so final machining is not necessary. A miter saw cut and a belt grinder squares the two cut ends.
For quick placement of the GCDC accelerometer data logger, a bottom portion of the plastic enclosure is glued to the inside of the cube. A small thumb screw allows quick mounting of the printed circuit board into the plastic enclosure.
An X6-2 accelerometer unit is used for this example. However, this calibration method is applicable to both the X6-2 and X6-1A devices (or any low g-force accelerometer). Separate calibration factors must be determined for high gain and low gain settings of the accelerometer. Therefore, perform the following instructions with the accelerometer set to high gain and again at low gain.
The X6-2 is configured to sample at 20 Hz, high gain, and no deadband. This calibration method does not need a significant amount of data so a low sample rate is recommended. The following example configuration file works well with the test method:
The six positions of the tumble test place each axis in the line of positive and negative gravity. While one axis is registering gravity, the other two axes are perpendicular to gravity and therefore register 0g. The ideal output relationship of the sensor is a line. The slope of the line is determined by using the measured values for positive and negative gravity. Then, the offset (or intercept value) is calculated using the values measured for 0 g.
The data collected with the tumble test can be imported into a spreadsheet and easily analyzed. The analysis should be performed using the "counts" output of the accelerometer (not converted g-force). The new slope and offset values are substituted into the g-force conversion equation to provide calibrated g-force output.
The example data illustrated in Figure 1 is imported into a spreadsheet to determine the scale and offset factors.
The scale factor for each axis is calculated as follows:
The offset is calculated using the data registered by the sensor when the axis was perpendicular to gravity. This occurs 4 times for a 6 position tumble test.
The ideal conversion factors stated in Equation 1 are replaced with the new factors for each axis, which results in Equation 3, 4, and 5.
X-Axis Equation 3
Y-Axis Equation 4
Z-Axis Equation 5