JP5967741B1 - Conveying device and vibration suppression control method thereof - Google Patents

Abstract

The present invention provides a vibration suppression control method and a conveying device that can reduce a lateral vibration that occurs in an elevating carriage even when the natural angular frequency changes every moment as the elevating carriage moves up and down. A vibration suppression control method for a conveying apparatus 10 is such that a control unit 104 obtains a first natural angular frequency of vibration when an elevating carriage 102 on which a conveyed product 20 is placed is at a first height position. In addition, the acceleration time of the traveling carriage that suppresses the vibration induced based on the first natural angular frequency is obtained as a provisional acceleration time, and the lifting carriage 102 on which the conveyed product 20 is placed is at the second height position. A step of calculating a second natural angular frequency of vibration in a certain case and calculating a deceleration time of the traveling carriage in which the vibration derived based on the second natural angular frequency is suppressed as a temporary deceleration time. [Selection] Figure 6

Description

  The present invention relates to, for example, a transport apparatus including a traveling carriage that travels along an installation surface, and a lifting carriage that is provided on the traveling carriage and moves up and down, and a vibration suppression control method thereof.

Patent Document 1 discloses a stacker crane having a traveling carriage capable of reciprocating traveling on a traveling rail, an elevating mast erected on the traveling carriage, and an elevating platform that carries a transport object and moves up and down along the elevating mast. The vibration control method is described.
The most common form of travel speed pattern for a stacker crane is a so-called trapezoidal speed pattern based on commands for constant acceleration time, constant speed, constant deceleration time and travel distance. A speed command based on the trapezoidal speed pattern is outputted from the control device to the traveling carriage and the lifting platform on which the conveyed product is placed, and the traveling carriage and the lifting carriage reach the target position.
However, when the traveling carriage stops, the lifting platform viewed from the traveling carriage swings due to inertial force, and a waiting time is required until the magnitude of the lateral swing is attenuated to an allowable value or less.
Here, when the traveling carriage is stopped at a constant speed from the state where the lifting carriage is not shaken, the position y (side shaking) of the lifting carriage viewed from the running carriage is expressed by the following equation.

y = (β / ω _n ² ) · (cos (ω _n t) −1) Formula (1)

Here, β is the deceleration of the traveling carriage, ω _n is the natural angular frequency, t is the deceleration time from the start of deceleration to the deceleration stop, and ω _n t is the phase angle from the start of deceleration to the deceleration stop. In addition, there is a case to be referred to the phase angle ω _{n t} and the phase angle θ.

If the height position of the lifting platform is fixed, the natural angular frequency ω _n is constant. Therefore, if the deceleration time t is set to the deceleration time T3 represented by the following equation so that the phase angle ω _n t is a positive integer n times 2π, the value of (cos (ω _n t) −1) Is zero, and the position (lateral shake) y of the lifting platform as seen from the traveling carriage is zero.

T3 = 2nπ / ω _n formula (2)

  In the trapezoidal speed pattern, acceleration starts and ends and deceleration starts and ends at four inflection points of speed, and the acceleration, which is a differential value of speed, increases, so the strength to the machine, vibration, abnormal noise, etc. May occur. Therefore, this acceleration is usually reduced by S-shaped acceleration / deceleration at each inflection point.

In this respect, in Patent Document 2, in the traveling carriage, correction speed commands are added during a minute time at the four places where the start and end of acceleration of the S-shaped trapezoidal speed and the start and end of deceleration are added. A technique is described in which a reverse waveform is applied to the lateral vibration waveform to cancel the lateral vibration, thereby reducing the lateral vibration magnitude of the lift carriage.
As an example, a corrected speed command Vrev when an S-curve acceleration / deceleration (two-stage moving average acceleration / deceleration) command is added to a speed command based on a trapezoidal speed pattern and a corrected speed command is further added can be obtained by the following equation.

Vrev = a / ω _n ² formula (3)

Here, a is a second-order differential value of velocity or a differential value of acceleration, and ω _n is a natural angular frequency.
The natural frequency Nc of the horizontal oscillation of the lift carriage is small, and the natural angular frequency ω _{n at} 2 Hz is obtained by the following equation.

ω _n = 2 · π · Nc = 2 · π · 2 = 12.57 (rad / s) Equation (4)

The second-order differential value of acceleration or the differential value a of acceleration when the minute time Δt of acceleration is 0.05 s and the constant acceleration α is 1 m / s ² is obtained by the following equation.

a = α / Δt = 1 / 0.05 = 20 (m / s ³ ) Formula (5)

  Therefore, by substituting Equation (4) and Equation (5) into Equation (3), the corrected speed command Vrev is expressed by the following equation.

Vrev = a / ω _n ² = 20 / 12.57 ² = 0.127 (m / s) Equation (6)

  The correction speed Vrev is stepped in a minute time Δt, and the constant acceleration α at the rising edge and the deceleration β at the falling edge are obtained by the following equations, respectively.

α = dVrev / dt equation (7A)
β = −dVrev / dt Formula (7B)

  As can be seen from these equations (7A) and (7B), when the speed response of the AC servo is good, the absolute values of acceleration and deceleration are remarkably large.

JP 2010-30728 A Japanese Patent No. 3750633

In the technique described in Patent Document 1, the time of the acceleration region and the deceleration region is set to a time that is an integer multiple of twice or more of the vibration period, and the symmetrical absolute values are the same acceleration and deceleration, The horizontal run-out of the lift truck carrying the transported goods is reduced.
However, when the traveling carriage and the lifting carriage are operated simultaneously and the lifting carriage moves on a diagonal line, the elevating carriage on which the transported article is placed changes the natural vibration period with the change in height. The time of the deceleration region is different in length, and it is not possible to sufficiently reduce the lateral swing of the lifting carriage on which the conveyed product is placed. In addition, the data of the natural vibration period at the height position of the lifting carriage on which the conveyed product is placed is a combination of the parameters of the mass of the conveyed product and the height position, and is a huge amount.

In the technique described in Patent Document 2, when the natural frequency at the height position of the lifting carriage on which the transported object is placed is 0.5 to 10 Hz, the lateral swing of the lifting carriage on which the traveling object is traveling is placed. The correction speed is added to suppress this.
However, the acceleration generated at the correction speed may cause adverse effects (strength, vibration, and sound) on the transport device.

  An object of the present invention is to provide a vibration damping control method and a conveying device that can reduce the lateral vibration generated in the lifting cart even when the natural angular frequency changes with the lifting and lowering of the lifting cart. .

A vibration damping control method for a transfer device according to the first invention that meets the above-described object includes a traveling carriage that travels along an installation surface,
An elevating carriage that is provided in the traveling carriage and moves up and down with a transported object;
A control unit for controlling the traveling carriage and the elevating carriage, and a vibration damping control method for a conveying apparatus comprising:
Obtaining a relationship between a height position of the lifting carriage and a natural angular frequency of vibration generated in the lifting carriage;
Based on the relationship, the control unit obtains a first natural angular frequency of the vibration when the carriage on which the transport object is placed is at a first height position, and is a positive integer multiple of 2π. Is calculated by dividing the first natural angular frequency by a temporary acceleration time , and based on the relationship, the vibration of the lift carriage with the transported object on the second height position is calculated. Obtaining a second natural angular frequency, and calculating a temporary deceleration time obtained by dividing a positive integer multiple of 2π by the second natural angular frequency ;
The control unit obtains a minute time obtained by equally dividing the provisional acceleration time, and each natural angular vibration corresponding to each height position of the lifting carriage according to each elapsed time from the start of acceleration to the center time of each minute time. each micro phase angle multiplied by the fine small time number, up to the point where the acceleration time of the temporary has elapsed calculates the phase angle of the first tentative integrated phase angle of the first tentative positive of 2π A first correction coefficient obtained by dividing the positive integer multiple of 2π by the first temporary phase angle so as to approach an integral multiple is obtained, and a correction obtained by multiplying the temporary acceleration time by the first correction coefficient Calculating acceleration time, obtaining a minute time obtained by equally dividing the temporary deceleration time, and each unique position corresponding to each height position of the lift carriage by each elapsed time from the start of deceleration to the center time of each minute time Each minute phase angle obtained by multiplying the angular frequency by the minute time is used as the temporary deceleration time. Time points until calculates the phase angle of the second tentative integrated, the as the phase angle of the second tentative approaches the positive integer multiple of 2 [pi, the 2 [pi positive number several times said second tentative Calculating a corrected deceleration time obtained by multiplying the provisional deceleration time by the second correction coefficient ;
The control unit generating a first speed command of the traveling carriage according to a first trapezoidal speed pattern defined at least by the corrected acceleration time and the corrected deceleration time;
And a step of driving the traveling carriage in accordance with the first speed command to suppress the vibration.

