Calculation device and method

Abstract

To provide an arithmetic unit and a method capable of inexpensively realizing speedup and high precision of speed and acceleration operations.SOLUTION: An amount of displacement C and an atmospheric parameter inputted at first and second sampling intervals Δt, ΔT respectively are held by first and second latch circuits, a difference between the amount of displacement C held by the first latch circuit and the most recent amount of displacement C is calculated by a first addition / subtraction circuit, a difference between an atmospheric parameter α held by the second latch circuit and the most recent atmospheric parameter α is calculated by a second addition / subtraction circuit, the atmospheric parameter α held by the second latch circuit is multiplied by a difference in the amount of displacement C by a first multiplication circuit, and output of the first multiplication circuit and output of the second multiplication circuit are added by a second multiplication circuit step for multiplying the amount of displacement C held by the first latch circuit by the difference in the atmospheric parameter α by a second multiplication circuit, and an addition circuit.SELECTED DRAWING: Figure 2

Description

Technical Field

[0001] The present invention relates to an arithmetic device and method, and particularly to an arithmetic device and method using the interference phenomenon of laser light.

Background Art

[0002] In a machine tool equipped with a numerical control device (NC (Numerical Control) machine tool), not only the accuracy when moving to a designated position but also the ability to reach a designated speed are emphasized. Regarding the performance related to such speed, the moving amount of the NC machine tool is measured at a predetermined sampling interval, and the speed and acceleration are calculated from this displacement amount.

[0003] Generally, speed is obtained as the time derivative of the displacement amount, and acceleration is obtained as the time derivative of the speed. However, when actually measuring the displacement amount, since the measurement sampling interval is finite, it is impossible to calculate the derivative value in a strict sense. Therefore, generally, instead of differentiation, variation is used to calculate the speed and acceleration.

[0004] Assuming that the displacement amount, speed, and acceleration of the measurement object are X, V, and A respectively, and the measurement sampling interval is Δt, the speed V and acceleration A are obtained by the following equations.

[0005] V = {X(t + Δt) - X(t)} / Δt A = {V(t + Δt) - V(t)} / Δt

Prior Art Documents

Patent Documents

[0006]

Patent Document 1

Non-Patent Documents

[0007]

Non-Patent Document 1

[0008] However, as mentioned above, the calculation method using variational calculus presents the following problems.

[0009] First, since the refractive index of the atmosphere is affected by atmospheric parameters (e.g., temperature, pressure, and humidity), high-precision displacement measurements using laser interferometry require correction by multiplying the measured displacement by the ratio of the refractive index (or its reciprocal) (Edren's empirical formula; see Non-Patent Literature 1).

[0010] Typically, changes in atmospheric parameters are much slower than changes in displacement. Therefore, to reduce costs, the measurement rate of atmospheric parameters is generally lower than that of displacement. However, when calculating the derivative of measurements taken at different sampling intervals using the above formula, errors due to sampling timing (errors that are not meaningful as purely physical phenomena) occur.

[0011] Figure 4 shows an example where the sampling interval for the displacement amount C(t) of the object being measured is Δt, and the sampling interval for the atmospheric parameter α(t) is ΔT, with ΔT > Δt (ΔT = 3Δt).

[0012] As shown in Figure 4, if we keep the value of α(t) constant for the period until the next sampling timing and calculate the product αC, the change in αC becomes concentrated at the sampling timing of α. Furthermore, when calculating ΔαC, abnormal behavior occurs in accordance with the sampling timing of α.

[0013] Furthermore, even if the value of α(t) during the period until the next sampling timing is not kept constant during interpolation, the result of the ΔαC calculation may change depending on the interpolation method, or it may be influenced by values ​​other than the actually measured values. Also, if variational calculus is performed after interpolation, the mathematical relationship with differentiation disappears.

[0014] Next, one might consider using a moving average method to reduce randomly occurring measurement errors. For example, if we let the measured values ​​be x0, x1, ..., xn, ... and take a moving average of N points for velocity, the intermediate N-1 velocity values ​​will cancel each other out, as shown in the equation below. This is the same result as simply setting the sampling interval to NΔt, and does not reduce the error.

