JP5697149B2 - Acceleration sensor characteristic evaluation method and program - Google Patents

Description

  The present invention relates to a characteristic evaluation method and program for an acceleration sensor used as, for example, a displacement measuring means, and more particularly to a characteristic evaluation method and program for identifying the sensor main axis direction and sensitivity of the acceleration sensor.

  For example, the calibration method of the triaxial acceleration sensor is defined in ISO16063 (reference: Non-patent document 1), ISO5347 (reference: Non-patent document 2), etc. It is assumed that the sensor spindle direction of each axis matches. However, this assumption is not always guaranteed. In addition, since the above-described calibration method inputs acceleration in the linear motion direction to the acceleration sensor, in general, in order to know the input acceleration, the displacement sensor data is differentiated twice or the mass of the acceleration sensor. And force must be measured simultaneously. As a result, it is technically difficult to realize highly accurate calibration.

  A sensor in one direction among the acceleration sensors can basically detect only the acceleration in the principal axis direction in principle. However, in an actual acceleration sensor, there is an error in the direction that occurs at the time of manufacture and attachment, so it is difficult to completely match the package direction of the acceleration sensor with the direction of each sensor spindle. Further, even in the acceleration sensor of a micro electro mechanical system (MEMS) device that is widely used at present, it is not easy to make the package direction of the acceleration sensor coincide with each sensor main axis direction with high accuracy. As a result of this mismatch in direction, for example, a phenomenon occurs in which the sensor in the x-axis direction detects acceleration in the y-axis or z-axis direction. In general, the degree of detection of acceleration that is not in the original detection direction is called lateral sensitivity, and is often described in a data sheet of the acceleration sensor.

According to a conventional acceleration sensor characteristic evaluation method, a cube block (corresponding to a package) in which an acceleration sensor is mounted on a table is fixed so that the x-axis direction defined in the acceleration sensor matches the vibration x-axis direction of the table. Sine wave in the x-axis direction to obtain the principal axis sensitivity _Sxx for the x-axis, and the acceleration sensor is mounted on the table so that the y-axis direction defined for the acceleration sensor matches the vibration x-axis direction of the table The cube block (corresponding to the package) is fixed and the table is sine wave-excited in the y-axis direction to obtain the lateral sensitivity S _xy with respect to the x-axis. A cubic block (corresponding to a package) with an acceleration sensor mounted on the table is fixed so that it coincides with the sine wave in the z-axis direction and the x-axis Determine the horizontal sensitivity S _xz related. Similarly, sensitivities S _yx , S _yy , S _yz , S _zx , S _zy , and S _zz related to the parallel evolution rate are obtained. Thereby, acceleration can be calculated as an accurate three-dimensional vector (see: Patent Document 1 and Non-Patent Document 3).

WO2005 / 095998

ISO 16063-1: Methods for the calibration of vibration and shock transducers Part 1, Basic concepts, 1998 ISO 5347: Methods for the calibration of vibration and shock pick-ups, 1993 Akira Umeda et al., "Study on the calibration method of a three-axis accelerometer using a three-dimensional vibration generator and a laser interferometer as a three-dimensional accelerometer," Japan Society of Mechanical Engineers, Journal, Volume 70, No. 697, 2007, pp.38 -45

  However, according to the conventional acceleration sensor characteristic evaluation method described above, there is a problem that the cost, the measurement time, and the measurement accuracy are inferior.

  Therefore, according to the present invention, the moment of inertia and the frictional force are made independent of the phase, and the necessary torque is made constant at any phase due to the weight balance, so that the acceleration sensor is positioned at an angle with respect to the outside world. The sensor main axis direction and sensitivity of the acceleration sensor are identified by using an acceleration sensor characteristic evaluation device that enables constant-speed circular motion in a held state and enables high-precision simultaneous measurement of two axes even in a minute time.

  In order to solve the above-described problems, an acceleration sensor characteristic evaluation method according to the present invention includes a table, at least two links that are connected to the table and have the same length, are infinitely rotatable, and are parallel to each other. A 123 coordinate system of the acceleration sensor package is rotated using the first rotation matrix with respect to the xyz coordinate system of the table of the acceleration sensor characteristic evaluation apparatus having a driving means for synchronously rotating the acceleration sensor package. And a step of fixing the table using the first rotation matrix, and performing a vibration by a constant-speed circular motion on the xy plane of the xyz coordinate system by the driving means after the rotation is fixed by the driving means. Calculating a first projection direction on the xy plane of the xyz coordinate system in the principal axis direction of each sensor using the output voltage; and the z-axis of the xyz coordinate system and the xy of the xyz coordinate system Calculating a first plane including a first projection direction on the surface, and converting the first plane of the xyz coordinate system to the first plane of the 123 coordinate system using an inverse matrix of the first rotation matrix Rotating the 123 coordinate system of the acceleration sensor package with respect to the xyz coordinate system of the table using a second rotation matrix different from the first rotation matrix, and fixing the acceleration sensor package to the table; After the rotation is fixed to the rotation matrix of 2, the table is excited by a constant velocity circular motion on the xy plane of the xyz coordinate system by the driving means, and the output voltage of the sine wave of each sensor in the acceleration sensor package is used. Calculating a second projection direction on the xy plane of the xyz coordinate system in the principal axis direction of the sensor, and a second plane including the z axis of the xyz coordinate system and the second projection direction on the xy plane of the xyz coordinate system And the second plane of the xyz coordinate system Using the inverse of the rotation matrix of 2 to convert to the second plane of the 123 coordinate system, and calculating the intersection of the first and second planes of the 123 coordinate system as the principal axis direction of each sensor of the acceleration sensor package The step of performing. In addition, the method includes a step of calculating the sensitivity of each sensor based on an output voltage from each sensor corresponding to an inner product of a unit vector in the principal axis direction of each sensor of the acceleration sensor package and an input acceleration vector by a constant velocity circular motion.

