CN102455683B - Number control device and friction compensation method - Google Patents

Abstract

The present invention provides a numerical control device and a friction compensation method, which can accurately estimate the friction force or friction torque from the low-speed region to the high-speed region in the feed drive mechanism of the double-nut preloading method, and is not limited to super-sized balls Preloading method. Therefore, the numerical control device can correct the limit protrusion. Quadrant protrusion is a phenomenon in which the movement trajectory deviates to the outside of the command trajectory. In the feed drive mechanism of the double nut preload method, the ball screw shaft is reversed to produce the first quadrant protrusion. The feed drive mechanism of the double nut preloading method produces the second quadrant projection when the table moves a predetermined amount after the table is reversed. The numerical control device can estimate with high precision the increase in frictional force generated in two stages in the double nut preloading method using two approximate expressions.

Description

Numerical control device and friction compensation method

technical field

The invention relates to a numerical control device and a friction compensation method.

Background technique

The machine tool controls the motor for two-axis circular interpolation motion. The machine tool cannot reverse immediately when the direction of rotation of the motor is reversed. The reason is the frictional influence of the feed drive mechanism. If the quadrant is changed (the moving direction of the moving body is reversed) during arc cutting, the actual moving trajectory of the moving body deviates to the outside of the commanded trajectory. The phenomenon that the moving track is deviated to the outside is a quadrant protrusion, which makes the machining accuracy worse.

The motor control device disclosed in Japanese Patent Laying-Open No. 210273 of 2008 calculates a speed signal by performing differential calculation on an actual position signal of a moving body. The motor control device integrates the speed signal to generate a displacement signal from a position where the moving body reverses the direction of motion and obtains an absolute value. The motor control device obtains the rate of change of the friction force or the friction torque with respect to the displacement using a model representing the relationship between the displacement and the friction force or the friction torque. The motor control device multiplies the rate of change with respect to displacement by the speed signal to obtain the rate of change with respect to time. The motor control device performs integral calculation on the rate of change with respect to time to estimate frictional force or frictional torque. The motor control device estimates the frictional force or frictional torque independently of the speed or acceleration before and after reversing the direction of motion.

The motor control device mainly supports the feed drive mechanism of the oversized ball preloading method. The oversized ball preload type feed drive mechanism has a nut and ball screw shaft. The feed drive mechanism of the double nut preload method has two nuts and a ball screw shaft. In the feed drive mechanism of the double nut preload method, the ball screw shaft reverses to generate the first quadrant projection, and the second quadrant projection occurs when the movable body moves a predetermined amount. The motor control unit does not support the double nut preload method to correct for the second quadrant protrusion.

In addition to the ball screw shaft, the friction factors of the machine tool include linear guides and bearings. Linear guides and bearings increase mechanical rigidity by applying high preload. Therefore, the friction torque characteristic at the time of reverse rotation changes suddenly. Other friction factors are the oil seal and the seal components of the movable chip guard. The oil seal is installed on the motor shaft. The oil seal is used to prevent cutting oil from entering the inside of the motor. The seal prevents chips from entering the ball screw shaft and linear guide.

Sealing parts and oil seals are rubber materials. The friction torque during reverse rotation changes more slowly than that of linear guides and the like. The friction characteristic when the machine tool is in reverse is the synthesis of two kinds of reverse friction characteristics.

The motor control device uses only a single tanh function for a model representing the relationship between the displacement from the reversed position and the friction torque. The motor control device does not take into account the above two reverse friction characteristics. Therefore errors will occur. The two kinds of inversion friction characteristics are characteristics having changes in two aspects: a sharp change in friction torque after inversion and a slow change in friction torque after inversion.

The motor control device uses a model representing 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 control device uses a model to obtain the rate of change of the frictional force or frictional torque with respect to the displacement as a function of the displacement signal represented by an absolute value. The motor control device multiplies the rate of change with respect to displacement by the speed signal to calculate the rate of change of frictional force or friction torque with time. The motor control device performs integral calculation on the rate of change with respect to time to estimate frictional force or frictional torque. Therefore, when the speed is high, the integral error becomes large, and the error of the estimated friction force or friction torque becomes large.

