JP2981465B1 - Method and apparatus for measuring moment of inertia - Google Patents

Abstract

An object of the present invention is to provide a method and an apparatus for measuring a moment of inertia which are easy to use and have extremely high measurement accuracy. Kind Code: A1 Abstract: A moment of inertia measuring device includes a rotating body on which an object to be measured can be detachably mounted, a torque detector for detecting torque applied around a rotating axis of the rotating body, and a torque detector around a rotating axis of the rotating body. A rotation angle detector 11 for detecting a rotation angle, rotation driving means 7, 8, 9, 10 for externally applying a rotational movement to the rotating body 4, a storage for storing a numerical calculation program for implementing the above method, and a torque A signal processing unit 22 including a processor for calculating the moment of inertia by executing the numerical calculation program based on the detection signals of the detector 3 and the rotation angle detector 11 and generating a drive signal for giving a desired angle change; An electric control device 20 having a motor driving unit 24 for driving the electric motor 7 as a driving means is provided.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for measuring the moment of inertia of a rotating part, in particular an electrical and mechanical rotating part, and to an apparatus for implementing the method.

[0002]

2. Description of the Related Art The moment of inertia of an electrical or mechanical component plays an important role in the dynamic motion characteristics of the electrical or mechanical component accompanying the rotary motion. For example, rotors of various electric motors, OA
It is important to correctly evaluate the moment of inertia around the rotation axis of disk drive mechanisms of equipment, video or audio equipment, and rotating parts of automobiles (brake disks, clutch plates, rotors of turbochargers, etc.). This also applies to mechanical parts with circular motion, such as robot arms. Furthermore, knowledge of the moment of inertia is also important in the design of exercise equipment, for example, the head of a golf club. Especially in a servo system using a motor as the drive source,
In order to correctly understand the response frequency characteristics of the whole system including this kind of rotating parts, it is extremely important to know the moment of inertia of the parts.

[0003] However, a practical device capable of measuring the moment of inertia accurately and with a simple operation has not yet been provided on the market. Therefore, when knowledge of the moment of inertia is required, the development designer of the device merely obtains the moment of inertia of the part in a laboratory as necessary. Rotational motion is given around the rotation axis of the rotating body directly connected to the object to be measured by using an appropriate rotation driving device, and the time t
The rotation angle θ (t) of the object around the rotation axis and the rotation torque m (t) are measured at

[Outside 4] Is obtained from equation (1). Therefore, if the torque M (t) and the rotational angular acceleration d ² θ (t) / d ² t at each time point t can be measured, the moment of inertia I can be obtained in principle. However, in practice, it is difficult to provide a rotational motion that maintains the rotational angular acceleration constant over a certain period, so that the torque and the rotational angle θ (t) or the rotational angular velocity dθ (t) / dt It is necessary to obtain a value, and to obtain the rotation angular acceleration, it is necessary to further differentiate the rotation angle or the rotation angular velocity with time. In such an operation, since the actual measured values of the torque and the rotation angle or the rotation angular velocity include unavoidable time fluctuations, only the moment of inertia whose measurement accuracy is significantly reduced is obtained.

In the case where the moment of inertia I needs to be measured with high accuracy, the rotation angle meter and the torque meter are separately calibrated in this system while the object to be measured is incorporated in a mechanism for giving a rotational movement. There is a need. This calibration needs to be performed relatively frequently, especially due to aging of both detectors.

[0005]

SUMMARY OF THE INVENTION An object of the present invention is to provide a method and a device for measuring the moment of inertia, which are easy to use and yet have extremely high measurement accuracy. Furthermore, it is desirable that the calibration of this measuring device be simple.