  The acceleration sensor characteristic evaluation program according to the present invention includes a table, at least two links that are connected to the table and have the same length and are infinitely rotatable and parallel, and driving for synchronously driving these links. The acceleration sensor package 123 is rotated with respect to the xyz coordinate system of the acceleration sensor characteristic evaluation apparatus table using the first rotation matrix to fix the acceleration sensor package to the table, and then the table is driven. By means of a constant velocity circular motion on the xy plane of the xyz coordinate system by means and using the sinusoidal output voltage of each sensor in the acceleration sensor package on the xy plane of the xyz coordinate system in the principal axis direction of each sensor A procedure for calculating a first projection direction and a procedure for calculating a first plane including the z-axis of the xyz coordinate system and the first projection direction on the xy plane of the xyz coordinate system , A procedure for converting the first plane of the xyz coordinate system to the first plane of the 123 coordinate system using the inverse matrix of the first rotation matrix, and the 123 coordinate system of the acceleration sensor package with respect to the xyz coordinate system of the table Is rotated using a second rotation matrix different from the first rotation matrix to fix the acceleration sensor package to the table, and then the table is driven by a constant velocity circular motion on the xy plane of the xyz coordinate system by the driving means. Performing a second projecting direction on the xy plane of the xyz coordinate system in the principal axis direction of each sensor using the sine wave-like output voltage of each sensor in the acceleration sensor package; A procedure for calculating the second plane including the second projection direction on the xy plane of the xyz coordinate system, and the second plane of the xyz coordinate system using the inverse matrix of the second rotation matrix and the second plane of the 123 coordinate system. The procedure for converting to a plane of 2 and the 123rd coordinate system It is intended to and a procedure for calculating the line of intersection of the second plane as the main axis of the respective sensors of the acceleration sensor package. Further, a procedure is provided for calculating the sensitivity of each sensor based on the output voltage from each sensor in accordance with the inner product of the unit vector in the principal axis direction of each sensor of the acceleration sensor package and the input acceleration vector by constant velocity circular motion.

  According to the present invention, the concept of lateral sensitivity used in the conventional acceleration sensor characteristic evaluation method is not necessary, and the direction of the sensor main axis is calculated using the rotation matrix and its inverse matrix. Excellent in measurement accuracy.

It is a figure which shows the acceleration sensor characteristic evaluation apparatus which concerns on this invention. It is a perspective view which shows the detail of the acceleration sensor characteristic evaluation apparatus of FIG. It is a fragmentary sectional view of the acceleration sensor characteristic evaluation apparatus of FIG. It is a perspective view which shows the actual sensor main-axis direction in the acceleration sensor package of FIGS. The acceleration sensor characteristic evaluation apparatus shown in FIGS. 1 to 3 is for explaining the operation in the case of a sensor main axis of 123 coordinate system = xyz coordinate system and ideally arranged, (A) is a vector diagram, and (B) is a single axis. It is a figure which shows an acceleration signal (output voltage). The acceleration sensor characteristic evaluation apparatus of FIGS. 1 to 3 is for explaining the operation in the case of a sensor main axis of 123 coordinate system = xyz coordinate system and practical arrangement, where (A) is a vector diagram and (B) is a single axis. It is a figure which shows an acceleration signal (output voltage). 3 is a flowchart showing the operation of the control circuit of FIGS. 1 and 2. FIG. 8 is a diagram for supplementarily explaining the flowchart of FIG. 7. It is a figure which shows the significant attitude | position of the sensor main axis | shaft of the acceleration sensor package of FIGS. Figure 7 shows an example of a rotation matrix R _a in FIG. 8, (A) is a number of the matrix, (B) the xyz coordinates when rotated 123 coordinate system rotation matrix R _a of (A) The 123 coordinate system after rotation with respect to the system is shown, and (C) is a photograph showing the actual acceleration sensor package of the 123 coordinate system after _Ra rotation. 7 and 8 show an example of the rotation matrix R _b , where (A) is the numerical value of the matrix, and (B) is the xyz coordinates when the 123 coordinate system is rotated by the rotation matrix R _b of (A). It is a photograph which shows the actual acceleration sensor package of the 123 coordinate system after the rotation with respect to a system.

  FIG. 1 is a diagram showing an acceleration sensor characteristic evaluation apparatus according to the present invention.

