JP2012108892A - Numerical control device and method for friction compensation - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a numerical control device capable of estimating a friction force or a friction torque in a range from low speed to high speed with high accuracy to calibrate a quadrant projection even in a feed drive mechanism of a double nut pre-load system, and to provide a method for friction compensation.SOLUTION: An inventive numerical control device estimates a friction force or a friction torque in a range from low speed to high speed with high accuracy not only in a feed drive mechanism of over-size ball pre-load system but also in that of double nut pre-load system. Therefore, the numerical control device can calibrate a quadrant projection. The quadrant projection is a phenomenon in which a movement trajectory issues more outward than a command trajectory. The feed drive mechanism of double nut pre-load system causes the quadrant projection of a first thread ridge by inversion of a ball screw axis. The feed drive mechanism of double nut pre-load system causes further the quadrant projection of a second thread ridge when a table moves by a predetermined amount after the inversion. The numerical control device estimates the increase of the frictional force arising in two steps in the double nut pre-load system with high accuracy by using two approximate expressions.

Description

  The present invention relates to a numerical controller and a friction compensation method.

  The machine tool controls the motor to perform a biaxial circular interpolation motion. Machine tools cannot be reversed immediately when the direction of motor rotation is reversed. The reason is the influence of the friction of the feed drive mechanism. When the quadrant changes during arc cutting (when the moving direction of the moving body is reversed), the actual moving track of the moving body goes outside the command track. The phenomenon in which the movement trajectory goes out is a quadrant projection, and the processing accuracy is deteriorated.

  The motor control device disclosed in Patent Document 1 differentiates an actual position signal of a moving body to obtain a speed signal. The motor control device integrates the speed signal and generates a displacement signal from a position where the moving body reverses the direction of motion to obtain an absolute value. The motor control device obtains the rate of change of the frictional force or the frictional torque with respect to the displacement using a model that represents the relationship between the displacement and the frictional force or the frictional torque. The motor control device obtains the rate of change with respect to time by multiplying the rate of change with respect to the displacement by the speed signal. The motor controller estimates the friction force or friction torque by integrating the rate of change with time. The motor control device estimates the frictional force or frictional torque without being affected by the speed or acceleration before and after the direction of motion is reversed.

JP 2008-210273 A

  However, the motor control device disclosed in Patent Document 1 mainly corresponds to an oversize ball preload type feed drive mechanism. The oversize ball preload type feed drive mechanism includes one nut and a ball screw shaft. The double nut preload type feed drive mechanism includes two nuts and a ball screw shaft. In the double nut preload type feed driving mechanism, the ball screw shaft is inverted to form a first quadrant projection, and when the moving body moves a predetermined amount, a second quadrant projection is generated. The motor control device does not correspond to the double nut preload system, and there is a problem that the quadrant projection of the second mountain cannot be corrected.

  In addition to the ball screw shaft, the friction factor of the machine tool is a linear guide and a bearing. Linear guides and bearings provide high preload to increase machine rigidity. Therefore, the friction torque characteristic at the time of reversal changes suddenly. Another friction factor is the oil seal and the seal member of the movable chip cover. The oil seal is attached to the motor shaft. The oil seal prevents cutting oil from entering the motor. The seal member prevents chips from entering the ball screw shaft and the linear guide portion. The seal member and the oil seal are rubber materials. The friction torque at the time of reversal changes more slowly than a linear guide or the like. The friction characteristics of a machine tool during reversal are a combination of two types of reversal friction characteristics.

  However, the motor controller uses only a single tanh function for a model representing the relationship between the displacement from the reverse position and the friction torque. The motor control device does not consider the two types of reverse friction characteristics described above. The two types of reverse friction characteristics are characteristics having both a sudden change in friction torque after inversion and a gentle change in friction torque after inversion. Therefore, there is a problem that an error occurs.

  Furthermore, the motor control device of Patent Document 1 uses a model that represents the relationship between the displacement from the position where the moving body reverses the direction of motion and the frictional force or frictional torque. The motor controller uses a model to determine the rate of change of the friction force or friction torque with respect to the displacement as a function of the displacement signal expressed as an absolute value. The motor control device calculates the rate of change of the friction force or the friction torque with respect to time by multiplying the rate of change with respect to the displacement by the speed signal. The motor control device estimates the friction force or the friction torque by integrating the rate of change with respect to the time. Therefore, when the speed is high, the integration error becomes large, and the error of the estimated friction force or friction torque becomes large.

  An object of the present invention is to provide a numerical control device and a friction compensation method capable of correcting a quadrant projection by accurately estimating a friction force or a friction torque from a low speed to a high speed region even in a double nut preload type feed drive mechanism. It is.

  The numerical control device according to the first aspect of the present invention includes a feed mechanism that has a ball screw shaft and a ball nut externally fitted to the ball screw shaft and moves a moving body fixed to the ball nut, and the ball screw shaft. A motor that rotates the motor, a position detection mechanism that detects the position of the moving body that has been moved by the motor, and a speed so that the position of the moving body detected by the position detection mechanism matches the position command generated by the control unit. A speed generation unit that generates a command, a speed detection mechanism that detects the speed of the motor, and a torque command that generates a speed command so that the speed detected by the speed detection mechanism matches the speed command generated by the speed generation unit. A torque generation unit; a friction estimation unit that estimates a friction force or a friction torque generated after the rotation direction of the motor is reversed; and the torque based on the friction or the friction torque estimated by the friction estimation unit. In the numerical control apparatus including a correction unit that corrects a command, the ball nut is formed of a pair of ball nuts, and the friction force or the friction torque caused by the feed mechanism in which the moving direction of the moving body increases after reversal is obtained. A first friction estimating unit for estimating a friction force or a friction torque that increases due to the ball screw shaft and the pair of ball nuts after the moving direction of the moving body is reversed by a predetermined amount after the moving direction is reversed. A friction estimation unit is provided, and the friction estimation unit adds the friction force or the friction torque estimated by each of the first friction estimation unit and the second friction estimation unit.

  In the numerical control device according to the first aspect, the quadrature protrusion can be corrected because the friction force or the friction torque can be estimated with high accuracy even in the feed mechanism of the double-nut preload system.

  In the first aspect, the pair of ball nuts includes a plurality of balls, and the predetermined amount is at least one of the plurality of balls including the pair of ball nuts and the ball screw after the moving direction of the moving body is reversed. It is good also as a distance which the said mobile body moves until it contacts with an axis | shaft at three points. Therefore, the second friction estimation unit can estimate a friction force or a friction torque that increases due to the ball screw shaft and the pair of ball nuts after the moving direction of the moving body has been reversed and then moved by a predetermined amount.

  In the first aspect, the real position estimating unit that estimates the real position of the moving body corresponding to the position command, and the moving direction of the moving body is reversed based on the real position estimated by the real position estimating unit. The first friction estimation unit and the second friction estimation unit may be approximate equations using the displacement calculated by the calculation unit as a variable. Therefore, the numerical control device has a frictional force or frictional torque caused by the feeding mechanism that increases after the moving direction of the moving body is reversed, and a frictional force or frictional torque that increases due to the ball screw shaft and the pair of ball nuts. Easy to calculate.

