Method for determining the variable rotation index of an eccentric rotor

Abstract

To calculate a more accurate moment of inertia or friction torque, a variable rotation index, and a bearing friction index with good accuracy.SOLUTION: Assuming that a rotation angle at analysis start time is θ1 and a rotational angular velocity at the time is ω1, a rotation angle θ from the start of measurement, ω12 which is the square of the rotational angular velocity ω1 at analysis start time, and a [-2Tfm / I] which is an average bearing friction index are substituted in the formula below to find the value of E. (Formula 11). The value of [ω2-E] which is a difference between the square of an instantaneous rotational angular velocity ω and the value of E is calculated, and [ω2-E+C] derived by introducing the value of C into the difference value so that the variation center of the difference becomes 0 is approximated using a trigonometric function -A sin(θ+θ0) of an amplitude A regarding the rotation angle θ from the start of measurement. (Formula 9). The value of amplitude A obtained from the trigonometric function approximation of the amplitude A based on the above formula is determined to be the variable rotation index A of an eccentric rotor, and a phase difference θ0 is determined.SELECTED DRAWING: None

Description

[Technical field]

[0001] The present invention relates to a method for determining the gravity of an eccentric rotor, the fluctuation rotation index of the moment of inertia and an index representative of bearing friction from rotational angular velocity measurements. [Background technology]

[0002] In rotating machines such as engines, turbines, and motors, as well as wheels and tires, the moment of inertia is an important physical quantity that affects performance. Measurement of friction is also necessary. Although the moment of inertia can be calculated from design drawings due to advances in CAD, it is not measured despite its importance. In addition, for rotating machines for which design drawings are not available, such as rotating machines made by third parties, the moment of inertia cannot be obtained unless it is actually measured. Therefore, there is a high demand for a versatile method of measuring the moment of inertia for comparing the performance of rotating machines. One method of measuring the moment of inertia is to attach a weight to a string wrapped around a rotating body, measure the time it takes for the weight to fall using a stopwatch, etc., and estimate the moment of inertia from the measured time, but this method makes it difficult to measure the falling situation. In addition, friction of the bearings causes measurement errors and makes it difficult to measure accurately.

[0003] Friction tests are one of the performance evaluation tests for bearings used in rotating machines such as engines, turbines, and motors. In friction tests, the torque (friction torque) of structures such as rotating shafts and bearings during rotation is measured. Conventional friction tests use strain gauges to measure the strain of these structures and calculate the friction torque from this strain. However, strain gauges have low sensitivity to stress caused by minute torques such as friction. In addition, the zero point is easily shifted by residual strain, and errors are easily generated by strain associated with deformation caused by vibrations and shocks that occur in structures such as shafts and bearings during friction measurement. In addition, some commercially available torque meters use optical systems to measure minute torsional deformations of the shaft, but these are not suitable for measuring minute torques.

[0004] As a method for solving the above problems in measuring the moment of inertia, a method has been proposed in which a weight is attached to a string wrapped around a rotating body and the time it takes for the weight to fall is measured using a phototransistor signal (see Patent Document 1). This method allows for highly accurate time measurement.

[0005] As a method for solving the problems in friction measurement described above, a method has been proposed in which a rotating body supported by a bearing is rotated steadily, then made to rotate by its own inertia, and the friction torque is calculated from the relationship between the time from the start point of free-running to the stop point and the rotation angle of the rotating body (see Patent Documents 2 and 3).

[0006] The essential problem with the method of dropping a weight attached to a string wrapped around a rotating body is that friction occurs between the rotating body and the bearing that supports the rotating body, and this friction changes depending on the speed at which the body is dropped. The method in Patent Document 1 does not solve the above problem, and the estimated value of the moment of inertia based on the measured drop time is affected by friction. In the methods of Patent Documents 2 and 3, friction torque is calculated with constant friction resistance regardless of the rotational angular velocity or angular acceleration of the rotating body, but the shear resistance of the lubricating oil film in the bearing is proportional to the speed due to the viscous nature of Newtonian fluid. Therefore, when the rotational angular velocity or rotational angular acceleration of the rotating body changes and the relative speed between the shaft and the bearing changes, the shear resistance of the lubricating oil film changes, and the frictional resistance changes accordingly. Since the above methods do not take such changes in frictional resistance into account, it is not possible to measure the friction torque with high accuracy.

[0007] In contrast, Patent Document 4 describes a method in which a rotating body supported rotatably on a bearing to be measured is rotated by applying a rotational torque to the rotating body, and then the change in the rotational angular velocity during free-running rotation of the rotating body when the application of the rotational torque is stopped, i.e., the rotational angular acceleration, is calculated, and the friction torque is calculated from the rotational angular acceleration and the inertia moment of the rotating body. Patent Document 4 also describes a method for measuring the inertia moment from the rotation fluctuation when the rotating body is an eccentric mass. In the method described in Patent Document 4, an eccentric weight whose inertia moment, mass, and center of gravity position are known is added to a rotating body whose inertia moment is unknown to form a rotating assembly, and the inertia moment of this rotating assembly is measured. Then, the measured inertia moment is divided by the known inertia moment of the eccentric weight to calculate the inertia moment of the rotating body, and at the same time, the friction torque corresponding to the instantaneous rotation speed of the rotating body is calculated. In other words, in this method, the inertia moment and the friction torque are measured simultaneously. The method of Patent Document 4 utilizes rotational fluctuation and damping to measure friction torque, which is a cause of error in moment of inertia measurement, in accordance with the situation, and is therefore an advanced, highly accurate measurement method that directly and simultaneously resolves the error causes of Patent Documents 1 to 3. [Prior art documents] [Patent documents]

[0008] [Patent Document 1] Japanese Patent Publication No. 53-148487 [Patent Document 2] Japanese Patent Application Publication No. 11-142263 [Patent Document 3] Japanese Patent Application Publication No. 11-241957 [Patent Document 4] JP 2014-157159 A Summary of the Invention [Problem to be solved by the invention]

[0009] In the method described in Patent Document 4, an optical or inductance type rotation angle detection device (rotary encoder) measures the relationship between the rotation angle of a rotating body and time, and calculates the rotation angular velocity and rotation angular acceleration from the measurement results, or determines the rotation angular velocity of a rotating body using measurements from an optical tachometer, a magnetic tachometer, and a speedometer using the Doppler effect, and determines the rotation angular acceleration from the change in the data sampling time interval and the rotation angular velocity. The above-mentioned rotation angle detection devices, tachometers, and speedometers measure the rotation angle and rotation angular velocity without contacting the rotating body, so that the effects of vibrations and shocks generated in structures such as shafts and bearings can be eliminated.

[0010] The method described in Patent Document 4 is physically and mathematically perfect when the rotation angle and time measurements are performed without error, but has real problems in engineering and technology, such as manufacturing errors and measurement errors. The rotation angular acceleration is calculated from the relationship between the rotation angle and time, or the measurement results of the rotation angular velocity. In this case, the errors contained in the relationship between the rotation angle and time or the measured value of the rotation angular velocity are amplified when calculating the numerical difference when calculating the rotation angular acceleration. In the method described in Patent Document 4, it has been clarified by experiment that the manufacturing error (or angular velocity measurement accuracy) of the rotary encoder should be within ±0.02% of the rotation angle to be measured, and in order to accurately determine the moment of inertia and friction torque of the rotating body, it is necessary to keep the error in the original measurement within 0.02%. However, there is a problem in that it is practically impossible to keep the manufacturing error within this range with an inexpensive rotary encoder with a measurement angle interval of 1°.

[0011] Although the explanation has been given here with an example of determining the moment of inertia of a rotating body and the friction torque of a bearing, the same problem exists when determining values ​​related to rotation fluctuations (center of gravity, gravity), such as the formula for calculating the moment of inertia of a rotating body and the friction torque, and the coefficients included in the formula. In this specification, the values ​​related to the moment of inertia of a rotating body and the bearing friction are referred to as the fluctuation rotation index and the bearing friction index.