  As shown in FIG. 1, links 3-1, 3-2 and 3-3 having the same length r, for example, 50 mm, are connected to each vertex of a regular triangular table 2 for fixing the acceleration sensor package 1. The links 3-1, 3-2 and 3-3 are parallel to each other, and can rotate infinitely with respect to the rotation axes 4-1, 4-2 and 4-3 as indicated by arrows R 1, R 2 and R 3. is there. Therefore, if the bias of the bearing is ignored, the moment of inertia and the frictional force of the table 2 are constant without depending on the phase, and the table R2, that is, the acceleration sensor package 1, holds the posture with respect to the outside and the arrow R0 As shown in FIG. 4, complete constant-speed circular motion with the radius r of the link 3-1, 3-2, 3-3 is possible. The angle θ of the constant velocity circular motion is detected by a rotary encoder 2 a provided on the table 2. As a result, the acceleration sensor package 1 is simultaneously subjected to sinusoidal vibration in the x direction and the y direction, thereby enabling the biaxial simultaneous measurement of the acceleration sensor package 1. In addition, since the known displacement of the acceleration sensor package 1 is guaranteed by a perfect circle whose radius is the length r of the links 3-1, 3-2 and 3-3, the measurement value of the acceleration sensor package 1 can be corrected. It becomes.

The sinusoidal uniaxial acceleration signal v _{out_1} , the biaxial acceleration signal v _{out_2} and the triaxial acceleration signal v _{out_3} of the acceleration sensor package 1 are supplied to the control circuit (computer) 10 in synchronization with the angle signal E of the rotary encoder 2a. As a result, the control circuit 10 calculates the sensor main axis direction and sensitivity of the acceleration sensor package 1 from the uniaxial acceleration signal _{vout_1} , the biaxial acceleration signal _{vout_2,} and the triaxial acceleration signal _{vout_3} .

In Figure 1, the coordinate system of the fixed portion of the acceleration sensor characteristic evaluation apparatus and xyz, to the base vector vectors e _x, e _y, and e _z. The coordinate system of the acceleration sensor package 1 is 123, and its base vectors are vectors e ₁ , e ₂ , and e ₃ . In the formulas and drawings of the specification, the vector is expressed in bold instead of the display “vector”.

  2 is a perspective view showing details of the acceleration sensor characteristic evaluation apparatus of FIG. 1, and FIG. 3 is a partial cross-sectional view of the acceleration sensor characteristic evaluation apparatus of FIG. 2, particularly, a cross-sectional view of links 3-2 and 3-3. Is shown.

  As shown in FIGS. 2 and 3, the links 3-1, 3-2 and 3-3 are fixed by screws between the two support plates 5-1 and 5-2. The support plates 5-1 and 5-2 are supported by four support columns 6-1, 6-2, 6-3, and 6-4. Each of the links 3-1, 3-2 and 3-3 is represented by the distance between the rotary shafts 4-1, 4-2 and 4-3 and the holding shafts 8-1, 8-2 and 8-3 of the table 2. They have the same length r and can rotate infinitely in synchronization with r as the radius. As a result, when the links 3-1, 3-2 and 3-3 are synchronously rotated with the radius r, the table 2, that is, the acceleration sensor package 1 also moves circularly with the radius r.

  In order to prevent the load from being biased during rotation, the links 3-1, 3-2, 3-3 have counterweights 7-1, 7-1 ′, 7-2, 7-2 ′, 7-3 and 7-3 ′ are provided to balance the mass. For example, in the link 3-2, M1 is the center of mass of the counterweights 7-2 and 7-2 ′, M2 is the center of mass of the entire counter 3-2 excluding the counterweights 7-2 and 7-2 ′, and M3 Is the center of mass of 1/3 of both the acceleration sensor package 1 and the table 2. “1/3” is a value corresponding to the number of links. If the number of links is n, 1/3 becomes 1 / n. In this case, the weights of the counterweights 7-2 and 7-2 'are determined so that 1/3 of the mass of both the acceleration sensor package 1 and the table 2 is applied to the holding shaft 8-2. As a result, even if the links 3-1, 3-2, and 3-3 rotate, the counter weights 7-1, 7-1 ', 7-2, 7-2', 7-3, and 7-3 ' Since the center of mass of each included link 3-1, 3-2, 3-3 is on the rotating shaft 4-1, 4-2, 4-3 of each link 3-1, 3-2, 3-3, Centrifugal force, that is, translational force is not generated on the rotating shafts 4-1, 4-2, and 4-3, and thus stable rotation can be obtained. Further, the product of the distance r from the center of mass (corresponding to the position of the holding shaft) of the acceleration sensor package 1 and the table 2 to the rotation axis and the mass of the acceleration sensor package 1 and the table 2 together for a certain rotation axis; If the distance r ′ from the center of mass of each counterweight to the rotation axis and the sum of the products of each counterweight match, the total mass of the acceleration sensor package 1 and table 2 and the total mass of each counterweight do not match. May be. That is, the mass of the sensor system × the length r = the mass of the counterweight system × the length r ′ may be satisfied.

  Since the table 2 and the links 3-1, 3-2, 3-3 are a combination of three parallel link structures, if only one of the links 3-1, 3-2, 3-3 is driven and rotated, 3 The three links 3-1, 3-2, and 3-3 are driven to rotate synchronously. 2 and 3, only the link 3-3 is driven by the drive motor 9 via the rotating plate 9a.

  Further, assuming that the apparatus is placed vertically and the acceleration sensor package 1 always operates while receiving gravitational acceleration g, the respective mass centers M1, M2, and M3 are made to coincide in the height direction of the apparatus. Therefore, almost no torque is required when the device is rotated at any inclination, and a very smooth rotation can be expected, and the device can be miniaturized.