In the first aspect, the approximate expression f ₁ (x ′) of the first friction estimation unit and the approximate expression f ₂ (x ′) of the second friction estimation unit are obtained after reversing the moving direction of the moving body. The moving force of the moving body is decomposed into a first inclination component and a second inclination component whose inclination is gentler than the first inclination component with respect to the amount of movement after reversing the frictional force or friction torque that changes from The displacement from the reversal position is x ′, the rising friction force or friction torque from the reversal of the first inclination component is f _c0 , the rising distance constant of the first inclination component is a ₀ , and the second inclination component The rising distance constant is a ₁ , the total value of dynamic friction force or dynamic friction torque that changes after the moving direction of the moving body is reversed f _c1 , and the ball that increases after moving the predetermined amount after the moving direction of the moving body is reversed Due to the screw shaft and a pair of ball nuts Friction or dynamic friction torque f _c2, the predetermined amount b, a ₂ rising distance constant frictional force or friction torque increases after reversing the moving direction of the moving body after said predetermined amount b _move, the sign function As sgn, the approximate expression f ₁ (x ′) of the first friction estimation unit and the approximate expression f ₂ (x ′) of the second friction estimation unit may be set as the following expressions. Therefore, the numerical control device easily generates the frictional force or frictional torque caused by the feeding mechanism that increases after the moving direction of the moving body is reversed, and the frictional force or frictional torque that increases due to the ball screw shaft and the pair of ball nuts. Can be calculated.

In the first aspect, the approximate expression f ₁ (x ′) of the first friction estimation unit and the approximate expression f ₂ (x ′) of the second friction estimation unit are obtained after reversing the moving direction of the moving body. The frictional force or frictional torque that changes from 1 is decomposed into a first inclination component and a second inclination component whose inclination is gentler than the first inclination component with respect to the movement amount after reversal, and the moving direction of the moving body is reversed. The displacement from the position is x ′, the rising friction force or friction torque from the reversal of the first inclination component is f _c0 , the rising distance constant of the first inclination component is a ₀ , and the rising edge of the second inclination component is The distance constant is a ₁ , the total value of dynamic friction force or dynamic friction torque that changes after the moving direction of the moving body is reversed f _c1 , and the ball screw that increases after moving the predetermined amount after the moving direction of the moving body is reversed Movement caused by a shaft and a pair of ball nuts Friction force or dynamic friction torque f _c2, the predetermined amount b, a ₂ rising distance constant frictional force or friction torque increases after reversing the moving direction of the moving body after said predetermined amount b _move, the sign function As sgn, the approximate expression f ₁ (x ′) of the first friction estimation unit and the approximate expression f ₂ (x ′) of the second friction estimation unit may be set as the following expressions. Therefore, the numerical control device easily generates the frictional force or frictional torque caused by the feeding mechanism that increases after the moving direction of the moving body is reversed, and the frictional force or frictional torque that increases due to the ball screw shaft and the pair of ball nuts. Can be calculated.

In the first aspect, the approximate expression f ₁ (x ′) of the first friction estimation unit and the approximate expression f ₂ (x ′) of the second friction estimation unit are obtained after reversing the moving direction of the moving body. The moving force of the moving body is decomposed into a first inclination component and a second inclination component whose inclination is gentler than the first inclination component with respect to the amount of movement after reversing the friction force or friction torque that changes from The displacement from the reversal position is x ′, the rising friction force or friction torque from the reversal of the first inclination component is f _c0 , the rising distance constant of the first inclination component is a ₀ , and the second inclination component The rising distance constant is a ₁ , the total value of dynamic friction force or dynamic friction torque that changes after the moving direction of the moving body is reversed f _c1 , and the ball that increases after moving the predetermined amount after the moving direction of the moving body is reversed Due to the screw shaft and a pair of ball nuts Friction or dynamic friction torque f _c2, the predetermined amount b, a ₂ rising distance constant frictional force or friction torque increases after reversing the moving direction of the moving body after said predetermined amount b _move, the sign function As sgn, the approximate expression f ₁ (x ′) of the first friction estimation unit and the approximate expression f ₂ (x ′) of the second friction estimation unit may be set as the following expressions. Therefore, the numerical control device easily generates the frictional force or frictional torque caused by the feeding mechanism that increases after the moving direction of the moving body is reversed, and the frictional force or frictional torque that increases due to the ball screw shaft and the pair of ball nuts. Can be calculated.

In the first aspect, the approximate expression f ₁ (x ′) of the first friction estimation unit and the approximate expression f ₂ (x ′) of the second friction estimation unit are obtained after reversing the moving direction of the moving body. The moving force of the moving body is decomposed into a first inclination component and a second inclination component whose inclination is gentler than the first inclination component with respect to the amount of movement after reversing the friction force or friction torque that changes from The displacement from the reversal position is x ′, the rising friction force or friction torque from the reversal of the first inclination component is f _c0 , the rising distance constant of the first inclination component is a ₀ , and the second inclination component The rising distance constant is a ₁ , the total value of dynamic friction force or dynamic friction torque that changes after the moving direction of the moving body is reversed f _c1 , and the ball that increases after moving the predetermined amount after the moving direction of the moving body is reversed Due to the screw shaft and a pair of ball nuts Friction or dynamic friction torque f _c2, the predetermined amount b, a ₂ rising distance constant frictional force or friction torque increases after reversing the moving direction of the moving body after said predetermined amount b _move, the sign function As sgn, the approximate expression f ₁ (x ′) of the first friction estimation unit and the approximate expression f ₂ (x ′) of the second friction estimation unit may be set as the following expressions. Therefore, the numerical control device easily generates the frictional force or frictional torque caused by the feeding mechanism that increases after the moving direction of the moving body is reversed, and the frictional force or frictional torque that increases due to the ball screw shaft and the pair of ball nuts. Can be calculated.

Further, in the first aspect, the approximate expression of the second friction estimation unit increases the displacement from the moving direction reversal position of the moving body by x ′, and increases after moving the predetermined amount after the moving direction of the moving body is reversed. The frictional force or frictional torque that increases after moving the predetermined amount b after reversal of the moving direction of the moving body is represented by f _c2 , the predetermined amount b by the dynamic friction force or dynamic friction torque caused by the ball screw shaft and the pair of ball nuts. The following equation may be used as an approximate expression f ₂ (x ′) of the second friction estimation unit, where a ₂ is a rising distance constant and sgn is a sign function. Therefore, the numerical controller can easily calculate the frictional force or frictional torque that increases due to the ball screw shaft and the pair of ball nuts.

  A friction compensation method according to a second aspect of the present invention includes a ball screw shaft and a ball nut that is fitted around the ball screw shaft, a feed mechanism that moves a moving body fixed to the ball nut, and the ball screw shaft. The position of the moving body detected by the position detection mechanism and the position generated by the control unit are performed by a numerical control device that includes a motor that rotates the motor and a position detection mechanism that detects the position of the moving body moved by the motor. A speed generation step for generating a speed command so that the command matches, a speed detection step for detecting the speed of the motor, a speed detected by the speed detection step, and a speed command generated by the speed generation step match A torque generation step for generating a torque command, a friction estimation step for estimating a friction force or a friction torque generated after reversing the rotation direction of the motor, and a friction estimated in the friction estimation step And a correction step of correcting the torque command based on a friction torque, wherein the ball nut is formed of a pair of ball nuts, and the moving mechanism in which the moving direction of the moving body increases after reversal is provided. A first friction estimation step for estimating a frictional force or frictional torque caused by the frictional force, and a frictional force that increases due to the ball screw shaft and the pair of ball nuts after the moving direction of the moving body has been reversed by a predetermined amount and then moved. Or a second friction estimation step for estimating a friction torque, wherein the friction estimation step adds the friction force or the friction torque estimated in each of the first friction estimation step and the second friction estimation step. And

  In the friction compensation method according to the second aspect, the quadrature protrusion can be corrected because the friction force or the friction torque can be estimated with high accuracy even in the double nut preload type feed mechanism.