[0012] The problem that the present invention aims to solve is to obtain a more accurate moment of inertia, friction torque, variable rotation index, and bearing friction index with high accuracy by a robust calculation formula and data processing method that do not use angular acceleration for the manufacturing error of a rotation angle detection device (rotary encoder). In addition, while Patent Document 4 sets the measurement division angle to the small side of 15° or less, the aim is to set this to 1° or even smaller values, and to present a calculation formula and data processing method that are robust against the influence of an increase in the manufacturing error rate, as well as a convenient calculation method that automatically processes data such as the experiment (measurement) start trigger (z-phase pulse of the rotary encoder) and the mounting direction of the eccentric mass (angle from the horizontal of the center of gravity direction of the eccentric mass when the z-phase pulse of the rotary encoder is generated). This eliminates the need for precision adjustment during device assembly, significantly shortening the work time and labor required for adjustment, and is also convenient for data analysis after the experiment. [Means for solving the problem]

[0013] In order to solve the above problems, the method for determining a bearing friction index according to the present invention comprises the steps of: Rotating the eccentric rotor by applying a rotational torque to the eccentric rotor that is rotatably supported by the bearing to be measured; Stopping the application of the rotational torque, and sequentially measuring a rotation time Δt [s] or a speed per unit angle Δθ [rad] of the eccentric rotor from a measurement start, which is an arbitrary time point after the start of rotation of the eccentric rotor by self-propelled rotation, until the eccentric rotor rotates J (J is an integer), A method for determining an index representing bearing friction (bearing friction index) by sequentially determining a rotation angle and a rotation angular velocity during J rotations of the eccentric rotor from the unit angle Δθ [rad] and the rotation time Δt [s], or from the unit angle Δθ [rad] and the speed, The rotation time Δt [s] is measured n times (n = 2π / Δθ, n is an integer) while the eccentric rotor makes one rotation. The number of measurements 2Jπ / Δθ until the eccentric rotor makes J rotations is 2Jπ / Δθ. The rotation angle at the start of the analysis of the measurement is θ1 [rad], the rotation angular velocity at that time is ω1 [rad / s], and the rotation angle immediately after the jth measurement is θ j+1 [rad], and the rotational angular velocity at that time is ω j+1 [rad / s], and the rotational angular velocity immediately after k rotations (k is an integer) from the start of the analysis is ω nk+1 [rad / s], and the average friction torque of the bearing is T fm When the moment of inertia of the eccentric rotor is I, The rotation angle θ j+1 [rad] is calculated using the following formula:

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[0014] In the above-mentioned bearing friction index determination method, when k=1, the average bearing friction index and the average rotational angular velocity are respectively expressed by the following equations.

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[0015] In the above-described bearing friction index determination method, the instantaneous bearing friction index based on the instantaneous rotation angular velocity can be obtained from an approximation formula that expresses the relationship between the average bearing friction index and the average rotation angular velocity in each divided measurement section. Specifically, the average bearing friction index [-2T fm / I] is the average rotational angular velocity ω m Expressing this as an approximate function of the instantaneous bearing friction index [-2T f / I] and angular velocity ω. In other words, if the approximation formula is the function Func, T fm = Func(ω m ) When T f = Func(ω) It can be expressed as:

[0016] In the above-mentioned method for measuring the bearing friction index, the word "sequentially" in "sequentially measure", "sequentially obtain" and "sequentially calculate" means "for each unit angle". Therefore, when measuring the rotation time per 1° of the rotation angle of the eccentric rotor while the eccentric rotor rotates by self-propelled rotation, the rotation angular velocity, [-2T fm / I] is also calculated from the value of the rotational angular velocity for each 1° of rotation angle and the value of the rotational angular velocity one rotation ahead. For J rotations, the calculation interval is moved every 1° from the first calculation, and (J-1) × 360 [-2T fm / I] and ω m The following calculation is required:

[0017] The eccentric rotor refers to a rotor whose center of gravity is not located on the central axis of rotation. The eccentric rotor can be composed of a shaft whose center of gravity is located on the central axis of rotation and which is rotatably supported by a bearing, and an eccentric weight attached to the shaft whose center of gravity is not located on the central axis of rotation.

[0018] If the size, weight (mass) and center of gravity of the eccentric rotor are known, the moment of inertia I of the eccentric rotor can be calculated. fm / I] and ω m From the approximate equation obtained from the graph showing the relationship between the average friction torque T fm can be calculated. In addition, as shown in Figures 9 to 11, from the relationship between the average angular velocity per revolution and the average friction, we calculated the friction based on the angular velocity that changes for every small rotation angle (1° in this case), and compared the instantaneous value with the one-revolution average value, and confirmed that there is no numerical problem in considering the one-revolution average value as the instantaneous value. From this, we inductively determined that the one-revolution average [-2T fm / I] and ω m and the instantaneous [-2T f / I] and ω. In other words, the approximation formula and the coefficients included in this approximation formula, [-2T f The relationship between the value of [I] and ω corresponds to the bearing friction index.

[0019] In addition, a method for determining a fluctuation rotation index according to the present invention, which is made to solve the above problem, comprises the steps of: Rotating the eccentric rotor by applying a rotational torque to the eccentric rotor that is rotatably supported by the bearing to be measured; Stopping the application of the rotational torque, and sequentially measuring a rotation time Δt [s] or a speed of the eccentric rotor per unit angle Δθ [rad] during a period in which the eccentric rotor rotates by self-propelled rotation and then rotates J (J is an integer) from the start of measurement; A method for determining a variable rotation index by sequentially determining a rotation angle and a rotation angular velocity during J rotations of the eccentric rotor from the unit angle Δθ [rad] and the rotation time Δt [s], or the unit angle Δθ [rad] and the velocity, The angle between the horizontal line and the line connecting the center of rotation and center of gravity of the eccentric rotor at the start of the measurement of the rotation time is θ0, the rotation angle at the start of data analysis among the values ​​measured based on the start of the measurement is θ1, and the rotation angular velocity at that time is ω1. The angle θ from the start of the measurement and the square of the measured rotation angular velocity ω1 are expressed as ω1. 2 and the bearing friction index [-2T f / I] and calculate the value of E by substituting them into the following formula:

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[0020] Furthermore, a method for determining a fluctuation rotation index according to the present invention, which is made to solve the above problem, comprises the steps of: Rotating the eccentric rotor by applying a rotational torque to the eccentric rotor that is rotatably supported by the bearing to be measured; Stopping the application of the rotational torque, and sequentially measuring the rotation time Δt [s] or speed of the eccentric rotor per unit angle Δθ [rad] during J (J is an integer) rotations of the eccentric rotor after the start of measurement, after the eccentric rotor has rotated by self-propelled rotation; A method for determining a variable rotation index by sequentially determining a rotation angle and a rotation angular velocity during J rotations of the eccentric rotor from the unit angle Δθ [rad] and the rotation time Δt [s], or from the unit angle Δθ [rad] and the velocity, The angle between the horizontal line and the line connecting the center of rotation and center of gravity of the eccentric rotor at the start of the measurement of the rotation time is θ0, the rotation angle at the start of the measurement when data analysis begins is θ1, and the rotation angular velocity at that time is ω1. The angle θ from the start of the measurement and the square of the measured rotation angular velocity ω1 are ω1. 2 and the average bearing friction index [-2T fm / I] and substitute into the following formula to find the value of E,

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[0021] The method of determining the fluctuating rotation index described above is an analysis of vibration components that takes into account instantaneous friction, and makes it possible to measure and analyze the fluctuating rotation index with greater accuracy than the method described in Patent Document 4.