  1 to 3, the number of links 3-1, 3-2 and 3-3 is 3 in consideration of control stability, machining accuracy, etc., but the number of links is 2 or 4 or more. May be. Further, the acceleration sensor package 1 is, for example, a capacitance acceleration sensor, but the present invention can also be applied to other acceleration sensors.

FIG. 4 shows unit vectors s ₁ , s ₂ , and s ₃ in the actual sensor main axis direction in the acceleration sensor package 1 of FIGS. Note that s ₁ , s ₂ , and s ₃ also indicate the respective sensor spindles. The unit vectors s ₁ , s ₂ , s ₃ can be represented by direction cosines for the 123 coordinate system.
s ₁ = [c ₁₁ , c ₁₂ , c ₁₃ ] ^t
s ₂ = [c ₂₁ , c ₂₂ , c ₂₃ ] ^t
s ₃ = [c ₃₁ , c ₃₂ , c ₃₃ ] ^t
However, t means transposition. Ideally, the sensor main axis direction coincides with the coordinate direction of the acceleration sensor package 1,
c _ij = δ _ij
Where δ _ij is the Kronecker symbol,
i = 1, 2, 3
j = 1, 2, 3
That means
c _ii = 1
c _ij = 0 (i ≠ j)
However, in practice, as shown in FIG. 4, the sensor main axis direction does not coincide with the coordinate direction of the acceleration sensor package 1, and as a result, when i = j, c _ij is a value close to 1, that is,
c _ij ≒ 1
When i ≠ j, c _ij is close to 0, that is,
c _ij ≒ 0
It is.

1 to 3, as shown in FIG. 5A, the sensor coordinate axes s ₁ , s ₂ , and s ₃ are ideally arranged by matching the 123 coordinate system of the acceleration sensor package 1 with the xyz coordinate system. The operation of will be described.

That is, when the acceleration sensor package 1 shown in FIGS. 1 to 3 is circularly moved at a constant speed, an input acceleration vector a applied to each sensor main axis of the acceleration sensor package 1 by centrifugal force and gravity is expressed in an xyz coordinate system (= 123 coordinate system). In terms of
a = [r | ω | ² cosθ, r | ω | ² sinθ, -g] ^t
Where r is the radius of rotation of the acceleration sensor package 1,
ω is an angular velocity vector of rotation of the acceleration sensor package 1,
θ is an encoder angle, that is, an angle formed by the links 3-1, 3-2, 3-3 and the unit vector e _x ,
g is the gravitational acceleration.
The inner product s _i · a of the two vectors can be regarded as a value obtained by dividing the voltage generated by the vector a by the sensitivity among the output voltages of the sensors of the sensor spindles s _i . Therefore, when the sensor spindles s ₁ , s ₂ , and s ₃ are ideally arranged, that is, when c _ii = 1 and c _ij = 0 (i ≠ j), θ = 0 ° for the sensor spindle s ₁ Output voltage v _{out_1} is maximum when θ = 180 °, output voltage v _{out_1} is minimum when θ = 180 °, and for sensor spindle s ₂ , output voltage v _{out_2} is maximum when θ = 90 °, and θ = 270 ° The output voltage v _{out — 2} is minimum, and the output voltage v out — ₃ is constant for the sensor spindle s ₃ . FIG. _5B shows the output voltage v _{out_1} corresponding to the sensor main axis s _{1. When} θ = 0 °, the acceleration, that is, the output voltage v _{out_1} is maximum, and when θ = 180 °, the acceleration, that is, the output voltage v _{out_1} is minimum. It has become.

In FIG. 1 to FIG. 3, as shown in FIG. 6A, the 123 coordinate system of the acceleration sensor package 1 is made coincident with the xyz coordinate system and the sensor main axes s ₁ , s ₂ , s _{3 in} the actual arrangement are used. The operation will be described.

In this case, c _ii ≈ 1, c _ij ≈ 0 (i ≠ j), and the sensor main axis s ₁ is different from θ = 0 ° if the deviation of the projection direction on the xy plane is Δθ ₁ Output voltage v _{out_1} is maximum when θ = Δθ ₁ , different from θ = 180 °, output voltage v _{out_1} is minimum when θ = 180 ° + Δθ ₁ , and projection direction on the xy plane for sensor main axis s ₂ if the deviation between Δθ _2, θ = 90 ° is different from θ = 90 ° + output voltage when the [Delta] [theta] ₂ v _{OUT_2} up, θ = 270 ° different from θ = 270 ° + when [Delta] [theta] ₂ output voltage v _{OUT_2} Is minimal. Furthermore, for the sensor main axis s _3, if a projection direction of displacement of the xy plane and [Delta] [theta] _3, the output voltage v _{OUT_3} when theta = [Delta] [theta] ₃ is the maximum, the output voltage v _{OUT_3} when θ = 180 ° + Δθ ₃ is Minimal. FIG. 6B shows an acceleration signal (output voltage) v _{out — 1} corresponding to the sensor main axis s ₁ .

Thus, in practice, the sensor spindles s ₁ , s ₂ , and s ₃ deviate from the 123 coordinate direction, but there is always an encoder angle θ that maximizes the output voltage of the sensor spindles s ₁ , s ₂ , and s _3. . Furthermore, even if the 123 coordinate system of the acceleration sensor package 1 is arbitrarily set with respect to the xyz coordinate system, that is, regardless of the posture of the acceleration sensor package 1, the acceleration sensor characteristic evaluation apparatus shown in FIGS. When the acceleration sensor package 1 is circularly moved at a constant speed using, there is always an encoder angle θ at which the output voltages of the sensor spindles s ₁ , s ₂ , and s ₃ are maximum. The present invention uses the latter to calculate unit vectors s ₁ , s ₂ , and s ₃ in the sensor main axis direction.