FIG. 2 is a diagram showing a part of the structure of a machine tool 20. It is a block diagram which shows the detailed structure of the numerical control apparatus 10 and a feed mechanism. 3 is a cross-sectional view of a feed drive mechanism A. 6 is a cross-sectional view of a periphery of a sphere 37 in the feed drive mechanism A. FIG. 4 is a cross-sectional view of a feed drive mechanism B. It is a figure which shows the contact state of the bulb | ball 47 of the feed drive mechanism B. FIG. FIG. 5 is an enlarged view of an error between an ideal arc locus and an actual locus of the feed drive mechanism A. FIG. 5 is an enlarged view of an error between an ideal arc locus and an actual locus of the feed drive mechanism B. It is the graph which showed the relationship between the motor torque of the feed drive mechanism A, and the distance from an inversion position. It is the graph which showed the relationship between the motor torque of the feed drive mechanism B, and the distance from an inversion position. It is the figure which showed the relationship between the table displacement amount of the feed drive mechanism A, and a friction torque. It is the figure which showed the relationship between the table displacement amount of the feed drive mechanism B, and a friction torque. 3 is a block diagram showing a configuration of a friction compensator 13. FIG. It is the figure which showed the relationship between the amount of table displacement, and friction torque when estimating friction torque using only the 1st term of Formula (1) as an approximate expression. It is the figure which showed the relationship between the amount of table displacement and friction torque when estimating friction torque only using Formula (1) as an approximate expression. It is the figure which showed the relationship between a table displacement amount and friction torque when estimating friction torque using Formula (3) (Formula (1) + Formula (2)) as an approximate expression of this invention. It is the figure which showed the relationship between the amount of table displacement, and friction torque when estimating friction torque using Formula (3) (Formula (4) + Formula (5)) as an approximation formula of this invention. It is the figure which showed the relationship between a table displacement amount and friction torque when estimating friction torque using Formula (3) (Formula (1) + Formula (6)) as an approximate expression of this invention. It is the figure which expanded the error of an ideal circular locus and the actual locus of cases 2, 3, and 6. It is the block diagram which showed the structure when the control block of patent document 1 was changed into the objective of this invention. It is the figure which showed the relationship between the amount of table displacement and friction torque when the friction torque at the time of non-high-speed operation | movement is estimated by the compensation system 1 and the compensation system 2. FIG. It is the figure which showed the relationship between the amount of table displacement, and a friction torque when the friction torque at the time of high-speed operation | movement is estimated by the compensation system 1 and the compensation system 2. FIG. It is the figure which showed the relationship between a table displacement amount and a friction torque when estimating a friction torque using (Formula (1) + Formula (5)) as an approximate expression of this invention. It is the figure which showed the relationship between the amount of table displacement, and a friction torque when estimating a friction torque using (Formula (4) + Formula (2)) as an approximate expression of this invention.

  Embodiments of the present invention will be described below with reference to the drawings. A numerical controller 10 shown in FIG. 1 is an embodiment of the present invention. The numerical control device 10 controls the axial movement of the machine tool 20 in accordance with a path commanded by the machining program and cuts the workpiece fixed to the table 3.

  An example of the table mechanism of the machine tool 20 will be described with reference to FIG. The table mechanism includes a base 1, an intermediate table 50, and a table 3. The base 1 is rectangular. The intermediate table 50 moves on the base 1. The table 3 moves on the intermediate table 50. Table 3 is an example of the moving body of the present invention.

  The base 1 has a pair of linear guides 6A. The pair of linear guides 6A guide the intermediate table 50 in the uniaxial direction. The ball screw shaft 4A and a nut (not shown) are disposed between the pair of linear guides 6A. The intermediate table 50 is fixed to the nut. The intermediate table 50 has a pair of linear guides 6B at the top. The linear guide 6B guides the table 3 in a direction orthogonal to the uniaxial direction. The ball screw shaft 4B and the nut 5 (see FIG. 2) are disposed between the pair of linear guides 6B.

  As shown in FIG. 2, the table 3 includes a block 51 at the bottom. The block 51 slides on the rail 61 of the linear guide 6B. The pair of bearings 7 support the ball screw shaft 4B. The pair of bearings 7 are fixed to the intermediate table 50. The bearing 7 has a bearing 8 inside. The intermediate table 50 includes a block (not shown) at the lower end. The block slides on a rail (not shown) of the linear guide 6A.

  A pair of bearings (not shown) supports the ball screw shaft 4A. The pair of bearings are fixed to the base 1. The bearing has a bearing (not shown) inside.

  As shown in FIG. 1, the base 1 supports a motor 2A at the top. The shaft of the motor 2A and the ball screw shaft 4A are connected by a coupling (not shown). The motor 2A has an oil seal (not shown) around the shaft portion.

  As shown in FIG. 2, the intermediate table 50 supports the motor 2B at the end. The shaft of the motor 2B and the ball screw shaft 4B are connected by a coupling 9. The motor 2B has an oil seal 52 around the shaft portion. The table 3 has fixed covers 53 at both ends. The seal member 55 is fixed to the end of the movable cover 54 opposite to the end on the table side. The seal member 55 is made of rubber. The seal member 55 prevents chips and the like from entering between the fixed cover 53 and the movable cover 54.

  The feed drive mechanism 56 moves the table 3 in the uniaxial direction. The feed drive mechanism 56 includes a ball screw shaft 4 </ b> B and a nut 5. The feed drive mechanism that moves the intermediate table 50 in the uniaxial direction has the same configuration as the feed drive mechanism 56 of the table 3. The feed mechanism of the table 3 includes at least a feed drive mechanism 56, a linear guide 6B, a block 51, a motor 2B, a coupling 9, an oil seal 52, a movable cover 54, a seal member 55, and a bearing 7.

  The configuration of the numerical control device 10 will be described. As shown in FIG. 1, the numerical controller 10 is connected to the motors 2A and 2B. The table 3 moves in the biaxial direction by driving the motors 2A and 2B.

  The ball screw shafts 4A and 4B and the nuts 5 convert the rotational motions of the motors 2A and 2B into the linear motion of the table 3 in the biaxial direction. The numerical control device 10 controls the position, speed, and acceleration of the table 3 by controlling the motors 2A and 2B.

  As shown in FIG. 2, the rotary encoder 60 is attached to the motors 2A and 2B. FIG. 2 does not show the motor 2A and the rotary encoder 60 on the motor 2A side. The rotary encoder 60 detects the positions of the motors 2A and 2B. The numerical controller 10 calculates the position of the table 3 based on the positions of the motors 2A and 2B and the pitch of the ball screw shafts 4A and 4B (interval between screw threads).

  The host controller outputs a position command signal to the position controller 11. The rotary encoder 60 outputs position detection signals of the motors 2A and 2B to the position controller 11. The position controller 11 generates a speed command signal so as to match the position command signal and the position detection signal, and applies the speed command signal to the speed controller 12. The differentiator 16 converts the position detection signal into a speed detection signal and applies it to the speed controller 12.

  The speed controller 12 generates a torque command signal so as to match the speed command signal and the speed detection signal, and applies the torque command signal to the adder 14. The friction compensator 13 generates a friction compensation signal based on the position command signal from the host controller and applies it to the adder 14. The friction compensation signal is a signal for compensating for a frictional force generated when the rotation directions of the motors 2A and 2B are reversed. The adder 14 adds the torque command signal from the speed controller 12 and the friction compensation signal from the friction compensator 13. The adder 14 adds the friction-compensated torque command signal to the current control amplifier 15. The current control amplifier 15 functions as a torque controller. The current control amplifier 15 controls the currents of the motors 2A and 2B so as to generate a torque that is as faithful as possible to the friction-compensated torque command signal.

  The configuration and operation of the position controller 11, speed controller 12, adder 14, current control amplifier 15, and differentiator 16 are well known. Therefore, the configuration and operation of the friction compensator 13 directly related to the present invention will be described focusing on the principle.