[0015]

number

[0016] Furthermore, the same result is obtained by taking the variation of the moving average.

[0017]

number

[0018] Next, there is a method of approximating velocity and acceleration using the least squares method (for example, Patent Document 1). Specifically, there is a method of approximating velocity from the slope of a straight line approximated by the least squares method from the displacement over a certain section. There is also a method of approximating acceleration from the coefficient of the quadratic curve approximated by the least squares method from the displacement over a certain section. Furthermore, there is a method of approximating acceleration from the coefficient of the quadratic curve. Moreover, the amount of calculation increases in proportion to the approximation interval (the number of measurements used in the least squares calculation).

[0019] As described above, realizing the functionality to determine velocity and acceleration values ​​with high accuracy requires a large amount of computation, resulting in long computation times and expensive configurations.

[0020] The present invention has been made in view of such circumstances, and an object thereof is to provide an arithmetic device and method capable of realizing high-speed and high-precision calculation of speed and acceleration at low cost.

Means for Solving the Problems

[0021] In order to solve the above problems, an arithmetic device according to a first aspect of the present invention includes a first latch circuit that holds a displacement amount C input at a first sampling interval Δt, a second latch circuit that holds an atmospheric parameter α input at a second sampling interval ΔT longer than the first sampling interval Δt, a first addition / subtraction circuit that calculates a difference between the displacement amount C held in the first latch circuit and the latest displacement amount C, a second addition / subtraction circuit that calculates a difference between the atmospheric parameter α held in the second latch circuit and the latest atmospheric parameter α, a first multiplication circuit that multiplies the difference between the atmospheric parameter α held in the second latch circuit and the displacement amount C, a second multiplication circuit that multiplies the difference between the atmospheric parameter α and the displacement amount C held in the first latch circuit, and an addition circuit that adds the outputs of the first multiplication circuit and the second multiplication circuit to calculate a time derivative of the product of the displacement amount C and the atmospheric parameter α.

[0022] The calculation method according to the second aspect of the present invention includes: a step of holding a displacement amount C input at a first sampling interval Δt by a first latch circuit; a step of holding an atmospheric parameter α input at a second sampling interval ΔT longer than the first sampling interval Δt by a second latch circuit; a step of calculating, by a first addition / subtraction circuit, a difference between the displacement amount C held in the first latch circuit and the latest displacement amount C; a step of calculating, by a second addition / subtraction circuit, a difference between the atmospheric parameter α held in the second latch circuit and the latest atmospheric parameter α; a step of multiplying, by a first multiplication circuit, the atmospheric parameter α held in the second latch circuit and the difference in the displacement amount C; a step of multiplying, by a second multiplication circuit, the displacement amount C held in the first latch circuit and the difference in the atmospheric parameter α; and a step of calculating, by an addition circuit, a time derivative of the product of the displacement amount C and the atmospheric parameter α by adding the outputs of the first multiplication circuit and the second multiplication circuit.

Advantages of the Invention

[0023] According to the present invention, a variation that maintains the mathematical properties of differentiation is used, and it is possible to achieve high-speed and high-precision calculation of speed and acceleration at a low cost.

Brief Description of the Drawings

[0024] [Figure 1] FIG. 1 is a diagram showing a measuring device according to an embodiment of the present invention. [Figure 2] FIG. 2 is a diagram showing a first example of a hardware configuration for performing a differential operation in an arithmetic unit. [Figure 3] FIG. 3 is a diagram showing a second example of a hardware configuration for performing high-speed least-squares speed approximation and least-squares acceleration approximation in an arithmetic unit. [Figure 4] FIG. 4 is a diagram for explaining the influence of sampling timing on a variation operation.

Modes for Carrying Out the Invention

[0025] Hereinafter, embodiments of the computing device and method according to the present invention will be described with reference to the attached drawings.

