JP5757526B2 - Diagnostic method for synchronization accuracy of rotating biaxial motion - Google Patents

Description

  The present invention relates to a method for diagnosing rotational biaxial motion, that is, synchronization accuracy of rotational motion about two orthogonal axes.

  Conventionally, a three-axis control machining center having three orthogonal translation axes has been used for machining parts used in industrial products such as molds, and the accuracy of synchronous control of any two axes of the three-axis control machining center. In order to diagnose this, the DBB (Double Ball Bar) method is generally used.

  According to the DBB method, a transducer is built in, and a telescopic bar is held on two axes of a three-axis control machining center, and a circular motion command is given. Then, by measuring the amount of change in the expansion and contraction of the bar during the operation of the three-axis control machining center, the radial distance variation that occurs in the circular motion, that is, the deviation from the reference circle is detected. The accuracy of is diagnosed.

In recent years, in order to cope with more complicated machining of parts, a 5-axis control machining center in which two axes of rotation are added to three axes of translation is becoming widespread (for example, see Patent Document 1).
FIG. 10a is a perspective view showing an example of a 5-axis control vertical machining sensor. As shown in FIG. 10a, the 5-axis control vertical machining center is obtained by mounting an inclined circular table 10 having an A axis and a C axis as rotation axes on a table of a 3-axis control vertical machining center. The 5-axis control vertical machining center is an operation mode in which two rotation axes are indexed (fixed) and processed with three translation axes, an operation mode in which only one rotation axis is indexed and machining is performed with three translation axes and one rotation axis, and It can operate in an operation mode in which machining is performed by simultaneously operating two rotation axes and three translation axes.

However, according to the DBB method, it is possible to diagnose the accuracy of the synchronous motion of the three axes including any one of the two rotational axes (A axis and C axis) of the five-axis control vertical machining center. The synchronization accuracy of the biaxial motion could not be diagnosed (see, for example, Patent Document 2).
In order to diagnose the synchronization accuracy of the rotating biaxial motion, there is only a very expensive method such as using an expensive high-precision gyro sensor. Even if the DBB method can be developed to diagnose the synchronization accuracy of the rotating biaxial motion, an expensive sensor is also required for implementing the DBB method, which is costly.

  Further, the diagnosis of the synchronization accuracy of the rotating biaxial motion is necessary not only when the end plate 11 is moved not only in the 5-axis control machining center but also in the parallel mechanism as shown in FIG. 10b.

JP 2008-73813 A JP 2004-219132 A

  Accordingly, an object of the present invention is to provide a method capable of easily diagnosing the synchronization accuracy of a rotating biaxial motion at a low cost.

  In order to solve the above-mentioned problems, the present invention is a method for diagnosing the synchronization accuracy of rotational motion around two orthogonal axes, and (1) a flat surface that is rotatably supported around the two axes. (2) The plate is periodically moved from the horizontal position around one of the two axes at an angle given by the amplitude of the sine function. And rotating the sphere around the other of the two axes periodically with an angle given by an amplitude of a sine function that is + 90 ° out of phase with the sine function. Rolling on the plate surface without sliding movement, and (3) detecting the deviation of the trajectory of the sphere on the plate surface from a pre-calculated reference circle, thereby rotating the plate around the two axes. It is obtained by constituting the method characterized by diagnosing the motion of synchronization accuracy.

  In the above configuration, when the trajectory of the movement of the sphere on the plate surface is an ellipse and the major and minor axes of the ellipse are aligned with the two axes, an error occurs in the amplitude of the rotational motion around the two axes. The amplitude error can be quantitatively detected based on the fact that the amplitude error is proportional to the difference between the lengths of the major axis and the minor axis of the ellipse.

  Alternatively, when the trajectory of the movement of the sphere on the plate surface is an ellipse, and the major axis or minor axis of the ellipse does not match the two axes, the amplitude and phase difference of the rotational motion around the two axes It is determined that an error has occurred, or that an error has occurred only in the phase difference of the rotational motion around the two axes, and the phase difference error has the major axis or the minor axis out of the two axes. The phase difference error can also be detected quantitatively based on the fact that it is in a proportional relationship with the angle formed by the closer axis.