In the vibration damping control method of the transport device according to the first invention,
A method for obtaining a relationship between a height position of the lifting carriage and the natural angular frequency of the vibration generated in the lifting carriage,
Obtaining a relationship between a height position of the lifting carriage on which the transported object is not placed and the natural angular frequency of the vibration generated in the lifting carriage as data by actual measurement or calculation;
Obtaining a linear regression equation for each height interval in which the data can be considered to be represented by linear approximation;
From the natural angular frequency calculated by the linear regression equation, a relational expression for calculating the natural angular frequency when the lifting carriage carrying the transported object of an arbitrary mass is at an arbitrary height position is obtained. And a step.

In the vibration damping control method of the transport device according to the first invention,
The control unit generates a second speed command of the lifting cart according to a second trapezoidal speed pattern defined by the corrected acceleration time and the corrected deceleration time of the traveling cart, and the first speed command and the It is also possible to output both the second speed command and drive both the traveling carriage and the lifting carriage.

In the vibration damping control method of the transport device according to the first invention,
0 and the control unit, the first correction coefficient is the ratio of the corrected acceleration time for acceleration time of the provisional, also reduced. When exceeding the range of 98 to 1.02, it is preferable that the corrected acceleration time is set as a new temporary acceleration time and the corrected acceleration time is calculated again.

In the vibration damping control method of the transport device according to the first invention,
0 and the control unit, the second correction factor is the ratio of the modified deceleration time for deceleration time of the provisional, also reduced. When exceeding the range of 98 to 1.02, it is preferable that the corrected deceleration time is set as the new temporary deceleration time and the corrected deceleration time is calculated again.

In the vibration damping control method of the transport device according to the first invention,
The first height position is preferably an acceleration start position of the lifting carriage.

In the vibration damping control method of the transport device according to the first invention,
The second height position is preferably a deceleration completion position of the lifting carriage.

A transport device according to a second invention that meets the above-described object is a traveling carriage that travels along an installation surface;
An elevating carriage that is provided in the traveling carriage and moves up and down with a transported object;
A controller that controls the traveling carriage and the lifting carriage based on a speed command represented by a trapezoidal speed pattern,
The lifting / lowering on which the transport object is placed based on the relationship between the mass of the transport object, the height position of the lift carriage, and the natural angular frequency of the vibration generated in the lift truck, which is determined in advance by the control unit. A first natural angular frequency of the vibration when the carriage is at the first height position is obtained, and a temporary acceleration time is calculated by dividing a positive integer multiple of 2π by the first natural angular frequency. In addition, based on the relationship, a second natural angular frequency of the vibration when the carriage on which the transported object is placed is at a second height position is obtained, and a positive integer multiple of 2π is calculated . the step of calculating a temporary deceleration time divided by the natural angular frequency of 2 to obtain the minute time obtained by equally dividing the acceleration time of the temporary, the lift according to the elapsed time to the center of the time for each minute time since the start of acceleration Each natural angular frequency corresponding to each height position of the carriage is multiplied by the minute time. The small phase angle, to the point where the acceleration time of the temporary has elapsed calculates the phase angle of the first tentative integrated, so that the phase angle of the first tentative approaches the positive integer multiple of 2 [pi, the 2 [pi A first correction coefficient obtained by dividing a positive integer multiple of the first correction phase angle by the first temporary phase angle is calculated, and a correction acceleration time obtained by multiplying the temporary correction time by the first correction coefficient is calculated. The minute time obtained by equally dividing the deceleration time is obtained, and each natural angular frequency corresponding to each height position of the lifting carriage by each elapsed time from the start of deceleration to the center time of each minute time is multiplied by the minute time. each minute phase angle is, up to the point where the deceleration time of the temporary has elapsed calculates the phase angle of the second tentative integrated, so that the phase angle of the second tentative approaches the positive integer multiple of 2 [pi, A second correction coefficient obtained by dividing the positive multiple of 2π by the second temporary phase angle is obtained, and the second deceleration coefficient is calculated at the temporary deceleration time. A command generator for executing a step of calculating a corrected deceleration time multiplied by a correction coefficient of 2 and a step of generating a speed command of the traveling vehicle based on a trapezoidal speed pattern defined at least by the corrected acceleration time and the corrected deceleration time Have

According to the first aspect of the present invention, it is possible to suppress the lateral shake that occurs in the lift carriage.
According to invention of Claim 2, the natural angular frequency which changes with the height positions of the raising / lowering carriage which carried the conveyed product can be calculated | required easily.
According to the third aspect of the present invention, the time required for the lifting carriage to reach the target position is reduced.
According to the fourth aspect of the present invention, it is possible to further suppress the lateral shake of the lift carriage.
According to the fifth aspect of the present invention, it is possible to further suppress the lateral shake of the lift carriage.
According to the invention described in claim 6, the provisional acceleration time can be easily obtained.
According to the seventh aspect of the present invention, the temporary deceleration time can be easily obtained.
According to the eighth aspect of the present invention, it is possible to provide a transfer apparatus in which the lateral movement of the lifting carriage is suppressed.

It is a block diagram of the conveying apparatus which concerns on one embodiment of this invention. (A) And (B) is explanatory drawing which shows the instruction | command by the trapezoidal speed pattern with respect to the driving | running | working trolley and the raising / lowering trolley with which the same conveying apparatus is respectively provided. It is an analysis model of the horizontal run-out of the raising / lowering cart which the conveyance apparatus has. It is a graph which shows the relationship (data of Table 1) between the height position of the raising / lowering cart which this conveyance apparatus has, and a natural angular frequency. (A), (B), and (C) are explanatory drawings which respectively show the raising / lowering carriage in the position of the lower limit of a movable range, the raising / lowering carriage, and the raising / lowering carriage which loaded the conveyed product. It is a flowchart which shows the vibration suppression control method of the conveyance apparatus. (A) And (B) is explanatory drawing which shows the temporary trapezoidal speed pattern of a driving | running | working cart and a raising / lowering cart, respectively.

Next, embodiments of the present invention will be described with reference to the accompanying drawings for understanding of the present invention. It should be noted that in the drawing, illustration of parts not related to the description may be omitted.
As shown in FIG. 1, the transport apparatus 10 according to an embodiment of the present invention includes a traveling carriage 101, an elevating carriage 102, and a control unit 104, and moves a conveyed product 20 placed on the elevating carriage 102 to a predetermined height. It can be transported to the target position. The conveyance device 10 is, for example, a stacker crane.
1 is a model simulating an actual stacker crane. Hereinafter, description will be made based on this model.

  The traveling carriage 101 can move in the horizontal direction along the installation surface. The traveling carriage 101 is fixed to a slider nut 24 that moves in the longitudinal direction of the ball screw 22 by a ball screw 22. The ball screw 22 is driven by a travel drive motor (AC servomotor) SVM1 through a coupling 26.

  The carriage 102 can move in the vertical direction on which the conveyed product 20 is placed. The elevating carriage 102 can move up and down along a portal mast 30 that is fixed to the traveling carriage 101 and extends in the vertical direction. The lifting carriage 102 is fixed to the timing belt 32 and moves up and down as the timing belt 32 rotates. The timing belt 32 is bridged between an upper pulley 34U provided on an upper portion of the portal mast 30 and a lower pulley 34L. The lower pulley 34L is a lifting drive motor (AC) fixed to the traveling carriage 101. Servo motor) Driven by SVM2.

The control unit 104 includes servo drivers SVA1 and SVA2 and a command generator CNT, and can control the travel drive motor SVM1 and the lift drive motor SVM2.
The servo drivers SVA1 and SVA2 are respectively connected to the travel drive motor SVM1 and the lift drive motor SVM2 and can drive the motors SVM1 and SVM2.
The command generator CNT can generate and output commands for driving the motors SVM1 and SVM2 to the servo drivers SVA1 and SVA2.
Note that the calculation performed by the command generator CNT to generate a command is realized by a program executed by a CPU mounted on the command generator CNT.

