JPWO2020080544A1 - Measuring device, parts for measuring device and arithmetic processing device for measuring device - Google Patents

Abstract

Further improve the sensitivity of the measuring device. Therefore, in a measuring device that detects a value corresponding to a physical quantity to be measured by using the amplitudes of two vibrating bodies, an existing cantilever (1B) and a cantilever (1B) as one of the two vibrating bodies are used. ), An actuator (22) that applies a force in the displacement direction set in advance, a vibration displacement detection unit including a displacement meter (23) of the cantilever (1B), and the cantilever (1B) are virtually coupled to each other. The cantilever (1A) is simulated as the other one of the two vibrating bodies, and the actuator (22) is driven based on the cantilever (1A) and the vibration displacement of the cantilever (1B) detected by the vibration displacement detection unit. It is provided with an arithmetic processing device that executes a coupled control process to be controlled.

Description

The present invention relates to a measuring device for measuring mass, elasticity, etc. from the vibration behavior of a vibrating body such as a cantilever, a component for the measuring device, and an arithmetic processing device for the measuring device.

Conventionally, as a technique for measuring mass and elasticity, two cantilever of the same shape are provided on the same support member so as to enable coupled vibration, and the measurement target added to the cantilever is based on the shape of the natural vibration mode of the two cantilever. A technique for measuring a minute mass of an object is disclosed (see, for example, Patent Document 1). By coupling two cantilever, it is said that minute changes in mass and elasticity can be detected with higher sensitivity than when one cantilever is used. Coupling here means that a part of two cantilever is connected by a very weak spring so that the displacement of one influences the displacement of the other.

Japanese Unexamined Patent Publication No. 2014-190771

M Manav, A Srikantha Phani, Edmond Cretu, "Mode Localization and Sensitivity in Weakly Coupled Resonators", IEEE Sensors Journal, VOL.19, NO.8, April 15, 2019, p.2999-3007 Chun Zhao, Graham S Wood, Jianbing Xie, Honglong Chang, Suan Hui Pu, Michael Kraft, "A three degrees-of-freedom Weakly coupled Resonator Sensor With Enhanced Stiffness Sensitivity", Journal of Microelectromechanical Systems, VOL.25, NO. 1, February 2016, p. 38-51

In the above-mentioned prior art, it is known that the lower the coupling effect of the two cantilever is, the higher the sensitivity is, and the closer the physical characteristics of the two cantilever are, the higher the sensitivity is. However, there is a limit in mechanical design and manufacturing to manufacture a cantilever that sufficiently satisfies these two conditions. Therefore, it has been difficult to achieve higher sensitivity.
In addition, manufacturing two cantilever that can be coupled is technically more difficult than manufacturing one cantilever, and has disadvantages such as deterioration of production yield, deterioration of complexity, and cost increase. It was happening.

Therefore, the present invention has been made by paying attention to the above-mentioned conventional unsolved problems, and an object of the present invention is to provide a measuring device having higher sensitivity, a component for the measuring device, and an arithmetic processing device for the measuring device. There is.

In order to solve the above problems, in the present invention, one of the two coupled cantilever levers is removed. Then, instead of the removed cantilever, the force that should be applied to the other cantilever when two cantilever are coupled is theoretically calculated in real time and applied to the actuator attached to the other cantilever. As a result, only the other cantilever is vibrated as if the two cantilever were vibrating in combination. By doing this, only one cantilever should be manufactured, and the physical characteristics of the cantilever can be ideally brought close to each other, and the coupling effect can be ideally reduced. , It becomes possible to solve the above problems.

That is, according to one aspect of the present invention, it is a measuring device that detects a value corresponding to a physical quantity to be measured by using the amplitudes of the two vibrating bodies, and is actually present as one of the two vibrating bodies. The actual vibrating body, the actuator that applies a force in the displacement direction set in advance to the actual vibrating body, and the vibration displacement detection unit that detects the vibration displacement of the actual vibrating body are virtually coupled with the actual vibrating body. The virtual vibrating body is simulated as the other one of the two vibrating bodies, and the actuator is driven and controlled based on the virtual vibrating body and the vibration displacement of the actual vibrating body detected by the vibration displacement detection unit. A measuring device including an arithmetic processing device that executes processing is provided.

Further, according to another aspect of the present invention, there are a component for the measuring device of the above aspect, an actual actual vibrating body, an actuator that applies a force in a preset displacement direction to the actual vibrating body, and an actual vibration. A component for a measuring device including a vibration displacement detecting unit for detecting a vibration displacement of a body is provided.
Further, according to another aspect of the present invention, the arithmetic processing device for the measuring device of the above aspect is virtually coupled to the real vibrating body by using the vibration displacement of the real vibrating body. An arithmetic processing device for a measuring device that simulates a virtual vibrating body and generates a signal for driving and controlling an actuator is provided.

According to one aspect of the present invention, a measuring device having higher sensitivity can be easily realized.

It is explanatory drawing for demonstrating the mass measuring method in the measuring apparatus to which this invention is applied. It is a figure which shows an example of the equivalent model of the dynamical system of a vibrating part. It is a schematic block diagram which shows an example of the measuring apparatus. It is a top view which shows an example of the actual vibrating body part. It is a front view which shows an example of the actual vibrating body part. It is a block diagram which shows an example of the dynamics of the whole measuring device. It is a figure for demonstrating the verification result. It is a figure for demonstrating the verification result. It is explanatory drawing for demonstrating the modification of the measuring apparatus to which this invention is applied. It is a figure which shows an example of the equivalent model of the dynamical system of the vibrating part in the modification.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
It should be noted that the following detailed description describes many specific specific configurations to provide a complete understanding of embodiments of the present invention. However, it is clear that other embodiments can be implemented without being limited to such specific specific configurations. In addition, the following embodiments do not limit the invention according to the claims. Also, not all combinations of features described in the embodiments are essential to the means of solving the invention.
In this embodiment, a case where the mass of the object to be measured is measured by the measuring device will be described.