In the above-described configuration, the sphere preferably has a two-layer structure including a spherical core and a jacket surrounding an outer surface of the core, and more preferably, the core is made of a metal or the like. The outer cover is formed of a flexible material such as rubber.
Furthermore, when the outer cover is made of rubber, the plate is preferably made of an acrylic plate.

  According to the present invention, a sphere is placed on a flat plate surface that is supported so as to be rotatable independently of each other about two rotation axes, and the plate is moved by a sine function that is 90 degrees out of phase with each other about the two axes. The rotation accuracy of the rotating biaxial motion is diagnosed by periodically rotating it at an angle given by the amplitude and detecting the deviation from the reference circle of the trajectory of the sphere on the plate surface. Diagnosis can be performed very easily and at low cost without using an expensive DBB or high-precision gyro sensor as in the prior art.

Fig. 2 is a flow diagram of a method according to the present invention. It is a perspective view which shows the state which put the ball | bowl in the predetermined position on the plate surface in a horizontal position. It is the side view which looked at FIG. 2 in the y-axis direction, and is a figure which shows the state which inclined angle (theta) to the x-axis direction. It is a photograph which shows a series of processes of the experiment which makes a ball roll a pendulum. It is the graph which plotted the measured value of the height and deflection width of the ball | bowl at the end of the pendulum movement when carrying out the rolling pendulum movement of the ball | bowl. It is the graph which plotted the measured value of the time until the inclination | tilt angle | corner rolls a predetermined distance when a sphere rolls on the inclined plate surface. It is a top view which illustrates the locus | trajectory of the motion of the sphere on a plate surface. It is a graph which shows the relationship between the difference | error of an amplitude when the error has arisen in the amplitude of biaxial rotational motion, and the difference of the length of the major axis and minor axis of the elliptical orbit of the sphere on a plate. Relationship between phase difference error and angle between major axis of elliptical orbit of sphere on plate and x-axis when error occurs in both amplitude and phase difference of biaxial rotational motion, or only phase difference It is a graph which shows. (A) is a perspective view showing an example of a 5-axis control vertical machining center, and (b) is a perspective view showing an example of a parallel mechanism.

  Hereinafter, preferred embodiments of the present invention will be described with reference to the accompanying drawings. FIG. 1 is a flow diagram of a method according to the present invention. Referring to FIG. 1, according to the present invention, first, as shown in FIG. 2, a flat support is rotatably supported independently of each other around two axes 3 and 4 whose diagnostic accuracy of rotational motion is to be diagnosed. A sphere 2 is placed at a predetermined position on the plate surface 1a (S1 in FIG. 1). In FIG. 2, the x axis and the y axis are set on the two axes 3 and 4 respectively.

In this case, the sphere 2 preferably has a two-layer structure including a spherical core and a jacket surrounding the outer surface of the core, and more preferably, the core is a high-density material such as metal. The jacket is formed from a flexible material such as rubber.
Furthermore, when the outer cover is made of rubber, the plate 1 is preferably made of an acrylic plate.
In this embodiment, a mouse ball (diameter 22 mm, mass 31 g, rubber jacket) incorporated in a computer mouse is used as the sphere 2, and an acrylic plate is used as the plate 1.

Next, the plate 1 is moved from the horizontal position around one of the two axes (for example, the y-axis) by an angle θ = θ ₀ sin ωt given by the amplitude of the sine function (where θ ₀ is from the horizontal position) And ω is an angular velocity, and t is time.) And the sine function around the other of the two axes (for example, the x-axis). Rotating the sphere 2 without sliding movement on the plate surface 1a by periodically rotating with an angle θ ′ = θ ₀ sin (ωt + 90 °) given by the amplitude of a sine function that is + 90 ° out of phase (S2 in FIG. 1).