  The feed drive mechanism has a friction force caused by the first friction source and the second friction source, respectively. The frictional force resulting from the first friction source is the preload of the block of the linear guide, the preload of the nut portion of the ball screw shaft, and the preload of the bearing. The rigidity of the feed drive mechanism increases as the preload increases, and the frictional force increases. The frictional force resulting from the second friction source is the sliding resistance of the seals of the oil seal 52 and the movable cover 54. The friction force increases as the sealing performance increases.

  The frictional force changes abruptly when the motion direction of the table 3 is reversed. When the movement direction of the table 3 is reversed, the rotation direction of the ball screw shafts 4A and 4B is reversed. For example, the numerical control apparatus 10 performs the circular cutting by performing the above-described circular interpolation motion using two orthogonal axes. There are cases where the control system cannot cope with changes in frictional force. The upper graph in FIG. 1 shows the error between the ideal arc trajectory and the actual trajectory. Portions 71 to 74 surrounded by an ellipse are quadrant projections. The friction compensator 13 estimates and compensates for the friction force when the movement direction of the table 3 is reversed with high accuracy. Therefore, the numerical controller 10 can make the quadrant protrusion as small as possible.

  The quadrant protrusion is caused by a change in frictional force generated in the feed drive mechanism. Quadrant projections are generated differently depending on the preloading method of the ball screw shaft. The structure and characteristics of the ball screw shaft preload system will be described. The ball screw shaft preload system includes an oversized ball preload system and a double nut preload system.

  As shown in FIG. 3, the oversize ball preload type feed drive mechanism A is a system in which preload is applied by a single nut 35 (hereinafter referred to as a nut 35). The nut 35 is a ball nut. The nut 35 includes a ball 37 inside. As shown in FIG. 4, the ball 37 always contacts the nut 35 and the ball screw shaft 34 at four points. The feature of the oversize ball preloading method is that the size of the nut 35 is small and the load is light. Therefore, the oversize ball preload system is adopted for small machine tools.

  As shown in FIG. 5, the double nut preload type feed drive mechanism B includes two nuts 45 and 46. The nuts 45 and 46 are ball nuts. The spacer 48 is between the nuts 45 and 46. As shown in FIGS. 6A, 6 </ b> B, and 6 </ b> C, the ball 47 moves according to the moving direction of the nuts 45 (not shown in FIG. 6) and 46. The ball 47 changes at any time by two-point or three-point contact with the nuts 45 and 46 and the ball screw shaft 44. A white arrow in FIG. 6 indicates the rotation direction of the sphere 47.

  For example, as shown in FIG. 6A, the nut 46 moves in one direction. Since the ball 47 contacts the nut 46 at one point and the ball screw shaft 44 at two points, the ball 47 contacts at three points. As shown in FIG. 6B, the nut 46 is in the middle of reversal of movement. Since the ball 47 contacts the nut 46 at one point and the ball screw shaft 44 at one point, the ball 47 contacts at two points. Therefore, the friction is smaller than that of the three-point contact. As shown in FIG. 6C, the nut 46 is moved in the opposite direction with the moving direction reversed. Since the ball 47 contacts the nut 46 at two points and the ball screw shaft 44 at one point, the ball 47 contacts at three points. Therefore, the friction increases again. The feature of the double nut preload system is high rigidity. Therefore, large machine tools etc. adopt the double nut preload system.

  The effect of the ball screw shaft preload system on the quadrant projection will be described. The error with respect to the ideal trajectory when the circular interpolation motion was performed using the numerical control devices that drive and control the feed drive mechanisms A and B was examined.

  7 and 8 are enlarged views of an error between an ideal arc locus and an actual locus. The feed speed is 3 m / min and the command radius is 25 mm. One scale is 5 μm.

  The locus error is a quadrant projection. In both the results of FIGS. 7 and 8, the quadrant protrusions are generated around 0 °, 90 °, 180 °, and 270 °. The direction of motion of the X axis is reversed between 0 ° and 180 °. The direction of movement of the Y axis is reversed at 90 ° and 270 °. The quadrant projections in the vicinity of each reversal position are the response of the servo system to the change of the frictional force on the circular locus. The friction force is the friction force when the direction of motion is reversed.

  As shown in FIG. 7, in the feed drive mechanism A, the quadrant protrusion is a mountain. The feed drive mechanism A is an oversize ball preload system. As shown in FIG. 8, in the feed drive mechanism B, the quadrant protrusions are two ridges. The feed drive mechanism B is a double nut preload system. The reason is as follows. The first peak of the quadrant projection is the effect of friction when the quadrant changes. The second peak of the quadrant projection is the effect of friction that increases when the ball goes from two-point contact to three-point contact with the nut and ball screw shaft.

  The behavior of the frictional resistance during reversal of the ball screw shaft alone was investigated. 9 and 10 are graphs showing the relationship between the distance from the reversal position of the ball screw shaft and the motor torque [Nm].

  As shown in FIG. 9, in the oversize ball preload system, the motor torque rises at a stroke and becomes constant after reversal. As shown in FIG. 10, in the double nut preload system, the motor torque increases slightly after inversion and becomes constant, and then gradually increases and becomes constant again. While the sphere is in contact at two points from the reverse position, the motor torque slightly increases and becomes constant. The sphere changes from a two-point contact state to a three-point contact state. In the case described above, a two-point contact state and a three-point contact state are mixed. Therefore, the motor torque increases slowly. After that, all spheres are in three-point contact. Therefore, the motor torque becomes a maximum value and is constant.

  FIG. 11 and FIG. 12 show the relationship between the amount of table displacement and the friction torque in the micro arc motion of the machine tool. The feed speed is 5 mm / min, and the command radius is 0.1 mm. In micro arc motion, the friction force is not affected by speed and acceleration.

  As shown in FIG. 11, in the oversized ball preload system, the motor torque exhibits a non-linear spring characteristic after the movement direction is reversed. The motor torque becomes a substantially constant value when the displacement increases to some extent. The motor torque locus draws a hysteresis loop. As shown in FIG. 12, in the double nut preload system, the motor torque changes in a gentle step shape at a position of 0.065 mm after the movement direction is reversed. The step-like change is the cause of the quadrant protrusion being doubled. The numerical controller 10 focuses on the friction characteristics of the double nut preload system. The numerical control device 10 can compensate for the two quadrant projections by estimating the frictional force or the frictional torque with high accuracy.

  A detailed configuration of the friction compensator 13 and a friction compensation method by the friction compensator 13 will be described with reference to FIG. The friction compensator 13 includes an actual position estimation unit 21, a differentiator 22, a sign inversion detection unit 23, an integrator 24, a first friction characteristic estimation unit 26, a second friction characteristic estimation unit 27, an adder 28, and a response delay compensation unit 29. At least. The first and second friction characteristic estimation units 26 and 27 include an absolute value calculation unit and a polarity calculation unit. The absolute value calculator obtains the absolute value of the input signal. The polarity calculator obtains the polarity of the signal obtained by time differentiation of the input signal.

  The host controller inputs the position command signal to the actual position estimating unit 21. The actual position estimation unit 21 uses a model of a servo control system that performs the feed movement of the table 3. The actual position estimation unit 21 estimates the actual position of the table 3 corresponding to the position command signal and generates an actual position signal. The actual position estimation unit 21 may be configured with, for example, a first-order lag element. The differentiator 22 is connected to the actual position estimation unit 21. The differentiator 22 differentiates the actual position signal and outputs it as a speed signal. The sign inversion detection unit 23 and the integrator 24 are connected to the differentiator 22.

  The sign inversion detection unit 23 detects that the sign of the speed signal is inverted. The sign inversion detection unit 23 outputs a reset signal. The integrator 24 restores the actual position signal by integrating the speed signal. The integrator 24 resets the integral value to zero for each reset signal output from the sign inversion detection unit 23. The integrator 24 generates a displacement signal from a position where the table 3 reverses the direction of motion.