[0006]

SUMMARY OF THE INVENTION According to the present invention, a rotating body on which an object to be measured can be detachably mounted is rotated by a rotation driving mechanism, and the torque m (t) applied around the rotation axis is reduced. A detector, and a rotation angle θ (t) around the rotation axis is detected by a rotation angle detector, and a method of measuring the moment of inertia I _{x of the} object around the rotation axis, comprising the following steps: the first time point t _s and subsequent second time point t _e over the measurement period in the torque application period [t _s, t _e] full rotation angle Θ rotation body is rotated between the seek (t _s, t _e) Obtaining a torque m (t) corresponding to a number of time points t in the measurement period; double numerically integrating the obtained value of the torque m (t) with respect to the measurement period; values M (t _s, t _e) of the torque of the full rotation angle Θ (t _s, t _e) measuring at that time divided by A case of obtaining the moment of inertia, the object attached to the rotating body, not performed, respectively, the object to be measured from the moment of inertia I ₁ of the measuring system fitted with an object to be measured is mounted for when not worn Moment of inertia I of the measuring system
Moment of inertia I of the object to be measured by subtracting _0
x has been solved by

[0007] Further, the present invention provides a rotary body 4 for detachably mounting an object to be measured, a torque detector for detecting a torque applied around a rotation axis of the rotary body 3, A rotation angle detector 11 for detecting a rotation angle of the main body 4 about a rotation axis; a rotation drive means 7, 8, 9, 10, for applying a rotational movement to the rotation main body 4 from outside; A storage device for storing a numerical calculation program, a torque detector 3 and a rotation angle detector 11
A signal processing unit 22 including a processor for executing the numerical calculation program based on the detected signal to calculate the moment of inertia, and generating a drive signal for giving a desired angle change to drive the electric motor 7 of the rotary drive means The problem is solved by a moment of inertia measuring device comprising an electric control device 20, having a motor drive 24,

[0008] Other advantageous configurations according to the invention are set out in the dependent claims.

[0009]

DESCRIPTION OF THE PREFERRED EMBODIMENTS According to the above configuration of the present invention,
In the moment of inertia measuring device used, a torque detector and a rotation angle detector are incorporated in a rotating shaft for rotating a test piece, and a single rotating motion shown in FIG. 1 is applied to the rotating shaft by using an appropriate rotating drive means. . In particular, it is advantageous to select the rotational angular velocity dθ / dt so as to exhibit a half-period sine wave.

The measuring method according to the present invention is generally shown by mathematical expressions. First, three modes are used for measurement, and these modes are designated by symbols i = 0 to 2. That is, the 0th measurement mode (i = 0): Measurement in a no-load state where no test piece is mounted on the measurement system. The first measurement mode (i = 1): The state in which a test piece to be actually measured is mounted. Measurement 2nd measurement mode (i = 2): Measurement with a reference weight having a known moment of inertia attached. If it is desired to distinguish between the quantities described below with respect to these measurement modes, i = 0, 1 and 2 denote the 0th, 1st and 2nd measurement modes, respectively, with a subscript i indicating the corresponding quantity. To be added.

The rotational moment application period [t _A,
t _B] suitable period within _{[t s, t e] (} t A ≦ t s <t e
≦ t _B ) as a measurement period, and a double integral value M of the torque m (t) applied to the rotating shaft during the measurement period in the i measurement mode.
(t _s, t _e )

[Outside 5] Becomes Further, when the rotational angular acceleration d ² θ (t) / d ² t in Expression (1) is integrated twice, the value at that time corresponds to the angle し た at which the rotary shaft is actually rotated by the torque applied to the rotary shaft. Therefore, the angle theta that the rotating shaft is rotated during the measurement (t _s, t _e) is composed of Figure 1, theta and _{(t s, t e) =} Θ (t e) -Θ (t s) (3) .

Further, I ₀ is the moment of inertia of the measuring system under no load, I _x is the moment of inertia of only the test piece, and I _s
When the moment of inertia of the calibration weight only, the i moment of inertia I _i of the entire measurement system obtained in measurement _{mode, I i = I 0 + I} x δ i1 + I s δ i2 (i = 0, 1, 2) (4 ) It can be expressed as. Here, δ _ij is 1 when i = j, and is 0 when i ≠ j.

Further, when the equations (1) are double-integrated using the quantities defined above, the moment of inertia I in the i-th measurement mode is obtained.
_i is

[Outside 6] Can be expressed as

From the equation (4), the moment of inertia I _X of the test piece is given by

[Outside 7] Can be obtained as Here, since the measurement time does not always coincide with the measurement of I ₀ and I ₁ , to distinguish between them, a dash “′” symbol such as the first and last time points t _s ′ and t _e ′ of the measurement period of I ₁ is used. I attached.