  Next, the operation of the control circuit 10 of FIG. 1 will be described with reference to the flowchart of FIG. 7 and FIG.

First, in step 701, by rotating the rotation matrix R _a by 123 coordinate system, i.e. the acceleration sensor package 1 from state 123 coordinate system relative xyz coordinate system shown in FIG. 8 (A) is coincident fixed (B in FIG. 8). It will be described later value of the rotation matrix R _a.

Next, in step 702, the drive motor 9 shown in FIGS. 2 and 3 is operated, and the table 2, that is, the acceleration sensor package 1 is subjected to constant-speed circular motion on the xy plane of 0.1 Hz, for example. In this state, the unit vectors s _i (i = 1, i = 1, _y) in the direction of each sensor main axis using the uniaxial acceleration signal v out — 1, the biaxial acceleration signal v _{out —} 2, and the triaxial acceleration signal v _{out —} 3 captured in synchronization with the encoder angle θ. Get the projection angle θ _ia to the xy plane of (2, 3). The unit vector s _ia 'in the projection direction on the xy plane of the unit vector s _i at this time is
[cosθ _ia , sinθ _ia , 0] ^t
It becomes.

Next, in step 703, it sets a unit vector s _ia 'and unit vectors e _z plane phi _ia including planar phi _ia xyz coordinate system unit normal vector n _ia a'. That means
n _ia '= e _z × s _ia '
_{= [-Sinθ ia, cosθ ia,} 0] t
It becomes.

Next, in step 704, the plane φ _ia of the xyz coordinate system is converted into a plane φ _ia of the 123 coordinate system shown in FIG. This plane phi _ia of 123 coordinate system is set at 123 coordinate plane phi _ia unit normal vector n _ia of '. That means
n _ia = R _a ^-1 n _ia '
= R _a ^t n _ia '

Next, in step 705, the 123 coordinate system, that is, the acceleration sensor package 1 is rotated by the rotation matrix R _b different from R _a from the state in which the 123 coordinate system coincides with the xyz coordinate system shown in FIG. To fix (FIG. 8D). The value of the rotation matrix _Rb will be described later.

Next, in step 706, the drive motor 9 shown in FIGS. 2 and 3 is operated to excite the table 2, that is, the acceleration sensor package 1, with a constant-speed circular motion on the xy plane of 0.1 Hz, for example. In this state, the unit vector s _i (i = 1,2,3) in the direction of each sensor main axis to the xy plane using the uniaxial acceleration signal v _{out_1} , the biaxial acceleration signal v _{out_2,} and the triaxial acceleration signal v _{out_3} Obtain the projection angle θ _ib . The unit vector s _ib ′ in the projection direction on the xy plane of the unit vector s _i at this time is
[cosθ _ib , sinθ _ib , 0] ^t
It becomes.

Next, in step 707, it sets a vector s _i and unit vector e _z unit normal vector of the xyz coordinate system of the plane phi _ib the plane phi _ib comprising n _ib '. That means
n _ib '= e _z × s _ib '
_{= [-Sinθ ib, cosθ ib,} 0] t
It becomes.

Next, in step 708, the plane φ _ib in the xyz coordinate system is converted into a plane φ _ib in the 123 coordinate system shown in FIG. This plane phi _ib of 123 coordinate system is set at 123 the coordinate system of the plane phi _ib unit normal vector n _ib of '. That means
n _ib = R _b ^-1 n _ib '
= R _b ^t n _ib '

Next, in step 709, the sensor main axis s _i is obtained from the intersection line of the planes φ _ia and φ _ib of the 123 coordinate system. That is, as shown in FIG.
s _i = ± (n _ia × n _ib ) / | n _ia × n _ib |
However, n _ia and n _ib are vectors, and n _ia × n _ib represents an outer product.

  Finally, in step 710, the sensitivity is calculated. The sensitivity will be described later.

The direction of the sensor main axis s _i may be set so that the cosine component c _ij that is normally the maximum among the components of the vector s _i is positive, but may be matched with the measured value of the output voltage.

Further, the two rotation matrices R _a and R _{b to be} determined are set so that the angle formed by the two normal vectors n _ia ′ and n _ib ′ becomes as large as possible in all directions (i = 1, 2, 3). Must be set. Since actual measurement includes various errors, it is desirable that the angle formed by the two planes φ _ia and φ _ib including the sensor principal axis s _i is as close to 90 ° as possible. Also, if the rotation axis (e _z ) and one of the sensor spindle directions s _i are set to be nearly parallel, the amplitude of the sensor output power v _{out_1 in} that direction must be reduced. . If the magnitude of the error on the xy plane when the sensor principal axis in a certain direction is projected onto the xy plane is l _e , the measurement accuracy of the projection angle θ _i is the projection length of the unit vector s _{i in} the sensor principal axis direction. When l _s , l _e / l _s . Accordingly, the projection length of the sensor spindle direction s _i on the rotation surface of the apparatus needs to be as large as possible for the sensor spindle s _{i in} all directions.