<Conventional mass measurement method>
First, a mass measurement method using a vibrating part having two vibrating bodies (for example, a cantilever) having the same spring rigidity and mass and being provided on the same support member so as to be capable of coupled vibration. explain.

First, of the two vibrating bodies, a feedback value proportional to the vibrating speed (displacement speed) of one vibrating body is positively fed back to give equal excitation inputs to the two vibrating bodies. As a result, self-excited vibration is generated in the two vibrating bodies. Here, in order to generate self-excited vibration, the feedback gain is gradually increased (or decreased) from a preset value. Then, first, self-excited vibration is generated only in the low-order natural vibration mode. The amplitude ratio of the two vibrating bodies at this time strictly corresponds to the low-order natural vibration mode.
On the other hand, the object to be measured is added to one of the two vibrating bodies, and the amplitude ratio when self-excited vibration occurs is measured. Then, for example, the mass of the object to be measured is measured from the change in the amplitude ratio when the object to be measured is added to the amplitude ratio when the object to be measured is not added.

FIG. 1A is a diagram showing a configuration example of the vibrating unit 1 when measuring the mass of the object to be measured by using such a mass measuring method.
As shown in FIG. 1A, the vibrating portion 1 includes a cantilever 1A, a cantilever 1B, a support member 1C, and an overhang portion 1D.
Both the cantilever 1A and 1B are made of the same material and shape, and are juxtaposed (coupled) with the support member 1C in a cantilever state in which one end is fixed to the support member 1C and the other end is a free end. There is. That is, the cantilever 1A and 1B have the same spring rigidity and mass.

Further, the root portions of the cantilever 1A and 1B on the fixed end side are connected by an overhang portion 1D projectingly formed on the support member 1C. The overhang portion 1D serves as a vibration transmission portion that transmits vibrations between the cantilever 1A and 1B, and the overhang portion 1D has a structure in which the cantilever 1A and 1B vibrate in a coupled manner.
In FIG. 1A, an object to be measured is attached to the cantilever 1B, and the cantilever 1A and 1B are displaced from the outside as velocity feedback to generate self-excited vibration in the cantilever 1A and 1B.

<Mass measurement method in this embodiment>
The measuring device according to the present embodiment measures the mass of the object to be measured by using such a mass measuring method, as shown in FIG. 1B, the cantilever 1A and the overhang portion 1D (support member 1C). Is realized as a virtual model on an arithmetic processing device composed of a digital signal processor (DSP) or the like.

[Equivalent model]
FIG. 2 is a diagram showing an example of an equivalent model of the dynamical system of the vibrating unit 1 included in the measuring device according to the present embodiment.
As shown in FIG. 2, the vibrating portion 1 is an equivalent model of a "spring-mass (mass) -damper" system (hereinafter, also referred to as a coupled model) in consideration of two coupled cantilever levers 1A and 1B. .) Think as.
In the coupled model shown in FIG. 2, the cantilever 1A has a first spring a1 having a spring constant k whose one end is supported by the support member 1C and a first damper a2 having a damping constant c whose one end is supported by the support member 1C. , A model including a first object a3 having a mass m supported at the other ends of the first spring a1 and the first damper a2.

Similarly, as shown in FIG. 2, the cantilever 1B has a second spring b1 having a spring constant k whose one end is supported by the support member 1C and a second damper b2 having a damping constant c whose one end is supported by the support member 1C. A model in which a second object b3 having a mass m supported at the other end of the second spring and the second damper is provided, and an object to be measured having a mass Δm is added to the second object b3 having a mass m. It becomes. That is, the cantilever 1A and 1B have the same mass as the first spring a1 or the second spring b1 having the same spring constant k and the first damper a2 or the second damper b2 having the same damping constant c, respectively. It is a model including the first object a3 and the second object b3, respectively.

Further, in the coupled model shown in FIG. 2, as shown in FIG. 2, the first object a3 and the second object b3 are connected by a third spring c1 having a spring constant kc. The third spring c1 having the spring constant kc corresponds to the overhang portion 1D in FIG. 1, and represents the coupled effect of the two cantilever 1A and 1B.
Then, in the measuring device according to the present embodiment, the portion surrounded by the broken line in FIG. 2 is simulated as a virtual model.

Here, in the equivalent model shown in FIG. 2, an exciting force F is further applied to the support points of the cantilever (virtual vibrating body) 1A and the cantilever (real vibrating body) 1B from the outside. At this time, the equations of motion of the system (coupling model of FIG. 2) are as shown in the following equations (1) and (2). The equation (1) shows the equation of motion of the virtual model including the cantilever 1A, and the equation (2) shows the equation of motion of the actual cantilever 1B.
m · (d ² x1 / dt ² ) + c · (dx1 / dt)
+ (K + kc) ・ x1-kc ・ x2 = F
… (1)
(m + Δm) · (d ² x2 / dt ² ) + c · (dx2 / dt)
-Kc · x1 + (k + kc) · x2 = F
… (2)

Incidentally, (1) and (2) in the formula, x1 is the displacement of the cantilever 1A, dx1 / dt is the first derivative value of the displacement of the cantilever ^1A, d 2 x1 / dt ² is the second order differential value of the displacement of the cantilever 1A, x2 displacement of the cantilever 1B, dx2 / dt is the first derivative value of the cantilever ^1B, d ² x2 / dt 2 is the second order differential value of the cantilever 1B.