[0022] The variable rotation index A is calculated using the variable rotation index determination method described above, and the moment of inertia I of the eccentric rotor is calculated from the variable rotation index. Furthermore, the average bearing friction index [-2T fm / I], the moment of inertia I and the average bearing friction index [-2T fm The average friction torque can be determined from the moment of inertia I and the bearing friction index [-2T f / I], the instantaneous friction torque can be determined. This method, when used in conjunction with the combination of a rotating body and an eccentric weight described in Patent Document 4, can become a highly accurate measurement and analysis method for the moment of inertia measuring instrument. In addition, the fluctuation rotation index is the amplitude A of the vibration component of the difference between the value of E and the square of the rotation angular velocity ω (Figure 15); if this is determined from actual measurements, then from equation (1) of [math 10], when the mass and center of gravity are known, it amounts to measuring the moment of inertia, and when the moment of inertia and mass are known, it amounts to measuring the center of gravity position. In this experiment, the mass and center of gravity are assumed to be known and measured in some way. In addition, when gravity is unknown, such as on Earth, a test machine with known mass, center of gravity, and moment of inertia can be created and used as a gravity measurement device based on the variable rotation index. Effect of the Invention

[0023] In the method of determining the bearing friction index and the variable rotation index of the present invention, friction elements such as the friction torque of the bearing are obtained using the rotation angular velocity, which is then used to estimate the fluctuation in friction torque corresponding to the change in angular velocity with respect to the rotation angle, and the friction component is removed from the fluctuation of the square of the rotation angular velocity to obtain the variable rotation index, so that the measurement accuracy of the variable rotation index associated with friction is improved, and the measurement accuracy of the quantities possessed by the rotating body, such as the moment of inertia, can be improved from the relationship in [Equation 10]. As a result, the measurement accuracy of the moment of inertia is improved, and the accuracy of calculating the friction torque from the friction index is also improved. [Brief description of the drawings]

[0024] [Figure 1] FIG. 1 is a front view showing a schematic diagram of an apparatus equivalent to the apparatus described in Patent Document 4, which was created to verify the validity of the present invention, for measuring a variable rotation index (here, moment of inertia) and a bearing friction index. [Figure 2A] Plan view (a) and cross-sectional view (b) showing an eccentric weight. [Figure 2B] Plan views (a), (b), and cross-sectional views (c), (d) of the two clutch discs that make up the clutch. [Diagram 3] An illustration of the bow section cut off from the eccentric weight. [Figure 4] A conceptual diagram of a rotary encoder pulse waveform. [Diagram 5]4 is a diagram for explaining the relationship between the position of the center of gravity of a rotating body consisting of a shaft and an eccentric weight and the rotation angle. FIG. [Figure 6] FIG. 4 is a graph showing the relationship between the square of the measured angular velocity and the rotation angle. [Figure 7] A diagram showing the relationship between [-2Tfm / I] and ωm during one rotation. [Figure 8] Stribeck diagram showing the characteristics of friction. [Figure 9] FIG. 4 is a diagram showing the relationship between angular velocity ω and average angular velocity ωm and the rotation angle. [Figure 10] FIG. 4 is a diagram showing the relationship between friction torque Tf and average friction torque Tfm and the rotation angle. [Figure 11] 4 is a diagram showing the relationship between angular velocity ω and friction torque Tf, and between average angular velocity ωm and average friction torque Tfm. [Figure 12] A graph showing the relationship between [-2Tf / I] and angular velocity ω. [Figure 13] A graph showing the history of [-2Tf / I] obtained from the history of angular velocity ω. [Figure 14] A graph showing the relationship between the square of the angular velocity ω (ω2) and E in [Equation 8], which includes the integral of the bearing friction index. [Figure 15] This is a graph showing the results of trigonometric approximation of E in [Equation 8], which contains the integral of the square of the angular velocity ω (ω2) in the experiment and the bearing friction index. [Figure 16] Graph showing friction torque measurements by the graph method (values ​​for all bearings, here for two bearings) [Figure 17] A graph showing the measured values ​​of friction torque due to the moment of inertia obtained by processing only the numerical values ​​(values ​​for all bearings, here for two bearings). DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0025] In the bearing friction index determination method of the present invention, Rotating the eccentric rotor by applying a rotational torque to the eccentric rotor that is rotatably supported by the bearing to be measured; Stopping the application of the rotational torque; Sequentially measuring a rotation time Δt [s] or a speed per unit angle Δθ [rad] of the eccentric rotor from a measurement start, which is an arbitrary time point after the start of rotation due to the free-running rotation of the eccentric rotor, until the eccentric rotor rotates J (J is an integer), A method for determining an index representing bearing friction by sequentially determining a rotation angle θ and a rotation angular velocity ω during J rotations of the eccentric rotor from the unit angle Δθ [rad] and the rotation time Δt [s], or from the unit angle Δθ [rad] and the velocity, The rotation time Δt [s] is measured n times (n = 2π / Δθ, n is an integer) while the eccentric rotor makes one rotation. The number of measurements 2Jπ / Δθ until the eccentric rotor makes J rotations is 2Jπ / Δθ. The rotation angle at the start of the analysis of the measurement is θ1 [rad], the rotation angular velocity at that time is ω1 [rad / s], and the rotation angle immediately after the jth measurement is θ j+1 [rad], and the rotational angular velocity at that time is ω j+1 [rad / s], and the rotational angular velocity immediately after k rotations (k is an integer) from the start of the analysis is ω nk+1 [rad / s], and the average friction torque of the bearing is T fm When the moment of inertia of the eccentric rotor is I, The rotation angle θ j+1 [rad] is calculated using the following formula:

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[0026] In addition, taking into account the swell fluctuations over one rotation, the value of half a rotation ω n / 2+1 For example, the average rotational angular velocity may be calculated by a simple averaging process using the following formula:

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[0027] The rotational angular velocity can be obtained by measuring the relationship between the rotation angle of the eccentric rotor and time. Rotary encoders of various types, such as optical, magnetic, and electromagnetic induction types, can be used to measure the relationship between the rotation angle of the eccentric rotor and time. When determining the rotational angular velocity from the rotation angle and speed, in addition to rotary encoders, devices such as speedometers that use the Doppler effect can be used.

[0028] Hereinafter, an embodiment of a test device used to verify the method for measuring the variable rotation index and the bearing friction index of the present invention will be described with reference to the drawings. This test device was produced based on Patent Document 4. 1 is a front view showing the overall configuration of the test device 100. In FIG. 1, the test device 100 is roughly divided into a drive system 10, a holding device 20 for a rotor and a bearing, and a detection system 30.

[0029] The bearing and rotating body holding device 20 has a pair of bearing holding legs 21, 21 erected on a base 40 installed on a floor surface, and a pair of bearings 200 to be measured are fixed to the upper part of the holding legs 21. The pair of bearings 200 rotatably support a shaft 201, and an eccentric weight 22 is attached to the middle part of the shaft 201 so as to rotate integrally with the shaft 201. The left and right ends of the shaft 201 protrude leftward from the left bearing 200 and rightward from the right bearing 200, respectively. In the example of the device shown in FIG. 1, as shown in FIG. 2A, the eccentric weight 22 has a shape obtained by cutting out a bow-shaped portion (the portion marked with the reference symbol 22a in FIG. 2A) from a cylindrical body. Incidentally, the eccentric weight 22 was produced for the purpose of checking the validity of the measurements in the verification experiment, and its center of gravity and moment of inertia were of a known shape. However, in actual measurements, the shape of the eccentric weight is arbitrary, and therefore the center of gravity and moment of inertia are unknown.

[0030] As shown in FIG. 1, the drive system 10 includes a slide mechanism 101 arranged on the left side of the base 40 and reciprocating in the left-right direction, a bearing stand 102 and a motor 103 fixed on the slide mechanism 101, a power supply unit 104, a pair of bearings 105 fixed on the bearing stand 102, a drive shaft 106 supported rotatably on the pair of bearings 105 and rotated by the motor 103, pulleys 107A, 107B and a belt 108 that transmit the rotational force of the motor 103 to the drive shaft 106, and clutch disks 111 and 112 provided on the right end of the drive shaft 106 and the left end of the shaft 201, with their protrusions and recesses lightly meshing with each other.