The commands that the command generator CNT outputs to the servo driver SVA1 and the servo driver SVA2 are acceleration (constant acceleration) periods I to II and constant speed periods as shown in FIGS. 2 (A) and 2 (B), respectively. This is a speed command based on a trapezoidal speed pattern determined by II to III and deceleration (constant deceleration) periods III to IV.
The traveling carriage 101 and the lifting carriage 102 move in parallel according to the speed command output from the command generator CNT. As a result, the lifting carriage 102 moves to the target position with the shortest path. Further, the lateral vibration (vibration in the traveling direction of the traveling carriage 101) when the elevating carriage 102 stops can be suppressed.

Next, the magnitude of the lateral deflection of the lifting carriage 102 viewed from the traveling carriage 101 will be described.
In an analysis model (see FIG. 3) in which the lifting platform 102 on which the portal mast 30 and the transported article 20 of the transport apparatus 10 are placed is regarded as a one-degree-of-freedom vibration system, the equation of motion of the lifting carriage 102 on which the transported article 20 is placed is It is represented by the following formula.
In the analysis model, the height position of the lifting carriage 102 (the height position from the lower end portion serving as the fixed end of the portal mast 30 to the center of the lifting carriage 102) h (see FIG. 1) does not change. It is fixed. Further, the viscous damping coefficient of the portal mast 30 is omitted because it is extremely small.

− (Mw + Md) · (d ² x / dt ² ) −k _s (x−u) = 0 Formula (A1)

Here, Mw is the mass of the conveyed product 20, Md is the mass of the lifting carriage 102, x is the position of the lifting carriage 102, u is the position of the traveling carriage 101, and k _s is the equivalent spring constant of the portal mast 30.

  The position (lateral deflection) y of the lifting carriage 102 viewed from the traveling carriage 101 is expressed by the following equation.

  y = x-u Formula (A2)

When the natural angular frequency and omega _n, natural angular frequency omega _n, the equivalent spring constant of the portal mast 30 k _s, and relational expression below formula mass of the mass and lifting carriage 102 of the transfer material 20 (Mw + Md) It becomes.

k _s / (Mw + Md) = ω _n ² formula (A3)

  Substituting equation (A2) and equation (A3) into equation (A1) yields:

d ² y / dt ² + ω _n ² = −d ² u / dt ² formula (A4)

Here, since d ² u / dt ² is the acceleration α1 (positive constant value) of the traveling carriage 101, the expression (A4) is as follows.

d ² y / dt ² + ω _n ² = −α1 Formula (A5)

  The solution of this differential equation is as follows.

y = (α1 / ω _n ² ) · (cos (ω _n t) −1)
= (Α1 / ω _n ² ) · (cos (θ) −1) Formula (A6)

Here, t is the elapsed time from the start of acceleration, ω _n t is the phase angle at time t, and θ is the phase angle.

The following can be understood from the equation (A6).
When the height position (height position from the fixed end of the lower part of the portal mast 30 to the center of the lift carriage 102) h is fixed and the natural angular frequency ω _n is constant, the acceleration time (acceleration Time from start to completion of acceleration) The phase angle θ at T1 is expressed by the following equation.

θ = ω _n · T1 Formula (A7)

If the phase angle θ is a positive integer n times 2π, (cos (θ) −1) becomes zero, and the lateral swing of the lifting carriage 102 (the position of the lifting carriage 102 as viewed from the traveling carriage 101) y is acceleration. It is zero regardless of α1 and the natural angular frequency ω _n .
Therefore, in order to make the lateral runout y of the lifting carriage 102 viewed from the traveling carriage 101 zero, the acceleration time T1 is obtained by dividing the positive integer n times 2π by the natural angular frequency ω _n as shown in the following equation. Must be set to a value.

T1 = 2nπ / ω _n formula (A8)

Expression (A8) holds true not only for the acceleration time T1 but also for the deceleration time T3.
The acceleration time T1 obtained by this equation (A8) is an example of the acceleration time of the traveling carriage 101 that is derived based on the natural angular frequency and in which lateral vibration (vibration) is suppressed, and the deceleration time T3 is It is an example of the deceleration time of the traveling vehicle 101 that is guided based on the natural angular frequency and in which the lateral vibration is suppressed.
However, when the elevating carriage 102 moves up and down, the natural angular frequency ω _n changes every moment, for example, as shown in FIG.
Therefore, in order to suppress the lateral deflection y of the transport apparatus 10, it is important to obtain the natural angular frequency ω _nh at an arbitrary height position h of the lifting carriage 102 as accurately as possible.
However, the combination data of the mass Mw of the conveyed product 20 and the height position h of the elevating carriage 102 is an enormous amount, and it is not easy to obtain the natural angular frequency ω _nh .
Therefore, a method for obtaining the natural angular frequency ω _nh at the height position h for each of A) the lifting carriage 102 not loaded with the transported object 20 and B) the lifting carriage 102 loaded with the transported object 20 will be described.

Here, the natural angular frequency ω _n , the natural angular frequency ω _nh , the natural angular frequency ω _nh (s), the natural angular frequency ω _nh (s + d), the natural angular frequency ω _nh (d), the natural angular frequency The number ω _nh (d + w) and the natural angular frequency ω _nh (s + d + w) are respectively defined as follows.

(1) Natural angular frequency ω _nh (s)
The natural angular frequency ω _nh (s) is a natural angular frequency of the lateral run-out y mainly composed of the portal mast 30 excluding the lift carriage 102 and the conveyed product 20.

(2) Natural angular frequency ω _nh (s + d)
The natural angular frequency ω _nh (s + d) is the natural angular frequency of the lateral shake y in the state shown in FIG. 5B, and the lifting carriage 102 on which the conveyed product 20 is not loaded is at an arbitrary height position h. It is the natural angular frequency in a certain case.

(3) Natural angular frequency ω _nh (d)
In the state shown in FIG. 5B, the natural angular frequency ω _nh (d) is zero in mass of the portal mast 30 and parts such as the upper pulley 34U attached to the portal mast 30 (excluding the traveling carriage 101). Is the natural angular frequency of the lateral runout y at an arbitrary height h of the lift carriage 102.

(4) Natural angular frequency ω _nh (d + w)
In the state shown in FIG. 5C, the natural angular frequency ω _nh (d + w) has zero mass of parts (excluding the traveling carriage 101) such as the portal mast 30 and the upper pulley 34U attached to the portal mast 30. Is the natural angular frequency of the lateral deflection y at an arbitrary height h of the lifting carriage 102 (mass Md) loaded with the conveyed product 20 (mass Mw).

(5) Natural angular frequency ω _nh (s + d + w)
The natural angular frequency ω _nh (s + d + w) is the natural angular frequency of the lateral vibration y in the state shown in FIG. 5C, and is an arbitrary value of the lifting carriage 102 (mass Md) loaded with the conveyed product 20 (mass Mw). Is the natural angular frequency at a height h.

(A) Natural angular frequency ω _nh (s + d) at the height position h of the lift carriage 102 on which the conveyed product 20 is not loaded.
The data of the natural angular frequency ω _nh (s + d) at a predetermined height position of the lifting / lowering carriage 102 (the mass Md of the lifting / lowering carriage 102 alone) on which the conveyed product 20 is not loaded is obtained by actual measurement or calculation, and can be regarded as a straight line. Each data is aggregated by a linear regression formula in the interval. For example, in FIG. 4, the least square method is used, and the height position h ( m ) and the natural angular frequency ω _nh (s + d) of the lifting carriage 102 on which the conveyed product 20 is not loaded are measured for each of the height sections 1 to 5. ) (Rad / s) is expressed by a linear regression equation as shown below.

Section 1 (0 ≦ h < 0.168 ): ω _nh (s + d) = 20.94 Formula (B1a)
Section 2 ( 0.168 ≦ h < 0.285 ): ω _nh (s + d) = 20.52-8.426h Formula (B1b)
Section 3 ( 0.285 ≦ h < 0.518 ): ω _nh (s + d) = 23.77-12.93h Formula (B1c)
Section 4 ( 0.518 ≦ h < 0.672 ): ω _nh (s + d) = 22.70-11.02h Formula (B1d)
Section 5 ( 0.672 ≦ h < 0.791 ): ω _nh (s + d) = 19.29−5.92h Formula (B1e)

  In FIG. 4, each straight line is a straight line passing through data located at the boundary between the height interval 1 to the interval 5, and is different from the above-described linear regression equation.