Here, the external excitation force F applied to the cantilever 1A and 1B so that self-excited oscillation is generated is applied as shown in the following equation (3) by using the displacement x2 of the cantilever 1B. Note that b in the equation (3) is a feedback gain set to generate self-excited oscillation. The feedback gain b is set to the value of the feedback gain when self-excited oscillation occurs in an actual measurement environment. This feedback gain b does not need to be updated if the measurement environment does not change, and may be updated when the measurement is performed under a different measurement environment.
F = b · dx2 / dt… (3)

Equations (1) and (2) can be rewritten into the following equations (4) and (5) using the equation (3).
m · (d ² x1 / dt ² ) + c · (dx1 / dt)
+ (K + kc) · x1-kc · x2 = b · (dx2 / dt)
… (4)
(m + Δm) · (d ² x2 / dt ² ) + c · (dx2 / dt)
-Kc · x1 + (k + kc) · x2 = b · (dx2 / dt)
… (5)

Equations (4) and (5) can be replaced with the following equations (6) and (7).
m · (d ² x1 / dt ² ) + c · (dx1 / dt)
+ (K + kc), x1-kc, x2-b, (dx2 / dt) = 0
… (6)
(m + Δm) · (d ² x2 / dt ² ) + c · (dx2 / dt)
+ K · x2 = kc · (x1-x2) + b · (dx2 / dt)
… (7)

In the present embodiment, the equation of motion of Eq. (6) is virtually simulated by using a quartic Runge-Kutta method in an arithmetic processing unit. Further, the right side in the equation (7) is applied to the actual cantilever 1B as the excitation force F.
Here, in order to virtually simulate the equation (6) with the arithmetic processing device, the state variable X is set to the following equation (8), the equation (6) is converted into the equation of state, and then the fourth-order Runge- It is solved using the Kutta method, and the state quantity (equation (10)) is derived from the state quantity (equation (9)) at time t after the unit step time, that is, at time t + h. The displacement of the virtual cantilever 1A at this time is obtained as x1 (t + h), and the velocity is obtained as dx1 (t + h).

Note that x1 (t) and dx1 (t) / dt in the equation (9) use the numerical calculation results. Further, x2 (t) and dx2 (t) / dt utilize the displacement measurement result of the actual cantilever 1B.
Next, in the equation of motion of Eq. (7), that is, the equation of motion of the actual cantilever 1B, the term on the right side is represented by the excitation force F.
That is, the equation of motion (7) is expressed by the following equation (11), where F is the exciting force.
(m + Δm) · (d ² x2 / dt ² ) + c · (dx2 / dt)
+ K · x2 = F
… (11)

Therefore, the exciting force F required to reproduce the equation (7) is expressed by the following equation (12).
F = kc · (x1-x2) + b · (dx2 / dt)
… (12)
That is, the exciting force F required to realize the equation (7) is a velocity feedback component (linear velocity feedback component) for self-excited oscillation and a displacement feedback (linear displacement feedback) for simulating the coupled effect. It becomes the sum with the component).
From the above, it is possible to understand the calculation required for simulating the coupled cantilever and the information to be fed back.

[Example of verification of equivalent model]
Next, in order to verify whether the simulation method of the virtual coupled model shown in FIG. 2 is correct, measurement was performed using a macro cantilever. This measurement was performed by the measuring device 100 shown in FIGS. 3 to 5 simulating the virtual coupled model shown in FIG. In the measuring device 100, an additional mass as a measurement object was attached at a position 10 mm from the tip of the macro cantilever in which the fixed end of the actual cantilever 1B was joined to the piezo actuator, and measurement was performed.

[Measuring device configuration]
FIG. 3 is a schematic configuration diagram showing an example of the measuring device 100.
The measuring device 100 uses a virtual body unit 11 including an actual cantilever 1B, a displacement meter 23 for detecting the amplitude of the cantilever 1B, and an actuator for vibrating the cantilever 1B, and a detection signal from the displacement meter 23. An arithmetic processing device 12 composed of a digital signal processor (DSP) or the like that simulates the movement of the cantilever 1A and performs coupled control processing for controlling the actuator, and the actuator 22 according to a command signal from the arithmetic processing device 12. A drive circuit 13 for driving the device and a display device 14 are included.

As shown in the top view of FIG. 4 and the front view of FIG. 5, the actual vibrating body portion 11 includes an actual cantilever 1B, a support member 21 that supports one end of the cantilever 1B, and an actuator 22 that vibrates the support member 21. A displacement meter (vibration displacement detection unit) 23 including a laser displacement sensor or the like for detecting the displacement of the tip of the cantilever 1B is provided. The parts shown in FIGS. 4 and 5 correspond to the parts for the measuring device.
As shown in FIG. 5, the support member 21 supports one end of the elongated plate-shaped cantilever 1B so that the width direction of the cantilever 1B is perpendicular to the vertical direction.
Further, the support member 21 includes a holding portion 21a for holding the cantilever 1B and a guide portion 21b for slidably supporting the holding portion 21a in a direction orthogonal to the longitudinal direction of the cantilever 1B. The holding portion 21a and the guide portion 21b are slidably supported via a linear bearing or the like.

The actuator 22 includes, for example, a uniaxial piezo actuator and the like, includes a shaft portion 22a that expands and contracts, a support portion 22b that supports one end of the shaft portion 22a, and a holding portion 21a at the other end of the shaft portion 22a. Is fixed. The expansion and contraction direction of the shaft portion 22a and the guide direction of the holding portion 21a in the guide portion 21b are arranged so as to coincide with each other, and the actuator 22 expands and contracts the shaft portion 22a in response to a drive signal from the drive circuit 13 to expand and contract the shaft portion 22a. The 21a moves with the guide portion 21b as a guide, and the cantilever 1B held by the holding portion 21a moves. As a result, the actuator 22 is moved so as to alternately repeat the expansion and contraction of the shaft portion 22a, so that the holding portion 21a vibrates, and as a result, the cantilever 1B vibrates.

The displacement meter 23 is arranged at a position where the distance between the tip of the cantilever 1B and the tip of the cantilever 1B can be measured, and measures the distance to the tip of the cantilever 1B. The amplitude of the cantilever 1B can be detected by calculating the displacement of the distance to the tip of the cantilever 1B detected by the displacement meter 23.