[0031] As shown in FIG. 2B, the clutch discs 111 and 112 have a circular outer shape and have holes 1111 and 1121 in the center into which the drive shaft 106 and the shaft 201 are fitted. Four recesses 115 and four protrusions 116 extending radially are formed on the opposing surfaces of the clutch discs 111 and 112, respectively. The shape and position of the recesses 115 of the clutch disc 111 correspond to the shape and position of the protrusions 116 of the clutch disc 112, and the shape and position of the protrusions 116 of the clutch disc 111 correspond to the shape and position of the recesses 115 of the clutch disc 112. With this configuration, when the bearing base 102 is moved rightward by the slide mechanism 101 and the clutch disc 111 comes into contact with the clutch disc 112, and the recesses 115 and the protrusions 116 mesh with each other, the drive shaft 106 and the shaft 201 are connected. As a result, the rotational force of the drive shaft 106 is transmitted to the shaft 201. Hereinafter, the clutch discs 111 and 112 will be collectively referred to as the clutch 110.

[0032] Detection system 30 includes rotary encoder 301 that detects the rotation angle of shaft 201, and device control and analysis device 303 that determines the rotation angular velocity of shaft 201 based on measurement control and measurement device (hardware) 302. Detection signals of Z phase (1 pulse per revolution) and A phase (n pulses per revolution, n=360 in this example) of rotary encoder 301 are input to measurement control and measurement device 302. When the Z phase detection signal is input, it is used as a trigger to start measurement and the interval time between the A phase and Z phase pulses is reduced by 5×10 -9 s with extremely high accuracy. The rotary encoder 301 is held by a holding plate 310 fixed to the right-side bearing holding leg 21. The measurement control and measuring device 302 can be linked by software to a device control and analyzing device 303, which is a computer consisting of a CPU or the like, to realize each function.

[0033] 1 during operation, the positions of each part are defined as follows. Power is supplied from power supply device 104 to motor 103, causing shaft 201 and eccentric weight 22 to rotate. Free-running rotation begins when slide mechanism 101 is slid to separate clutch disk 111 and clutch disk 112 of clutch 110. When power is supplied from power supply device 104 to motor 103, rotary encoder 301 transmits a pulse signal to measurement control and measurement device 302, which waits for a command sent from device control and analysis device 303. When a measurement command is received from device control and analysis device 303 to measurement control and measurement device 302, measurement begins with the measurement trigger (first z-phase pulse signal) of rotary encoder 301. If the angle of the center of gravity of the rotating body (eccentric weight + shaft + clutch) from the horizontal plane at this moment is θ0 (see Figure 5), this θ0 becomes the starting point of the rotation angle θ (i.e., when θ = 0), and is defined as the "measurement start" point. Measurement control and measurement device 302 continues to send the pulse sent from rotary encoder 301 and its time measurement data to equipment control and analysis device 303. This continues for J rotations until a stop command is received from equipment control and analysis device 303 to measurement control and measurement device 302. The data is analyzed by equipment control and analysis device 303. The angle (θ in Figure 5) when data analysis processing is started by equipment control and analysis device 303 is set as θ1. Angle θ1 is an angle based on the measurement start point (angle from θ0, which is the measurement start point). For convenience of analysis, θ1 is usually θ1>0, but θ1=0 may also be used.

[0034] To summarize the above, the following can be said: Start of free-running rotation: Stop torque supply (disengage clutch). The angle θ at this time is undetermined (not measured). Start of measurement: A measurement trigger (first z-phase pulse signal) is input to the measurement control and measurement device 302. Z-phase pulse signals after the start of measurement are ignored. The angle θ at this time is set to "0", and Δt [s] between Δθ [rad] is measured, and the device control and analysis device 303 calculates the angle θ and angular velocity ω [rad / s] by adding Δθ after the start of measurement. Analysis start: This is carried out by the device control and analysis device 303. θ is the angle after the start of measurement, which is 0, and θ1 is the analysis start angle for the period when the experimental measurement values ​​are favorable for analysis. θ1 is a value starting from the start of measurement, and since measurements have already been made, the value of θ1 is large. The θ1 and ω1 in the formula are the values ​​at this time. It is possible to start measurement before the start of free-running rotation, but analysis is started with the measured value after free-running rotation. In this case, in order to find the direction of the center of gravity θ0, whether the angle θ is selected as the reference point before or after the start of free-running rotation, the reference point (θ=0) must always be the time when the z-phase pulse occurs as the measurement start point, and Δθ must be added according to the subsequent A-phase or equivalent pulse, but the measurement data before free-running rotation is discarded. Therefore, the order of operations is not fundamentally different from the start of free-running rotation, the start of measurement, and the start of analysis, and the order of operations does not overturn the basic concept of this invention.

[0035] The rotary encoder 301 may be an optical encoder, a magnetic encoder, an electromagnetic induction encoder, or the like, and any of these types of encoders may be used. An optical encoder has a light-emitting element, a light-receiving element, and a disk with many radially formed slits, and detects the rotation angle position information of the shaft 201 as an optical pulse signal. A magnetic encoder has a permanent magnet and a magnetic sensor, and detects the rotation angle position information of the shaft 201 as a change in a magnetic field. An electromagnetic induction encoder detects the change in a magnetic field generated between an induction coil (excitation coil) and a fixed coil (detection coil) as the rotation angle position information.

[0036] <Experiment> Next, an experiment conducted using the above-mentioned test device 100 to find an index related to variable rotation caused by an eccentric weight (variable rotation index) and an index related to friction of the bearing 200 (bearing friction index) will be described. In the experiment, a sliding bearing was used as the bearing 200, and a magnetic type was used as the rotary encoder 301. In addition, an eccentric weight 22, clutch 112, and shaft 201 with the dimensional specifications shown in Table 1 below were used. The eccentric weight 22, clutch 112, and shaft 201 are adhesively fixed to each other, and together they constitute the eccentric rotor of the present invention. [Table 1]

[0037] 3, the eccentric weight 22 is made up of the remaining portion obtained by cutting off the sector-shaped arcuate portion 22a with a central angle β, and in Table 1, D1 and D2 of the eccentric weight 22 represent the outer and inner diameters of the cylinder before the arcuate portion 22a is cut off, L1 represents the length excluding the arcuate portion from the diameter, and L2 represents the thickness. In addition, D1 of the clutch 112 represents the outer diameter, D2 represents the inner diameter, L1 represents the entire axial length, and L2 represents the axial length excluding the protrusion 116. In addition, D1 and L1 of the shaft 201 represent the diameter and length of the portion held by the bearing 200, and D2 and L2 represent the diameter and length of the portion protruding from the bearing 200 and connected to the rotary encoder.

[0038] The following description is based on the assumption that the units of D1, D2, L1, and L2 in Table 1 have been converted from mm to m. The center of gravity positions (in Table 1, shown as distances (m) from the center of rotation) and moments of inertia of the eccentric weight 22, clutch 112, shaft 201, and entire rotor (= eccentric rotor) shown in Table 1 are values ​​calculated from the above-mentioned dimensional specifications. For example, the density of eccentric weight 22 is ρ, and the inner radius is r i (=inner diameter D2 of eccentric weight 22 × (1 / 2)), outer radius is R i (=Outer diameter D1 of eccentric weight 22 × (1 / 2)), thickness is b i (=thickness L2 of eccentric weight 22), the moment of inertia I i , center of gravity position r g can be obtained from the following formulas (2) and (3), where β is the central angle of the arched portion 22a (see FIG. 3).

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[0039] Equations (2) and (3) are equations described in Patent Document 4. In this embodiment, the calculated values ​​of the above equations (2) and (3) are compared with the measured values ​​to determine the validity of the method of the present invention. The true value is the sum of the moment of inertia of the shaft 201 and the moment of inertia of the clutch 112 to the moment of inertia of the eccentric weight 22 calculated from equation (2), and corresponds to the value of the moment of inertia (moment of inertia of the rotating body) shown in the lower right column of Table 1. If the true value of the moment of inertia coincides with the moment of inertia calculated from the position and mass of the center of gravity of the eccentric weight 22 calculated from equation (2) and the measured value of the variable rotation index, the measurement can be applied to any rotating body of different shapes.