Contents of the invention

The problem to be solved by the invention

The object of the present invention is to provide a numerical control that can estimate the frictional force or frictional torque from the low-speed range to the high-speed range with high precision even in the feed drive mechanism of the double nut preloading method, and correct the confining projection. Device and friction compensation method.

The numerical controller of the first invention includes a feed mechanism, a motor, a position detection mechanism, a speed generator, a speed detector, a torque generator, a friction estimation unit, a correction unit, a first friction estimation unit, and a second friction estimation unit. The feed mechanism has a ball screw shaft and a ball nut, and is used to move the moving body. The ball nut is externally fitted to the ball screw shaft. The moving body is fixed on the ball nut. The electric motor rotates the ball screw shaft. The position detection means detects the position of the moving body moved by the motor. The speed generation unit generates a speed command for matching the position of the moving body detected by the position detection means with the position command generated by the control unit. The speed detection mechanism detects the speed of the motor. The torque generator generates a torque command for matching the speed detected by the speed detection means with the speed command generated by the speed generator. The friction estimating unit estimates frictional force or frictional torque generated when the rotation direction of the motor is reversed. The correction unit corrects the torque command based on the friction force or friction torque estimated by the friction estimation unit. The ball nut consists of a pair of ball nuts. The first friction estimating section estimates a frictional force or a frictional torque caused by the feed mechanism that increases after the moving direction of the moving body is reversed. The second friction estimating unit estimates a friction force or a friction torque that increases due to the ball screw shaft and the pair of ball nuts after the moving body moves a predetermined amount after the moving direction of the moving body is reversed. The friction estimating unit adds the friction force or friction torque respectively estimated by the first friction estimating unit and the second friction estimating unit. The feed mechanism of the double nut preload method has a ball screw shaft fitted with a pair of nuts. The feed mechanism of the double nut preloading method generates friction force or friction torque due to the structure of the feed mechanism and friction force or friction torque due to the structure of the support mechanism of the moving body. The first friction estimating section estimates a frictional force or a frictional torque caused by the feed mechanism that increases after the moving direction of the moving body is reversed. The second friction estimating unit estimates a friction force or a friction torque that increases due to the ball screw shaft and the pair of ball nuts after the moving body moves a predetermined amount after the moving direction of the moving body is reversed. The friction estimating unit adds the friction force or friction torque estimated by the first friction estimating unit and the second friction estimating unit. Therefore, the numerical control device can estimate the frictional force or frictional torque with high precision even in the feed mechanism of the double nut preloading method, and thus can correct the protrusion of the limit.

In the numerical controller of the second invention, the pair of ball nuts has a plurality of balls. The predetermined amount is the distance when the moving body moves to a point where at least one of the plurality of balls comes into three-point contact with the pair of ball nuts and the ball screw shaft after the moving direction of the moving body is reversed. In the feed mechanism of the double nut preload method, the state where the ball is in two-point contact with a pair of nuts and the ball screw shaft alternates with the state where the ball is in three-point contact with a pair of nuts and the ball screw shaft. Friction force or friction torque increases as the balls change from two-point to three-point contact. Therefore, the second friction estimating unit can estimate the frictional force or friction torque that increases due to the ball screw shaft and the pair of ball nuts after the moving body moves a predetermined amount after the moving direction of the moving body is reversed.

A numerical control device according to a third invention includes an actual position estimation unit and a calculation unit. The actual position estimating unit estimates the actual position of the moving object corresponding to the position command. The calculating unit calculates the displacement after the moving direction of the moving body is reversed based on the actual position estimated by the actual position estimating unit. The first friction estimating unit and the second friction estimating unit are approximations. The approximate expression is an expression in which the displacement calculated by the calculation unit is used as a variable. Therefore, the numerical control device can easily calculate the frictional force or frictional torque due to the feed mechanism that increases from the reversal of the moving direction of the mobile body, and the frictional force that increases due to the ball screw shaft and the pair of ball nuts or friction torque.