[Block diagram showing the dynamics of the measuring device]
FIG. 6 is a block diagram showing an example of the dynamics of the entire measuring device 100.
Here, it is necessary to convert the equations (1) to (12) described in the dimensional form into a dimensionless quantity in the calculation by the arithmetic processing unit 12 composed of the DSP or the like. When the equations (6) and (7) are made dimensionless, they can be expressed by the following equations (13) and (14).
(d ² x1 ^* / dt ^{* 2} ) + γ ・ (dx1 ^* / dt ^* )
+ (1 + kc ^* ) ・ x1 ^* -kc ^*・ x2 ^*
−β ・ (dx2 ^* / dt ^* ) = 0
… (13)

(1 + δ) ・ (d ² x2 ^* / dt ^{* 2} )
+ Γ ・ (dx2 ^* / dt ^* ) + x2 ^*
= Kc ^*・ (x1 ^* −x2 ^* ) + β ・ (dx2 ^* / dt ^* )
… (14)
The symbol "*" in the equation (14) indicates a dimensionless quantity, and x1 ^* and x2 ^* correspond to x1 and x2, respectively. In addition, t ^* = (k / m) ^1/2 · t, γ = c / (m · k) ^1/2 , kc ^* = kc / k, β = b / (m · k) ^1/2 , δ = Δm / m.

FIG. 6 is a block diagram of equations (13) and (14).
As shown in FIG. 6, the displacement x2 of the cantilever lever 1B is detected by the displacement meter 23, multiplied by the gain G1 of the displacement meter 23 by the calculator 31, and then converted into a digital signal by the AD converter (ADC) 32 for calculation. It is processed by the processing device 12. That is, the output of the AD converter 32 passes through the LPF (low-pass filter) unit 34 and the differentiator (vibration velocity detection unit) 35 after the gain G2 is multiplied by the arithmetic unit 33, and then the first-order differential value dx2 of the displacement x2. ^It is converted to * / dt ^* and input to the multiplier 36, and β · (dx2 ^* / dt ^* ) is output from the multiplier 36. A feedback component for self-oscillation is created by multiplying the first-order differential value dx2 ^* / dt ^* of the displacement x2 ^{* by the velocity feedback gain β.} This feedback component is input to the adder 37.

The output x2 ^* of the arithmetic unit 33 is further input to the arithmetic unit 38, and is also input to the arithmetic unit 39 directly or via the differentiator 40.
^{The arithmetic unit 39 obtains the displacement x1 *} of the virtual cantilever 1A by using the Runge-Kutta method based on ^{the output x2 *} of the arithmetic unit 33 and the output dx2 ^* / dt ^{* of the differentiator 40.} The displacement x1 ^* is input to the arithmetic unit 39, and the difference between the ^{displacement x1 *} and the displacement x2 ^{* is output from the arithmetic unit 39. By multiplying this difference by the displacement feedback gain kc *} for coupling the virtual cantilever 1A and the real cantilever 1B with the multiplier 41, a feedback component for simulating the coupled rigidity is created. This feedback component is input to the adder 37. ^{The output β · (dx2 *} / dt ^* ) of the multiplier 36 as the speed feedback component ^{and the output kc · (x1 *} −x2 ^* ) of the multiplier 41 as the displacement feedback component are added by the adder 37 and vibrated. It is output as the input displacement Δx. The excitation input displacement Δx is input to the arithmetic unit 42, multiplied by the gain G3, and then output to the actuator 22 via the DA converter (DAC) 43. That is, the output of the DA converter 43 is multiplied by the piezoelectric constant d33 of the actuator 22 (piezo actuator) by the multiplier (feedback control unit) 44, and is input to the cantilever 1B as the excitation input displacement Δx. As a result, a feedback loop that simulates the coupled effect of a virtual vibrating body is constructed.
The gains G2 and G3 are set based on, for example, a representative length and a representative time for converting a dimensionless quantity into a dimensional quantity.

[Characteristics of cantilever 1B used in verification experiment]
Next, the characteristics of the actual cantilever 1B used in the measuring device 100 will be described.
The material of the cantilever 1B is C5191P (phosphor bronze plate). The shape of the cantilever 1B is 210 [mm] in length from the fixed end, 15 [mm] in width, and 0.3 [mm] in thickness. The natural frequency f1 of the cantilever 1B is 3.964 Hz, and the dimensionless attenuation coefficient γ is 1.770 × 10 ^-3 .

〔inspection result〕
In the measuring device 100 having the above configuration, ^{by setting the displacement feedback gain kc *} to an arbitrary value, the coupled rigidity of the virtual cantilever 1A and the actual cantilever 1B can be set to a desired value. I checked if it was. Specifically, the confirmation was performed using the change state of the secondary mode natural frequency f2 of the actual cantilever 1B when the ^{displacement feedback gain kc *} for simulating the virtual coupled rigidity was changed.
FIG. 7A shows ^{a value set as the displacement feedback gain kc *} and a measured value of the secondary mode natural frequency f2 of the actual cantilever 1B at that time. The secondary mode natural frequency f2 of the cantilever 1B can be obtained, for example, from the frequency analysis of the free vibration of the cantilever 1B detected from the detection value of the displacement meter 23.

Further, FIG. 7B shows the correspondence between the ^{set value set as the displacement feedback gain kc * and the experimental value kce *} of the coupled stiffness calculated from the secondary mode natural frequency f2. In FIG. 7B, the horizontal axis is ^{the set value set as the displacement feedback gain kc *} , and the vertical axis is the experimental value kce ^* of the coupled rigidity. The experimental value kce ^* of the coupled rigidity was calculated from the following equation (15). Equation (15) is derived from equations (13) and (14) with the velocity feedback gain set to β = 0, and an experiment of coupled rigidity when the velocity feedback gain is set to β = 0. The value kce ^* can theoretically be expressed by Eq. (15). Note that δ and γ in the equations (13) and (14) are coefficients representing the characteristics of the actual cantilever 1B, and here, both δ and γ are set to zero.
^{kce * = (1/2) × {} (f2 / f1) 2 -1}
… (15)