[0026] [Measuring device] Figure 1 shows a measuring device according to one embodiment of the present invention.

[0027] As shown in Figure 1, the measuring device 10 according to this embodiment includes a laser light source 12, an interferometer 14, and a corner cube prism 16. In the following description, a three-dimensional Cartesian coordinate system is used in which the direction parallel to the optical axis of the laser beam L0 is defined as the X direction, and the direction parallel to the perpendicular direction is defined as the Y direction.

[0028] The corner cube prism 16 is an example of a retroreflector that reflects incident light parallel to and in the opposite direction to the direction of incidence (retroreflection). Specifically, the corner cube prism 16 is formed by combining three flat plates that have the property of reflecting laser light at right angles to each other to form part of a cube. The image of the reflected light retroreflected by such a corner cube prism 16 is an inverted image of the incident light. Note that in Figure 1, the reflective surfaces of the corner cube prism 16 are simplified to show only two surfaces.

[0029] The corner cube prism 16 is attached to the object to be measured and is installed to be movable in the linear axis direction (direction of the white arrow in the diagram).

[0030] Here, the linear axis refers to the axis parallel to the geometrically correct straight line of the linear shape of the object being measured.

[0031] In this embodiment, an example is described in which the displacement is measured by installing the interferometer 14 on the fixed part and the corner cube prism 16 (reflecting mirror) on the moving part. However, it is also possible to measure the displacement by installing the corner cube prism 16 (reflecting mirror) on the fixed part and the interferometer 14 on the moving part.

[0032] The laser light source 12 includes, for example, a He-Ne laser tube and emits laser light L0 in the +X direction having a polarization component perpendicular to the plane of the paper in Figure 1. In the following explanation, polarization perpendicular to the plane of the paper is called "vertical polarization," and polarization horizontal to the plane of the paper is called "horizontal polarization." In the figure, vertically polarized laser light may be shown with an arrowhead, and horizontally polarized laser light may be shown with a double arrow.

[0033] The quarter-wave plate 18 is an optical element containing a birefringent material, which creates a 90° phase difference between two mutually orthogonal polarization components. The quarter-wave plate 18 is positioned with its anisotropic axis tilted at 45° with respect to the plane of the paper. Therefore, the longitudinally polarized laser light L0 that passes through the quarter-wave plate 18 becomes circularly polarized laser light, that is, laser light that is a combination of longitudinally and transversely polarized light.

[0034] The Polarizing Beam Splitter (PBS) 20 is an optical element designed to transmit one polarization component of incident light, which is a mixture of two mutually orthogonal polarization components, while reflecting the other polarization component by a dielectric multilayer coating. Of the circularly polarized laser light L0, the transversely polarized component (first polarization component) of the laser light L1 passes through the polarizing beam splitter 20 and travels in a straight line, while the longitudinally polarized component (second polarization component) of the laser light L2 is reflected (bent) by the dielectric multilayer coating of the beam splitter at a 90° angle to the optical axis. Hereinafter, the longitudinally polarized laser light L2 reflected by the polarizing beam splitter 20 will be referred to as the "reference light".

[0035] The transversely polarized laser light L1, which has passed through the polarizing beam splitter 20 and traveled in a straight line, exits the interferometer 14, is reflected by the corner cube prism 16 installed on the object to be measured, and returns to the interferometer 14. Hereafter, the transversely polarized laser light L1 that has returned to the interferometer 14 will be referred to as the "measurement light".

[0036] The unpolarized beam splitter (hereinafter referred to as the beam splitter) 22 is an optical element manufactured to transmit 50% of the incident light and reflect 50%. The measurement light L1 transmitted through the beam splitter 22 and the reference light L2 reflected by the beam splitter 22 are combined by the beam splitter 22. Hereinafter, the combined light obtained by combining the measurement light L1 transmitted through the beam splitter 22 and the reference light L2 reflected by the beam splitter 22 will be called "composite light".