In the numerical control device of the fourth invention, the approximate expression f ₁ (x') of the first friction estimating unit and the approximate expression f ₂ (x') of the second friction estimating unit are changed after reversing the moving direction of the moving body The friction force or friction torque is decomposed into a first slope component and a second slope component whose slope is smaller than the first slope component with respect to the moving amount of the moving body after the moving body reverses the moving direction. x' is the displacement of the moving body from the position where the moving direction is reversed. f _c0 is the frictional force or frictional torque with which the first slope component rises from reverse rotation. a ₀ is the rising distance constant of the first slope component. a ₁ is the rising distance constant of the second slope component. f _c1 is the total value of the dynamic friction force or dynamic friction torque that changes after the moving direction of the moving body is reversed. f _c2 is the dynamic friction force or dynamic friction torque caused by the ball screw shaft and a pair of ball nuts that increases after the moving body moves a predetermined amount after the moving direction of the moving body is reversed. b is a predetermined amount. a ₂ is a rising distance constant of the frictional force or friction torque that increases after the mobile body has moved a predetermined amount b after the moving direction of the mobile body is reversed. sgn is a symbolic function. The approximate expression f ₁ (x') of the first friction estimator and the approximate expression f ₂ (x') of the second friction estimator are the following expressions. Therefore, the numerical control device can easily calculate the frictional force or frictional torque due to the feed mechanism that increases from the reversal of the moving direction of the mobile body, and the frictional force that increases due to the ball screw shaft and the pair of ball nuts or friction torque.

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; tanh</span>}<span\; class="notranslate">\; (</span>\frac{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span>}{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; sgn</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; dx</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; tanh</span>}<span\; class="notranslate">\; (</span>\frac{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span>}{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; sgn</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; dx</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; tanh</span>}<span\; class="notranslate">\; (</span>\frac{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; b</span>}}{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; sgn</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; dx</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&DoubleRightArrow;</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; sgn</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; dx</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; )</span>$

In the numerical control device of the fifth invention, the approximate expression f ₁ (x') of the first friction estimating unit and the approximate expression f ₂ (x') of the second friction estimating unit are changed after reversing the moving direction of the moving body The friction force or friction torque is decomposed into a first slope component and a second slope component whose slope is smaller than the first slope component with respect to the moving amount of the moving body after the moving body reverses the moving direction. x' is the displacement of the moving body from the position where the moving direction is reversed. f _c0 is the frictional force or frictional torque with which the first slope component rises from reverse rotation. a ₀ is the rising distance constant of the first slope component. a ₁ is the rising distance constant of the second slope component. f _c1 is the total value of the dynamic friction force or dynamic friction torque that changes after the moving direction of the moving body is reversed. f _c2 is the dynamic friction force or dynamic friction torque caused by the ball screw shaft and a pair of ball nuts that increases after the moving body moves a predetermined amount after the moving direction of the moving body is reversed. b is a predetermined amount. a ₂ is a rising distance constant of the frictional force or friction torque that increases after the mobile body has moved a predetermined amount b after the moving direction of the mobile body is reversed. sgn is a symbolic function. The approximate expression f ₁ (x') of the first friction estimator and the approximate expression f ₂ (x') of the second friction estimator are the following expressions. Therefore, the numerical control device can easily calculate the frictional force or frictional torque due to the feed mechanism that increases from the reversal of the moving direction of the mobile body, and the frictional force that increases due to the ball screw shaft and the pair of ball nuts or friction torque.

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; exp</span>}\frac{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span>}{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; sgn</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; dx</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; exp</span>}\frac{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span>}{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; sgn</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; dx</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; exp</span>}\frac{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; sgn</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; dx</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&DoubleRightArrow;</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; sgn</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; dx</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; )</span>$

In the numerical controller of the sixth invention, the approximate expression f ₁ (x') of the first friction estimating unit and the approximate expression f ₂ (x') of the second friction estimating unit are changed after reversing the moving direction of the moving body The friction force or friction torque is decomposed into a first slope component and a second slope component whose slope is smaller than the first slope component with respect to the moving amount of the moving body after the moving body reverses the moving direction. x' is the displacement of the moving body from the position where the moving direction is reversed. f _c0 is the frictional force or frictional torque with which the first slope component rises from reverse rotation. a ₀ is the rising distance constant of the first slope component. a ₁ is the rising distance constant of the second slope component. f _c1 is the total value of the dynamic friction force or dynamic friction torque that changes after the moving direction of the moving body is reversed. f _c2 is the dynamic friction force or dynamic friction torque caused by the ball screw shaft and a pair of ball nuts that increases after the moving body moves a predetermined amount after the moving direction of the moving body is reversed. b is a predetermined amount. a ₂ is a rising distance constant of the frictional force or friction torque that increases after the mobile body has moved a predetermined amount b after the moving direction of the mobile body is reversed. sgn is a symbolic function. The approximate expression f ₁ (x') of the first friction estimator and the approximate expression f ₂ (x') of the second friction estimator are the following expressions. Therefore, the numerical control device can easily calculate the frictional force or frictional torque due to the feed mechanism that increases from the reversal of the moving direction of the mobile body, and the frictional force that increases due to the ball screw shaft and the pair of ball nuts or friction torque.