(B) The natural angular frequency ω _nh (s + d + w) at the height position h of the lifting carriage 102 loaded with the conveyed product 20.
If the mass Mw of the conveyed product 20 can be obtained by actual measurement or calculation, the natural angular frequency ω _nh (s + d + w) at an arbitrary height position h of the lifting carriage 102 loaded with the conveyed product 20 can be obtained. In addition, if the mass Mw of the conveyed product 20 is known from, for example, information associated with the drawing, the natural angular frequency ω _nh (s + d + w) can be obtained using the information.
The theory and specific calculation formula will be described below.

The natural angular frequency ω _nh (s + d) is a value obtained by synthesizing the natural angular frequency ω _nh (s) and the natural angular frequency ω _nh (d), and the following relationship is established by Duncare's equation.

1 / (ω _nh (s + d)) ² = 1 / (ω _nh (s)) ² + 1 / (ω _nh (d)) ²
Formula (B2)

Then, the natural angular frequency ω _nh (d) is obtained by the following equation.

ω _nh (d) = ((A · B) / (A−B)) ^1/2 formula (B3)

Here, A = (ω _nh (s)) ² and B = (ω _nh (s + d)) ² .

That is, the natural angular frequency ω _nh (d) is obtained by substituting the natural angular frequency ω _nh (s) and the natural angular frequency ω _nh (s + d) obtained by actual measurement or calculation into the equation (B3). Can do. In particular, if the natural angular frequency ω _nh (s + d) is known, if the height position h of the lifting carriage 102 is known, for example, the natural angular frequency ω _nh (s + d) is substituted into a linear regression equation represented by the equations (B1a) to (B1e). It can be obtained without actual measurement or calculation.

Next, a relational expression between the natural angular frequency ω _nh (d + w) and the natural angular frequency ω _nh (d) is obtained.
The natural angular frequency ω _nh (d) is obtained by the following equation.

ω _nh (d) = (k _s / Md) ^1/2 formula (B4)

Here, k _s is the equivalent spring constant of the portal mast 30, and Md is the mass of the lifting carriage 102.

The natural angular frequency ω _nh (d + w) is obtained by the following equation.

ω _nh (d + w) = (k _s / (Md + Mw)) ^1/2 formula (B5)

The relational expression between the natural angular frequency ω _nh (d + w) and the natural angular frequency ω _nh (d) is expressed as shown in the following expression by the expressions (B4) and (B5). Regardless of the spring constant k _s , it is determined only by the mass Md of the lifting carriage 102 and the mass Mw of the conveyed product 20.

ω _nh (d + w) = (Md / (Md + Mw)) ^1/2 · ω _nh (d) Equation (B6)

Here, the natural angular frequency ω _nh (s + d + w) is a value obtained by synthesizing the natural angular frequency ω _nh (s) and the natural angular frequency ω _nh (d + w). To do.

1 / (ω _nh (s + d + w)) ² = 1 / (ω _nh (s)) ² + 1 / (ω _nh (d + w)) ²
Formula (B7)

Then, the natural angular frequency ω _nh (s + d + w) is expressed by the following formula (an example of a relational expression for calculating the natural angular frequency when the lifting carriage on which the transport object of an arbitrary mass is placed is at an arbitrary height position). Desired.

ω _nh (s + d + w) = ((A · C) / (A + C)) ^1/2 formula (B8)

Here, A = (ω _nh (s)) ² and C = (ω _nh (d + w)) ² .

That is, the natural angular frequency ω _nh (s + d + w) is the natural angular frequency ω _nh (s) obtained by actual measurement or calculation and the natural angular frequency ω _nh (d + w) obtained from the equation (B5). Can be obtained by substituting

In this way, the natural angular frequency ω _nh (s) obtained by actual measurement or calculation and the data of the natural angular frequency ω _nh (s + d) at each height position h of the lifting carriage 102 of mass Md are obtained beforehand by actual measurement or calculation. The data amount can be suppressed by collecting each data by a linear regression equation in a height section that can be regarded as a straight line.
Further, if the mass Mw of the conveyed product 20 is known, the natural angular frequency ω _nh (s + d + w) is a value obtained by measuring or calculating the natural angular frequency ω _nh (s) and the natural angular frequency ω _nh (d + w) in advance. It can be easily obtained by substituting into the equation (B8).

Next, a vibration suppression control method (see FIG. 6) of the transport device 10 will be described.
As described above, the acceleration time T1 and the deceleration time T3 (see FIG. 2) are set as shown in the equation (A8) in order to make the position (side roll) y of the lifting carriage 102 viewed from the traveling carriage 101 zero. Needs to be set to a value obtained by dividing a positive integer n times 2π by the natural angular frequency ω _nh (s + d + w).
Therefore, the command generator CNT of the control unit 104 generates a speed command based on a trapezoidal speed pattern for the traveling carriage 101 and the lifting carriage 102 according to the following steps.

(Step S1: Data acquisition of natural angular frequency ω _nh (s + d) at each height position h)
The user obtains data of the natural angular frequency ω _nh (s + d) by actual measurement or calculation. If the natural angular frequency ω _nh (s + d) is known from information associated with the drawing, the information may be used. As a result, for example, measurement data as shown in Table 1 is obtained.

  Next, based on the obtained data, the user obtains, for example, a linear regression equation as shown in equations (B1a) to (B1e). The obtained linear regression equation is set in the command generator CNT (see FIG. 1).

(Step S2: Determination of setting parameters)
The user determines the following setting parameters PA1 to PA3, PB1, and PB2 that define trapezoidal speed patterns (see FIGS. 2A and 2B) for the traveling carriage 101 and the lifting carriage 102, respectively. Note that the acceleration time T1, the constant speed time T2, and the deceleration time T3 are the same for each of the trapezoidal speed patterns of the traveling carriage 101 and the lifting carriage 102.

(1) Setting parameter for traveling carriage 101 determined by user 1) Setting parameter PA1: Start point position (current position) Pstart
2) Setting parameter PA2: end point position (target position) Pstop
3) Setting parameter PA3: acceleration α1
The operation time Ttotal1 shown in FIG. 2A is the time required for the traveling carriage 101 to move from the start point position Pstart to the end point position Pstop.

(2) Setting parameter for lifting vehicle 102 determined by user 1) Setting parameter PB1: Height position (current position) H _{bottom of} starting point
2) Setting parameter PB2: End position height position (target position) H _top

(Step S3: setting of temporary acceleration time T1tmp and temporary deceleration time T3tmp)
First, command generator CNT is natural angular frequency omega _nbottom at the height position of the starting point of the lifting carriage 102 carrying the conveyed object 20 _{H bottom} (an example of a first height position and a acceleration starting position) (the 1 (an example of the natural angular frequency) is obtained from the linear regression equation obtained in step S1 (for example, the equations (B1a) to (B1e)), and the temporary acceleration time is calculated by the following equation so as to satisfy the equation (A8). Set T1tmp.

T1tmp = 2nπ / ω _nbottom formula (C1a)

  However, n is a positive integer.

Next, the command generator CNT has a natural angular frequency at a height position H _top (an example of the second height position, which is a deceleration completion position) at the end of travel of the lift carriage 102 on which the conveyed product 20 is placed. ω _ntop (an example of the second natural angular frequency) is obtained from the linear regression equation obtained in step S1 (for example, Equation (B1a) to Equation (B1e)), and so as to satisfy Equation (A8), A temporary deceleration time T3tmp is set.

T3tmp = 2nπ / ω _ntop equation (C1b)

  However, n is a positive integer.

When the provisional acceleration time T1tmp and provisional deceleration time T3tmp are set, the provisional trapezoidal speed pattern shown below is defined based on the setting parameters PA1 to PA3 and the setting parameters PB1 and PB2 determined by the user in step S2. The parameters are determined.
1) Temporary constant speed Vc1tmp of traveling carriage 101
2) Temporary deceleration β1tmp of traveling carriage 101
3) Temporary constant speed time T2tmp
4) Temporary constant speed Vc2tmp of the lifting carriage 102
5) Temporary acceleration α2tmp of the lifting carriage 102
6) Temporary deceleration β2tmp of the lifting carriage 102

(Step S4: Correction of temporary acceleration time T1tmp and temporary deceleration time T3tmp)
When the speed command is generated based on the setting parameters PA1 to PA3, PB1, PB2, and the temporary parameters, the lateral shake y is suppressed. However, since the natural angular frequency ω _nh (s + d + w) that changes every moment as the elevating carriage 102 rises is not sufficiently taken into consideration, the effect is limited.
Therefore, the command generator CNT corrects the temporary acceleration time T1tmp and the temporary deceleration time T3tmp as follows.