In the calculation method so far, the rotation angle detector and the torque detector have been already calibrated, and the output signal of each detector indicates the absolute value of the corresponding amount. However, when actually producing the measurement system, it is necessary to calibrate the output signals of both detectors and the value of the actual detection amount. Next, this case will be described. Between the detection signal e _a (t) of the rotation angle detector and the actual rotation angle θ (t), and between the detection signal e _b (t) of the torque detector and the actually applied torque m
Assuming that the proportional coefficients between (t) are c _a and c _b , respectively, θ (t) = c _a · e _a (t) (7) m (t) = c _b · e _b (t) (8) It can be expressed as. Using the proportional coefficients c _{a and} c _b ,
Detection signal measurement period of e _b (t) of the double time integral value M of the torque m (t) by (2) a torque detector [t _s, t _e] in the double integration value E _b (t _s, Using t _e )

[Outside 8] It can be expressed as. At the same time, the total rotation angle Θ (t _s, t _e) the rotary body is actually rotated during the measurement _{period, Θ (t s, t e} ) = c a [e a (t e) -e a (t _{s)] ≡c a E a (} t s, a t _e) (10).

By substituting Equations (8) and (9) into Equation (5) for the 0th measurement mode and the 1st measurement mode, respectively _, the ratios K and C of the proportional coefficients c _{a and} c _b are obtained.

[Outside 9] Using,

[Outside 10] Becomes

Using equations (11) and (12), from equation (4), the moment of inertia I _x of the test piece is

[Outside 11] Can be obtained as Note that the display of the parameters t _{s and} t _e indicating the measurement period of E _{a and} E _b is omitted here for better visibility. Similar omissions are made in the following equations.

Similarly, the moment of inertia I _S known from the zeroth measurement mode and the second measurement mode is

[Outside 12] Can be obtained as Therefore, the known moment of inertia I _S , the detection signals E _a0 and E _a2 of the rotation angle detectors in both measurement modes, and the value E _{b0 obtained} by double time integration of the torque detector,
From E _b2, the ratio K of the proportionality coefficient is

[Outside 13] Can be obtained as Here, it should be noted that if a calibration weight is used, the value of K can be determined without actually measuring the values of the proportional coefficients c _a and c _b .

[0019]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention will be described below in more detail with reference to the drawings showing preferred embodiments.

In the moment of inertia measuring device whose main part is shown in FIG. 2, the test piece 1 is attached to one end of the rotating body 4 via the torque detector 3 in order to detect the torque applied to the rotating body 4. The chuck 2 is fixedly connected. The rotating body 4 is rotatably fixed to a gantry 6 via a bearing 5. The gantry 6 is fixed to a floor or a table (neither is shown) via a suitable support member (not shown). A pulley 8 is connected to the other end of the rotating body 4, and a rotor of a rotating angle detector 11 for detecting a rotating angle position of the rotating body is further connected to an axial end of the pulley 8. The main body 11 is fixed to a part of the gantry 6.

Further, an electric motor 7 is provided near the rotating body 4 of the gantry 6 for transmitting a rotating motion to the rotating body 4, and a pulley 9 is fixed to a tip of a shaft of the electric motor 7. I have. A belt 10 that transmits torque at an appropriate reduction ratio is stretched between the pulley 8 and the pulley 9.

Since the center axis of the rotary body 4 and the center axis of the chuck 2 are arranged concentrically, a torque can be applied around the center axis C ₀ of the test piece 1 as shown by an arrow. Accordingly, in this apparatus will measure the central axis C ₀ around the moment of inertia of the test piece 1. Furthermore, in order to perform calibration of the measurement system, no load, i.e. remove the test piece 1 from the chuck 2, nothing or state not mounted, the state of mounting a calibration weight having a known moment of inertia to the center axis C ₀ around realizable.