As shown in FIG. 7B, the intrinsic frequency f1 of the cantilever 1B obtained from the free vibration experiment when the ^{displacement feedback gain kc *} and the experimental value kce ^* of the coupled rigidity, that is, the displacement feedback gain kc ^{* is given. And it was confirmed that the relationship with the experimental value kce *} of the coupled rigidity obtained from the equation (15) using the secondary mode natural frequency f2 of the cantilever 1B is almost located on the straight line of the inclination “1”. That is, it was confirmed that by adjusting the displacement feedback gain kc ^* , a virtual cantilever 1A connected to the cantilever 1B can be simulated with ^{the experimental value kce * of the desired coupled rigidity.}

FIG. 8 shows, in the measuring device 100, when the displacement feedback gain kc ^* is kc ^* = 0.01 (FIG. 8 (a)) and when kc ^* = 0.005 (FIG. 8 (b)). The relationship between the amplitude ratio and the mass ratio of the cantilever 1A and 1B is shown.
In FIGS. 8A and 8B, the horizontal axis is the mass ratio and the vertical axis is the amplitude ratio (x1 / x2).
From FIGS. 8A and 8B, it can be seen that the amplitude ratio decreases monotonically as the mass ratio increases. That is, it was confirmed that the mass can be measured from the amplitude ratio.
Further, from FIGS. 8A and 8B, ^{it can be seen that the smaller the displacement feedback gain kc *, the} larger the amount of change in the amplitude ratio with respect to the change in the mass ratio. In other words, by changing the displacement feedback gain kc ^*, it is possible to adjust the mass of the measuring sensitivity of the measuring object, the more the displacement feedback gain kc ^* is small, it was confirmed that the measurement sensitivity is further improved.

From the above, by simulating the equivalent model shown in FIG. 2 by the arithmetic processing device 12 of the measuring device 100, the measurement added to the cantilever 1B using the virtual cantilever 1A coupled in coupling and the existing cantilever 1B. It can be seen that the mass of the object can be measured.
Further, in the measuring device 100, since the displacement feedback proportional to the difference in displacement between the actual cantilever 1B and the virtual cantilever 1A is given to the cantilever 1B, the coupled rigidity can be simulated. Further, by adjusting the displacement feedback gain kc ^* , any coupled rigidity can be simulated.

Then, by using the Runge-Kutta method, the coupled cantilever 1A and 1B can be simulated in real time. Therefore, the mass of the object to be measured can be measured from the ratio of the amplitude of the cantilever 1B to which the object to be measured is attached and the amplitude of the virtual cantilever 1A.
Further, the measurement sensitivity of the mass of the object to be measured can be adjusted by arbitrarily changing the coupled rigidity. Further, the coupled rigidity can be changed arbitrarily, that is, the coupled rigidity can be made smaller than the case where two existing cantilever are connected and connected by machining. .. That is, it is possible to realize a measuring device 100 with higher accuracy.

Further, as described above, since the cantilever 1A and the overhang portion 1D are virtually simulated by the arithmetic processing unit 12, the measuring device that measures the mass of the object to be measured using one existing cantilever. This can be realized only by mounting the simulation device 100a including the arithmetic processing unit 12, the drive circuit 13, and the display device 14 shown in FIG. Therefore, the accuracy of the measuring device can be easily improved by adding the simulating device 100a to the existing measuring device.

<Modification example>
[1] In the above embodiment, the measuring device 100 may be configured so that the amplitude of self-excited oscillation can be suppressed to be smaller.
That is, the exciting force is F, and the value represented by the following equation (16) is used.
F = kc · (x1-x2) + b · (dx2 / dt)
+ F (x, (dx / dt))… (16)

In addition, f (x, (dx / dt)) in the equation (16) is a nonlinear velocity feedback component, and its phase needs to be anti-phase or in-phase with dx2 / dt. For example, if f (x, (dx / dt)) is set as shown in the following equation (17) and bn in the equation (17) is adjusted, the amplitudes of the virtual cantilever 1A and the real cantilever 1B can be reduced. It can be suppressed. As a result, it is possible to suppress the vibration of the cantilever 1A and 1B from diverging, and it is possible to suppress the divergence, so that the linear mode can be measured with high accuracy.

In this case, the equations of motion shown in Eqs. (1) and (2) can be expressed by the following equations (18) and (19).
f (x, (dx / dt)) = bn · (dx2 / dt) ³
… (17)
m · (d ² x1 / dt ² ) + c · (dx1 / dt)
+ (K + kc) ・ x1-kc ・ x2
= B · (dx2 / dt) + bn · (dx2 / dt) ³
… (18)
(m + Δm) · (d ² x2 / dt ² ) + c · (dx2 / dt)
-Kc · x1 + (k + kc) · x2
= B · (dx2 / dt) + bn · (dx2 / dt) ³
… (19)

[2] In the above embodiment, a case where a cantilever having the same shape and characteristics as the actual cantilever 1B is assumed as the virtual cantilever 1A has been described, but the present invention is not limited to this. The virtual cantilever 1A and the real cantilever 1B may have the same natural frequency, and may not have the same shape as long as the natural frequencies are the same. The higher the accuracy with which the natural frequencies of the cantilever 1A and 1B match, the higher the measurement accuracy with the measuring device 100. The term "identical" as used herein includes not only cases where they are exactly the same, but also cases where there is a difference (for example, a deviation of 1% to 2%) that can be regarded as substantially the same. When the eigenfrequency of the cantilever 1B that can be actually measured within the measurable range is used and the eigenfrequency of the cantilever 1A and 1B is adjusted to be the same, the difference between the eigenfrequency of the two is the minimum. Including the case where

[3] In the above embodiment, the arithmetic processing unit 12 may further execute the initial processing. For example, the actuator 22 is driven to drive only the actual cantilever 1B, and the frequency at the time of self-excited oscillation is acquired. Specifically, while observing the vibration state of the cantilever 1B, the feedback gain is changed to acquire the frequency at the time when the cantilever 1B starts to vibrate, that is, the resonance frequency. This is set as the eigenfrequency, and the information based on the acquired eigenfrequency is set as the information necessary for simulating the virtual cantilever 1A. After that, the cantilever 1A is simulated using the set information. This initial processing may be performed at a preset timing such as, for example, at the start of measurement for a series of measurement objects or periodically. The natural frequency is a theoretical value, and the frequency that actually resonates is the resonance frequency. Unless the influence of viscosity is strong, the resonance frequency is almost equal to the natural frequency.
The initial process may include a process for setting the feedback gain b.