[0040] In this experiment, the motor 103 was started and the shaft 201 was rotated at a constant rotational angular velocity (approximately 15 Hz, 900 rpm), after which the clutch disks 111, 112 were separated and the shaft 201 was rotated independently. The output pulses of the rotary encoder 301 during the independent rotation were input to the measurement control and measurement device 302 (a pulse measurement and analysis device (WE7000) manufactured by Yokogawa Measurement Corporation), and the data was processed by the device control and analysis device 303. The signals input from the rotary encoder 301 to the measurement control and measurement device 302 were A-phase and Z-phase (one pulse per revolution) pulse signals. The Z-phase pulse signal was used as a trigger to start measurement. Note that a B-phase pulse signal may be input to the measurement control and measurement device 302 instead of the A-phase pulse signal.

[0041] FIG. 4 shows the pulses of the rotary encoder 301. If the angle between two successive pulses is Δθ [rad] and the time is Δt [s], then the angular velocity ω (= Δθ / Δt) [rad / s] can be calculated from the measured value of Δt and Δθ. Note that Δt1 and Δt2, ω1 and ω2 in FIG. 4 are used to explain the relationship between the pulse, the measurement time Δt, and the angular velocity ω, and the subscripts to these symbols represent the "rotation angle θ (of the eccentric rotor) immediately after the jth measurement in this invention." j+1 It does not correspond to the j in "[rad]".

[0042] If the angular position of the eccentric rotor when the central pulse in Figure 4 is transmitted is θ [rad], this is the angle immediately after measuring Δt1 [s]. If the angular velocity corresponding to Δt1 is ω1 [rad / s] and the angular velocity corresponding to the next measured value, Δt2 [s], is ω2 [rad / s], then the angular velocity ω at the angle θ [rad] can be expressed by the following equation. ω=(ω1+ω2) / 2=Δθ(1 / Δt1+1 / Δt2) / 2 [rad / s]

[0043] Therefore, the jth Δt j Angular velocity ω immediately after measurement of [s] j+1 The rotation angle at that time is θ j+1 [rad], j+1th measurement value is Δt j+1 If [s], it can be expressed by the following equation. ω j+1 =Δθ(1 / Δt j +1 / Δt j+1 ) / 2 [rad / s] After the measurement starts, Δt is measured continuously, and the angle θ is the angle from the start of the measurement. After the measurement starts, θ1 and ω1 are determined at the start of the analysis, so the Δt value before angle θ1 is also measured.

[0044] In addition to the above, the angular velocity ω j+1 may be calculated from the following formula: ω j+1 =2Δθ / (Δt j +Δt j+1 ) In addition, if the angle is the position shifted by Δθ / 2 from the pulse position, that is, the rotation angle θ1 [rad] at the start of the analysis is Δθ / 2 after the pulse, and the jth Δt j Measure the angular velocity ω j =Δθ / Δt j In this case, the rotation angle θ j [rad] may be Δθ / 2 after the jth pulse. Also, if Δθ becomes small, the correction of Δθ / 2 after the pulse is ignored and the correction of Δt after the j+1th pulse is j+1 The measurement is ω j+1 ≒Δθ / Δt j+1 or ω j+1 ≒Δθ / Δt j However, this has almost no effect on the numerical calculations. Furthermore, when using angular velocity or velocity measurement means other than time measurement, the angular velocity or velocity measurement means is connected to the measurement control and measurement device (hardware) 302, and the measurement control and measurement device 302 takes in data in response to a pulse command from the rotary encoder 301. Therefore, the angular velocity calculated using the measurement value at the angle of the pulse position calculated by the above-mentioned formula [Equation 1] becomes the rotational angular velocity of that angle.

[0045] In this experiment, the time interval between the rising edge (voltage rise) of the A-phase (1°) pulse and the rising edge (voltage rise) of the next pulse was continuously measured. At the same time, the time interval between the rising edge (voltage rise) of the Z-phase (1 pulse per rotation) pulse and the rising edge (voltage rise) of the next pulse was also continuously measured. This allows the rotation time per unit angle of 1° to be measured sequentially, and the rotation angular velocity per unit angle of 1° can be obtained sequentially. In order to standardize the measurement start angle, the rising edge (voltage rise) of the Z-phase pulse was used as a measurement start trigger for the measurement control and measurement device 302. Note that the time interval between the falling edge (voltage fall) of the pulse and the falling edge (voltage fall) of the next pulse may be measured, and it is possible to appropriately select whether to use the time interval of the rising edge of the pulse or the time interval of the falling edge. In addition, the A-phase pulse may be replaced with a B-phase pulse, or may be replaced with a bar (reverse pulse) of the A-phase pulse or B-phase pulse.

[0046] Prior to the verification of the experimental results, the variable rotation index and bearing friction index of the present invention will be explained. The definitions of the symbols used in the following explanation are as follows. Formulas and symbols are based on SI units, kg, m, s, and N, unless otherwise specified. F: Friction force (for sliding bearings, the integral value of the shear stress on the bearing inner shaft surface) [N] g: Gravitational acceleration [m / s 2 〕 I: Moment of inertia of the rotating body [kg m 2 〕 M: Mass of the rotating body [kg] (r g is the center of gravity of the rotating body), mass of the eccentric weight [kg] (r g is the center of gravity of the eccentric weight) r: inner radius [m] r g : Distance between the axis of rotation and the center of gravity (eccentric distance) [m] (if M is the mass of the rotating body, it is the center of gravity of the rotating body; if M is the mass of an eccentric weight, it is the center of gravity of the eccentric weight) In addition, Mr. g will be the same whether M is the mass of the rotating body or the mass of the eccentric weight. R: Radius or shaft radius (radius from the center of rotation to the friction point) [m] t: time (s) T: Torque [Nm] W: Load [N] α: Angular acceleration of the rotating body [rad / s 2 〕(negative value during deceleration) θ: Rotation angle of the rotor from the start of measurement (rad) μ: Friction coefficient ω: Angular velocity of the rotating body (rotational angular velocity) [rad / s] ρ: Density [kg / m 3 〕 Subscripts f: Friction m: average x,y: horizontal, vertical axis direction

[0047] <Friction torque> The friction torque T acting between the rotating shaft and the sliding bearing of a rotating body (eccentric weight + shaft + clutch) as shown in Fig. 5 is f[Nm] is expressed by the following formula (4). Here, θ0 is the rotation angle [rad] of the center of gravity of the rotating body from the horizontal line at the start of the measurement of the rotation angle, θ is the rotation angle starting from θ0, and θ0+θ is the rotation angle [rad] of the center of gravity of the rotating body from the horizontal line at the time of the measurement of the rotation angle. In addition, the friction torque T f is the sum of the friction torques of all the bearings, and in the case of the device used in this embodiment, it is the sum of the friction torques of two bearings. The average friction torque T fm The same is true in the case of

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[0048] In Patent Document 4, an equation equivalent to equation (4) is described in which θ0 is removed from equation (4). This is because the state at the start of measurement (when the z-phase pulse trigger occurs) is set to a state where the center of gravity of the eccentric weight is located on a horizontal plane passing through the center of rotation of the rotor. However, the work of adjusting the attachment position of the eccentric weight to achieve the above state is very time-consuming. Therefore, in this embodiment, the angle θ0 representing the position of the center of gravity of the eccentric weight at the start of measurement (when the z-phase pulse trigger occurs) is introduced into the equation. In other words, in this embodiment, after the eccentric weight is attached arbitrarily and measured, the value of θ0 is set so that the phases match, and the adjustment work of the attachment position of the eccentric weight is not required.

[0049] The angular velocity ω and angular acceleration α are described by the following equations, so they can be calculated numerically using Figure 4.

