Force sensor with dynamic error correction function, and dynamic error correction method considering base acceleration.

Abstract

When attempting to estimate and correct the dynamic error of a force sensor based on its output, this was impossible if the acceleration of the force sensor base was not zero. [Solution] By using the measured or estimated acceleration value of the force sensor's base, it becomes possible to estimate and correct the dynamic error of the force sensor from the force sensor's output itself.

Description

Technical Field

[0001] It relates to the technical field of a dynamic calibration method for force sensors.

Background Art

[0002] In Patent Document 1 below, an invention regarding a dynamic error correction method for a force sensor is disclosed, which utilizes that most of the dynamic errors of a highest-accuracy type (strain gauge type) force sensor can be explained by the inertial force (= product of effective mass and acceleration) around the sensing part of the sensor. However, in the inventions up to the previous time, the dynamic errors caused by the acceleration motion (such as vibration) of the base of the force sensor were not considered. The dynamic errors caused by the acceleration motion of the base of the force sensor are often not negligible, and this point has been a major problem.

Patent Document 1

[0003] Force, which is one of the basic physical quantities, is usually measured using a force sensor. A force sensor mechanically deforms (strains) in response to a force and converts that deformation (strain) into an electrical signal such as a voltage. Depending on the element responsible for its action, commonly used force sensors are classified as follows. (1) A strain gauge type force sensor uses a strain gauge attached to an elastic body. (2) A piezo element type force sensor uses a piezo element. (3) A capacitance type force sensor uses two conductor plates supported by an elastic structure.

[0004] Force sensors require calibration of the relationship between standard force and output using known forces. Currently, force sensors are calibrated under static conditions using gravity acting on a mass standard (standard weight). In static force standards, two types of forces are distinguished: tensile force and compressive force. Currently, dynamic force standards have not been established, meaning that dynamic calibration methods for force sensors have not been established. However, several methods for dynamic calibration of force sensors have been researched and developed. For example, a method has been researched and developed in which a mass is attached to the force sensor and the entire system is vibrated by a vibrator to apply a time-varying force (dynamic force) to the force sensor. On the other hand, the author has been researching and developing the Levitation Mass Method, a method in which a levitated mass is made to collide with a fixed force sensor, and the force acting on the force sensor is determined as the product of the mass and its acceleration.

[0005] One field where force measurement is necessary is materials testing. Generally, in materials testing machines, force is applied to the non-test material by an actuator, and the force (stress) and displacement (strain) acting on the test material at that time are measured. A force sensor is attached to measure force (stress), and a position sensor is attached to measure displacement (strain). The force applied to the test material is often a "fluctuation force," but the force sensor used is calibrated only with a "static force standard," and not with a dynamic force standard. Therefore, it is strictly impossible to [a] evaluate the uncertainty of the magnitude of the measurement value and [b] evaluate the uncertainty of the measurement value in the time axis for the force sensor measurement value when a "fluctuation force" is applied. This is a serious problem in force measurement. By applying the levitation mass method, it is possible to realize a materials testing machine that measures force based on the definition of force F=Ma without using a force sensor.

[0006] The "levitation mass method" is a method for generating and measuring "fluctuating forces" characterized by the high-precision measurement of the inertial force acting on a levitated and supported inertial mass using an optical interferometer. In the levitation mass method, the inertial force acting on a levitated and supported object (inertial mass) is measured with high precision using an optical interferometer. During the experiment, the optical interferometer measures only the Doppler shift frequency f of the signal light directed at the object. From this Doppler shift frequency f, the object's velocity v, position x, acceleration a, and inertial force F are determined by numerical differentiation, numerical integration, etc.

[0007] The levitation mass method measures time-varying force (dynamic force) based on the definition of force (F=ma), enabling highly accurate measurements. Its applications are diverse. Representative published papers on dynamic calibration methods for force sensors using the levitation mass method include the following: [Non-Patent Document 1] Y. Fujii, “Measurement of the electrical and mechanical responses of a force transducer against impact forces”, Rev. Sci. Instrum., Vol.77, No.8, 085108-1-5, 2006. [Non-Patent Document 2] Y. Fujii, "Method for correcting the effect of the inertial mass on dynamic force measurements", Meas. Sci. Technol., Vol. 18, No. 5, pp. N13-N20, 2007. [Non-Patent Document 3] Y. Fujii, “Toward establishing dynamic calibration method for force transducers”, IEEE Trans. Instrum. Meas., Vol.58, No.7, pp.2358-2364, 2009. [Non-Patent Document 4] Y. Fujii, “Toward dynamic force calibration”, Measurement, Vol.42, No.7, pp.1039-1044, 2009