Theoretically, it is possible to identify the spindle direction and sensitivity with the highest accuracy by performing measurement in three orthogonal orientations with respect to the three axes. Problems due to inconsistencies in measurement conditions, such as changes in temperature, temperature, and input voltage. Also, it is desirable that the number of measurements is small in terms of cost. In the present invention, if the orientation of the acceleration sensor package 1 is properly adjusted, three planes including the sensor principal axis directions s _i in three directions can be obtained simultaneously by one uniform circular motion. It is possible to identify all sensor spindle directions s _i .

In the case of an ideal three-axis acceleration sensor, the posture that takes all the projection lengths of the sensor spindles s _{i in} all directions to be equal is a finite rotation group, and postures that are significantly different in the present invention are as shown in FIG. There are four for the xy plane. Among these four postures, the combination of two arbitrary postures results in the same plane including sensors in any one of the three sensor main axes. Therefore, if the two postures of the sensor with respect to the xyz coordinate system are expressed by the rotation matrices R _a and R _b expressed by the equation (1), the sum of the projection lengths of the sensors in all directions is made equal by two uniform circular motions. Considering that the combination of R _a '(cosα = √ (3/5)) or the outer product of the normal vectors of two planes is larger, the angle between the two planes is closer to 90 °. Candidates are combinations of postures (cosα = √ (7/3) of R _a ') in which the product of the projection length of two times per sensor and the product of the normal vectors are equal. .

According to the inventors' experiment, in order to increase the projection lengths of the _three sensor main axes s ₁ , s ₂ , and s ₃ with respect to the xy plane, the rotation matrices R _a and R _b are represented by (A) in FIG. Settings were made as shown in FIG. In this case, in R _a in FIG. _10A and R _b in FIG. 11A, the angle α in the equation (1) is an acute angle where cos α = 1 / √3. 10B and 11B show the xyz coordinate system when the 123 coordinate system is rotated by the rotation matrices R _a and R _b of FIG. 10A and FIG. 11A. FIG. 10C and FIG. 11C are photographs showing an actual acceleration sensor package of the 123 coordinate system after R _a and R _b rotation. In either case of FIG. 10 or FIG. 11, the projection length of the sensor principal axis s _i with respect to the xy plane is 1 / √2 or more.

An example of the projection angles θ _ia and θ _ib on the xy plane obtained by steps 702 and 706 of FIG. 7 with respect to the sensor main axis s _i rotated by the rotation matrices R _a and R _b of FIGS. Shown in the table.

The projection angle Δθ _{i in} Table 1 was obtained under the following conditions. The acceleration sensor package 1 has a rotation radius r of 50 mm and a rotary encoder 2a of 324000ppr. However, the number of pulses of the rotary encoder may vary depending on the required accuracy. In order to avoid the influence of the vibration of the gear head, the end of the drive motor 9 is circular, and the mechanism is rotated using the table 2 whose surface is covered with rubber. The average error of the rotation frequency at the time of 0.1Hz drive by PID control is about 1%. Input acceleration in the range of 0.002 to 0.2 m / s ² (0.2 to 20 gal) can be set.

Using the above-mentioned apparatus, a vibration experiment of constant velocity circular motion of the acceleration sensor package 1 of the MEMS device was performed. This excitation condition is an excitation frequency of 0.5 Hz, and the acceleration received by the sensor is a maximum of about 0.5 m / s ² . If the effect of offset voltage change over time is not negligible, it is necessary to perform baseline correction. However, the sensor used in this experiment has a stable voltage change rate of 1% or less, and correction is not performed. The output voltage obtained by the measurement performs nonlinear curve approximation. By comparing the obtained approximate sine wave and the input acceleration obtained from the rotary encoder 2a, the deviation Δθ _i between the plane including the sensor main axis direction and the package angle was measured.

Two planes φ _ia and φ _ib including the same direction of the actual sensor main axis s _i are obtained with the sensors in different postures, and the intersecting line indicates the direction of the actual sensor main axis s _i . At this time, a state where the two planes φ _ia and φ _{ib of} the 123 coordinate system are close to each other is avoided.

  Next, the sensitivity calculation step 710 in FIG. 7 will be described in detail.

In the actual acceleration sensor package 1, the sensor sensitivity differs in the sensor main axis direction even in the same package. Further, the offset voltage v off — _i also changes due to temperature drift or the like. When the sensor sensitivity of the sensor main axis s _i and kappa _i, strictly speaking, kappa _i is input acceleration a, is a non-linear function that depends on the temperature T, the input voltage v _in. Further, the voltage v _{out_i} output from the sensor of the sensor spindle s _i is _expressed by the equation (2).
The sensor sensitivity κ _i is considered to be less affected by changes in temperature and input voltage if the measurement is performed in a room where the temperature is kept constant for a short time. In this case, the sensor sensitivity kappa _i can be approximated to have a variable only _{a κ i = k i s i} · a (k i is a constant, which means the sensitivity to only the acceleration sensor main axis s _i). In this case, the equation (2) is expressed by the following equation.
Note that v off — _i changes almost linearly for a short time. Therefore, in this apparatus, a voltage of the same phase with each other, the v _{Off_i} can be removed by taking for example a v _{OUT_I} when the theta = 0 °, the difference between v _{OUT_I} when the θ = 360 °. In addition, this device can also remove the v _{off_i} term from the average value of the output voltage at the start of measurement and at the end of measurement, using the fact that the input acceleration is a sine wave for each sensor in the main spindle direction. it can.