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[0050] If the manufacturing error of a rotary encoder is δ, then when the error in the output pulse at a certain timing is +δ, there is a high probability that the error in the next output pulse will be -δ. When this is introduced into the calculation of acceleration, the deviation from the true value of acceleration is roughly as follows:

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[0051] In other words, while the manufacturing error of the angular velocity results in an error in the angular velocity, the error of the angular acceleration may be 100 times or more larger than the manufacturing error. As can be seen from the above formula, the angular acceleration α is more affected by the accuracy of the angular interval of the output pulse of the rotary encoder 301 than the angular velocity ω, and if the accuracy of the angular interval of the rotary encoder 301 is poor, the angular acceleration α is unstable. The manufacturing accuracy δ of the rotary encoder and the instability of the angular acceleration α have been confirmed by experiments. Therefore, it is necessary to derive and analyze a formula that does not use angular acceleration in order to aim for measurements at the limit where the pulse interval is shortened to 1°, 0.5°, or even 0.1° using a rotary encoder with poor manufacturing accuracy. Note that the influence of the manufacturing error on the angular acceleration is the same even if an angular velocity measuring means other than the rotary encoder is used.

[0052] If the time interval of the output pulse of the rotary encoder 301 is t and the angle is θ, the angular velocity ω and the angular acceleration α are expressed by the following equations, which mathematically describe the laws of physics.

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[0053] Since the experimental data is processed using numerical calculations, the angular acceleration α is eliminated. By setting ωdt = dθ and dω = αdt, equation (4) is transformed into an equation that does not use the angular acceleration α. ​​In the equation below, θ1 indicates the first rotation angle sampled from the start of the rotation angle analysis.

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[0054] From the above, we can derive the following equation (5) which does not use angular acceleration. Here, we assume that the rotating body rotates continuously multiple times. ω1 in the above equation is a value corresponding to θ1, and is kept constant from the start to the end of the analysis. Therefore, ω1 in equation (5) is treated differently from ω1 in equations [Equation 2] and [Equation 4].

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[0055] The rotation angle sampled at the i-th point from the start of the rotation angle analysis is called θ i+1 The friction torque at that time is T fi , and the angle step is Δθ, the first term on the right hand side of equation (5) is expressed as the integral value from the start of the analysis to the jth point, as shown below.

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[0056] Therefore, the average friction torque when the rotation angle is measured n times from the start of the analysis is T fm Then, equation (5) can be transformed into the following equation (6). Here, ω = ω in equation (5) n+1 , θ=θ n+1 has been replaced with.

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[0057] The rotational angular velocity obtained from the measurement of the first rotation time in any one rotation is ω1, and the rotational angular velocity obtained from the measurement of the last (first of the next rotation) rotation time is ω n+1 Then, if it rotates once in n times, then θ n+1 Since -θ1 = 2π, the trigonometric function term in equation (6) becomes "0", the term affected by gravity disappears from equation (6), and the relationship between the average friction torque and moment of inertia is expressed by the following equation (7).

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[0058] Also, the average angular velocity of one rotation ω m is expressed by the following equation (8).

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[0059] In addition, although the average friction torque and average angular velocity for one rotation are calculated using equations (7) and (8), these can be expanded to multiple rotations as in equations (2) and (3). Equation (8) can also be expressed as equations (6) and (7). In addition, the pulse interval time Δt of the rotary encoder 301 is continuously measured at 1° rotation angle intervals, and the experimental angular velocity ω can be calculated using the following formula. ω=Δθ / Δt[rad / s] A more precise explanation has already been given using FIG.

[0060] Figure 6 shows the squared value of the angular velocity (ω 2 ) and the angle θ [rad] after the measurement trigger for the center of gravity position when Δt is measured. The angle from the horizontal line is θ+θ0 [rad]. In FIG. 6, the horizontal axis is the angle θ, and the vertical axis is ω 2 Also, FIG. 7 shows the ω 2was substituted into equations (7) and (8) to obtain [-2T fm / I] value (unit is [rad / s 2 ]) and average angular velocity ω m The graph below plots the vertical and horizontal coordinates of -2T fm / I" is called the average friction index value.

[0061] Deceleration due to friction is known to have the characteristics of the Stribeck diagram shown in Figure 8. In Figure 8, η [Pa s] represents the viscosity of the oil that slides the bearing. Friction torque T f [Nm] is the friction force around the bearing (tangential resistance force) F [N] multiplied by the radius of the rotating shaft (length of the arm), so if the friction coefficient is μ and the force applied to the bearing is W [N], the friction coefficient μ can be expressed by the following formula. μ = F / W

[0062] In addition, if the radius of the bearing is R [m] and the width is B [m], the friction torque T f [Nm], average surface pressure P m [Pa] is expressed by the following formula: T f =FR P m =W / (BR) During high speed rotation, the force acting on the bearing is mainly centrifugal force W, and during low speed rotation, the force acting on the bearing is mainly gravity W.

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[0063] In this experiment, the value η of the horizontal axis of the Stribeck diagram in Fig. 8 is constant. m is a function of ω. Also, the sudden increase in the friction coefficient μ in the low-speed direction (left direction) of the Stribeck diagram is due to contact between the shaft and the sliding bearing. Therefore, this region was not used in the calculation of friction torque, and only the friction characteristics in the region in Figure 8 where the friction coefficient μ increases monotonically were used. In other words, P m When is constant, the friction torque T fIn addition, Fig. 7 shows negative values, and the reason why the low-speed side rises in the figure is because the centrifugal force becomes smaller, P m This is because the load decreases and friction decreases.

[0064] Figure 9 shows the history of angular velocity ω and the average angular velocity ω obtained from the actual measurement of the pulse interval time Δt of a rotary encoder every 1°. m FIG. 10 shows the relationship between the average friction torque T fm and average angular velocity ω m The relationship between friction torque T f and the angular velocity ω, the friction torque T f History and average friction torque T fm In both Fig. 9 and Fig. 10, the horizontal axis is the angle θ. The angle θ is eliminated from Fig. 9 and Fig. 10, and the relationship between the angular velocity ω and the friction torque T f The relationship between the average angular velocity ω m and the average friction torque T fm The relationship between the average friction index value [-2T fm / I] to the friction index value [-2T f / I], the average angular velocity ω m The horizontal and vertical axes are the friction index value [-2T f The graph in Fig. 12 shows the friction index value [-2T f Table 2 shows an approximate formula that expresses the relationship between [I] and angular velocity ω. [Table 2]

[0065] Figure 13 shows the friction index value [-2T f 1 is a graph showing the history of [I / I] versus the angle θ.

[0066] <Analysis of moment of inertia> Next, let the rotational fluctuation be the square of the angular velocity ω 2 In order to analyze this, we transformed equation (5) into an equation using simple trigonometric functions as follows:

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[0067] Here, we focus on the equation (10) and calculate the friction index value [-2T f Using the value of [I], calculate the value E of the following formula, and combine this with ω 2 The relationship between the rotation angle θ is shown in FIG.

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[0068] As can be seen from Fig. 14, the ω calculated from the measured ω 2 The value E changes almost linearly with respect to the fluctuation and attenuation of

[0069] The difference between the method using equation (4) of [Equation 15] of the present invention and the method using [Equation 2] described in Patent Document 4 is whether the equation expressing the friction torque is written as "θ+θ0" or "θ". However, such a difference in the equation affects the necessity of work such as accurately adjusting the installation position of the eccentric weight so that the angle from the horizontal direction at the start of measurement is zero by not using θ0, and determining the angle θ1 at which the analysis is started by the measurement control and measuring device 302 and the device control and analyzing device 303 before the analysis. These work are very time-consuming work in experiments and can take several days, so it is practically advantageous to be able to eliminate these work. The fact that the θ0 and θ1 selected to be convenient for the numerical calculation of the equation and analysis process become the true values ​​of θ0 and θ1 of the device even if the device is assembled appropriately in a short time can be said to be a major advance in engineering and technology compared to the measurement method shown in Patent Document 4.

[0070] In the above explanation, the horizontal direction was used as the reference for angles, but even if the reference is changed, if the physical phenomenon is the same, only the mathematical description changes. Also, the sine function sin and the cosine function cos can be mathematically converted simply by having a phase difference of π / 2. Therefore, an equation expressed using the sine function sin can be changed to an equation using the cosine function cos.