(Step S4-1: Correction of Temporary Acceleration Time T1tmp of Traveling Car 101)

In the temporary trapezoidal speed pattern of the lifting carriage 102 as shown in FIG. 7B, a minute time Δt obtained by dividing the temporary acceleration time T1tmp by N is obtained by the following equation.
N is a positive integer.

  Δt = T1tmp / N Formula (C2)

  The central time Δtc of N equally divided times is obtained by the following equation.

  Δtc = Δt / 2 Formula (C3)

The k-th (k is an integer) elapsed time t _{k at} the center of the time divided N times from the start of acceleration is obtained by the following equation.

t ₁ = 1 · Δt _c
t ₂ = 3 · Δt _c = 3 · t ₁
...
t _k = (2k−1) · Δt _c = (2k−1) · t ₁ formula (C4)

Height h _k of the lifting carriage 102 in the elapsed time t _k is calculated by the following equation.

h _k = (1/2) · α 2 · t _k ² + H _bottom
= (1/2) · α2 · (2k−1) ² · t ₁ ² + H _bottom equation (C5)

The linear regression represented by the linear regression formula (for example, formula (B1a) to formula (B1e)) obtained in step S1 for the natural angular frequency ω _nhk (s + d) at each height position h _k of the lifting carriage 102. It is _obtained by substituting the height position h _k for each of the height positions h of the lifting carriage 102 of the formula. Similarly, using these values, according to the formulas (B3), (B6), and (B8), the natural angular frequency ω _nhk (d) corresponding to each height position h _k and the natural angular frequency ω _nhk (d + w) and natural angular frequency ω _nhk (s + d + w) are sequentially calculated to be obtained.
The sum of values obtained by multiplying each natural angular frequency ω _nhk (s + d + w) by the minute time Δt is a temporary phase angle θ1tmp (an example of the first phase angle) at the time when the temporary acceleration time T1tmp has elapsed. It is obtained by the following formula.

  A first correction coefficient ζ1 obtained by dividing a positive integer n times 2π by a temporary phase angle θ1tmp is obtained from the following equation.

  ζ1 = 2nπ / θ1tmp (C7)

  A corrected acceleration time T1rev obtained by multiplying the temporary acceleration time T1tmp by the first correction coefficient ζ1 is obtained from the following equation.

  T1rev = ζ1 · T1tmp (C8)

By setting the corrected acceleration time T1rev obtained by the equation (C8) as the normal acceleration time T1, the phase angle at the acceleration end time (constant speed movement start time) approaches a positive integer n times 2π, and the end point The lateral deflection y of the lift carriage 102 loaded with the conveyed product 20 at the height position H _top is reduced.
Even a small first modification coefficients ζ1 determined by the formula (C7) 0. If it exceeds the range of 98 to 1.02, the calculation is repeated again with the corrected acceleration time T1rev as a new temporary acceleration time T1tmp. The first correction coefficient ζ1 is 0 . If it is in the range of 98 to 1.02, the lateral runout y of the lift carriage 102 becomes smaller.

(Step S4-2: Correction of Temporary Deceleration Time T3tmp of Traveling Truck 101)
Corresponding to the provisional phase angle θ3tmp (an example of the second phase angle) and the first modification coefficient ζ1 at the time when the provisional deceleration time T3tmp has passed, similar to the modification of the provisional acceleration time T1tmp of the traveling carriage 101 described above. A second correction coefficient ξ3 is obtained. A corrected deceleration time T3rev obtained by multiplying the temporary deceleration time T3tmp by the second correction coefficient ξ3 is obtained from the following equation, and the obtained corrected deceleration time T3rev is set as a regular deceleration time T3.

  T3rev = ξ3 · T3tmp (C9)

By setting the corrected deceleration time T3rev obtained by the equation (C9) as the normal deceleration time T3, the phase angle at the end of the deceleration approaches a positive integer n times 2π, and the conveyance at the end position height position H _top is performed. The lateral deflection y of the lifting carriage 102 loaded with the objects 20 is reduced.
Even a small second correction coefficient ζ3 is 0. If it exceeds the range of 98 to 1.02, the calculation is repeated again with the corrected deceleration time T3rev as a new temporary deceleration time T3tmp. The second correction coefficient ζ3 is 0 . If it is in the range of 98 to 1.02, the lateral runout y of the lift carriage 102 becomes smaller.

(Step S5: Generation of speed command)
The command generator CNT defines a trapezoidal speed pattern (an example of a first trapezoidal speed pattern) for the traveling carriage 101 based on the setting parameters PA1 to PA3, the corrected acceleration time T1rev, and the corrected deceleration time T3rev determined by the user. Therefore, other parameters necessary for the calculation are calculated again, and a speed command (an example of a first speed command) for the traveling carriage 101 is generated.
Further, the command generator CNT generates a trapezoidal speed pattern (an example of a second trapezoidal speed pattern) for the lifting carriage 102 based on the setting parameters PB1, PB2, the corrected acceleration time T1rev, and the corrected deceleration time T3rev determined by the user. Other parameters necessary for the regulation are calculated again, and a speed command (an example of a second speed command) for the lifting carriage 102 is generated.

(Step S6: Driving of traveling cart and lifting cart)
The speed commands generated by the command generator CNT are input to the servo drivers SVA1 and SVA2, respectively, and the traveling carriage 101 and the lifting carriage 102 are driven according to the speed instructions.

As a result, since the traveling carriage 101 rises at the acceleration time T1 and the deceleration time T3 such that the lateral shake y of the lifting carriage 102 approaches zero, the lateral shake y is suppressed.
In addition, since the lifting carriage 102 reaches the target position with a substantially shortest path as viewed from the installation surface of the transfer apparatus 10, the time for the lifting carriage 102 to reach the target position is reduced.

As described above, according to the vibration suppression control method of the transport device 10, the horizontal runout y of the lift carriage 102 when the lift carriage 102 reaches the target height position and stops is suppressed. The waiting time until the magnitude of the signal decays below the allowable value is shortened. Further, the time required for the lifting carriage 102 to reach the target position is reduced.
That is, the time required for transporting the transported object 20 is shortened.

  In the present embodiment, the vibration suppression control method when the lifting carriage is raised has been described. However, the horizontal vibration y can be suppressed by the same vibration suppression control method when the lifting carriage is lowered.

  Next, an embodiment using the transfer device (actual machine model) 10 shown in FIG. 1 will be described, and the vibration suppression control method of the transfer device 10 will be further described.

The main specifications of the transport device (actual machine model) 10 are as follows.
(1) Portal mast 30
The portal mast 30 includes two plate-like members 302 and 304 extending in the vertical direction with a space therebetween. The lower ends of the plate-like members 302 and 304 are fixed to the traveling carriage 101, and the upper ends are fixed to the beam 306. The material of each of the plate-like members 302 and 304 is aluminum, and the length, width, and thickness in the vertical direction are 880 mm, 30 mm, and 3 mm, respectively.
(2) Traveling cart 101
The traveling drive motor (AC servomotor) SVM1 has a capacity of 0.1 kW. The lead pitch of the ball screw 22 is 6 mm.
(3) Lifting carriage 102
The mass Md of only the lifting carriage 102 is 0.310 kg, and the mass Mw of the conveyed product 20 is 0.265 kg. The capacity of the lifting drive motor (AC servomotor) SVM2 is 0.1 kW.

First, as a comparative example, the transport apparatus 10 was controlled according to the following trapezoidal speed pattern (see FIG. 2).
As a result, the total amplitude of the lateral deflection y of the lifting carriage 102 when the traveling carriage 101 and the lifting carriage 102 reached the target position and stopped was about 30 mm.
(1) Trapezoidal speed pattern / travel distance L of the traveling carriage 101 = 0.192 (m)
・ Acceleration α1 = 0.8 (m / s ² )
・ Deceleration β1 = 0.7 (m / s ² )
・ Constant speed Vc1 = 0.272 (m / s)
・ Acceleration time T1 = 0.34 (s)
・ Constant speed time T2 = 0.34 (s)
・ Deceleration time T3 = 0.39 (s)

(2) Trapezoidal speed pattern / movement distance L = 0.24 (m) of the lifting carriage 102
・ Acceleration α2 = 1.0 (m / s ² )
・ Deceleration β2 = 0.87 (m / s ² )
・ Constant speed Vc2 = 0.34 (m / s)
・ Acceleration time T1 = 0.34 (s)
・ Constant speed time T2 = 0.34 (s)
・ Deceleration time T3 = 0.39 (s)

  Next, as an example, the transport apparatus 10 was controlled according to the above-described steps S1 to S6 (see FIG. 6). Hereinafter, each step S1 to S6 will be described.