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; tanh</span>}<span\; class="notranslate">\; (</span>\frac{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span>}{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; sgn</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; dx</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; tanh</span>}<span\; class="notranslate">\; (</span>\frac{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span>}{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; sgn</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; dx</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; exp</span>}\frac{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; sgn</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; dx</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&DoubleRightArrow;</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; sgn</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; dx</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; )</span>$

In the numerical control device of the seventh invention, the approximate expression f ₁ (x') of the first friction estimating unit and the approximate expression f ₂ (x') of the second friction estimating unit are changed after reversing the moving direction of the moving body The friction force or friction torque is decomposed into a first slope component and a second slope component whose slope is smaller than the first slope component with respect to the moving amount of the moving body after the moving body reverses the moving direction. x' is the displacement of the moving body from the position where the moving direction is reversed. f _c0 is the frictional force or frictional torque with which the first slope component rises from reverse rotation. a ₀ is the rising distance constant of the first slope component. a ₁ is the rising distance constant of the second slope component. f _c1 is the total value of the dynamic friction force or dynamic friction torque that changes after the moving direction of the moving body is reversed. f _c2 is the dynamic friction force or dynamic friction torque caused by the ball screw shaft and a pair of ball nuts that increases after the moving body moves a predetermined amount after the moving direction of the moving body is reversed. b is a predetermined amount. a ₂ is a rising distance constant of the frictional force or friction torque that increases after the mobile body has moved a predetermined amount b after the moving direction of the mobile body is reversed. sgn is a symbolic function. The approximate expression f ₁ (x') of the first friction estimator and the approximate expression f ₂ (x') of the second friction estimator are the following expressions. Therefore, the numerical control device can easily calculate the frictional force or frictional torque due to the feed mechanism that increases from the reversal of the moving direction of the mobile body, and the frictional force that increases due to the ball screw shaft and the pair of ball nuts or friction torque.

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; exp</span>}\frac{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span>}{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; sgn</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; dx</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; exp</span>}\frac{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span>}{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; sgn</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; dx</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; tanh</span>}<span\; class="notranslate">\; (</span>\frac{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; b</span>}}{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; sgn</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; dx</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&DoubleRightArrow;</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; sgn</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; dx</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; )</span>$

In the numerical controller of the eighth invention, the approximate expression of the second friction estimation unit is the following expression. x' is the displacement of the moving body from the position where the moving direction is reversed. f _c2 is the dynamic friction force or dynamic friction torque caused by the ball screw shaft and a pair of ball nuts that increases after the moving body moves a predetermined amount after the moving direction of the moving body is reversed. b is a predetermined amount. a ₂ is a rising distance constant of the frictional force or friction torque that increases after the mobile body has moved a predetermined amount b after the moving direction of the mobile body is reversed. sgn is a symbolic function. Therefore, the numerical control device can easily calculate the frictional force or frictional torque due to the ball screw shaft and the pair of ball nuts.

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\frac{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; b</span>}}{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; sgn</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; dx</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0</span>}\mathrm{<span\; class="notranslate">\; or</span>}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&DoubleRightArrow;</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; sgn</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; dx</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; )</span>$