[0037] Note that the measurement light L1 reflected by the beam splitter 22 and the reference light L2 (the component directed towards the X in the figure) transmitted through the beam splitter 22 are not used.

[0038] The combined light, synthesized via beam splitter 22, is split by beam splitter 24. In the combined light split by beam splitter 24, the polarization and synthesis state are maintained in the same state as before synthesis.

[0039] The combined light L3a that passes through the beam splitter 24 passes through the polarizing plate 26 and is received by the photodetector 28. The combined light L3b reflected by the beam splitter 24 is reflected by the mirror 30, passes through the quarter-wave plate 32 and the polarizing plate 34 and is received by the photodetector 36.

[0040] Polarizing plates 26 and 34 are optical elements manufactured to transmit light only in a specific direction (transmission axis) and block light in the other direction. When two polarized lights are incident at 45° different angles relative to the transmission axis, the sum of the two lights is transmitted.

[0041] The light-receiving elements 28 and 36 are optical elements for obtaining the intensity of the interference light of the combined light L3a and L3b, respectively, and output electrical signals (voltages) corresponding to the intensity of the combined light L3a and L3b. The light-receiving elements 28 and 36 are, for example, photodiodes.

[0042] The speed axis of the quarter-wave plate 32 is positioned perpendicular to the plane of the paper. Therefore, of the composite wave L3b that passes through the quarter-wave plate 32, only the transversely polarized light becomes light with a 90° phase delay.

[0043] The transmission axes of polarizers 26 and 34 are positioned at a 45° angle to the plane of the paper. The composite wave L3a entering polarizer 26 has no phase shift, so the sum of vertical and horizontal polarization is output. Therefore, the photodetector 28 outputs a voltage equal to the intensity of the sum of vertical and horizontal polarization. On the other hand, the composite wave L3b entering polarizer 34 has horizontal polarization that is 90° behind in phase, so the sum of vertical polarization and horizontal polarization that is 90° behind in phase is output. Therefore, the photodetector 36 outputs a voltage equal to the intensity of the sum of vertical polarization and horizontal polarization that is 90° behind in phase.

[0044] For the photodetector 28, the intensity increases when the optical path difference between vertically polarized and transversely polarized light is an integer multiple of the wavelength, and decreases in between. In other words, a voltage is output that has a sinusoidal relationship with respect to the optical path difference.

[0045] On the other hand, for the photodetector 36, the intensity increases when the distance obtained by adding 1 / 4 of the wavelength to the optical path difference between the vertically polarized and horizontally polarized light coincides with an integer multiple of the wavelength, and decreases in the intermediate range. In other words, a voltage is output that has a cosine function relationship with respect to the optical path difference.

[0046] As described above, the output of the photodetector 28 is a voltage that has a sinusoidal relationship with respect to the optical path difference. If the object to be measured is located at the optical path difference where the sinusoidal wave is at its maximum or minimum value, the light intensity will decrease regardless of the direction of movement. Therefore, the photodetector 28 alone cannot determine which direction the object has moved from this position.

[0047] In this embodiment, the light-receiving element 36 acquires a signal that is a sinusoidal wave with a phase difference of 90°, so it is possible to determine which direction of movement has occurred even using the maximum and minimum optical path difference of the light-receiving element 28.

[0048] The outputs (interference signals) A1 and A2 from the photodetectors 28 and 36 are input to the interpolator circuit 38 of the calculation unit 40. The interpolator circuit 38 outputs a counter value representing the interference signal (a counter value indicating how many times the wavelength the object being measured has moved).

[0049] [Hardware Configuration 1] Figure 2 shows a first embodiment of the hardware configuration for performing differential operations in the arithmetic unit.

[0050] When measuring displacement using the measuring device 10 described above, the wavelength of the laser light is affected by the refractive index of the atmosphere, particularly atmospheric parameters (e.g., atmospheric temperature, pressure, and humidity). Therefore, in order to measure the displacement with high accuracy, it is necessary to correct the displacement obtained by the measuring device 10 by multiplying it by the ratio of the refractive index (or its reciprocal) (Edren's empirical formula; see Non-Patent Literature 1). In this example, the hard wafer configuration involves multiplying the displacement obtained by the measuring device 10 by the atmospheric parameters and then differentiating the result with respect to time.