  Thus, the sphere 2 oscillates simply on the plate surface 1a when viewed on the zx plane due to the rotational motion of the plate 1 around the y-axis, and at the same time, the yz plane due to the rotational motion of the plate 1 around the x-axis. When viewed from above, the plate surface 1a undergoes a single vibration with a phase shifted by + 90 ° from the simple vibration. As a result, when viewed on the xy plane, the sphere 2 rolls in a circular orbit on the plate surface 1a.

In this case, the values of θ ₀ and ω are determined so that the circular orbit of the sphere 2 becomes a predetermined reference circle. The method for determining the values of θ ₀ and ω is as follows.
Now, consider the case where the plate 1 is rotated about the x-axis and the y-axis in FIG. FIG. 3 is a view showing a state in which the plate 1 is fixed around the x axis, rotated around the y axis, and inclined by an angle θ in the x direction.

In FIG. 3, the coordinate system fixed to the plate 1 is Σ _m (X _m Y _m Z _m coordinate system), and the coordinate system fixed at the center of gravity of the sphere 2 is Σ _B (X _B Y _B Z _B coordinate system). ). The forces acting on the sphere 2 are assumed to be a frictional force f, a centrifugal force p, and gravity Mg. In FIG. 3, F represents the resultant force of the frictional force f and the centrifugal force p.

At this time, the equation of motion of the sphere 2 rolling on the plate surface 1a is that the sphere 2 ignores the influence of the rubber jacket as a solid body having a constant density, and θ (t) = θ ₀ sin ωt (in FIG. 3). The value of θ measured clockwise from the horizontal position is assumed to be positive.) Further, an attenuation term proportional to the velocity of the sphere 2 is added, and the following equation is obtained.
Here, ^m X _B is the X coordinate of the coordinate system Σ _B viewed from the coordinate system Σ _m , M is the mass of the sphere 2, g is the gravitational acceleration, and D is the attenuation coefficient.

The equation of motion for the rotational motion around the center of gravity of the sphere 2 is as follows.
Here, I is the moment of inertia around the center of the sphere 2, and r is the radius of the sphere 2.

Equation (2)
From the equations (1) and (3),
Get.

Further, since the ball 2 rolls without slipping, the following equation is established.
Here, r is the radius of the sphere 2 and φ is the rotation angle of the sphere 2.
And by differentiating equation (5) with time t,
Get.

By substituting Equation (6) and the moment of inertia I = (2/5) Mr ² of a sphere with uniform density into Equation (4),
Or, D _M = D / M,
Get.

Even when the plate 1 is fixed around the y-axis and rotated around the x-axis, except for the point that θ ′ = θ ′ ₀ sin (ωt + 90 °) in the equation (9), It is the same.
Thus, considering the case where θ is sufficiently small, the equation of motion of the sphere 2 on the XY plane is
It becomes.

Next, the attenuation coefficient D is measured. This is done as follows. A cylindrical pendulum made of the same material as the plate 1 (made of acrylic in this embodiment) (with a diameter of 128 mm) is placed sideways, and a ball 2 is placed on the inner wall surface of the cylinder to form a rolling pendulum. Then, as shown in FIG. 4, the sphere 2 is held by hand and released from the state where it is stationary at the initial position h ₁ (height 64 mm = cylinder radius R) of the cylindrical inner wall surface. Move the pendulum up. Each time the ball 2 reaches the end of the pendulum movement, the height h ₂ , h ₃ , h ₄ ,... H _n of the ball 2 at that time is measured, and the swing widths b ₀ , b ₀ ′ are measured. , B ₁ , b ₁ ′ (measured by a dash symbol indicating a return path). The measurement results are shown in the graph of FIG. In the graph of FIG. 5, the vertical axis represents height or runout width (mm), and the horizontal axis represents elapsed time (s). Also, ● represents the height, and ○ represents the swing width.

  Moreover, in this experiment, as a result of measuring the period of the rolling pendulum, an actual measurement value of 0.53 seconds was obtained. On the other hand, assuming that the ball 2 rolls without slipping, the period of this rolling pendulum obtained by theoretical calculation is 0.546 seconds. From this, the ball 2 rolls without slipping during the pendulum movement. It was confirmed that it was moving.