The friction compensation method of the ninth invention is a method performed by a numerical controller. The numerical controller includes a feed mechanism, a motor, and a position detection mechanism. The feed mechanism has a ball screw shaft and a ball nut, and is used to move the moving body. The ball nut is externally fitted to the ball screw shaft. The friction compensation method includes a speed generating step, a speed detecting step, a torque generating step, a friction estimating step, a correcting step, a first friction estimating step, and a second friction estimating step. The speed generating step generates a speed command for matching the position of the moving body detected by the position detection means with the position command generated by the control unit. The speed detection process detects the speed of the motor. The torque generating step generates a torque command for matching the speed detected by the speed detection means with the speed command generated by the speed generating unit. The friction estimating step estimates the friction force or friction torque generated when the rotation direction of the motor is reversed. In the correction step, the torque command is corrected based on the friction force or friction torque estimated by the friction estimation unit. The ball nut consists of a pair of ball nuts. The first friction estimating process estimates the frictional force or frictional torque caused by the feed mechanism that increases after the moving direction of the moving body is reversed. The second friction estimating step estimates the frictional force or frictional torque that increases due to the ball screw shaft and the pair of ball nuts after the moving body moves a predetermined amount after the moving direction of the moving body is reversed. The friction estimating step adds up the friction force or friction torque respectively estimated in the first friction estimating step and the second friction estimating step. The feed mechanism of the double nut preload method has a ball screw shaft fitted with a pair of nuts. The feed mechanism of the double nut preloading method generates friction force or friction torque due to the structure of the feed mechanism and friction force or friction torque due to the structure of the support mechanism of the moving body. The first friction estimating process estimates the frictional force or frictional torque caused by the feed mechanism that increases after the moving direction of the moving body is reversed. The second friction estimating step estimates the frictional force or frictional torque that increases due to the ball screw shaft and the pair of ball nuts after the moving body moves a predetermined amount after the moving direction of the moving body is reversed. The friction estimating step adds the friction force or friction torque estimated by the first friction estimating step and the second friction estimating step. Therefore, the friction compensation method can estimate the frictional force or the frictional torque with high precision even in the feed mechanism of the double nut preloading method, and thus can correct the confining protrusion.

Description of drawings

FIG. 1 is a diagram showing part of the structure of a machine tool 20 .

FIG. 2 is a block diagram showing detailed configurations of the numerical controller 10 and the feed mechanism.

FIG. 3 is a sectional view of the feed drive mechanism A. FIG.

FIG. 4 is a cross-sectional view of the periphery of the ball 37 in the feed drive mechanism A. As shown in FIG.

FIG. 5 is a sectional view of the feed drive mechanism B. FIG.

FIG. 6 is a diagram showing the contact state of the ball 47 of the feed drive mechanism B. As shown in FIG.

FIG. 7 is a diagram obtained by amplifying the error between the ideal arc trajectory and the actual trajectory of the feed drive mechanism A. FIG.

FIG. 8 is a diagram obtained by amplifying the error between the ideal arc trajectory and the actual trajectory of the feed drive mechanism B. FIG.

9 is a graph showing the relationship between the motor torque of the feed drive mechanism A and the distance from the reverse position.

10 is a graph showing the relationship between the motor torque of the feed drive mechanism B and the distance from the reverse position.

FIG. 11 is a graph showing the relationship between the table displacement amount and the friction torque of the feed drive mechanism A. FIG.

FIG. 12 is a graph showing the relationship between the table displacement amount and the friction torque of the feed drive mechanism B. FIG.

FIG. 13 is a block diagram showing the configuration of the friction compensator 13 .

14 is a graph showing the relationship between the table displacement amount and the friction torque when the friction torque is estimated using only the first term of the formula (1) as an approximate formula.

15 is a graph showing the relationship between the table displacement amount and the friction torque when the friction torque is estimated using only Equation (1) as an approximate expression.

16 is a graph showing the relationship between table displacement and friction torque when friction torque is estimated using equation (3) (expression (1) + equation (2)) as an approximate equation in the present invention.

17 is a graph showing the relationship between table displacement and friction torque when friction torque is estimated using equation (3) (equation (4) + equation (5)) as an approximate equation in the present invention.

18 is a graph showing the relationship between table displacement and friction torque when friction torque is estimated using equation (3) (equation (1) + equation (6)) as an approximate equation in the present invention.

Fig. 19 is a diagram obtained by amplifying the error between the ideal arc trajectory and the actual trajectory of cases 2, 3, and 6.

FIG. 20 is a block diagram showing a configuration when the control module described in Patent Document 1 is changed according to the object of the present invention.

21 is a graph showing the relationship between the table displacement amount and the friction torque when the friction torque during non-high-speed operation is estimated using compensation method 1 and compensation method 2. FIG.