Now, the amplitude of the output voltage v _{out_i} obtained by the device from the equation (3) includes both the component of s _i · a determined by the sensor main axis direction and the input acceleration and the sensor sensitivity κ _i integrated. I understand that. In order to identify the two separately, either the sensor sensitivity κ _i or the direction of the sensor spindle s _i needs to be known. Since the direction of the sensor main axis s _i can not be identified only sensor sensitivity kappa _i in an unknown state, after obtaining the components of the unit vector s _i in the sensor main axis direction ahead in the manner described above, the inner product s _i · a The sensor sensitivity κ _i is calculated from the value of.

Now, when the unit vector s _i in the sensor spindle direction is known, the maximum voltage v _{out_i} (max) of the sensor of the sensor spindle s _i when the device is vibrated with constant velocity circular motion is set to v _{out_i} (max). _{When out_i} (min) is set, the difference between the two is expressed by equation (4).
The right side means twice the value obtained by multiplying the centrifugal force received from the apparatus by the sensor spindle s _i by the sensor sensitivity κ _i . If the rotational angular velocity | ω | of the device is constant, the sensor sensitivity κ _i can be specified from the single measurement data without removing the acceleration sensor package 1 from the device by using the equation (4). When the above is summarized and expressed using a tensor, Expression (5) is obtained.
Here, S is a direction tensor of the sensor spindle s _i , K is a sensitivity tensor, v _off and v _out are vectors indicating an offset voltage and an output voltage of each sensor, respectively. S is a matrix including the directions of the principal axes of the three sensors, but it can also be regarded as a coordinate transformation tensor composed of _three linearly independent oblique basis vectors s ₁ , s ₂ , and s ₃ . Further, when an expansion coefficient matrix is used, Expression (5) can be expressed as Expression (6).
As described above, a general three-axis acceleration sensor in which the actual directions of the sensors are not orthogonal to each other is an affine transformation in which an input acceleration vector space is converted into a voltage vector space by a tensor KS and a base coordinate is shifted to an offset voltage v _off. Therefore, if there is an inverse transformation, the acceleration vector a can be obtained.

From formulas (5) and (6), in order to obtain the characteristics of the triaxial acceleration sensor, it is not always necessary to separately obtain the tensor S and the tensor K, and they may be obtained in the form of the product KS. However, it should be noted that the offset voltage vector v _off may change with time. If K, S (or KS) and the vector v _off are known, the input acceleration vector a can be obtained from the output voltage vector v _out using the equation (7).

The inverse transformation T ⁻¹ exists except for abnormal situations such as the two axes of the multi-axis acceleration sensors overlapping or the sensitivity in a certain direction being zero. Since the acceleration sensors calibrated by the above method can obtain the input acceleration as a three-dimensional vector even if the actual sensor axis directions are not necessarily orthogonal to each other, highly accurate measurement is always possible if the sensor characteristics are stable. There is an advantage that can be. In addition, since the actual calculation only involves a 3 × 3 square matrix, high-speed calculation is possible, and it is considered advantageous for applications such as real-time processing after calibration, for example, dead reckoning for aircraft and automobiles.

Table 2 shows the unit vector s _i and the sensitivity in the sensor spindle direction obtained by calculation from Table 1 for each Δθ _i in two postures obtained in the experiment.

In other words, the maximum value of 2.3% is obtained when converted to lateral sensitivity from the calculated sensor principal axis direction vector s _i , and the standard value of the acceleration sensor package 1 data sheet (maximum 3%, standard 2%) Matched. The offset voltage was almost constant regardless of time (the maximum noise level was about 0.4 m / s ^{2 in} terms of acceleration). Regarding the sensitivity, a result almost similar to the value of 1000 mV / g (≈100 mV / (m / s ² )) in the data sheet was obtained. Moreover, when the result of Table 2 is shown in the form of Expression (5), Expression (8) is obtained.

  From this result, the acceleration sensor package 1 used as a sample was shown to be able to obtain the input acceleration in the form of a vector from the output voltage using the formula (5) or the formula (7). As described above, since the sensor spindle direction and sensitivity can be identified individually for each sensor, it is possible to cope with variations in individual sensors.

  Although the above-described acceleration sensor package 1 has a three-axis acceleration sensor, the present invention can also be applied to an acceleration sensor package including a two-axis acceleration sensor or a one-axis acceleration sensor.

1: Acceleration sensor package 2: Table 2a: Rotary encoder 3-1, 3-2, 3-3: Links 4-1, 4-2, 4-3: Rotating shaft 5-1, 5-2: Support plate 6 -1, 6-2, 6-3, 6-4: support columns 7-1, 7-1 ′, 7-2, 7-2 ′, 7-3, 7-3 ′: counterweight 8-1, 8-2, 8-3: Holding shaft 9: Drive motor 9a: Rotating plate 10: Control circuit

Claims (8)