(Step S1: Data acquisition of natural angular frequency ω _nh (s + d) at each height position h)
The height position h from the lower end portion serving as the fixed end of the portal mast 30 to the center of the lift carriage 102 was changed, and 23 data of the natural angular frequency at each height position h were measured. In addition, the raising / lowering carriage 102 does not load the conveyed product 20. Table 1 above shows the measurement results (data Nos. 3 to 12 are omitted). FIG. 4 is a graph corresponding to Table 1.
These data were expressed by formulas (B1a) to (B1e), which are five linear regression equations (correlation coefficients: 0.98 to 1.02) by the least square method.

From these formulas (B1a) to (B1e), it is possible to finally determine the natural angular frequency when the lifting carriage 102 on which the conveyed product 20 is loaded is at an arbitrary height position.
As an example, the transported object 20 (mass Mw = 0.265 kg) is loaded on the lifting carriage 102 (mass Md = 0.310 kg), and the height position H _top from the center of the lifting carriage 102 to the fixed end of the portal mast 30 is set. A specific procedure for obtaining the natural angular frequency ω _nh (s + d + w) at (791 mm) is shown below.

First, the measured values of the natural angular frequency ω _nh (s) of the transport device mainly composed of the portal mast 30 in the state where the lifting carriage 102 and the transported object 20 are not present are as follows.

ω _nh (s) = 20.94 (rad / s) Formula (D1)

Next, the natural angular frequency ω _nh (s + d) at the height position (h = 0.971 m) of the lifting carriage 102 is obtained from the formula (B1e) as follows.

ω _nh (s + d) = 14.61 (rad / s) Formula (D2)

Next, ω _nh (d) is as follows according to the equation (B3).

A = (ω _nh (s)) ² = 20.94 ² = 438.5 (rad / s) ²
B = (ω _nh (s + d)) ² = 14.61 ² = 213.5 (rad / s) ²
ω _nh (d) = ((A · B) / (A−B)) ^1/2 = 20 · 39 (rad / s)
Formula (D3)

Next, the natural angular frequency ω _nh (d + w) is as follows according to the equation (B6).

Md = 0.310 (kg)
Mw = 0.265 (kg)
ω _nh (d + w) = (Md / (Md + Mw)) ^1/2 · ω _nh (d)
= 14.97 (rad / s) Formula (D4)

Finally, the natural angular frequency ω _nh (s + d + w) is obtained as follows by substituting the natural angular frequency ω _nh (s) and the natural angular frequency ω _nh (d + w) into the equation (B8).

A = (ω _nh (s)) ² = (20.94) ² = 438.5 ((rad / s) ² )
C = (ω _nh (d + w)) ² = 14.97 ² = 224.1 ((rad / s) ² )
ω _nh (s + d + w) = ((A · C) / (A + C)) ^1/2 = 12.2 (rad / s)
Formula (D5)

Here, when the natural angular frequency ω _nh (s + d + w) was measured, the value (measured value) was 12.1 (rad / s). A comparison between this measured value and the calculated value obtained based on the previous equation (D5) is as follows.

ω _nh (s + d + w) / ω _nh (s + d + w) (actual value) = 1.01 Formula (D6)

That is, the error was 1% or less, and the natural angular frequency ω _nh (s + d + w) obtained in this example was a value within the target error range.

(Step S2: Determination of setting parameters)
The operating conditions of the traveling carriage 101 and the lifting carriage 102 are as follows. The acceleration α1 is the same as that in the comparative example.
A trapezoidal speed pattern that satisfies this operating condition was obtained. For each trapezoidal speed pattern of the traveling carriage 101 and the lifting carriage 102, the acceleration time T1, the constant speed time T2, and the deceleration time T3 are the same.

(1) Driving conditions of traveling vehicle 101 / start position Pstart = 0 (m)
・ End point position Pstop = 0.35 (m)
・ Acceleration α1 = 0.8 (m / s ² )
・ Constant speed Vc1 ≒ 0.35 (m / s)
・ Deceleration β1 ≦ 1 (m / s ² )
・ Operating time Ttotal1 ≒ 1.5 (s)

(2) Driving conditions of the lifting carriage 102 / height position of the starting point H _bottom = 0.552 (m)
・ End position height H _top = 0.791 (m)
・ Acceleration α2 ≦ 1 (m / s ² )
・ Constant speed Vc2 ≦ 0.35 (m / s)
・ Deceleration β2 ≦ 1 (m / s ² )
・ Operating time Ttotal2 = Ttotal1≈1.5 (s)

The following setting parameters were determined so as to satisfy the above operating conditions.
1) Setting parameter PA1: Start point position (current position) Pstart = 0 (m)
2) Setting parameter PA2: end point position (target position) Pstop = 0.35 (m)
3) Setting parameter PA3: acceleration α1 = 0.8 (m / s ² )
4) Setting parameter PB1: Height position of the starting point (current position) H _bottom = 0.552 (m)
5) Setting parameter PB2: End position height position (target position) H _top = 0.791 (m)

These setting parameters PA1 to PA3, PB1, and PB2 define conditions that the generated trapezoidal velocity pattern should satisfy at least. The setting parameters are not limited to these setting parameters PA1 to PA3, PB1, and PB2.
As a first example, instead of the setting parameter PA3 (acceleration α1), a constant speed Vc1 may be used as the setting parameter.
As a second example, the deceleration β1 may be used as the setting parameter instead of the setting parameter PA3 (acceleration α1).

(Step S3: setting of temporary acceleration time T1tmp and temporary deceleration time T3tmp)
First, a temporary acceleration time T1tmp and a temporary deceleration time T3tmp of the traveling carriage 101 were set.
The natural angular frequency ω _{nbottom at} the height position H _bottom = 0.552 (m) of the starting point of the lift carriage 102 on which the conveyed product 20 is loaded is 14.48 (rad / s) from the equation (B8). It was. Therefore, the provisional acceleration time T1tmp is set as follows from the formula (C1a).

T1tmp = 2π / ω _nbottom = 0.434 (s) Formula (E1a)

The temporary acceleration time T1tmp is a natural vibration period when the lifting carriage 102 is at the height position H _bottom .

The natural angular frequency ω _{ntop at} the height position H _top = 0.791 (m) of the end point of the lift carriage 102 on which the conveyed product 20 is loaded is 12.2 (rad / s) from the equation (B8). It was. Therefore, the provisional deceleration time T3tmp is set as follows according to the equation (C1b).

T3tmp = 2π / ω _ntop = 0.515 (s) Formula (E1b)

The temporary deceleration time T3tmp is a natural vibration period when the lifting carriage 102 is at the height position H _top .

  Next, based on the provisional acceleration time T1tmp and provisional deceleration time T3tmp set, and the setting parameters PA1 to PA3 and the setting parameters PB1 and PB2 determined by the user in step S2, the traveling vehicle shown in FIG. A temporary constant speed Vc1tmp and a temporary deceleration β1tmp of 101 were obtained from the following equations.

Vc1tmp = α1 · T1tmp = 0.8 · 0.434≈0.347 (m / s)
Formula (E2a)
β1tmp = Vc1tmp / T3tmp = 0.347 / 0.515≈0.674 (m / s ² )
Formula (E2b)

  Next, a temporary constant speed time T2tmp was obtained from the following equation.

(Vc1tmp) · (T1tmp / 2 + T2tmp + T3tmp / 2)
= (Pstop-Pstart) Formula (E3a)
T2tmp = (Pstop-Pstart)
/ (Vc1tmp)-(T1tmp / 2 + T3tmp / 2)
= (0.350-0.000) /0.347- (0.434 / 2 + 0.515 / 2)
= 0.5345 (s) Formula (E3b)

  The provisional constant speed Vc2tmp, provisional acceleration α2tmp, and provisional deceleration β2tmp of the lifting carriage 102 shown in FIG. 7B were obtained from the following equations.