[0051] Hereinafter, let C(t) be the displacement of the object being measured, and α(t) be the atmospheric parameter. If we define equation (1), obtained by differentiating the product of C and α (α×C) with respect to time (t), as a variation, we obtain equation (2).

[0052] x(t)=d(α×C) / dt=α×dC / dt+C×dα / dt …(1) x(t) = variation(α×C) = α×ΔC / Δt + C×Δα / ΔT …(2) In equation (2), Δt is the sampling interval for the displacement amount C(t) of the object being measured (first sampling interval), and ΔT is the sampling interval for the atmospheric parameter α(t) (second sampling interval). Here, Δt and ΔT are different, and Δt < ΔT.

[0053] As shown in Figure 2, the calculation unit 50 receives the displacement amount C(t) at a sampling interval Δt. The latch circuit (first latch circuit) 52 of the calculation unit 50 holds the displacement amount C(t) that was input at a sampling interval Δt.

[0054] Meanwhile, the calculation unit 60 receives atmospheric parameters α(t) at a sampling interval ΔT. The latch circuit 62 (second latch circuit) of the calculation unit 60 holds the atmospheric parameters α(t) that were input at a sampling interval ΔT.

[0055] The addition / subtraction circuit (first addition / subtraction circuit) 54 calculates the difference between the displacement amount C(t) held in the latch circuit 52 and the latest displacement amount C(t) input at the sampling interval Δt.

[0056] The multiplier circuit (first multiplier circuit) 56 multiplies the output of the adder / subtractor circuit 54 by the atmospheric parameter α(t) held in the latch circuit 62. This yields the first term of equation (2).

[0057] Similarly, the addition / subtraction circuit (second addition / subtraction circuit) 64 calculates the difference between the atmospheric parameter α(t) held in the latch circuit 62 and the latest atmospheric parameter α(t) input at the sampling interval ΔT.

[0058] The multiplier circuit (second multiplier circuit) 66 multiplies the output of the adder / subtractor circuit 64 by the displacement amount C(t) held in the latch circuit 52. This yields the second term of equation (2).

[0059] Next, the adder circuit 70 adds the outputs of the multiplier circuits 56 and 66. This completes the calculation of x(t) = variation(α × C), i.e., the velocity.

[0060] Furthermore, by inputting the variation (α × C) again into the hardware configuration related to this example, acceleration calculations can be performed.

[0061] As this example demonstrates, by using variational calculus that maintains the mathematical properties of differentiation, it is possible to prevent errors caused by sampling timing (errors that have no meaning as purely physical phenomena).

[0062] Furthermore, this example demonstrates that it is possible to achieve high accuracy in measured values ​​inexpensively using a circuit that includes a small number of latch circuits, addition / subtraction circuits, and multiplication circuits.

[0063] In this example, since speed and acceleration can be measured in a measuring device that utilizes the interference phenomenon of laser light, it is possible to establish performance evaluation criteria using speed and acceleration to evaluate the performance degradation of machine tools and the like over time.

[0064] In this embodiment, the atmospheric parameter α(t) was given as an example of a parameter to be multiplied by the displacement amount C(t), but the present invention is not limited to this. This example can also be applied when multiplying the displacement amount C(t) by other coefficients with different sampling rates (for example, coefficients related to thermal expansion).

[0065] [Hardware Configuration 2] Figure 3 shows a second embodiment of a hardware configuration for performing least-squares velocity approximation and least-squares acceleration approximation at high speed in the calculation unit.

[0066] The hardware configuration in this example calculates Pi, which is proportional to the displacement after filtering; Qi, which is proportional to the velocity after filtering; and Ri, which is proportional to the acceleration after filtering. Pi is proportional to the displacement of the most recent N samples; Qi is proportional to the slope of the linear approximation of the displacement of the most recent N samples; and Ri is proportional to the quadratic coefficient of the quadratic approximation of the displacement of the most recent N samples.