The first friction characteristic estimation unit 26 and the second friction characteristic estimation unit 27 are connected to the integrator 24. The first friction characteristic estimation unit 26 uses the approximate expression 1 described later. The first friction characteristic estimation unit 26 obtains the friction torque f ₁ (x ′) [N · m]. Friction torque f ₁ is increased after the table inverted. The second friction characteristic estimation unit 27 uses an approximate expression 2 described later. The second friction characteristic estimating unit 27 obtains the friction torque f ₂ (x ′) [N · m]. After the friction torque f ₂ table 3 inverted, increases after moving a predetermined amount. The adder 28 is connected to the first friction characteristic estimation unit 26 and the second friction characteristic estimation unit 27.

The adder 28 adds f ₁ (x ′) and f ₂ (x ′). The response delay compensation unit 29 is connected to the output terminal of the adder 28. The response delay compensation unit 29 is composed of an inverse function of the transfer function. The transfer function models the characteristics from the torque command signal to the torque that the motor 2 actually outputs. The torque command signal is input to the current control amplifier 15 (see FIG. 2). The response delay compensation unit 29 multiplies the estimated friction torque to generate a friction compensation signal.

The approximate expression 1 of the first friction characteristic estimation unit 26 and the approximate expression 2 of the second friction characteristic estimation unit 27 will be described. In the present embodiment, various parameters are defined as follows.
F (x ′) = total friction torque [N · m]
F ₁ (x ′) = friction torque increasing after table inversion [N · m]
F ₂ (x ′) = Friction torque [N · m] that increases after moving a predetermined amount after the table is reversed
F _c0 = Friction torque changing after table reversal is decomposed into two types of gradient components with respect to the amount of movement after reversal, and rising friction torque [N · m] from the reversal of the first gradient component
A ₀ = rise distance constant of the first slope component [mm]
A ₁ = rise distance constant of the second slope component [mm]
・ F _c1 = Total value of dynamic friction torque that changes after table reversal [N · m]
F _c2 = dynamic friction torque caused by the ball screw shaft and the pair of ball nuts increasing after moving the predetermined amount after the table is reversed (dynamic friction torque at the time of steady (three-point contact) between the ball screw shaft and the nut) [N · m]
A ₂ = Friction torque rising distance constant [mm] that increases after a predetermined amount of movement after the table is reversed
B = distance [mm] until f ₂ (x ′) starts to increase after the table is inverted
・ X ′ = displacement from the reversal position of the movement direction of the table [mm]
Sgn = sign function sgn is +1 when dx ′ / dt> 0, 0 when dx ′ / dt = 0, and −1 when dx ′ / dt <0. a ₁ , a ₂ , f _c1 , f _c2 , b are shown in the hysteresis curve when the circular interpolation motion is performed by the double nut method shown in FIG. The first slope component has a steeper slope than the second slope component.

Approximation formula 1 is as follows.
F ₁ (x ′) = f _c0 {tanh (| x ′ | / a ₀ ) −1/2} sgn (dx ′ / dt) + (f _c1 + f _c2 / 2−f _c0 / 2) {2 tanh ( | X ′ | / a ₁ ) −1} sgn (dx ′ / dt) (1)

  In the approximate expression described in Patent Document 1, the tanh function is a set. The present invention combines two sets of different tanh functions. The reason is to deal with both the first friction factor and the second friction factor. The first friction factor is a linear guide whose friction characteristics at the time of reversal change suddenly. The first slope is due to the first friction factor. The second friction factor is an oil seal or the like that changes more slowly than the first friction factor. The second slope component is attributed to the second friction factor.

Approximation formula 2 is as follows.
F ₂ (x ′) = _{fc 2} {tanh ((| x ′ | −b) / a ₂ ) −1/2} sgn (dx ′ / dt) (2)
When | x ′ | −b <0, f ₂ (x ′) = − f _c2 / 2 · sgn (dx ′ / dt). Equation (2) corresponds to the friction of the double nut preload system. The friction of the double nut preload system increases after the nut is reversed and moved a predetermined amount.

From the formulas (1) and (2), the approximate formula 3 of the total friction torque f (x ′) is the following formula.
F (x ′) = f ₁ (x ′) + f ₂ (x ′) (3)

The approximate expressions 1 and 2 may be exp functions instead of the tanh functions. For example, the approximate expressions 1 and 2 may be expressed as follows. The values a ₀ and a ₁ in formula (4) and a _{2 in} formula (5) are selected as appropriate values for a ₀ and a ₁ in formula ( ₁ ) and a _{2 in} formula (2). Therefore, equations (4) and (5) can draw almost the same curves as equations (1) and (2).
F ₁ (x ′) = f _c0 {1 / 2−exp (− | x ′ | / a ₀ )} sgn (dx ′ / dt) + (f _c1 + f _c2 / 2−f _c0 / 2) {1 −2exp (− | x ′ | / a ₁ )} sgn (dx ′ / dt) (4)
F ₂ (x ′) = f _c2 {1 / 2−exp {− (| x ′ | −b)} / a ₂ } sgn (dx ′ / dt) (5)
When | x ′ | −b <0, f ₂ (x ′) = − f _c2 / 2 · sgn (dx ′ / dt).

The approximate expression 2 can also be expressed as follows using a cos function. The approximate expression 2 has a gentle rise in the vicinity of | x ′ | −b = 0. The approximate expression 2 can draw a curve closer to the actual measurement data.
F ₂ (x ′) = − f _c2 / 2cos {{(| x ′ | −b) / a ₂ } π} sgn (dx ′ / dt) (6)
When | x ′ | −b <0 or | x ′ | −b−a ₂ > 0, f ₂ (x ′) = − f _c2 / 2 · sgn (dx ′ / dt).

In order to confirm the effect of the numerical controller 10 having the friction compensator 13, cases 1 to 5 were compared. Case 1 is a case where circular interpolation motion is performed by applying a conventional friction compensation method. Case 2 is a case where circular interpolation motion is performed by applying only the approximate expression 1 of the present invention. Case 3 is a case where circular interpolation motion is performed by applying the formula (1) as the approximate formula 1 and the formula (2) as the approximate formula 2 of the present invention. Case 4 is a case where circular interpolation motion is performed by applying Formula (4) as the approximate formula 1 and Formula (5) as the approximate formula 2 of the present invention. Case 5 is a case where circular interpolation motion is performed by applying Formula (1) as the approximate formula 1 and Formula (6) as the approximate formula 2 of the present invention. Case 1 refers to the approximate expression described in Japanese Patent Application Laid-Open No. 2008-210273, and f _c0 {tanh (| x ′ | / a ₀ ), which is the first term of the expression (1) described in the present invention, as an agreed approximate expression. ) -1/2} sgn (dx '/ dt) only. Cases 1 to 5 performed circular interpolation motion with a feed rate of 5 mm / min and a command radius of 0.1 mm. The result of comparing the relationship between the table displacement and the motor torque with the measured data is as follows. Also in cases 1 and 2, the definition of the parameters of the approximate expression used by the first and second friction characteristic estimation units 26 and 27 of the friction compensator 13 is the same as the above definition.

The result of case 1 will be described with reference to FIG. In FIG. 14, the actual measurement value is indicated by a thick line, and the value calculated by the approximate expression is indicated by a thin line. As the parameter, a value that can most closely approximate the rising characteristic after the inversion of the measured data is selected. In this example, f _c0 = 0.9 and a ₀ = 0.0025. As shown in FIG. 14, the value of the approximate expression of the motor torque matches the slope of the increase of 0.9 N · m in the first stage of the actual measurement value. The measured value rises gently after the first stage rise, and further rises in the second stage at about 70 μm after reversal. Since the approximate expression is a constant value, it does not match the actual measurement value. The reason is that the conventional approximate expression of Patent Document 1 only supports a single characteristic of only a sudden friction change after reversal by a linear guide or the like. Therefore, the conventional approximate expression cannot correct the friction characteristic of the oil seal or the like and the friction characteristic of the double nut preload system. Friction characteristics of oil seals change slowly after reversal. The friction characteristics of the double nut preloading method increase after the nut moves a predetermined distance after inversion.