Vc2tmp · (T1tmp / 2 + T2tmp + T3tmp / 2)
= (H _top −H _bottom ) Formula (E4a)
Vc2tmp = (H _top −H _bottom ) / (T1 / 2 + T2 + T3 / 2)
= (0.791-0.552)
/(0.434/2+0.5345+0.515/2)
= 0.239 / 1.009
≈ 0.237 (m / s) Formula (E4b)
α2tmp = Vc2tmp / T1tmp
= 0.237 / 0.434
≈ 0.546 (m / s ² ) Formula (E4c)
β2tmp = Vc2tmp / T3tmp
= 0.237 / 0.515
≈0.460 (m / s ² ) Formula (E4d)

(Step S4: Correction of temporary acceleration time T1tmp and temporary deceleration time T3tmp)
(Step S4-1: Correction of Temporary Acceleration Time T1tmp of Traveling Car 101)
N was set to 5, and a minute time ΔT1 obtained by dividing the provisional acceleration time T1tmp by 5 was obtained by the following equation (see FIG. 7B).

  ΔT1 = T1tmp / N = 0.434 / 5 = 0.0868 (s) Formula (E5)

  The central time ΔTc1 of the N (5) equally divided time is obtained by the following equation.

  ΔTc1 = ΔT1 / 2 = 0.0868 / 2 = 0.0434 (s) Formula (E6)

5 central k-th elapsed time t _k of the equally divided time from the start of acceleration determined by the following equation.

t ₁ = 1 · ΔTc1
t ₂ = 3 · ΔTc1
...
t _k = (2k−1) · ΔTc1 = (2k−1) · t ₁ formula (E7)

The elapsed times t ₁ , t ₂ , t ₃ , t ₄ and t ₅ were calculated according to the formula (E7), and the results were as follows.
t ₁ = 0.0434 (s)
t ₂ = 0.130 (s)
t ₃ = 0.217 (s)
t ₄ = 0.304 (s)
t ₅ = 0.391 (s)

The height h _k of the lifting carriage 102 at time t _k of the determined by the following equation.

h _k = (1/2) · α 2 · t _k ² +0.552 Formula (E8)

When the height positions of the lift carriage 102 at each time described above were calculated according to the equation (E8), the following results were obtained.
h ₁ = 0.553 (m)
h ₂ = 0.557 (m)
h ₃ = 0.565 (m)
h ₄ = 0.577 (m)
h ₅ = 0.594 (m)

When the natural angular frequency ω _nk (s + d + w) at each height position of the lifting carriage 102 loaded with the conveyed product 20 (mass 0.265 kg) is calculated according to the formula (B3), the formula (B6), and the formula (B8), It became as follows.
ω _n1 (s + d + w) = 14.45 (rad / s)
ω _n2 (s + d + w) = 14.40 (rad / s)
ω _n3 (s + d + w) = 14.30 (rad / s)
ω _n4 (s + d + w) = 14.10 (rad / s)
ω _n5 (s + d + w) = 13.90 (rad / s)

A value obtained by multiplying each natural angular frequency ω _nk (s + d + w) by a minute time ΔT1 = 0.0868 (s) obtained by dividing the temporary acceleration time T1tmp by 5 and summing these values. Is the provisional phase angle θ1tmp (rad / s). The provisional phase angle θ1tmp was calculated according to the formula (C6), and the following values were obtained.

  This provisional phase angle θ1tmp is a value smaller than 2π (6.28). Therefore, as shown below, if the first correction coefficient ζ1 is obtained by the equation (C7) and multiplied by the provisional acceleration time T1tmp, the correction phase angle θ1rev becomes 2π.

  ζ1 = 2π / θ1tmp = 2π / 6.175≈1.0175 Formula (E10)

  Therefore, the corrected acceleration time T1rev was obtained by the following calculation formula.

T1rev = ζ1 · T1tmp = 1.0175 · 0.434≈0.442 (s)
Formula (E11)

(Step S4-2: Correction of Temporary Deceleration Time T3tmp of Traveling Truck 101)
The corrected deceleration time T3rev was calculated in the same manner as the corrected acceleration time T1rev described above, and the following results were obtained.
Temporary deceleration time T3tmp = 0.515 (s)
Temporary phase angle θ3tmp at the end point of deceleration = 6.3475 (rad)
Second correction coefficient ζ3 = 2π / θ3 = 0.9899
・ Modified deceleration time T3rev = ζ3 · T3≈0.510 (s)

(Step S5: Generation of speed command)
The obtained corrected acceleration time T1rev and corrected deceleration time T3rev were respectively set as the original acceleration time T1 and deceleration time T3, and other parameters defining the trapezoidal speed pattern of the traveling carriage 101 were obtained.
It should be noted that the acceleration α1 (setting parameter PA3) of the traveling carriage 101 remains 0.8 (m / s ² ) without being changed.
The parameters defining the trapezoidal speed pattern of the traveling carriage 101 are as follows.

・ Acceleration time T1 = 0.442 (s)
・ Deceleration time T3 = 0.510 (s)
・ Constant speed Vc1 = 0.53636 (m / s)
Deceleration β1 = 0.6933 (m / s ² )
-Constant speed time T2 = 0.5138 (s)

  The constant speed Vc1, the deceleration β1, and the constant speed time T2 were obtained by the following equations.

Vc1 = α1 · T1rev
= 0.8 ・ 0.442
= 0.3536 (m / s) Formula (E12)

β1 = Vc1 / T3rev
= 0.3536 / 0.510
= 0.6933 (m / s ² ) Formula (E13)

Vc1 · (T1rev / 2 + T2 + T3 / 2) = (Pstop−Pstart)
Formula (E14)
T2 = (Pstop−Pstart) / (Vc1) − (T1 / 2 + T3 / 2)
= (0.350-0.000) /0.3536
-(0.442 / 2 + 0.510 / 2)
= 0.9898-0.476
= 0.5138 (s) Formula (E15)

  Other parameters that define the trapezoidal speed pattern of the lift carriage 102 are as follows.

・ Acceleration time T1 = 0.442 (s)
-Constant speed time T2 = 0.5138 (s)
・ Deceleration time T3 = 0.510 (s)
・ Constant speed Vc2 = 0.415 (m / s)
・ Acceleration α2 = 0.5464 (m / s ² )
Deceleration β2 = 0.4735 (m / s ² )

  The constant speed Vc2, the acceleration α2, and the deceleration β2 were obtained from the following equations.

Vc2 · (T1 / 2 + T2 + T3 / 2) = (H _top −H _bottom )
Formula (E16)
Vc2 = (H _top −H _bottom )
/ (T1rev / 2 + T2rev + T3rev / 2)
= (0.791-0.552)
/(0.442/2+0.5138+0.510/2)
= 0.239 / 0.9898
= 0.2415 (m / s) Formula (E17)

α2 = Vc2 / T1
= 0.2415 / 0.442
= 0.5464 (m ^{/ s} 2) formula (E18)

β2 = Vc2 / T1
= 0.2415 / 0.510
= 0.4735 (m ^{/ s} 2) formula (E19)

From the above calculation results, the trapezoidal speed pattern generated by the command generator CNT is as follows.
(1) Trapezoidal speed pattern / travel distance L (setting parameters PA1, PA2) of the traveling carriage 101 = 0.35 (m)
Acceleration α1 (setting parameter PA3) = 0.8 (m / s ² )
Deceleration β1 = 0.6933 (m / s ² )
・ Constant speed Vc = 0.3536 (m / s)
・ Acceleration time T1 = 0.442 (s)
-Constant speed time T2 = 0.5138 (s)
・ Deceleration time T3 = 0.510 (s)

(2) Trapezoidal speed pattern / moving distance L (setting parameters PB1, PB2) of the lift carriage 102 = 0.239 (m)
・ Acceleration α1 = 0.5464 (m / s ² )
・ Deceleration β1 = 0.4735 (m / s ² )
・ Constant speed Vc = 0.415 (m / s)
・ Acceleration time T1 = 0.442 (s)
-Constant speed time T2 = 0.5138 (s)
・ Deceleration time T3 = 0.510 (s)
(Step S6: Generation of speed command)
The transport device 10 was controlled according to the speed command based on the trapezoidal speed pattern described above.
As a result, the total amplitude of the lateral deflection y of the lifting carriage 102 when the traveling carriage 101 and the lifting carriage 102 reached the target position and stopped was 1 mm or less.