The torque sensor 3 is intended method for converting the amount of torque by detecting the amount twist elastic member beam being passed pointing axially C ₀ at both ends of the flanges, twist amount was attached to the beam It is detected using a strain gauge. The rotation angle detector 11 employs two magnetoresistive elements in series in a rotor part and has a permanent magnet built in a main body part.
A constant potential is applied to both ends of a series magnetoresistive element, and a relative rotation angle of the rotor can be detected from a voltage change at an intermediate tap.

As shown in FIG. 2, the attached electric control unit 20 of the moment of inertia measuring device comprises an arithmetic processing unit 22, a motor drive unit 24, an attached output display unit DSP, an input unit INH, and an output printing unit PRT. Have been. The input unit INH has function keys and numeric keys for designating a measurement mode (i = 0 to 2), designating the start of measurement, and inputting required input numerical values and the like, and designates or inputs all input commands with this unit. The results during or after the measurement can be sequentially displayed on the output display unit DSP, and the final measurement results can be printed out by the printer of the output printing unit PRT. The potential applied to the bridge of the strain gauges of the arithmetic processing unit 22 and the torque detector 3 and the input and output of the torque detection signal from the bridge are performed via the conductor L _1. extraction of the rotation angle detection signal from the application and the center tap of the bias current to the resistor element is performed via conductor L _2. The drive current of the motor is
Via conductors L ₃ are introduced to the electric motor 7, FIG. 1
Command signal S that gives the rotational angular acceleration d ² θ / dt ²
_c is determined by a command via the lead L ₄ from the storage device built in the arithmetic processing unit 22 program control signal introduced into the motor drive unit 24 (relative to the inverter circuit).

FIG. 3 shows a detailed circuit configuration of the arithmetic processing section 22 and the motor driving section 24. In the arithmetic processing unit 22, the conductor L
Detection signals of the torque sensor 3 that has been introduced through a ₁ is introduced into the first stage amplifier circuit A ₁ for the conversion filtering and impedance, the output signal sample and hold circuit via the SH analog-to-digital converter A / is input to the D _1. This digital detection signal is introduced into the central processing unit 26.
Similarly, the rotation angle detector 1 introduced via the conductor L ₂
The detection signal of _{No. 1} is introduced into the first-stage amplifier circuit A ₁ , and its output signal is converted into a digital detection signal by the analog / digital converter A / D ₁ and input to the central processing unit 26. Oscillator O
The frequency of the SC oscillation pulse is frequency-divided by a frequency divider DIV to an appropriate frequency and introduced into the sample-and-hold circuit SH via a lead L _S , and the sampling period is determined by the frequency-divided pulse period. Double time integrated value E _b relates to a torque stored once storage device all of the torque detection value obtained by sampling at regular time intervals e _b (t), calculated by integrating twice the detection value stored for the measurement period Is done. The central processing unit 26 has a first storage RAM for temporarily storing numerical values in the middle of calculation, a second storage RO for storing predetermined programs and numerical values and various mathematical expressions described above, and taking out and processing them as needed.
M, is one that is bus-connected, including an interface IO ₁ ~IO ₄ the microprocessor μP as a main unit. All of these elements or a plurality of specific sets can be used as a large-scale integrated IC.
FIG. 3 exemplifies this IC as reference numeral 26.

The motor drive unit 24 rectifies the commercial AC power, applies the output of the control circuit CTL to the collectors of the output transistors Tr ₁ and Tr ₂ and applies the output of the control circuit CTL to the bases of both transistors, and supplies a desired output current to the conductor L _3. Through the electric motor 7
Send to At this time, the control circuit CTL which plays a central role as a servomotor has an angular velocity dθ / d as shown in FIG.
t is to control the exciting current of the electric motor 7 so as to give a sine-wave-shaped rotation output having a substantially half cycle, and its output pattern is determined by a program numerical value stored in the storage ROM and an appropriate value designated by the input unit INH. It is supplied to the control circuit CTL by a conductive wire L ₄ by multiplying the a amplitude value. Furthermore,
The feedback monitoring signal introduced into the control circuit CTL, the detection signal S _I and the current applied to the motor, if necessary, the rotational position signal S _P and the rotational speed signal S _V is also introduced.