  As shown in FIGS. 14 and 15, there is a difference between the actually measured values in Cases 1 and 2 and the result of the approximate expression in the value of torque immediately before reversal. The actual torque command is the sum of the output of the speed controller 12 and the output of the approximate expression. The torque command is controlled to coincide with the actually measured value. The speed controller 12 outputs about −0.175 N · m immediately before inversion at −100 μm, for example. The actual torque command is a value obtained by offsetting the approximate expression by 0.175 N · m. Therefore, the approximate expression and the actual measurement value coincide with each other at the rising portion of the friction torque after the inversion.

The result of case 2 will be described with reference to FIG. Case 2 uses only the first term of formula (1) of the present invention. In FIG. 15, the actual measurement value is indicated by a thick line, and the value calculated by the approximate expression is indicated by a thin line. As the parameter, a value that can approximate the rising characteristic of the first stage after the inversion of the measured data is selected. In this example, f _c0 = 0.9, a ₀ = 0.0025, f _c1 = 0.625, and a ₁ = 0.031. As shown in FIG. 15, the change in friction after reversal is approximated by a combination of two sets of tanh functions. The measured value and the approximate expression agree with each other in the first stage of friction increase from 60 μm after inversion. The measured value and the approximate expression do not agree with the friction increase in the second stage. Therefore, the case 2 can cope with a slow reverse torque characteristic such as an oil seal, but cannot cope with the two-stage friction increase of the double nut preload system.

The result using the approximate expression 3 of the present invention will be described. FIG. 16 shows the case 3 where the approximate expression 1 and approximate expression 2 both use the tanh function. FIG. 17 shows the case 4 where the exp function is used for both the approximate expression 1 and the approximate expression 2. FIG. 18 shows the case 5 where the cos function of the equation (6) is used with the equation (1) as the approximation equation 2 in the approximate equation 1. The actual measurement value is indicated by a thick line, and the value calculated by the approximate expression is indicated by a thin line. As the parameters, values that can be approximated most closely to the measured data in cases 3 to 5 are selected. In case 3, f _c0 = 0.9, a ₀ = 0.0025, f _c1 = 0.45, a ₁ = 0.031, f _c2 = 0.35, a ₂ = 0.02, b = 0.075 It is. In case 4, f _c0 = 0.9, a ₀ = 0.0018, f _c1 = 0.45, a ₁ = 0.022, f _c2 = 0.35, a ₂ = 0.014, b = 0.075 It is. In case 5, f _c0 = 0.9, a ₀ = 0.0025, f _c1 = 0.45, a ₁ = 0.031, f _c2 = 0.35, a ₂ = 0.05, b = 0.06 It is. As shown in FIGS. 16 and 17, the value of the approximate expression 3 of the present invention for the motor torque matches the first increase in the first measured value and also matches the second increase. Approximation equation 3 corresponds to both the first and second increases in friction. Therefore, the cases 3 and 4 can cope with the two-stage friction increase of the double nut preload system.

The difference between the approximate expressions of cases 3 and 4 becomes almost the same curve when the values of a ₀ , a ₁ , and a ₂ are changed. Therefore, the result of using the approximate expression 3 in a combination of the approximate expression 1 as the expression (1) and the approximate expression 2 as the expression (5) is also a calculation result that closely approximates the actual measurement value. The result of using the approximate expression 3 in a combination of the approximate expression 1 as the expression (2) and the approximate expression 2 as the expression (4) is also a calculation result that closely approximates the actual measurement value.

  As shown in FIG. 18, the case 5 uses a cos function to increase the second stage friction. Therefore, the rise is smoother than cases 3 and 4 and is closer to the actually measured value. A calculation result using the approximate expression 3 in a combination of the approximate expression 1 as the expression (4) and the approximate expression 2 as the expression (6) is also a calculation result that closely approximates the actual measurement value as in the case 5.

  In order to investigate the reduction effect of quadrant protrusions in cases 2 and 3, the error between the ideal arc locus and the actual locus was examined. The actual trajectory shown in FIG. 19 is an arc trajectory when the feed speed is 6 m / min and the command radius is 50 mm. Case 6 is a comparative example. Case 6 is a case where no friction compensation was performed. In FIG. 19, case 2 is indicated by a long dotted line, case 3 is indicated by a solid line, and case 6 is indicated by a short dotted line.

  In case 6, there are two quadrant protrusions. The double quadrant projection is a characteristic of the double nut preload system. In Case 2, one of the two quadrant protrusions has disappeared. The second mountain remains. Case 2 is friction-compensated by only approximate expression 1 corresponding to only the first stage. Approximation formulas that correspond only after reversal can correspond to the oversize ball preloading method, but not the double nut preloading method. Therefore, the approximate expression corresponding only after inversion cannot eliminate the quadrant projections, so that the processing accuracy cannot be improved.

  In Case 3, the quadrant protrusions almost disappear in all the peaks. Case 3 is friction-compensated by the approximate expression 3 of the present invention. The reason is that the frictional force generated in two stages after the shaft reversal is estimated with high accuracy by the approximate expressions 1 and 2. Therefore, the numerical control device 10 can be adapted to any of the oversize ball preload type and double nut preload type feed drive mechanisms. The numerical control device 10 can also be applied to a machine tool having a composite reverse friction characteristic. Therefore, the numerical controller 10 can effectively improve the machining accuracy of the workpiece.

  The rotary encoder 60 is an example of the position detection means of the present invention. The position controller 11 is an example of speed generation means of the present invention. The differentiator 16 is an example of the speed detection means of the present invention. The speed controller 12 is an example of torque generating means of the present invention. The actual position estimating unit 21 is an example of the actual position estimating means of the present invention. The friction compensator 13 is an example of the friction estimation means of the present invention. The response delay compensation unit 29 is an example of a response delay correction unit of the present invention. The second friction characteristic estimation unit 27 is an example of a second friction estimation unit of the present invention. The first friction characteristic estimation unit 26 is an example of a first friction estimation unit of the present invention. The adder 28 is an example of the adding means of the present invention.

  As described above, the numerical controller 10 and the friction compensation method of the present embodiment can sufficiently cope with not only the oversize ball preload system but also the double nut preload system feed drive mechanism. In the double nut preload system, the ball contacts the nut and the ball screw shaft at two or three points according to the moving direction of the nut. In the double nut preloading system, the ball screw shaft is inverted to form a first quadrant protrusion, and when the table 3 is further moved by a predetermined amount, a second quadrant protrusion is generated. The conventional friction compensation method only supports the oversize ball preloading method. The conventional friction compensation method cannot eliminate the quadrant projection of the second mountain peculiar to the double nut preloading method. In the present embodiment, an increase in frictional force generated in two stages in the case of the double nut preloading method can be estimated with high accuracy using two approximate equations. The first peak of the quadrant projection is due to the friction characteristics after reversal. The friction characteristics after reversal include those in which the friction characteristics change suddenly after reversal and those in which the friction characteristics change slowly after reversal. An example of the former is based on a linear scale. An example of the latter is due to an oil seal in the motor shaft. In the present embodiment, two approximate equations can be used in consideration of the friction characteristics of the two. In this embodiment, in addition to the disappearance of the first quadrant projection, the second quadrant projection, which could not be disappeared in the past, can be surely eliminated. In this embodiment, the quadrant protrusion can be effectively eliminated even with a double nut preloading system or with an oil seal. This embodiment can improve processing accuracy reliably.