  Thus, the lateral runout y of the present example was 1 mm or less, while the lateral runout y of the comparative example was 30 mm. That is, the lateral shake y is significantly suppressed, and the effectiveness of the vibration suppression control method according to the present embodiment can be confirmed.

  Although the embodiments of the present invention have been described above, the present invention is not limited to the above-described embodiments, and all changes in conditions and the like that do not depart from the gist are within the scope of the present invention.

  Considering only the suppression of the lateral swing y of the lifting carriage 102, the traveling carriage 101 and the lifting carriage 102 do not necessarily have to move at the same acceleration time T1, constant speed time T2, and deceleration time T3, respectively. In the up-and-down operation of the lifting carriage 102 (running stop state), it is considered that the influence on the lateral deflection y of the lifting carriage is small. However, if the height position of the lift carriage changes, the natural angular vibration in the running direction changes. Therefore, according to this vibration suppression control method, the phase angle at the end point of the acceleration time T1 and the deceleration time T3 of the running carriage 101 is a positive 2π. This is intended to reduce the lateral run-out of the lift truck by making it an integral multiple of.

The first height position and the second height position can be arbitrarily set. However, the calculation is facilitated by setting the first height position to the height position H _bottom and the second height position to the height position H _top .

DESCRIPTION OF SYMBOLS 10 Conveying device 20 Conveyed object 22 Ball screw 24 Slider nut 26 Coupling 30 Gate type mast 32 Timing belt 34L Lower pulley 34U Upper pulley 101 Traveling carriage 102 Elevating carriage 104 Control part 302, 304 Plate member 306 Beam CNT Command generator SVA1 , SVA2 Servo driver SVM1 Traveling drive motor SVM2 Lifting drive motor

Claims (8)

A traveling carriage that travels along the installation surface;
An elevating carriage that is provided in the traveling carriage and moves up and down with a transported object;
A control unit for controlling the traveling carriage and the elevating carriage, and a vibration damping control method for a conveying apparatus comprising:
Obtaining a relationship between a height position of the lifting carriage and a natural angular frequency of vibration generated in the lifting carriage;
Based on the relationship, the control unit obtains a first natural angular frequency of the vibration when the carriage on which the transport object is placed is at a first height position, and is a positive integer multiple of 2π. Is calculated by dividing the first natural angular frequency by a temporary acceleration time , and based on the relationship, the vibration of the lift carriage with the transported object on the second height position is calculated. Obtaining a second natural angular frequency, and calculating a temporary deceleration time obtained by dividing a positive integer multiple of 2π by the second natural angular frequency ;
The control unit obtains a minute time obtained by equally dividing the provisional acceleration time, and each natural angular vibration corresponding to each height position of the lifting carriage according to each elapsed time from the start of acceleration to the center time of each minute time. each micro phase angle multiplied by the fine small time number, up to the point where the acceleration time of the temporary has elapsed calculates the phase angle of the first tentative integrated phase angle of the first tentative positive of 2π A first correction coefficient obtained by dividing the positive integer multiple of 2π by the first temporary phase angle so as to approach an integral multiple is obtained, and a correction obtained by multiplying the temporary acceleration time by the first correction coefficient Calculating acceleration time, obtaining a minute time obtained by equally dividing the temporary deceleration time, and each unique position corresponding to each height position of the lift carriage by each elapsed time from the start of deceleration to the center time of each minute time Each minute phase angle obtained by multiplying the angular frequency by the minute time is used as the temporary deceleration time. Time points until calculates the phase angle of the second tentative integrated, the as the phase angle of the second tentative approaches the positive integer multiple of 2 [pi, the 2 [pi positive number several times said second tentative Calculating a corrected deceleration time obtained by multiplying the provisional deceleration time by the second correction coefficient ;
The control unit generating a first speed command of the traveling carriage according to a first trapezoidal speed pattern defined at least by the corrected acceleration time and the corrected deceleration time;
And a step of driving the traveling vehicle according to the first speed command, wherein the control unit controls the vibration. In the vibration damping control method of the conveying apparatus according to claim 1,
A method for obtaining a relationship between a height position of the lifting carriage and the natural angular frequency of the vibration generated in the lifting carriage,
Obtaining a relationship between a height position of the lifting carriage on which the transported object is not placed and the natural angular frequency of the vibration generated in the lifting carriage as data by actual measurement or calculation;
Obtaining a linear regression equation for each height interval in which the data can be considered to be represented by linear approximation;
From the natural angular frequency calculated by the linear regression equation, a relational expression for calculating the natural angular frequency when the lifting carriage carrying the transported object of an arbitrary mass is at an arbitrary height position is obtained. And a vibration damping control method for the transfer device. In the vibration suppression control method of the conveying apparatus according to claim 2,
The control unit generates a second speed command of the lifting cart according to a second trapezoidal speed pattern defined by the corrected acceleration time and the corrected deceleration time of the traveling cart, and the first speed command and the A vibration damping control method for a transfer device that outputs a second speed command together and drives both the traveling carriage and the lifting carriage. In the vibration suppression control method of the conveyance apparatus of any one of Claims 1-3,
0 and the control unit, the first correction coefficient is the ratio of the corrected acceleration time for acceleration time of the provisional, also reduced. When exceeding the range of 98-1.02, the vibration suppression control method of the conveying apparatus which makes the said corrected acceleration time the new said temporary acceleration time, and recalculates the said corrected acceleration time. In the vibration suppression control method of the conveying apparatus according to claim 4,
0 and the control unit, the second correction factor is the ratio of the modified deceleration time for deceleration time of the provisional, also reduced. When exceeding the range of 98 to 1.02, the vibration damping control method of the transport device, in which the corrected deceleration time is set as the new temporary deceleration time and the corrected deceleration time is calculated again. In the vibration suppression control method of the conveying apparatus according to claim 4 or 5,
The vibration suppression control method for a transfer apparatus, wherein the first height position is an acceleration start position of the lift carriage. In the vibration suppression control method of the conveying apparatus according to claim 6,
The vibration suppression control method for a transfer apparatus, wherein the second height position is a deceleration completion position of the lifting carriage. A traveling carriage that travels along the installation surface;
An elevating carriage that is provided in the traveling carriage and moves up and down with a transported object;
A controller that controls the traveling carriage and the lifting carriage based on a speed command represented by a trapezoidal speed pattern,
The lifting / lowering on which the transport object is placed based on the relationship between the mass of the transport object, the height position of the lift carriage, and the natural angular frequency of the vibration generated in the lift truck, which is determined in advance by the control unit. A first natural angular frequency of the vibration when the carriage is at the first height position is obtained, and a temporary acceleration time is calculated by dividing a positive integer multiple of 2π by the first natural angular frequency. In addition, based on the relationship, a second natural angular frequency of the vibration when the carriage on which the transported object is placed is at a second height position is obtained, and a positive integer multiple of 2π is calculated . the step of calculating a temporary deceleration time divided by the natural angular frequency of 2 to obtain the minute time obtained by equally dividing the acceleration time of the temporary, the lift according to the elapsed time to the center of the time for each minute time since the start of acceleration Each natural angular frequency corresponding to each height position of the carriage is multiplied by the minute time. The small phase angle, to the point where the acceleration time of the temporary has elapsed calculates the phase angle of the first tentative integrated, so that the phase angle of the first tentative approaches the positive integer multiple of 2 [pi, the 2 [pi A first correction coefficient obtained by dividing a positive integer multiple of the first correction phase angle by the first temporary phase angle is calculated, and a correction acceleration time obtained by multiplying the temporary correction time by the first correction coefficient is calculated. The minute time obtained by equally dividing the deceleration time is obtained, and each natural angular frequency corresponding to each height position of the lifting carriage by each elapsed time from the start of deceleration to the center time of each minute time is multiplied by the minute time. each minute phase angle is, up to the point where the deceleration time of the temporary has elapsed calculates the phase angle of the second tentative integrated, so that the phase angle of the second tentative approaches the positive integer multiple of 2 [pi, A second correction coefficient obtained by dividing the positive multiple of 2π by the second temporary phase angle is obtained, and the second deceleration coefficient is calculated at the temporary deceleration time. A command generator for executing a step of calculating a corrected deceleration time multiplied by a correction coefficient of 2 and a step of generating a speed command of the traveling vehicle based on a trapezoidal speed pattern defined at least by the corrected acceleration time and the corrected deceleration time Conveying device having