[0027] To determine the moment of inertia I _x of the test piece to be measured, which as previously described, the proportional coefficient of the detection sensitivity of the torque sensor 3 of the detection sensitivity of the proportionality coefficient c _a and the rotation angle detector 11 c _b is determined by some method (for example, the nominal value of the detection sensitivity of each detector of the manufacturer can be used), and these values and their ratio K (Equation (9)) are stored in the storage ROM in advance. Keep it. Further, the rotation speed by the rotation drive system is set so that the rotation speed is within the range of the optimum measurement value of the torque detector 3 according to the weight of the test piece. This usually requires several preliminary tests by trial and error.
After determining the optimum rotation speed, the zeroth measurement mode is executed to perform measurement in a no-load state, and the inertia moment I _{0 of the} system itself is measured.
Ask for. This I ₀ is stored in the storage ROM, and the measurement in the first measurement mode is executed, and the moment of inertia _IX of the test piece is obtained from the equation (12).

Furthermore, when it is desired to increase the measurement accuracy, using the reference weight of known moment of inertia I _S, obtained in advance the ratio K of the proportional coefficient from the second measurement value of the measurement mode by the formula (14) Is stored again in the storage ROM, and the measurement in the first measurement mode is performed using K at this time, and the equation (1)
2) Obtain the moment of inertia _IX of the test piece from.

FIG. 4 shows the time change of the signal waveform obtained in each measurement step. waveform indicated by α in the measured detection signal e _b corresponding to the torque, the noise signals to increase frequently sudden to the original torque signal is superimposed. Signal E _b obtained by integrating twice the time by the equation (7) the measured detection signal e _b is very smooth, it has been made smooth for time integration. Note that the signal _Eb is shown inverted in time for convenience of explanation. In addition, the command signal of the rotational angular velocity to be executed at this time is shown as γ. It can be seen that a considerable noise signal is also superimposed on this signal γ. In any case, the smoothing by the twice time integration has a much higher measurement accuracy than the method of directly obtaining the torque from the torque value and the twice differential value of the rotation angle from the equation (1). This is because the numerical differentiation process gives a large error if the difference is obtained from the value of the angle including the error. Performs calibration test the calibration weight having a known moment of inertia I _s, was measured accuracy can easily guarantee within 0.3% of the maximum measurable moment of inertia.

The above description has been made with reference to a preferred embodiment, and various modifications and improvements can be made. For example, a slide resistance potentiometer that does not use a magnetoresistive element as a rotation angle sensor, or a commercially available rotation angle sensor that photoelectrically detects a tooth row of a gear can be used. In addition, it is also possible to pulse-drive a rotation driving motor and directly obtain the rotation angle from the control pulse. in this case,
No rotation angle detector is required, and a control pulse is used as the rotation angle signal. Further, as the torque detector, a commercially available digital torque meter which directly photoelectrically detects the twist at different positions in the axial direction of the elastic member fixedly connected between the flanges at both ends may be adopted.

In addition, a method of sampling the rotation angle by the arithmetic processing unit 22 of the attached electric control device 20 may be introduced. In that case, it may be inserted sample and hold circuit between the first-stage amplifier A ₂ and the analog-digital converter A / D _2. Such a method facilitates the introduction of a safety circuit that detects abnormal rotation angles one by one. However, in any case, it goes without saying that all the methods and apparatuses for realizing the structure defined in the claims fall within the scope of the present invention.

[0032]

As described above, according to the method and the apparatus for measuring the moment of inertia according to the present invention, the operation in use is very simple, and the measurement accuracy of the moment of inertia is nevertheless extremely high. Furthermore, the detection system of this measuring device can be easily calibrated. In that case. The inertial moment of various shaped specimens can be measured with an accuracy of less than 0.3%. Therefore, the individual design and development and quality control of the rotating body in the rotating machine can be accurately and quickly performed by the measuring method and the apparatus according to the present invention.