[0008] Despite a quarter-century of research and development at major national standards laboratories, a dynamic calibration method for force sensors has yet to be established. The following is considered a reasonable approach to establishing a dynamic calibration method. Stage 1: The force sensor targets a state where the base (pedestal) is not undergoing accelerated motion. Stage 2: This stage focuses on the state in which the base (pedestal) of the force sensor undergoes accelerated motion. Many studies start from the second stage (excitation with a vibrator, using each force sensor), but the base motion involves various acceleration and vibration states, making it difficult to comprehensively cover and integrate all force sensor usage environments and conditions. I believe this is the root cause of the misguided research and development of dynamic calibration methods over the past quarter-century.

[0009] Currently, the only widely used calibration method for force sensors is static calibration based on static force standards. In static calibration, compressive and tensile forces are generally treated separately. When dynamic calibration of force sensors becomes established and widespread, it is anticipated that a distinction will be made between cases where the base of the force sensor (pedestal, base section, mounting section, base, and rigid body section opposite the sensing element) does not undergo accelerated motion (= Stage 1 above) and cases where it does undergo accelerated motion (= Stage 2 above). In such cases, it is anticipated that using measured or estimated values ​​of the acceleration of the force sensor base, based on the present invention, will be essential. [Overview of the Initiative] [Problems that the invention aims to solve]

[0010] The present invention aims to provide a method for correcting the dynamic error of a force sensor (such as a strain gauge force sensor or a piezoelectric force sensor) using the output of the force sensor and an acceleration sensor installed on the force sensor base. [Means for solving the problem]

[0011] To achieve the above objective, the invention relating to claim 1 is a force sensor with a dynamic error correction function, or a dynamic error correction method that takes base acceleration into consideration, characterized by estimating and correcting the dynamic error of the force sensor using the measured or estimated value of the acceleration of the base of the force sensor. The invention relating to claim 2 is a force sensor with a dynamic error correction function as described in claim 1, or a dynamic error correction method that takes base acceleration into consideration, characterized in that the dynamic error of the force sensor is estimated and corrected using the measured or estimated value of the acceleration of the sensing part of the force sensor. The invention relating to claim 3 is a force sensor with a dynamic error correction function according to claim 1 or claim 2, or a dynamic error correction method that takes base acceleration into consideration, characterized in that the acceleration sensor can be installed at any position without being integrated with the force sensor.

[0012] The invention relating to claim 4 is a dynamic error correction device and a dynamic error evaluation method, characterized by measuring the acceleration of the base portion of a force sensor using an optical interferometer. This invention can be directly applied to force sensors that utilize the deformation of elastic or viscoelastic materials for force detection, such as strain gauge type force sensors, piezoelectric element type force sensors, and capacitance type force sensors. Furthermore, it can be applied to devices that evaluate the relationship between the dynamic error of the force sensor and the component due to the acceleration motion (vibration, etc.) of the force sensor's base (fixed position), as well as to dynamic calibration devices for force sensors. [Effects of the Invention]

[0013] Fig. 1 shows a schematic diagram and a model diagram (mass = spring = damper system) of an S-shaped strain gauge type force sensor (highest precision type). The equation of motion for the mass M1 can be expressed as follows using the load Fapply to the force sensor sensing part (above the mass M1), the force Fspring received by M1 from the spring, and the force Fdamper received by M1 from the damper. M1 a1 = Fapply – Fspring – Fdamper Here,

[0014] Fspring = k(x1 - x0) Fdamper = C (v1 - v0) If it can be assumed that the spring and the damper are ideal respectively, the following holds. M1 a1 = Fapply – k(x1 - x0) – C (v1 - v0) Expressing it in terms of the quantity Fapply to be measured, Fapply = k(x1 - x0) + C (v1 - v0) + M1 a1

[0015] In the static calibration of the force sensor, the relationship between the force sensor output (generally voltage output) and the load based on the force standard is obtained by distinguishing the types of loads (compression weight, tensile weight, increasing process, decreasing process). It is a necessary condition for an ideal force sensor that the spring constant k can be regarded as constant and that the "relationship between load and output" is a proportional relationship regardless of the type of load. In a more precise static calibration, the relationship between the force sensor output (generally voltage output) and the load based on the force standard is obtained as a function.