The table of the acceleration sensor characteristic evaluation apparatus comprising: a table; at least two infinitely rotatable and parallel links connected to the table and having the same length; and driving means for synchronously driving the links. Rotating the 123 coordinate system of the acceleration sensor package with respect to the xyz coordinate system using the first rotation matrix to fix the acceleration sensor package to the table;
After the rotation is fixed using the first rotation matrix, the table is subjected to vibration by a constant-speed circular motion on the xy plane of the xyz coordinate system by the driving means, and a sinusoidal waveform of each sensor in the acceleration sensor package is obtained. Calculating a first projection direction on the xy plane of the xyz coordinate system in the principal axis direction of each sensor using an output voltage;
Calculating a first plane including the z-axis of the xyz coordinate system and the first projection direction on the xy plane of the xyz coordinate system;
Transforming a first plane of the xyz coordinate system to a first plane of the 123 coordinate system using an inverse matrix of the first rotation matrix;
Rotating the 123 coordinate system of the acceleration sensor package with respect to the xyz coordinate system of the table using a second rotation matrix different from the first rotation matrix to fix the acceleration sensor package to the table;
After fixing the rotation used for the second rotation matrix, the table is subjected to vibration by a constant-speed circular motion on the xy plane of the xyz coordinate system by the driving means, and a sinusoidal waveform of each sensor in the acceleration sensor package is obtained. Calculating a second projection direction on the xy plane of the xyz coordinate system in the principal axis direction of each sensor using an output voltage;
Computing a second plane including the z-axis of the xyz coordinate system and the second projection direction on the xy plane of the xyz coordinate system;
Transforming a second plane of the xyz coordinate system into a second plane of the 123 coordinate system using an inverse matrix of the second rotation matrix;
Calculating an intersection of the first and second planes of the 123 coordinate system as a principal axis direction of each sensor of the acceleration sensor package. The first and second planes of the xyz coordinate system are represented by the following unit normal vector n _i ′.
n _i '= e _z × s _i '
Where e _z is the z-axis unit vector of the xyz coordinate system,
s _i ′ is a unit vector of the first and second projection directions of the xyz coordinate system,
The acceleration sensor characteristic evaluation method according to claim 1, wherein x is calculated by an outer product. The first of the 123 coordinate system unit vectors s _i of the principal axis direction of each sensor present on the line of intersection of the second plane,
s _i = ± (n _ia × n _ib ) / | n _ia × n _ib |
Where n _ia is a unit normal vector of the transformed first plane of the 123 coordinate system,
n _ib is the transformed unit normal vector of the second plane of the 123 coordinate system,
X represents the outer product,
The acceleration sensor characteristic evaluation method according to claim 1, which is calculated by :   2. The method of claim 1, further comprising: calculating sensitivity based on an output voltage from each sensor corresponding to an inner product of a unit vector in a principal axis direction of each sensor of the acceleration sensor package and an input acceleration vector by the constant velocity circular motion. 2. The acceleration sensor characteristic evaluation method described in 1. The table of the acceleration sensor characteristic evaluation apparatus comprising: a table; at least two infinitely rotatable and parallel links connected to the table and having the same length; and driving means for synchronously driving the links. After rotating the 123 coordinate system of the acceleration sensor package with respect to the xyz coordinate system using the first rotation matrix to fix the acceleration sensor package to the table, the table is attached to the xyz coordinate system by the driving means. First excitation on the xy plane of the xyz coordinate system in the principal axis direction of each sensor is performed using a sinusoidal output voltage of each sensor in the acceleration sensor package by performing vibration by constant velocity circular motion on the xy plane. A procedure for calculating the projection direction;
Calculating a first plane including a z-axis of the xyz coordinate system and a first projection direction on the xy plane of the xyz coordinate system;
Transforming the first plane of the xyz coordinate system to the first plane of the 123 coordinate system using an inverse matrix of the first rotation matrix;
After the 123 coordinate system of the acceleration sensor package is rotated using a second rotation matrix different from the first rotation matrix with respect to the xyz coordinate system of the table, the acceleration sensor package is fixed to the table, and then the table The xyz in the principal axis direction of each sensor using the sinusoidal output voltage of each sensor in the acceleration sensor package by performing excitation by constant velocity circular motion on the xy plane of the xyz coordinate system by the driving means A procedure for calculating a second projection direction on the xy plane of the coordinate system;
Calculating a second plane including a z-axis of the xyz coordinate system and a second projection direction on the xy plane of the xyz coordinate system;
Converting the second plane of the xyz coordinate system to the second plane of the 123 coordinate system using an inverse matrix of the second rotation matrix;
An acceleration sensor characteristic evaluation program comprising: calculating an intersection line of the first and second planes of the 123 coordinate system as a principal axis direction of each sensor of the acceleration sensor package. The first and second planes of the xyz coordinate system are represented by the following unit normal vector n _i ′.
n _i '= e _z × s _i '
Where e _z is the z-axis unit vector of the xyz coordinate system,
s _i ′ is a unit vector of the first and second projection directions of the xyz coordinate system,
6. The acceleration sensor characteristic evaluation program according to claim 5, wherein x is calculated by outer product. The first of the 123 coordinate system unit vectors s _i of the principal axis direction of each sensor present on the line of intersection of the second plane,
s _i = ± (n _ia × n _ib ) / | n _ia × n _ib |
Where n _ia is a unit normal vector of the transformed first plane of the 123 coordinate system,
n _ib is the transformed unit normal vector of the second plane of the 123 coordinate system,
X represents the outer product,
The acceleration sensor characteristic evaluation program according to claim 5, which is calculated by: 6. The method of calculating sensitivity according to an output voltage from each sensor according to an inner product of a unit vector in a principal axis direction of each sensor of the acceleration sensor package and an input acceleration vector by the constant velocity circular motion. The acceleration sensor characteristic evaluation program described in 1.