The present invention is not limited to the above embodiment, and various modifications can be made. For example, in the friction compensator 13 of the above embodiment, the first friction characteristic estimation unit 26 calculates the friction torque f ₁ (x ′) using the approximate expression 1. The second friction characteristic estimating unit 27 calculates the friction torque f ₂ (x ′) using the approximate expression 2. The friction compensator 13 calculates the total friction torque f (x ′) by adding the friction torques f ₁ (x ′) and f ₂ (x ′) using the approximate expression 3. The friction compensator 13 adds the total friction torque f (x ′) to the torque.

  For example, the friction compensator disclosed in Japanese Patent Application Laid-Open No. 2008-210273 may be modified to meet the object of the present invention. The friction compensator can compensate for the frictional force that increases in two stages by using two approximate equations 5 and 6 different from the above embodiment. The configuration and operation of the friction compensator 106 will be described. The friction compensator 106 is a modification of the friction compensator 13.

  The configuration of the friction compensator 106 will be described with reference to FIG. The friction compensator 106 has a part of the same configuration as the friction compensator 13 shown in FIG. The friction compensator 106 includes an actual position estimation unit 21, a differentiator 22, a sign inversion detection unit 23, an integrator 24, an adder 28, and a response delay compensation unit 29. The friction compensator 106 includes a third friction characteristic estimation unit 56 and a fourth friction characteristic estimation unit 57. The third friction characteristic estimation unit 56 is a substitute for the first friction characteristic estimation unit 26. The fourth friction characteristic estimation unit 57 is a substitute for the second friction characteristic estimation unit 27. The third friction characteristic estimator 56 and the fourth friction characteristic estimator 57 calculate differential values using approximate equations 5 and 6, which will be described later. The multiplier 59 and the integrator 60 are provided between the adder 28 and the response delay compensation unit 29.

  The adder 28 adds the differential values calculated by the third friction characteristic estimation unit 56 and the fourth friction characteristic estimation unit 57 and outputs the result to the multiplier 59. The multiplier 59 multiplies the differential value output from the adder 28 by the speed signal output from the differentiator 22 to calculate the rate of change of the friction torque with respect to time. The integrator 60 is connected to the output terminal of the multiplier 59. The integrator 60 integrates the change rate calculated by the multiplier 59 with time. The response delay compensation unit 29 is connected to the output terminal of the integrator 60.

  The response delay compensation unit 29 is composed of an inverse function of the transfer function. The transfer function models the characteristics from the torque command signal to the torque that the motor 2 actually outputs. The torque command signal is input to the current control amplifier 15 (see FIG. 2). The response delay compensation unit 29 multiplies the integration value output from the integrator 60 to generate a friction compensation signal.

  The approximate expressions 5 and 6 will be described. The third friction characteristic estimation unit 56 and the fourth friction characteristic estimation unit 57 use approximate expressions 5 and 6. The definition of various parameters in this modification is the same as when the approximate expressions 1 and 2 are defined.

The approximate expressions 5 and 6 are obtained by differentiating the approximate expressions 1 and 2 by x ′. The approximate expression 5 is an expression (7) obtained by differentiating the expression (1) by x ′.
Df ₁ / dx ′ = 2f _c0 / a ₀ {1-tanh ² (| x ′ | / a ₀ )} + 1 / a ₁ (2f _c1 + f _c2 −f _c0 ) {1-tanh ² (| x ′ | / A ₁ )} (7)

The approximate expression 6 becomes an expression (8) obtained by differentiating the expression (2) by x ′.
_{· Df 2 / dx '= f} c2 / a 2 {1-tanh 2 {(| x' | -b) / a 2}} ··· (8)
If | x ′ | −b <0, df ₂ / dx ′ = 0.

  The difference in effect was examined between the case where the friction compensation was performed by the friction compensator 13 of the above embodiment and the case where the friction compensation was performed by the friction compensator 106 of the present modification. The former method is the compensation method 1, and the latter method is the compensation method 2. In FIG. 21, the data of the compensation method 1 is indicated by a thin line, and the data of the compensation method 2 is indicated by a thick line.

  The error of friction compensation was investigated when the arc motion was performed at a non-high speed and when the arc motion was performed at a high speed. As shown in FIG. 21, when arc cutting was performed at a non-high speed, the friction torque when the friction compensation was performed by the compensation methods 1 and 2 was the same. As shown in FIG. 22, when arc cutting was performed at high speed, the friction torque when the friction compensation was performed by the compensation method 2 caused an error with respect to the compensation method 1. In the case of the compensation method 2, the rate of change of time with respect to the friction torque is once obtained, and time integration is performed on the obtained result. Therefore, the integration error cannot be ignored at high speed.

  As described above, when compensation similar to that of the present invention is performed by changing the control method of Japanese Patent Laid-Open No. 2008-210273, the same effect can be obtained at non-high speed. The method of the present invention is a method of simply calculating with a friction estimation formula expressed as a function of inversion distance and adding it to the torque command. The present invention can perform friction compensation with high accuracy from a low speed region to a high speed region, and the present invention is superior to the conventional method.

  In the above embodiment, the expression (1) used for the approximate expression 1 is a combination of two sets of tanh functions. Equation (4) is a combination of two sets of exp functions. Even if the first term is a combination of the tanh function and the second term is the exp function, the same effect can be obtained even if the first term is the exp function and the second term is the tanh function.

  In the above embodiment, the first term of the approximate expression 1 approximates the sudden friction change after reversal by the tanh function or the exp function. The sudden change in friction after reversal becomes a constant value immediately after sudden rise. Therefore, the first term of the approximate expression 1 may be approximated using a ramp function or a step function.

  In the above embodiment, the table 3 is a moving body. The moving body may be a mechanism that supports the main shaft holding the tool. Keep the table fixed. The mechanism may be composed of a spindle head and a column. The spindle head supports the spindle rotatably. The column supports the spindle head so as to be movable up and down or back and forth.

As the case 7, the expression (1) is used for the approximate expression 1, and the expression (5) is used for the approximate expression 2. In case 8, equation (4) is used for approximate equation 1 and equation (2) is used for approximate equation 2. In case 3, f _c0 = 0.9, a ₀ = 0.0025, f _c1 = 0.45, a ₁ = 0.031, f _c2 = 0.35, a ₂ = 0.014, b = 0.075 It is. In case 8, f _c0 = 0.9, a ₀ = 0.00025, f _c1 = 0.45, a ₁ = 0.031, f _c2 = 0.35, a ₂ = 0.014, b = 0.075 It is. FIG. 23 is a diagram of the case 7. FIG. 24 is a diagram of the case 8.

  Any one of the expressions (1) and (4) may be used as the approximate expression 1, and any of the expressions (2), (5), and (6) may be used as the approximate expression 2. Therefore, there are six ways.

  In the above embodiment, a double-nut preload feed mechanism is used. The present invention can achieve the same effect even in an offset preload type feed mechanism. The offset preload type feed mechanism has the same friction characteristics as the double nut preload type. The offset preload type feed mechanism is configured as a single nut by integrating a pair of nuts and a spacer.