[0016] In static calibration, in the general formula including the dynamic state Fapply = k(x1 - x0) + C (v1 - v0) + M1 a1 the velocity component and the acceleration component can be ignored, so Fapply_static = k(x1 - x0)= Fspring

[0017] This is the case. Typically, the voltage output Vout of the force sensor system (the output voltage of the bridge circuit connected to the strain gauge of the force sensor, etc.) is proportional to the displacement Δx (=x1-x0) of the force sensor itself, or the displacement Δx (=x1-x0) of the spring part (strain-generating body) of the force sensor. A proportional relationship holds between the output voltage Vout of the force sensor system and the load Fapply_static. Fapply_static = A Vout

[0018] This is expressed as follows. Note that A [N / V] is the proportionality constant. Roughly speaking, static calibration is the process of determining this proportionality constant A. Furthermore, in this case, A Vout is the force of the spring, A Vout= k(x1-x0)=Fspring It can be expressed as follows.

[0019] The reason why the displacement Δx (=x1-x0) of the force sensor itself and the displacement Δx (=x1-x0) of the spring part (strain-generating body) of the force sensor are represented by the same symbol is that we assume that only the spring part (strain-generating body) within the force sensor itself is soft and deformable.

[0020] In the current state where dynamic calibration methods are not yet established, using the proportionality constant A obtained by static calibration directly will result in the following dynamic error Fdynamic_error. Fdynamic_error = A Vout – Fapply = Fspring - Fapply = [k(x1-x0)] – [k(x1-x0) + C (v1-v0) + M1 a1] = - C (v1-v0) - M1 a1

[0021] We consider the estimation and correction of the inertial force M1a1 acting on the inertial mass M1 around the sensing element within the context of dynamic errors.

[0022] Figure 2 shows a model diagram of a force sensor assuming that damping is negligible and the spring is ideal (a model diagram of a mass-spring system). Fspring = k Δx = k (x1-x0) [N] Differentiating this with respect to time yields the following:

[0023] (d / dt)Fspring = k (v1-v0) [N / s] Furthermore, differentiating with respect to time yields the following: (d2 / dt2)Fspring = k (a1-a0) [N / s2] Transforming this equation yields the following:

[0024] a1- a0 = (1 / k) (d2 / dt2)Fspring Multiplying both sides by M1 and rearranging, a1M1 = (M1 / k) (d2 / dt2)Fspring + a0 M1 By pre-determining M1 and k, the inertial force component a1M1 of the dynamic error can be determined solely from the force sensor output Fspring and the base acceleration a0. a1M1 = (M1 / k) (d2 / dt2)Fspring + M1 a0

[0025] It is also conceivable to directly measure the acceleration a1 of the sensing element by attaching the acceleration sensor to a rigid body integrated with the sensing element. In that case, it would no longer be necessary to measure the acceleration of the base of the force sensor (the part of the force sensor that can be considered a rigid body attached to the base) in order to determine a1M1. However, attaching the acceleration sensor to a rigid body integrated with the sensing element presents problems such as space limitations, interference with the path through which the measured force is transmitted, and the need to add the mass of the acceleration sensor itself to M1. Furthermore, external forces acting on the acceleration sensor cable must be added to a1M1. In these respects, there are advantages to measuring the acceleration of the force sensor's base.

[0026] We consider the estimation and correction of the component C (v1-v0) due to the damper around the sensing element within the dynamic error.

[0027] Fdamper = C (v1-v0) As a first approximation, we assume the following holds: A Vout = Fspring = k Δx = k (x1-x0) Differentiating this with respect to time yields the following: (d / dt) A Vout = k (v1-v0) [N / s] When transformed,

[0028] (v1-v0) = A / k (d / dt) (Vout) Substituting this equation into the previously mentioned Fdamper = C (v1-v0), Fdamper = CA / k (d / dt) (Vout) By pre-determining C, A, and k, the damping force component Fdamper [= C (v1-v0)] of the dynamic error can be determined solely from the force sensor output Vout.