[4] In the above embodiment, the case where the arithmetic processing unit 12 performs the arithmetic processing has been described, but the present invention is not limited to this. For example, an analog circuit that performs the above arithmetic processing may be configured, and the arithmetic processing may be performed by this analog circuit. That is, when the length of the cantilever 1B becomes short, the vibration frequency of the cantilever 1B becomes high and higher speed calculation is required. Therefore, it is necessary to use a higher performance digital signal processor or the like as the arithmetic processing unit 12. Leads to increased costs. In this case, by configuring the arithmetic processing unit 12 shown in FIG. 3 with an analog circuit, it can be realized without using a high-performance digital signal processor or the like, that is, an increase in cost can be suppressed. ..

When the function of the arithmetic processing unit 12 is realized by an analog circuit, it is preferable to form an analog resonance circuit that outputs an electric signal equivalent to the equation (1). For example, by building a spring mass model with an LCR circuit, the model can be built as if the displacement signal of the real cantilever 1B was input to the fixed end of the virtual cantilever 1A, and it is coupled with the real cantilever 1B. The combined virtual cantilever 1A can be realized with higher accuracy.

[5] In the above embodiment, the case where a uniaxial piezo actuator is used as the actuator 22 has been described, but the present invention is not limited to this.
For example, any actuator that can reciprocate the fixed end of the cantilever 1B, such as a magnet, can be applied.
Further, in the above embodiment, the tip end side of the cantilever 1B may be vibrated. For example, any actuator that can vibrate the tip of the cantilever 1B, such as a magnet or a piezo actuator, can be applied.

[6] In the above embodiment, the case where the cantilever 1B for measuring the mass of the object to be measured is applied has been described, but the present invention is not limited to this.
For example, it may be applied to a probe used in an AFM (atomic force microscope) or the like to simulate a virtual model in which a real probe and a virtual probe are coupled.
The physical quantity to be measured is not limited to mass, but may be any of surface shape, elastic modulus, viscoelasticity, and force field. The force field here includes an electric field in space, a magnetic field in space, a spatial distribution of universal gravitation, and the like.

For example, when measuring the electric field to be measured, in the method of measuring using two existing cantilever, both cantilever may be affected by the electric field.
In the measuring device 100 of the present embodiment, since one cantilever 1A is a virtual cantilever, a situation equivalent to the case where the two cantilevers are arranged apart from each other to a position where the one cantilever is not affected by the electric field is virtualized. Can be realized. Therefore, it is possible to prevent both the two cantilever from being affected by the electric field, and the measurement accuracy can be improved accordingly.
Further, by measuring the spatial distribution of universal gravitational force, for example, the mass of a moving body can be detected. That is, since the universal gravitational force changes with the movement of the mass on the ground, the mass of the moving body can be detected by detecting the change in the universal gravitational force.

[7] In the above embodiment, the case where the laser displacement meter is used as the displacement meter 23 has been described, but the present invention is not limited to this. For example, a capacitance displacement sensor, an encoder, an optical displacement meter (for example, a displacement sensor using the optical lever method, etc.), a strain gauge, or the like can be used. Further, the eddy current may be measured and the displacement of the cantilever 1B may be detected from the displacement amount. In short, any method may be used as long as the displacement of the cantilever 1B can be detected.

[8] In the above embodiment, the case where the cantilever is used as the vibrating body has been described, but the present invention is not limited to this. It is also possible to apply a coil spring as a vibrating body.

[9] In the above embodiment, the case where the cantilever 1A and the overhang portion 1D are virtually simulated by the arithmetic processing unit 12 has been described, but the present invention is not limited to this. For example, the cantilever 1A and the cantilever 1B may be actually provided, and the existing cantilever 1A and the cantilever 1B may be configured to be virtually coupled by the arithmetic processing unit 12. In this case, for example, the amplitude of the cantilever 1A and the amplitude of the cantilever 1B are detected, and based on these, the cantilever 1A and the cantilever 1B are virtually coupled by using an equivalent model. The actuators that drive 1A and 1B may be controlled.

[10] In the above embodiment, a plurality of cantilever levers for improving sensitivity may be further provided between the cantilever 1A and the cantilever 1B.

FIG. 9 shows between the virtual cantilever CL1 corresponding to the virtual cantilever 1A, the real cantilever CLn (n is an integer of n ≧ 3) corresponding to the real cantilever 1B, and the cantilevers CL1 and CLn. It is explanatory drawing for demonstrating the method of measuring an atomic force using the vibrating part 1 which has one or a plurality of cantilever CLi (i is 2≤i≤n-1) for improving sensitivity. An atomic force to be measured is applied to an existing cantilever CLn, and this atomic force is measured.
In FIG. 9, the virtual cantilever CL1 and the real cantilever CLn have the same natural frequency. As a method of matching the natural frequencies, the virtual cantilever CL1, the sensitivity improving cantilever CL2 to CLn-1, and the existing cantilever CLn are made of the same material and shape, and have the same spring rigidity and mass. There is a method of forming the cantilever, a method of matching the ratio of the spring rigidity and the mass, and the like.

The cantilever CL2 to CLn-1 for improving the sensitivity are formed in the same manner as the cantilever CL1 and the cantilever CLn. That is, in the state of a cantilever beam in which one end is fixed to the support member 1C and the other end is a free end, the cantilever is juxtaposed to the support member 1C, and the root portion on the fixed end side of the adjacent cantilever is formed in the support member 1C. It is connected by an overhang portion 1D, and has a structure in which a virtual cantilever CL1, a cantilever CL2 to CLn-1 for improving sensitivity, and an existing cantilever CLn vibrate in a coupled manner.
The virtual cantilever CL2 to CLn-1 for improving the sensitivity is realized as a virtual model on the arithmetic processing unit in the same manner as the virtual cantilever CL1. If the virtual cantilever CL1 and the real cantilever CLn have the same specific frequency, the specific frequencies of the virtual cantilever CL2 to CLn-1 for improving the sensitivity are unique to the virtual cantilever CL1 and the real cantilever CLn. It does not have to be the same as the frequency.