Then, the attenuation coefficient D is obtained according to the following equations (12) and (13).
Here, δ is a logarithmic attenuation rate, and ζ is an attenuation ratio. M is the mass of the sphere 2 and k _κ = 5Mg / [7 (R−r)], where R is the radius of the cylinder and r is the radius of the sphere 2.
As a result of the calculation, an attenuation coefficient D = 0.053 was obtained in this experiment.

Since the above formulas (12) and (13) are calculation formulas when the centrifugal force does not act on the sphere 2, they are obtained in the above experiment so that the influence of the centrifugal force acting on the sphere 2 is reflected. Correct the value of the damping coefficient D. This correction is performed by numerical calculation using the above formulas (9) to (11).
That is, the radius of the reference circle is determined in advance in consideration of the radius of the sphere 2 and the size of the plate 1 (for example, 100 mm), and an appropriate D value (D = 0.053 correction value) in Equation (9). To calculate the value of the damping coefficient D such that the sphere 2 draws a reference circle, and θ ₀ (maximum rotation angle from horizontal position; hereinafter referred to as “maximum tilt angle”) and ω (angular velocity) ) Value.

By this numerical calculation, D = 0.016 is obtained as a damping coefficient taking into account the centrifugal force acting on the sphere 2. On the other hand, for θ ₀ and ω, there are an infinite number of pairs of θ ₀ and ω for one value of the radius of the reference circle. Therefore, an appropriate one that matches the actual situation is determined. To do.

In this case, first, an allowable numerical range of the maximum inclination angle θ ₀ is determined as follows.
In FIG. 2, when the plate 1 is tilted in the x-axis direction by an angle θ, the initial speed of the sphere 2 is set to zero, the moving distance L of the sphere 2, the acceleration a in the slope direction of the center of gravity of the sphere 2, and the time t Satisfies the following equation.

Then, the plate 1 is actually tilted and the sphere 2 is rolled in the x-axis direction, and the time t required to reach L = 60 cm is measured and this measured value is obtained according to the equations (14) and (15). Compare with the value. FIG. 6 is a graph showing the result of comparison between actual measurement values and theoretical values. In the graph of FIG. 6, the vertical axis and the horizontal axis represent time (s) and inclination angle (°) until L = 60 cm, respectively, ◯ represents an actual measurement value, and solid line represents a theoretical value.
From the graph of FIG. 6, it can be seen that the measured value and the theoretical value do not match when the inclination angle θ is small. This is because the sphere 2 performs a meandering motion. However, when the inclination angle θ is 2 ° or more, the sphere 2 starts a stable rolling motion, and the measured value and the theoretical value almost coincide.

From the experimental results, it was found that the maximum inclination angle θ ₀ is preferably 2 ° or more.
Since the length of the plate 1 in the x-axis direction and the rotational speed (angular velocity ω) around the y-axis are limited, if the maximum inclination angle θ ₀ is too large, the sphere 2 is moved on the plate surface 1a. It becomes impossible to make a single vibration in the x-axis direction. Considering this point, the preferable numerical range of the maximum inclination angle θ ₀ is determined to be 2 ° to 15 °.

Then, an appropriate value of the maximum inclination angle θ ₀ within a range of 2 ° to 15 ° is determined, and a corresponding value of ω is determined. For example, it is determined that the radius of the reference circle = 100 mm, the maximum inclination angle θ ₀ = 3 °, and ω = 0.5 rad / s (corresponding to the cycle T = 4.0 s).

In this way, the sphere 2 is placed on the plate surface 1a, and is simply oscillated in the xz plane and the yz plane, so that the sphere 2 rolls in a circular orbit on the plate surface 1a.
Then, by detecting the deviation of the trajectory of the motion of the sphere 2 on the plate surface 1a from the reference circle, the synchronization accuracy of the rotational motion about the two axes is diagnosed (S3 in FIG. 1).