DESCRIPTION OF SYMBOLS 1 Numerical controller 12 Speed controller 13 Friction compensator 21 Actual position estimation part 24 Integrator 29 Response delay compensation part 26 First friction characteristic estimation part 27 Second friction characteristic estimation part

Claims (9)

A feed mechanism that has a ball screw shaft and a ball nut that is externally fitted to the ball screw shaft, moves a moving body fixed to the ball nut, a motor that rotationally drives the ball screw shaft, and a movement that is moved by the motor A position detection mechanism that detects the position of the body, a speed generation unit that generates a speed command so that the position of the moving body detected by the position detection mechanism matches the position command generated by the control unit, and the speed of the motor A speed detection mechanism for detecting the torque, a torque generation unit for generating a torque command so that a speed detected by the speed detection mechanism and a speed command generated by the speed generation unit match, and a rotation direction of the motor is reversed A numerical control system comprising: a friction estimation unit that estimates a generated friction force or friction torque; and a correction unit that corrects the torque command based on the friction or friction torque estimated by the friction estimation unit. In the device,
The ball nut comprises a pair of ball nuts,
A first friction estimation unit that estimates a friction force or a friction torque caused by the feed mechanism that increases after the moving direction of the moving body is reversed, and
A second friction estimation unit that estimates a frictional force or a friction torque that increases due to the ball screw shaft and the pair of ball nuts after the moving direction of the moving body has been moved by a predetermined amount after reversing;
The numerical controller according to claim 1, wherein the friction estimation unit adds the friction force or the friction torque estimated by the first friction estimation unit and the second friction estimation unit. The pair of ball nuts has a plurality of balls,
The predetermined amount is a distance that the movable body moves until at least one of the plurality of balls contacts the pair of ball nuts and the ball screw shaft at three points after the moving direction of the movable body is reversed. The numerical control apparatus according to claim 1, wherein the numerical control apparatus is provided. An actual position estimating unit that estimates an actual position of the moving body corresponding to the position command;
A calculation unit that calculates the displacement after the moving direction of the moving body is reversed based on the actual position estimated by the actual position estimation unit;
The numerical control device according to claim 1, wherein the first friction estimation unit and the second friction estimation unit are approximate expressions using the displacement calculated by the calculation unit as a variable. The approximate expression f ₁ (x ′) of the first friction estimation unit and the approximate expression f ₂ (x ′) of the second friction estimation unit are friction forces that change after reversal of the moving direction of the moving body or The friction torque is decomposed into a first inclination component and a second inclination component whose inclination is gentler than the first inclination component with respect to the movement amount after reversing, and the displacement of the moving body from the reversing position in the movement direction is determined. x ′, the rising friction force or the friction torque from the reversal of the first inclination component is f _c0 , the rising distance constant of the first inclination component is a ₀ , and the rising distance constant of the second inclination component is a ₁ , The total value of dynamic friction force or dynamic friction torque that changes after the moving direction of the moving body is reversed, f _c1 , and a ball screw shaft and a pair of balls that increase after moving the predetermined amount after the moving direction of the moving body is reversed Dynamic friction force or dynamic friction torque caused by nut The f _c2, the predetermined amount b, a ₂ rising distance constant frictional force or friction torque increases after reversing the moving direction of the moving body after said predetermined amount b _move, the sign function as sgn,

The numerical control apparatus according to claim 3, wherein: The approximate expression f ₁ (x ′) of the first friction estimation unit and the approximate expression f ₂ (x ′) of the second friction estimation unit are friction forces that change after reversal of the moving direction of the moving body or The friction torque is decomposed into a first inclination component and a second inclination component having a gentler inclination than the first inclination component with respect to the movement amount after reversing, and the displacement of the moving body from the reversing position in the moving direction is represented by x. ', The rising friction force or friction torque from the reversal of the first inclination component is f _c0 , the rising distance constant of the first inclination component is a ₀ , the rising distance constant of the second inclination component is a ₁ , The total value of dynamic friction force or dynamic friction torque that changes after the reversal of the moving direction of the moving body is _fc1 , and a ball screw shaft and a pair of ball nuts that increase after moving the predetermined amount after reversing the moving direction of the moving body. Dynamic friction force or dynamic friction torque caused by f _c2, the predetermined amount b, a ₂ rising distance constant frictional force or friction torque increases after reversing the moving direction of the moving body after said predetermined amount b _move, the sign function as sgn,

The numerical control apparatus according to claim 3, wherein: The approximate expression f ₁ (x ′) of the first friction estimation unit and the approximate expression f ₂ (x ′) of the second friction estimation unit are friction forces that change after reversal of the moving direction of the moving body or The friction torque is decomposed into a first inclination component and a second inclination component whose inclination is gentler than the first inclination component with respect to the movement amount after reversing, and the displacement of the moving body from the reversing position in the moving direction is determined. x ′, the rising friction force or the friction torque from the reversal of the first inclination component is f _c0 , the rising distance constant of the first inclination component is a ₀ , and the rising distance constant of the second inclination component is a ₁ , The total value of dynamic friction force or dynamic friction torque that changes after the moving direction of the moving body is reversed, f _c1 , and a ball screw shaft and a pair of balls that increase after moving the predetermined amount after the moving direction of the moving body is reversed Dynamic friction force or dynamic friction torque caused by nut The f _c2, the predetermined amount b, a ₂ rising distance constant frictional force or friction torque increases after reversing the moving direction of the moving body after said predetermined amount b _move, the sign function as sgn,

The numerical control apparatus according to claim 3, wherein: The approximate expression f ₁ (x ′) of the first friction estimation unit and the approximate expression f ₂ (x ′) of the second friction estimation unit are friction forces that change after reversal of the moving direction of the moving body or The friction torque is decomposed into a first inclination component and a second inclination component whose inclination is gentler than the first inclination component with respect to the movement amount after reversing, and the displacement of the moving body from the reversing position in the moving direction is determined. x ′, the rising friction force or the friction torque from the reversal of the first inclination component is f _c0 , the rising distance constant of the first inclination component is a ₀ , and the rising distance constant of the second inclination component is a ₁ , The total value of dynamic friction force or dynamic friction torque that changes after the moving direction of the moving body is reversed, f _c1 , and a ball screw shaft and a pair of balls that increase after moving the predetermined amount after the moving direction of the moving body is reversed Dynamic friction force or dynamic friction torque caused by nut The f _c2, the predetermined amount b, a ₂ rising distance constant frictional force or friction torque increases after reversing the moving direction of the moving body after said predetermined amount b _move, the sign function as sgn,

The numerical control apparatus according to claim 3, wherein: The approximate expression of the second friction estimation unit is that the displacement from the moving direction reversal position of the moving body is x ′, and a pair of a ball screw shaft that increases after moving the predetermined amount after the moving direction of the moving body is reversed The dynamic friction force or the dynamic friction torque caused by the ball nut is f _c2 , the predetermined amount is b, and the rising distance constant of the friction force or the friction torque that increases after the predetermined amount b is moved after reversing the moving direction of the moving body is a. ₂ , sign function is sgn,

The numerical control apparatus according to claim 3, wherein: A feed mechanism that has a ball screw shaft and a ball nut that is externally fitted to the ball screw shaft, moves a moving body fixed to the ball nut, a motor that rotationally drives the ball screw shaft, and a movement that is moved by the motor A speed that is generated by a numerical control device having a position detection mechanism that detects the position of the body, and that generates a speed command so that the position of the moving body detected by the position detection mechanism matches the position command generated by the control unit A generating step, a speed detecting step for detecting the speed of the motor, a torque generating step for generating a torque command so that the speed detected by the speed detecting step matches the speed command generated by the speed generating step, A friction estimation step for estimating a friction force or a friction torque generated after reversing the rotation direction of the motor, and the torque command based on the friction or the friction torque estimated in the friction estimation step The friction compensation method and a correction step of correcting,
The ball nut comprises a pair of ball nuts,
A first friction estimation step for estimating a friction force or a friction torque caused by the feed mechanism that increases after the moving direction of the moving body is reversed, and
A second friction estimation step of estimating a frictional force or a friction torque that increases due to the ball screw shaft and the pair of ball nuts after the moving direction of the moving body has moved by a predetermined amount after reversing,
The friction compensation method, wherein the friction estimation step adds the friction force or the friction torque estimated in each of the first friction estimation step and the second friction estimation step.

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