[0067] If the calculations are performed according to the formula for calculating the above parameters, the computational complexity is large, and the computational complexity increases proportionally to the filter interval.

[0068] In contrast, the hardware configuration in this example can achieve the above calculations using only decimal latch circuits (80, 82, 84, 88, 98, and 108), addition and subtraction circuits (86, 96, and 106), and constant multiplication circuits (90-94 and 100-104).

[0069] The filtering of displacement, velocity, and acceleration using the least squares method is expressed by the following equation. Let x1, x2, ... be the series of displacement data, Δt be the sampling interval (equal intervals), and N be the filter length.

[0070] Given a data series of displacements x0, x1, x2, ..., a sampling interval of Δt (equal intervals), and a filter width of N, the i-th displacement, velocity, and acceleration are obtained by the following formulas.

[0071]

number

[0072] In this case, the sequence {Pi}i, {Qi}i, {Ri}i can be expressed by the following recurrence relation.

[0073]

number

[0074] As shown in Figure 3, this example demonstrates that the accuracy of measurements obtained by filtering (calculation of filtered displacement, filtered velocity, and filtered acceleration) can be achieved quickly and inexpensively.

[0075] Furthermore, the doubling circuit 90 in the circuit can be replaced with a single bit shift circuit, and the tripling circuit 100 can be replaced with a single bit shift and a single adder circuit, thus enabling the creation of faster and cheaper circuits.

[0076] Furthermore, if we restrict N to powers of 2, then 1 / 2 × (N 2 The +N) multiplication circuits 102 and 104 can also be replaced with two bit shifts and one adder, thus enabling the creation of even faster and cheaper circuits. [Explanation of symbols]

[0077] 10... Measuring device, 12... Laser light source, 14... Interferometer, 16... Corner cube prism, 38... Interporator circuit, 40... Calculation unit, 50, 60... Calculation unit, 52, 62... Latch circuit, 54, 64... Addition / subtraction circuit, 56, 66... ​​Multiplication circuit, 70... Addition circuit

Claims

1. A first latch circuit that holds the displacement amount C input at a first sampling interval Δt, A second latch circuit that holds atmospheric parameters α input at a second sampling interval ΔT which is longer than the first sampling interval Δt, A first addition / subtraction circuit that calculates the difference between the displacement amount C held in the first latch circuit and the latest displacement amount C, A second addition / subtraction circuit calculates the difference between the atmospheric parameter α held in the second latch circuit and the latest atmospheric parameter α, A first multiplication circuit multiplies the atmospheric parameter α held in the second latch circuit by the difference in the displacement amount C, A second multiplier circuit multiplies the displacement amount C held by the first latch circuit by the difference of the atmospheric parameter α, An adder circuit that adds the outputs of the first multiplier circuit and the second multiplier circuit to calculate the time derivative of the product of the displacement amount C and the atmospheric parameter α, A computing device equipped with the following features.

2. The first latch circuit holds the displacement amount C input at a first sampling interval Δt, The second latch circuit holds the atmospheric parameter α input at a second sampling interval ΔT that is longer than the first sampling interval Δt, The first step is to calculate the difference between the displacement amount C held in the first latch circuit and the latest displacement amount C using the first addition / subtraction circuit. The steps include: calculating the difference between the atmospheric parameter α held in the second latch circuit and the latest atmospheric parameter α using the second addition / subtraction circuit; The first multiplication circuit performs the step of multiplying the atmospheric parameter α held in the second latch circuit by the difference in displacement C, The second multiplication circuit performs the step of multiplying the displacement amount C held by the first latch circuit by the difference of the atmospheric parameter α, The steps include: adding the outputs of the first multiplier circuit and the second multiplier circuit using an adder circuit to calculate the time derivative of the product of the displacement amount C and the atmospheric parameter α; A calculation method comprising the following features.

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