That is, as shown in FIG. 7a, when the trajectory of the movement of the sphere 2 is a circle and coincides with or substantially coincides with the reference circle, it is determined that the synchronization error of the rotating biaxial movement does not occur.
Also, as shown in FIG. 7b, when the trajectory of the movement of the sphere 2 is an ellipse and the major and minor axes of the ellipse are aligned with the x-axis and the y-axis, a synchronization error, that is, a rotational biaxial motion It is determined that there is an error in the maximum inclination angle (amplitude) θ ₀ of.

In this case, if the synchronization error is constant, the error of the maximum inclination angle (amplitude) θ ₀ of the rotating biaxial motion is proportional to the difference between the major axis and the minor axis of the ellipse. Thus, the error of the maximum inclination angle (amplitude) θ ₀ of the rotating biaxial motion can be quantitatively diagnosed.

Also, as shown in FIG. 7c, when the trajectory of the movement of the sphere 2 is an ellipse and the major and minor axes of the ellipse do not match the x-axis and the y-axis, a synchronization error, that is, a rotational biaxial motion It is determined that there is an error in the maximum inclination angle (amplitude) θ ₀ and the phase difference α, or that only the phase difference α has an error.

  In this case, if the synchronization error is constant, the error of the phase difference α of the rotating biaxial motion is proportional to the angle between the major axis or the minor axis of the ellipse and the closest axis of the rotating two axes. Based on the proportional relationship, the error of the phase difference α of the rotating biaxial motion can be quantitatively diagnosed.

(Experiment)
The effect of the present invention was confirmed by experiments.
[Experiment 1]
A plate 1 made of the above-mentioned acrylic plate is attached to a robot (MOTOMAN-DIA10 made by Yaskawa Electric Co., Ltd.) that can rotate biaxially, and the above-mentioned sphere 2 (mouse ball [diameter 22 mm, mass 31 g, rubber) 2) (2 axis phase difference α = 90 °, period T = 3.3 s), the maximum inclination angle of 2 axes (x axis, y axis) satisfies the condition of θ ₀ + θ ′ ₀ = 6 ° Then, the biaxial rotation was performed so that the radius R of the reference circle was 100 mm, and the trajectory of the movement of the sphere 2 over time was photographed with a camera. Moreover, the gyro sensor was arrange | positioned at the plate 1, and the inclination angle regarding each axis | shaft of the plate 1 was measured during the biaxial rotation.

From the image photographed by the camera, the movement locus of the sphere 2 becomes an ellipse, the major and minor axes of the ellipse are aligned with the x-axis and the y-axis, and the change in the value of Δθ = θ ₀ −θ ′ ₀ It has been confirmed that the ratio of the major axis to the minor axis of the ellipse changes as the time elapses.
Based on the image taken by the camera and the measured value of the gyro sensor, the relationship between Δθ = θ ₀ −θ ′ ₀ and the difference between the corresponding major axis and minor axis length of the elliptical orbit of the sphere 2 is expressed. Examined.
On the other hand, using the equations (9) to (11), the simulation was performed under the conditions of D = 0.016 (D _M = 0.5), θ ₀ + θ ′ ₀ = 6 °, T = 3.3 s, and R = 100 mm. The relationship between Δθ = θ ₀ −θ ′ ₀ and the difference in length between the major axis and the minor axis of the corresponding ellipse was examined.
The results of the experiment and simulation are shown in the graph of FIG.

In the graph of FIG. 8, the vertical axis represents the difference (mm) between the major axis and the minor axis of the ellipse, and the horizontal axis represents Δθ (°). Further, in the graph, ◯ represents the result of the experiment, and the solid line represents the result of the simulation.
From the graph of FIG. 8, when the synchronization error is constant, the error Δθ of the maximum inclination angle (amplitude) of the rotational biaxial motion is proportional to the difference between the major axis and minor axis length of the elliptical orbit of the sphere 2. It was confirmed that there was.

[Experiment 2]
The same robot, plate 1 and sphere 2 as in Experiment 1 are used, a gyro sensor is arranged on the plate 1, and the maximum inclination angle of two axes (x axis, y axis) is θ ₀ + θ ′ ₀ = 6 °. Satisfying the conditions, the cycle T = 3.3 s, the radius R of the reference circle R = 100 mm, the biaxial rotational motion is shifted so that the phase difference α of the biaxial rotational motion gradually deviates from 90 °, and the sphere 2 over time The movement track was taken with a camera. In addition, a gyro sensor was disposed on the plate 1 and the tilt angle with respect to each axis of the plate 1 during the biaxial rotational movement was measured.