[0029] In this case, acceleration information from the base of the force sensor is not necessary. In this specification, the expression "base of the force sensor" means "the part attached to the base of the force sensor," "the base of the force sensor," or "the part of the base / lower part of the force sensor that is attached to the base and integrated with the base, and can be considered a rigid body." Typically, the "part attached to the base of the force sensor," along with the "base of the force sensor" and the "member to which the force sensor is attached," is made of a hard material such as metal or ceramic, and can be considered a rigid body compared to the softer parts of the force sensor, such as the strain-generating body. [Brief explanation of the drawing]

[0030] [Figure 1] Figure 1 shows a schematic diagram and a model diagram (mass = spring system) of an S-shaped strain gauge type force sensor (highest accuracy type). [Figure 2] Figure 2 is a schematic diagram showing the setting of the coordinate axes. [Figure 3]Figure 3 is a schematic diagram of a force sensor based on the present invention. [Figure 4] Figure 4 is a schematic diagram of a force sensor based on the present invention. [Figure 5] Figure 5 is a schematic diagram of a force sensor based on the present invention. [Figure 6] Figure 6 is a schematic diagram of a force sensor based on the present invention.

[0031] [Figure 7] Figure 7 is a schematic diagram of an apparatus for evaluating the response of a force sensor to an impact force, based on the levitation mass method. [Figure 8] Figure 8 shows an example of the measurement results of the force sensor's response to impact force, based on the levitation mass method. [Figure 9] Figure 9 shows a device for dynamic error correction that takes base acceleration into consideration, based on the present invention. [Modes for carrying out the invention] [Examples]

[0032] Example 1 is an embodiment based on claim 1. Figure 3 shows a force sensor according to the present invention. It is a force sensor equipped with an elastic body for acceleration measurement on its base. The method for correcting the dynamic error of a force sensor is characterized by estimating the acceleration a1 around the sensing part of the force sensor using the term obtained by the second derivative of the force sensor output Fspring with respect to time and the measured value a0 of an acceleration sensor installed on the base of the force sensor. By determining M1 and k in advance, the dynamic error a1M1 can be determined from only the force sensor output Fspring and the acceleration a0 of the base using the following formula.

[0033] a1M1 = (M1 / k) (d2 / dt2)Fspring + M1 a0 In this embodiment, the acceleration sensor is built into the force sensor. The base (aluminum) of the force sensor is hollowed out, and the acceleration sensor is mounted inside. This makes it possible to estimate and correct the inertial force component of the force sensor's dynamic error using the measured or estimated acceleration of the force sensor's base. In other words, by pre-determining M1 and k, the inertial force component a1M1 of the dynamic error can be determined solely from the force sensor output Fspring and the base acceleration a0.

[0034] a1M1 = (M1 / k) (d2 / dt2)Fspring + M1 a0 The sensing axis (sensitive axis) of the installed acceleration sensor is in the same direction as the sensitive axis of the force sensor shown in Figure 1. To investigate or correct for the influence of forces in two orthogonal axial directions (crosstalk / cross-correlation) on the sensing axis of the force sensor, it is conceivable to utilize two-axis or three-axis acceleration sensors. [Examples]

[0035] Example 2 is an embodiment based on claim 2. In Example 2, an acceleration sensor is built into both the lower and upper parts of the force sensor. This makes it possible to estimate and correct the dynamic error of the force sensor using the measured or estimated value of the acceleration a1 of the sensing part of the force sensor.

[0036] Regarding the estimation and correction of the inertial force M1a1 acting on the inertial mass M1 around the sensing element within the dynamic error, it can be calculated from the measured acceleration a1 of the force sensor's sensing element and the pre-measured final mass M1. Furthermore, regarding the estimation and correction of the damper component C(v1-v0) around the sensing element within the dynamic error, it can be estimated from the force sensor output alone using the following approximate formula.

[0037] Fdamper = CA / k (d / dt) (Vout) In Example 2, a0 and a1 are obtained from two acceleration sensors attached to the force sensor. By calculating their respective integral values ​​v0 and v1, the following can be calculated. Fdamper = C (v1-v0) If the accuracy of the accelerometer is sufficiently high, calculations and estimations using this formula will be more accurate. [Examples]

[0038] Example 3 is an embodiment based on claim 3. The acceleration sensor can be separated from the force sensor and installed at any position. This allows any type of force sensor to be used, increasing the degree of freedom. As shown in Figure 4, by fixing the member fixed to the sensing part and the added mass at any position, if the force to be measured is a force applied vertically from above to the top of the added mass shown in Figure 4, the influence of inertial forces acting on the added mass (M2 [kg]) and the elastic body (M3 [kg]) can be eliminated.