[0071] Using equation (10) and Figure 14, we calculate the displacement due to gravity. If "θ1 + θ0" is arbitrary, then ω 2 The effect of friction E in [Equation 8] is removed (E minus) ω 2 -E fluctuates (oscillates). The value of C is adjusted so that the center of the oscillation is "0 (zero)". This means that θ0 is the initial setting for the center of gravity direction (see Figure 5), and the relationship between the center of the oscillation and θ1 is examined. Figure 15 shows the results of adjusting the value of C so that the center of the oscillation is 0, based on the experimental results. As can be seen from Figure 15, in this case it can be approximated by a trigonometric function (note that although it is approximated by a sine function in Figure 15, it may also be approximated by a cosine function). If the amplitude of the sine function is A, then (2Mgr gOnce θ+θ0 is determined so that it coincides with the sine function, θ0 can be found from the phase difference. This will be explained in detail below.

[0072] The angle θ from the start of measurement and the measured ω 2 Once the history of (ω squared) is determined, the value of ω squared at the start of data analysis is also determined. Only the value of C on the left side of the above formula (10) shown below (hereafter referred to as "X") is not determined.

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[0073] Therefore, the value of C is determined so that the fluctuation will have a median value of 0 for the X value. If the amplitude of the fluctuation is A, and the fluctuation with a median value of 0 for the angle θ is approximated by a sine function sin, the direction of the center of gravity θ0 can be found by adjusting the phase. In other words, -Asin(θ+θ0) Adjust the amplitude A and determine θ0 so that the phase is aligned. This is the direction of the center of gravity of the eccentric weight at the start of measurement. In addition, the following relationship exists between this C value and A, θ0, and θ1.

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[0074] When the moment of inertia I of the entire rotating body is unknown, the specifications of the eccentric weight shown in Table 1 (mass M, distance r from the axis of rotation to the center of gravity) g ) can be used to calculate the moment of inertia I of the entire rotating body from the following formula. The moment of inertia I will be explained later. I=(2Mgr g ) / A

[0075] Also, the distance rg When one of the masses M is unknown, the value of that one can be found from the other and the value of the moment of inertia I. In other words, this is a method for measuring not only the moment of inertia I, but also the values ​​of other physical quantities that constitute variable rotation indices. Table 3 shows the values ​​of the moment of inertia of the rotating body found as described above. If the C value is not adjusted, the median value of the vibration in Figure 15 will deviate from 0. Therefore, the offset a0 is introduced in Table 3. Adjusting the value of a0 in Table 3 corresponds to adjusting the C value. Here, θ1 is taken to be an angle of sin(θ1+θ0)=0, that is, a0=0 (C=0). [Table 3]

[0076] The moment of inertia values ​​shown in Table 3 are the true values ​​of the moment of inertia calculated from the dimensions in Table 1, 7.5633E-03 [kgm 2 ], which is almost the same. Also, if the moment of inertia is known, the friction torque T f The results are shown in Figure 16.

[0077] In the present invention, the history of E in [Equation 8] can be calculated from the history of ω with respect to θ in the experiment using the approximation formula in Table 2. Therefore, the θ0 value, A value, and C value are assumed and substituted into Equation (9), and the virtual ω with respect to θ is calculated. 2 It is also possible to repeatedly calculate the above and compare it with the experimental values ​​in Figure 6 to determine the amplitude and friction based on the values ​​that minimize the deviation.

[0078] The above explanation is about the principle of measurement and an example of analysis using the device shown in Fig. 1, but it is troublesome to calculate the C value using the device control and analysis device 303 in Fig. 1, plot the graph shown in Fig. 15, and determine the values ​​in Table 3. Therefore, from equation (10), the following equation

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number

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[0079] Where:

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[0080] and,

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[0081] [Table 4]

[0082] Calculating one rotation from θ1=262[rad], the true value of the moment of inertia I of the rotor shown in Table 1 is 7.5633E-03[kgm 2 ], the value of the moment of inertia I shown in Table 4 was -2.26%. The friction torque calculated using this moment of inertia is shown in Figure 17.

[0083] The friction torque can also be calculated using the following formula (11). This is a method of calculating the average friction index value every time a rotating body rotates, and as described in Patent Document 4, the idea is that the friction during rotation is constant at an average value. In FIG. 13, the friction index value [-2T f / I] fluctuates, but the integral value of this is ω calculated from the measured ω as shown in Figure 14. 2Since the value E changes almost linearly with respect to the fluctuation and damping, it can also be expressed using the rotation average friction torque. fm / I" can be calculated from the following formula (11).

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[0084] In this case, formula (12) can be expressed as formula (13) below. Also, formula (10) can be simplified to formula (13) below.

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[0085] E is

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[0086] In addition, the following equation

[30]

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[30] , we obtain the following equation.

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[0087] Then, if the left side of the above equation

[45] is the experimental value f(θ),

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[0088] The above methods are all switched for each rotation. Compared to the previous method of integrating the instantaneous friction torque, the calculation accuracy of the amplitude A and the three constants a0, a1, and b1 is lower, but it is sufficient for practical purposes.

[0089] The present invention improves on the method described in Patent Document 4, and if the method for determining the variable rotation index is replaced with this method, it can be widely used to measure the moment of inertia and friction. In addition, if friction exists other than that of the bearing, it can be included in the data analysis as the bearing friction index or friction torque using the method of the present invention. Incidentally, the moment of inertia of the rotor of the motor can be measured by applying FIG. 1 and Patent Document 4, but in this case, the application of rotational torque and the halt of application of rotational torque are performed by supplying and halting the supply of power to the motor 103 by the power supply device 104 while the clutch disks 111 and 112 are in a joined state and the slide mechanism 101 is in a stopped state. Therefore, it becomes necessary to perform correction based on the rotational speed ratio. It is even better to make the drive system 10 in FIG. 1 only include the power supply device 104 and the motor 103, attach the clutch disk 111 directly to the motor shaft to maintain the state of being joined to the clutch disk 112, and apply and halt the application of rotational torque by supplying and halting the supply of power to the motor 103 by the power supply device 104. Preferably, a known eccentric weight 22 and detection system 30 are directly attached to the shaft of the motor 103, and a power supply unit 104 supplies and stops power to the motor to apply and stop the application of rotational torque. By performing free-running rotation, main measurement, and main analysis, it is possible to measure the moment of inertia of the armature, as well as the friction of the motor bearings and the resistance force generated in the rotor.

[0090] Finally, the accuracy of the rotary encoder used by the present inventor was ±0.01° (±1% per 1° pulse interval) as a result of measurement. If the angular velocity is measured with an accuracy of within ±2% of the true value, a pulse interval of 0.5° is possible. It was also determined that analysis of Patent Document 4 based on angular acceleration due to numerical differences at pulse intervals of less than 10° is not possible. Furthermore, the accuracy of the optical rotary encoder used by the present inventor in the past for measurements was ±0.001° (±0.1% per 1° pulse interval), so if the angular velocity is measured with an accuracy of within ±2% of the true value, a pulse interval of 0.05° is possible. However, it was determined that analysis of Patent Document 4 based on angular acceleration due to numerical differences at pulse intervals of less than 5° is not possible. The minimum value of the pulse interval depends on the manufacturing accuracy of the rotary encoder.