From the image taken by the camera, the locus of motion of the sphere 2 becomes an ellipse, and the major and minor axes of the ellipse do not match the x and y axes, and as the value of Δα = 90 ° −α changes. It was confirmed that the inclination angle of the major axis of the ellipse with respect to the x-axis changed.
And based on the image image | photographed with the camera, the relationship between (DELTA) (alpha) = 90 degrees-(alpha) and the angle (beta) which the long axis of the elliptical orbit of the sphere 2 corresponding to it makes with an x axis was investigated.
On the other hand, using the equations (9) to (11), the simulation was performed under the conditions of D = 0.016 (D _M = 0.5), θ ₀ + θ ′ ₀ = 6 °, T = 3.3 s, and R = 100 mm. The relationship between Δα = 90 ° −α and the angle β between the long axis of the corresponding ellipse and the x axis was examined.
The results of the experiment and simulation are shown in the graph of FIG.

In the graph of FIG. 9, the vertical axis represents the angle β (°) between the long axis of the ellipse and the x axis, and the horizontal axis represents Δα (°). Further, in the graph, ◯ represents the result of the experiment, and the solid line represents the result of the simulation.
From the graph of FIG. 9, when the synchronization error is constant, the phase difference error Δα is within the range of the elliptical orbit of the sphere 2 when the phase difference error Δα of the rotational biaxial motion is within the range of 0 ° to about 45 °. It was confirmed that the major axis is proportional to the angle formed by the x axis.

DESCRIPTION OF SYMBOLS 1 Plate 1a Plate surface 2 Sphere 3 One rotating shaft 4 The other rotating shaft 10 Inclined circular table 11 End plate

Claims (9)

A method for diagnosing the synchronization accuracy of rotational motion about two orthogonal axes,
(1) A sphere is placed at a predetermined position on a flat plate surface that is rotatably supported around the two axes.
(2) The plate is periodically rotated from one horizontal axis around one of the two axes at an angle given by the amplitude of the sine function, and the other of the two axes Rolling the sphere around the plate without sliding motion by periodically rotating around the axis with an angle given by the amplitude of the sine function that is + 90 ° out of phase with the sine function;
(3) A method of diagnosing the synchronization accuracy of the rotational motion about the two axes by detecting a deviation of the trajectory of the sphere on the plate surface from a pre-calculated reference circle. .   When the trajectory of the movement of the sphere on the plate surface is an ellipse, and the major axis and the minor axis of the ellipse are aligned with the two axes, there is an error in the amplitude of the rotational movement about the two axes. 2. The method according to claim 1, wherein the amplitude error is quantitatively detected based on a determination that the amplitude error is proportional to a difference between the major axis and the minor axis of the ellipse. the method of.   When the trajectory of the movement of the sphere on the plate surface is an ellipse and the major axis or minor axis of the ellipse is not aligned with the two axes, there is an error in the amplitude and phase difference of the rotational motion around the two axes. It is determined that an error has occurred or only an error has occurred in the phase difference of the rotational motion around the two axes, and the phase difference error is close to the major axis or the minor axis of the two axes. The method according to claim 1, wherein the phase difference error is quantitatively detected based on being proportional to an angle formed with the other axis.   The method according to claim 1, wherein a maximum rotation angle of the plate from the horizontal position is 2 ° to 15 °.   The method according to any one of claims 1 to 4, wherein the sphere has a two-layer structure including a spherical core and a jacket surrounding an outer surface of the core.   6. The method of claim 5, wherein the core is formed from a high density material and the jacket is formed from a flexible material.   The method according to claim 5 or 6, wherein the outer jacket is made of rubber.   The method according to claim 5, wherein the core is made of a metal.   9. The method according to claim 7, wherein the plate is made of an acrylic plate.