FIG. 10 is a diagram showing an example of an equivalent model (coupling model) of the dynamical system of the vibrating unit 1. In the coupled model shown in FIG. 10, the virtual cantilever CL1 has a first spring K1 having a spring constant k1 whose one end is supported by the support member 1C and a first spring K1 having a mass m1 supported by the other end of the first spring K1. It is a model including the object M1.
Similarly, the actual cantilever CLn is the nth spring Kn of the spring constant kn whose one end is supported by the support member 1C and the nth spring Kn of the nth spring Kn, as shown as a cantilever within the frame of the one-point chain line at the right end of FIG. The nth object Mn having a mass mn supported at the other end is provided, and the nth spring Kn is a model in which the spring constant kn is added with the spring rigidity Δk according to the interatomic force to be measured. ..

The virtual cantilever CLi (2 ≦ i ≦ n-1) for improving the sensitivity has a spring constant ki i-th spring Ki whose one end is supported by the support member 1C and a mass supported by the other end of the i-spring Ki. It is a model equipped with the i-th object Mi of mi.
Further, in the coupled model shown in FIG. 10, the first object M1 and the second object M2 are connected by a spring Kc1 having a spring constant kc, and similarly, adjacent objects are connected to each other by a spring having a spring constant kc, and are actually present. The nth object Mn corresponding to the cantilever CLn and the (n-1) th object Mn-1 corresponding to the cantilever CLn-1 for improving sensitivity are connected by a spring Kcn-1 having a spring constant kc. The springs Kc1 to Kcn-1 having the spring constant kc correspond to the overhang portion 1D in FIG. 9, and cause the coupled effect of the cantilever CL1 to CLn. In FIG. 10, the portion surrounded by the broken line is simulated as a virtual model.

When measuring in a measuring device having such a vibrating portion 1, among the cantilever supported by the support member 1C, an actual cantilever CLn is subjected to, for example, an atomic force to be measured, and the support member 1C is subjected to, for example, an atomic force. A vibration input is given to the cantilever CL1, which is a cantilever located at the end of the supported cantilever and is a virtual cantilever.
Here, in Non-Patent Document 1 and Non-Patent Document 2, in a measuring device using a resonator (cantilever), when a large number of resonators are weakly coupled, the sensitivity of the measuring device becomes higher as the number of resonators increases. It is stated that it can be done.

As described in Non-Patent Document 2, when the rigidity decreases (Δk <0), the amplitude ratio of the secondary mode is measured. On the contrary, when the rigidity increases (Δk> 0), the amplitude ratio in the primary mode is measured. Here, the case where the rigidity of the coupled model shown in FIG. 9 decreases will be described according to Non-Patent Document 1.
From the equation (13) of Non-Patent Document 1, the amplitude ratio of the first cantilever CL1 and the nth cantilever CLn in the secondary mode to the dimensionless rigidity change δ = Δk / k1 of the nth cantilever CLn is an2 ( The rate of change S2 (deviation from the amplitude ratio 1) is given by the following equation (20) (corresponding to the equation (13) of Non-Patent Document 1). In equation (20), αi has αi = mi / m1 (i = 2, ..., N), δ = Δk / k1, κ = kc / k1, and λp has n cantilever CL1 to CLn. It is a p-order eigenvalue in a measuring device provided with a vibrating part.

When there are two weakly coupled cantilever, the equation (20) can be expressed by the following equation (21).

Therefore, from the equation (20), it can be seen that the rate of change, that is, the sensitivity S2 is significantly improved when the following conditions are satisfied.
Condition 1 Increase the number n of cantilever as much as possible. That is, a large number of cantilever levers for improving sensitivity are provided.
Condition 2 αn = mn / m1 should be made as small as possible.
Condition 3 Each mass m2 to mn-1 of the cantilever CL2 to CLn-1 for improving the sensitivity is made larger than the mass m1 of the cantilever CL1.
Condition 4 The spring rigidity of each cantilever CL2 to CLn-1, that is, the spring constant k2 to kn-1, is made larger than the spring rigidity of the cantilever CL1, that is, the spring constant k1.

From the above, as shown in FIGS. 9 and 10, virtual cantilever CL2 to CLn-1 for improving sensitivity are provided between the virtual cantilever CL1 and the actual cantilever CLn, and the cantilever CL1 to CLn are vibrated in an coupled manner. It can be seen that the sensitivity is improved by increasing the number of.

Then, as shown in FIGS. 9 and 10, in the vibrating unit 1 according to the present embodiment, the virtual cantilever CL1 and the cantilever CL2 to CLn-1 for improving sensitivity are realized not as an actual cantilever but as a virtual cantilever. doing. Therefore, even if it is difficult to actually manufacture a plurality of cantilever, in the measuring device 100 according to the present embodiment, a virtual cantilever CL1 which is another cantilever other than the actual cantilever CLn and a cantilever for improving sensitivity are used. Since CL2 to CLn-1 are virtually simulated, it is possible to easily manufacture a high-sensitivity cantilever coupled with a large number of cantilever for improving sensitivity by manufacturing only the existing cantilever CLn. can. This is the most different point of this embodiment from Non-Patent Document 1 and Non-Patent Document 2. That is, while Non-Patent Document 1 and Non-Patent Document 2 assume that a large number of existing cantilever are coupled, it is technically difficult to manufacture, whereas this embodiment is an existing cantilever. Since only one cantilever is required, it is technically easy to manufacture. In the present embodiment, a virtual cantilever CL1 and a large number of cantilever CL2 to CLn-1 for improving sensitivity are "simulated", but in the present invention, an existing cantilever exists, and further, it is coupled. By combining an arithmetic processing device capable of executing the above with an existing cantilever, the performance superior to the known technology is realized, so that it does not correspond to the abstract concept.