[0091] In the above description, the description of units is omitted for some of the mathematical formulas, but the units of the mathematical formulas are determined by the units of the quantities represented by the symbols that make up the mathematical formulas. [Explanation of symbols]

[0092] 10...Drive system 100...Test equipment 101...Slide mechanism 102...Bearing stand 103...Motor 104…Power supply device 105...Bearing 106…Drive shaft 107A, 107B...Pulley 108...Belt 110…Clutch 111…Clutch disc 112…Clutch disc 115…Recess 116…Convex part 20...Bearing and rotor holding device 200...Bearing 201...Axis 21...Bearing retaining leg 22...Eccentric weight 30...Detection system 301...Rotary encoder 302…Measurement control and measuring device 303…Device control and analysis device 310...Retaining plate

Claims

1. Rotating the eccentric rotor by applying a rotational torque to the eccentric rotor that is rotatably supported by the bearing to be measured; The application of the rotational torque is stopped, and after the eccentric rotor rotates by self-propelled rotation, a rotation time Δt [s] or a speed of the eccentric rotor per unit angle Δθ [rad] is sequentially measured during J rotations (J is an integer) from the start of measurement; A method for determining a variable rotation index by sequentially determining a rotation angle and a rotation angular velocity during J rotations of the eccentric rotor from the unit angle Δθ [rad] and the rotation time Δt [s], or the unit angle Δθ [rad] and the velocity, The angle between the horizontal line and the line connecting the center of rotation and center of gravity of the eccentric rotor at the start of the measurement of the rotation time is defined as θ 0 Among the values ​​measured based on the start of the measurement, the rotation angle at the start of the analysis is θ 1 , the rotational angular velocity at that time is ω １ , the instantaneous friction torque is T ｆ , the moment of inertia of the eccentric rotor is I, the rotation angle θ from the start of the measurement and the rotation angular velocity ω at the start of the analysis １ ω, which is the square of １ ２ and the instantaneous bearing friction index [-2T ｆ / I] into the following formula to find the value of E, [0080] The difference between the square of the instantaneous rotational angular velocity ω and the value of E above, [ω ２ -E] was calculated, and the value of C was introduced into the difference value so that the center of the fluctuation of the difference becomes 0 [ω ２ -E + C] Based on the following formula 9, the trigonometric function of the amplitude A with respect to the rotation angle θ from the start of the measurement, −A sin(θ+θ 0 ) to approximate it, [0090] The value of the amplitude A obtained from the trigonometric approximation of the amplitude A based on the above formula is determined as a fluctuation rotation index A of the eccentric rotor, and the phase difference θ 0 A method for determining a fluctuation rotation index.

2. 2. The method for determining a variable rotation index according to claim 1, The integral value of the instantaneous bearing friction index with respect to the rotation angle is calculated by the following equation: １ Average bearing friction index [−2T ｆｍ A method for determining a fluctuation rotation index by approximating the fluctuation rotation index using the following equation expressed using [F1 / I] and the rotation angle. [0041]

3. Rotating the eccentric rotor by applying a rotational torque to the eccentric rotor that is rotatably supported by the bearing to be measured; The application of the rotational torque is stopped, and after the eccentric rotor rotates by self-propelled rotation, a rotation time Δt [s] or a speed of the eccentric rotor per unit angle Δθ [rad] is sequentially measured during J rotations (J is an integer) from the start of measurement; A method for determining a variable rotation index by sequentially determining a rotation angle and a rotation angular velocity during J rotations of the eccentric rotor from the unit angle Δθ [rad] and the rotation time Δt [s], or the unit angle Δθ [rad] and the velocity, The angle between the horizontal line and the line connecting the center of rotation and center of gravity of the eccentric rotor at the start of the measurement of the rotation time is defined as θ 0 The rotation angle at the start of the analysis is θ 1 , the rotational angular velocity at that time is ω １ , the rotation angle is θ １ The average friction torque in the measurement section between θ and T ｆｍ , the moment of inertia of the eccentric rotor is I, the rotation angle θ from the start of the measurement and the rotation angular velocity ω at the start of the analysis １ ω, which is the square of １ 2 and the average bearing friction index [-2T ｆｍ / I] into the following formula to find the value of E, ##EQU00011## The difference between the square of the instantaneous rotational angular velocity ω and the value of E above, [ω ２ -E] was calculated, and the value of C was introduced into the difference value so that the center of the fluctuation of the difference becomes 0 [ω ２ -E + C] Based on the following formula 9, the trigonometric function of the amplitude A with respect to the rotation angle θ from the start of the measurement, −A sin(θ+θ 0 ) to approximate it, [0090] The value of the amplitude A obtained from the trigonometric approximation of the amplitude A based on the above formula is determined as a fluctuation rotation index A of the eccentric rotor, and the phase difference θ 0 A method for determining a fluctuation rotation index.

4. The relationship between the variable rotation index A, the value of which is determined in the variable rotation index determination method according to any one of claims 1 to 3, and each quantity of the eccentric rotor is described by the following formula (1), and the quantities M, g, r of the eccentric rotor are calculated using the variable rotation index A and formula (1). ｇ , a method for determining the amount of any of I. [0010] In the formula (1), I is the moment of inertia of the eccentric rotor, M is the mass of the eccentric rotor, g is the gravitational acceleration, r ｇ (However, r ｇ >0) represents the distance between the center of gravity of the eccentric rotor and the center of rotation.

5. Rotating the eccentric rotor by applying a rotational torque to the eccentric rotor that is rotatably supported by the bearing to be measured; Stopping the application of the rotational torque, and sequentially measuring a rotation time Δt [s] or a speed per unit angle Δθ [rad] of the eccentric rotor during a period during which the eccentric rotor rotates J (J is an integer) from a measurement start, which is an arbitrary time point after the start of rotation due to the free-running rotation of the eccentric rotor; A method for determining an average friction torque and an instantaneous friction torque by sequentially determining a rotation angle and a rotation angular velocity during J rotations of the eccentric rotor from the unit angle Δθ [rad] and the rotation time Δt [s], or from the unit angle Δθ [rad] and the speed, The rotation time Δt [s] is measured n times (n=2π / Δθ, n is an integer) during one rotation of the eccentric rotor, and the measurement section during which the eccentric rotor makes J rotations is divided into one or more divided measurement sections, each of which corresponds to k (k is an integer and is determined for each divided measurement section, which will be described later) rotations of the eccentric rotor. For each of the one or more divided measurement sections, the rotation angle at the start of analysis of the divided measurement section out of the number of measurements 2Jπ / Δθ until the eccentric rotor makes J rotations in the divided measurement section is defined as θ. 1 [rad], and the rotational angular velocity at that time is ω １ [rad / s] (the subscript "1" indicates the start of the analysis, and the value of the symbol with the subscript "1" is determined for each divided measurement section and may have a different value from the same symbol in any of claims 1 to 3), and for j = 1, 2, ..., n k, the rotation angle from the start of the analysis of the divided measurement section to immediately after the j-th measurement is expressed as θ ｊ+1 [rad], and the rotational angular velocity at that time is ω ｊ+1 The angular velocity immediately after k rotations from the start of the analysis of the divided measurement section, that is, at the end of the analysis of the divided measurement section, is expressed as ω ｎｋ+1 [rad / s], and the average friction torque of the bearing in the divided measurement section is T ｆｍ When the moment of inertia of the eccentric rotor is I, For j = 1, 2, ..., nk, the rotation angle θ immediately after the j-th measurement from the start of the analysis ｊ+1 Calculate the value of [rad] from the following formula: [0010] Average bearing friction index [-2(T ｆｍ / I) [rad / s 2 Calculate the value of from the following formula: [0025] Average rotational angular velocity ω ｍ [rad / s], [0030] By setting the value of Calculating an average bearing friction index and an average rotational angular velocity for each of the divided measurement sections, and determining an approximation expression that expresses a relationship between the average bearing friction index and the average rotational angular velocity for each of the divided measurement sections; From the above approximation, the instantaneous bearing friction index [−2(T ｆ / I) [rad / s 2 ] relationship, The average bearing friction index [-2(T ｆｍ / I)] or the instantaneous bearing friction index [−2(T ｆ / I)], a fluctuating rotation index A is determined by the fluctuating rotation index determination method according to any one of claims 1 to 3, and a moment of inertia I of the eccentric rotor is determined from the fluctuating rotation index A by the method according to claim 4; The moment of inertia I and the average bearing friction index [-2T ｆｍ / I] and the average friction torque T ｆｍ and further determining the moment of inertia I and the instantaneous bearing friction index [-2T ｆ / I] and the instantaneous friction torque T ｆ A method for determining friction torque.

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