[0039] If the force to be measured is Fapply in Figure 6, the components of the dynamic error due to the added mass (M2 [kg]) and the inertial force of the elastic body (M3 [kg]) are M2 a2 and M3[(a1+a2) / 2], respectively. It is assumed that the elastic body is homogeneous, has a uniform cross-section, and deforms (stretches and compresses) uniformly in the vertical direction of Figure 6. That is, the acceleration of the center of gravity of the elastic body is assumed to be (a1+a2) / 2.

[0040] Fapply = Fspring + Fdamper + M2 a2 + M3[(a1+a2) / 2] + M1 a1 [Examples]

[0041] Example 4 is an embodiment based on claim 4. It is a dynamic error correction device and a dynamic error evaluation method characterized by measuring the acceleration of the base of a force sensor using an optical interferometer. Figure 7 shows the apparatus for evaluating the shock response of a force sensor based on the levitation mass method. Figure 8 shows the evaluation results of the shock response of the force sensor measured in Figure 7. Fmass is the inertial force Ma of the levitation mass (mass of the movable part of the static pressure linear air bearing) measured by the levitation mass method. Ftrans is the output of the force sensor (output based on the static calibration result). Since the uncertainty is sufficiently small, we treat it as the "true value" for convenience, and the dynamic error Fdynamic_error = Fdiff = Ftrans – Fmass.

[0042] In contrast, as shown in Figure 8, the second derivative of the force sensor output (d 2 / dt 2 )Ftrans, coefficient (-3.33 × 10 -7 Let Freg be the value obtained by multiplying by ). From Figure 8, the dynamic error Fdynamic_error = Fdiff = Ftrans – Fmass and the second derivative of the force sensor output (d 2 / dt 2 )Ftrans, coefficient (-3.33 × 10 -7 The value Freg, obtained by multiplying by ), shows good agreement. This indicates that the dynamic error of the force sensor can be estimated and corrected using the second derivative of the acceleration of the force sensor's sensing element. Figure 9 shows a device for dynamic error correction that takes base acceleration into consideration, based on the present invention. [Industrial applicability]

[0043] This invention provides a method for accurately estimating the dynamic error of a force sensor, including the dynamic error caused by the acceleration motion (such as vibration) of the base of the force sensor. This invention is considered to have significant advantages and usefulness in situations where dynamic calibration methods have not yet been established.

[0044] The force sensor based on this invention has a simple component configuration, consisting only of an acceleration sensor added to the base of the force sensor, making development and manufacturing easy. Despite this simplicity, it enables highly accurate estimation of the dynamic error of force sensors, including dynamic errors due to acceleration motion (such as vibration) of the force sensor base, which was previously impossible. This is expected to make a significant contribution in various fields. Its practicality is considered extremely high.

[0045] Market entry is expected for force sensors and dynamic calibration methods (devices) for force sensors. The force sensor market is expected to grow steadily in the future.

[0046] Potential application areas include measuring instruments such as material testing machines, production machinery, and production plants, as well as industrial robots, automotive safety systems, medical devices, and user interfaces for home appliances.

Claims

1. A force sensor with a dynamic error correction function, or a dynamic error correction method that takes base acceleration into consideration, characterized by estimating and correcting the dynamic error of the force sensor using the measured or estimated value of the acceleration of the base of the force sensor.

2. A force sensor with a dynamic error correction function, or a dynamic error correction method that takes base acceleration into consideration, according to claim 1, characterized in that the dynamic error of the force sensor is estimated and corrected using the measured or estimated value of the acceleration of the sensing part of the force sensor.

3. A force sensor with a dynamic error correction function according to claim 1 or claim 2, characterized in that the acceleration sensor can be installed at any position without being integrated with the force sensor, or a dynamic error correction method that takes base acceleration into consideration.

4. A dynamic error correction device and a dynamic error evaluation method, characterized by measuring the acceleration of the base of a force sensor using an optical interferometer.

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