Then, in the vibrating unit 1 according to the present embodiment, the cantilever CL2 to CLn-1 for improving the sensitivity is realized not as an actual cantilever but as a virtual cantilever. Therefore, it is easy to increase the number of cantilever simulated as the sensitivity improving cantilever, and the larger the number of cantilever to be coupled and vibrated, the more the sensitivity can be improved. In the techniques described in Non-Patent Document 1 and Non-Patent Document 2, the number of cantilever for improving sensitivity is limited to physical size, strength, cost, etc., and therefore cannot be increased endlessly.
Since the sensitivity can be easily improved in this way, even a physical quantity that could not be measured due to low sensitivity can be measured by improving the sensitivity as described above, and is easy to use. It can be improved and versatility can be increased.

Moreover, since the sensitivity can be easily improved in this way, even a lightweight substance or the like that could not be measured until now can be easily measured.
Further, as in the condition 2, the sensitivity is increased by making αn = mn / m1 as small as possible. Here, since m1 is the mass of the first object M1 possessed by the virtual cantilever CL1, in the present embodiment, the sensitivity can be improved as the mass m1 is virtually increased, and the sensitivity is easily improved. be able to. In the techniques described in Non-Patent Document 1 and Non-Patent Document 2, increasing the mass m1 is limited by physical size, strength, cost, and the like, and thus has a limit.

In the above embodiment, at least the natural frequencies of the virtual cantilever CL1 and the actual cantilever CLn need to be the same, but preferably, the spring rigidity of the cantilever CL2 to CLn-1 for improving the sensitivity is increased. It is preferably higher than the spring rigidity of the cantilever CL1 and CLn. Further, the cantilever CL2 to CLn-1 for improving the sensitivity does not necessarily have the cantilever CL2 to improve the sensitivity if the spring rigidity of the cantilever CL2 to CLn-1 for improving the sensitivity is higher than the spring rigidity of the cantilever CL1 and CLn. CLn-1s do not have to be the same material and shape, and may have different spring rigidity and mass.

It should be noted that the scope of the present invention is not limited to the illustrated and described exemplary embodiments, but also includes all embodiments that provide an effect equal to that of the object of the present invention. Moreover, the scope of the invention can be defined by any desired combination of specific features of all disclosed features.

1 Vibrating part 1A Cantilever (virtual vibrating body)
1B cantilever (actual vibrating body)
1C Support member 1D Overhang part 11 Actual vibrating body part 12 Arithmetic processing device 13 Drive circuit 14 Display device 21 Support member 21a Holding part 21b Guide part 22 Actuator 22a Shaft part 22b Support part 23 Displacement meter 100 Measuring device 100a Simulation device CL1 Virtual Cantilever CL2-CLn-1 Cantilever for improving sensitivity CLn Actual cantilever

Claims (10)

It is a measuring device that detects a value corresponding to a physical quantity to be measured by using the amplitudes of two vibrating bodies.
An actual real vibrating body as one of the two vibrating bodies and
An actuator that applies a force in a preset displacement direction to the actual vibrating body, and
A vibration displacement detection unit that detects the vibration displacement of the actual vibrating body,
The virtual vibrating body that is virtually coupled to the real vibrating body is simulated as the other one of the two vibrating bodies, and the virtual vibrating body and the vibration displacement detecting unit detect the above. An arithmetic processing device that executes coupled control processing that drives and controls the actuator based on the vibration displacement of the actual vibrating body, and
A measuring device characterized by being provided with. The measuring device according to claim 1, wherein the virtual vibrating body is represented by numerical information that simulates a physical model of the vibrating body coupled with the real vibrating body by a theoretical mathematical formula. The measurement according to claim 1 or 2, wherein the arithmetic processing device simulates the virtual vibrating body so that the natural frequency of the virtual vibrating body matches the natural frequency of the real vibrating body. Device. The arithmetic processing unit
A vibration velocity detection unit that detects the vibration velocity of the actual vibrating body,
A feedback control unit that drives the actuator with a feedback control signal,
With
The feedback control signal is
A linear displacement feedback component based on the difference between the vibration displacement of the actual vibrating body detected by the vibration displacement detecting unit and the vibration displacement of the virtual vibrating body simulated by the arithmetic processing device, and detected by the vibration velocity detecting unit. The measuring device according to any one of claims 1 to 3, further comprising a linear velocity feedback component based on the vibration velocity. The measuring device according to claim 4, wherein the feedback control signal includes a non-linear velocity feedback component in phase or antiphase with respect to the vibration velocity in order to suppress the amplitude of the actual vibrating body. The arithmetic processing device drives and controls the actuator, vibrates the actual vibrating body to acquire the resonance frequency at the resonance point, and sets information necessary for simulating the virtual vibrating body based on the acquired resonance frequency. The measuring device according to any one of claims 1 to 5, wherein the initial process is executed. The measuring device according to any one of claims 1 to 6, wherein the physical quantity is at least one of mass, surface shape, elastic modulus, viscoelasticity, and force field. .. In addition to the virtual vibrating body, the arithmetic processing device simulates another virtual vibrating body for improving sensitivity, which is virtually coupled between the virtual vibrating body and the real vibrating body. Claims 1 to 7, wherein a coupled control process for driving and controlling the actuator is executed based on the virtual vibrating body, the other virtual vibrating body for improving the sensitivity, and the vibration displacement. The measuring device according to any one item. The component for the measuring device according to any one of claims 1 to 8.
Real real vibrating body and
An actuator that applies a force in a preset displacement direction to the actual vibrating body, and
A vibration displacement detection unit that detects the vibration displacement of the actual vibrating body,
A component for a measuring device characterized by being provided with. The arithmetic processing unit for the measuring device according to any one of claims 1 to 7.
A measuring device characterized in that the vibration displacement of the actual vibrating body is used to simulate a virtual vibrating body that is virtually coupled to the actual vibrating body and to generate a signal for driving and controlling the actuator. Arithmetic processing device for.

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