[Brief description of the drawings]

Fig. 1 Rotational angle θ, rotational angular velocity dθ / dt (one dot is attached on θ) and rotational angular acceleration d ² θ / d ² t (two points on θ) Graph with time)

FIG. 2 is a block diagram of the entire measuring device,

FIG. 3 is a detailed circuit diagram of a motor control and arithmetic processing unit,

FIG. 4 is a graph illustrating an instantaneous value (α) of an actually measured torque, a total integrated value (β) obtained by double-time integration of the torque, and an instantaneous value (γ) of a rotation angle of a rotating body at that time.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Test piece 2 Chuck 3 Torque detector 4 Rotating main body 5 Bearing 6 Mount 7 Electric motor 8, 9 Pulley 10 Belt 11 Rotation angle detector 20 Electric control device 22 Arithmetic processing part 24 Motor drive part

Claims (4)

(57) [Claims] 1. A rotating body on which an object to be measured can be detachably mounted is rotated by a rotation driving mechanism, and a torque m (t) applied around a rotation axis is detected by a torque detector, and a rotation angle θ ( detecting each t) with the rotation angle detector, a method for measuring the moment of inertia I _x of the object about the rotation axis, the following process, the first time point t _s and subsequent in-torque application period the two time t _e over the measurement period [t _s, t _e] full rotation angle theta (t _s, t _e) the rotating body is rotated between the calculated torque corresponding to the number of time t in the measurement period m (t) the calculated numerically integrated double time value of-determined torque m (t) with respect to the measurement period, the value M (t _s, t _e) of, double-time integral torque full rotation the the angle Θ (t _s, t _e) by dividing by finding the moment of inertia of the measurement system at that time, to the rotary body In the case of mounting the body, performed respectively for the case where no attached, minus the inertia moment I ₀ of a measuring system not wearing an object to be measured from the moment of inertia I ₁ of the measuring system fitted with an object to be measured Is the moment of inertia I _{x of the} object to be measured. 2. A proportional coefficient c _a between the actual value θ (t) of the rotation angle and the value e _a (t) of the output signal of the rotation angle detector at that time, the actual value m (t) of the torque and the torque detection. The proportional coefficient c _b between the value e _b (t) of the output signal of the detector at that time is obtained, and the ratio K of both proportional coefficients is _expressed as follows. The measurement period [t _s, t
_e ] corresponds to a value obtained by integrating the detection signal E _a0 corresponding to the total rotation angle Θ (t _s, t _e ) of the rotating body and the value m (t) of the torque detection signal twice during this measurement period. To _{obtain the} double time integral values E _b0 to be measured, and with the object to be measured attached to the rotating body,
^{_{[t s ', t e'}} ] full rotation angle Θ of the rotating body in ^{_{(t s ', t e'}} )
A detection signal E _a1 which corresponds to the value of the torque detection signal m (t)
M (t _s ^′ _,
t _e ^′ ), and obtains the double time integral values E _b1 , respectively, and calculates the moment of inertia I _{x of the} object to be measured by The method of claim 1, wherein 3. Furthermore, the following process, with the moment of inertia I _s is fitted with a known reference weight to the rotating body, and the detection signal E _a2 corresponding to the rotation angle of the rotating body in the corresponding measurement period, the torque A double time integration value E _b2 corresponding to a value obtained by time integrating the detection signal twice with respect to the corresponding measurement period is obtained, and the ratio K of the proportionality coefficient is calculated as follows. 3. The method according to claim 2, wherein the value of K is used instead of the ratio of the proportionality factor K as defined in claim 2. 4. A rotating body (4) on which an object to be measured can be detachably mounted, a torque detector (3) for detecting a torque applied around a rotation axis of the rotating body (4), and a rotating body (4). A rotation angle detector (11) for detecting a rotation angle about a rotation axis of (1), a rotation driving means (7, 8, 9, 10) for externally applying a rotational movement to the rotation body (4); And a storage unit for storing a numerical calculation program for implementing the method according to any one of (1) to (3), and executing the numerical calculation program based on detection signals of the torque detector (3) and the rotation angle detector (11) to execute inertia A signal processing unit (22) including a processor for calculating a moment; and a motor drive unit (24) for generating a drive signal for giving a desired angle change to drive the electric motor (7) of the rotary drive means. Control device (20) Inertia measurement unit of an object, characterized in that it comprises a.