22 is a graph showing the relationship between the table displacement amount and the friction torque when the friction torque during high-speed operation is estimated using the compensation method 1 and the compensation method 2.

23 is a graph showing the relationship between the table displacement amount and the friction torque when the friction torque is estimated using (Equation (1)+Equation (5)) as an approximate equation according to the present invention.

24 is a graph showing the relationship between the table displacement amount and the friction torque when the friction torque is estimated using (Equation (4)+Equation (2)) as an approximate equation according to the present invention.

Detailed ways

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 axis movement of the machine tool 20 according to the path instructed by the machining program to cut the workpiece fixed on the table 3 .

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

The base 1 has a pair of linear guides 6A. A pair of linear guide rails 6A guides the intermediate table 50 in one axial 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 nuts. The intermediate table 50 has a pair of linear guide rails 6B on the upper part. The linear guide rail 6B guides the table 3 in a direction perpendicular to the above-mentioned one axis 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 slider 51 at its lower portion. The slider 51 slides on the rail 61 of the linear guide 6B. A pair of bearing housings 7 supports the ball screw shaft 4B. A pair of bearing housings 7 are fixed on the intermediate workbench 50 . The bearing housing 7 has a bearing 8 inside. The intermediate table 50 is equipped with a slider (not shown) at the lower end. The slider slides on a rail (not shown) of the linear guide rail 6A.

A pair of bearing housings (not shown) support the ball screw shaft 4A. A pair of bearing seats are fixed on the base 1. The bearing housing has a bearing (illustration omitted) inside.

As shown in FIG. 1 , a base 1 supports a motor 2A at its upper portion. The shaft of the motor 2A is connected to the ball screw shaft 4A via a coupling (not shown). The motor 2A has an oil seal (not shown) around the shaft.

As shown in FIG. 2 , the intermediate table 50 supports the motor 2B at its end. The shaft of the motor 2B is connected to the ball screw shaft 4B through a coupling 9 . The motor 2B has an oil seal 52 around the shaft. The table 3 has fixed covers 53 at both ends. The sealing member 55 is fixed to the end portion of the movable cover 54 opposite to the end portion on the table side. The sealing member 55 is formed of rubber. The seal member 55 prevents cutting 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 one axial direction. The feed drive mechanism 56 includes a ball screw shaft 4B and a nut 5 . The structure of the feed drive mechanism for moving the intermediate table 50 in one axis direction is the same as that of 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 rail 6B, a slider 51 , a motor 2B, a coupling 9 , an oil seal 52 , a movable cover 54 , a seal member 55 , and a bearing seat 7 .

The configuration of the numerical controller 10 will be described. As shown in FIG. 1 , numerical controller 10 is connected to motors 2A and 2B. Driven by motors 2A and 2B, table 3 moves in two axial directions.

The respective ball screw shafts 4A, 4B and the respective nuts 5 convert the rotational motion of the motors 2A, 2B into linear motions of the table 3 in two axial directions. Numerical controller 10 controls motors 2A, 2B to control the position, speed, and acceleration of table 3 .

As shown in FIG. 2 , a rotary encoder (rotary encoder) 60 is attached to the motors 2A, 2B. FIG. 2 does not illustrate the motor 2A and the rotary encoder 60 on the side of the motor 2A. The rotary encoder 60 detects the positions of the motors 2A, 2B. Numerical controller 10 calculates the position of table 3 from the positions of motors 2A, 2B and the pitches (intervals between screw threads) of ball screw shafts 4A, 4B.

The host controller outputs a position command signal to the position controller 11 . Rotary encoder 60 outputs position detection signals of motors 2A, 2B to position controller 11 . The position controller 11 generates a speed command signal in which the position command signal matches the position detection signal, and supplies it 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 in which the speed command signal matches the speed detection signal, and supplies it to the adder 14 . The friction compensator 13 generates a friction compensation signal according to the position command signal from the host controller and supplies it to the adder 14 . The friction compensation signal is a signal for compensating the 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 applies 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 current of the motors 2A, 2B so as to generate a torque as faithful as possible to the torque command signal after friction compensation.

The structures and actions of the position controller 11, the speed controller 12, the adder 14, the current control amplifier 15, and the differentiator 16 are well known. Therefore, the description will focus on the principle of the structure and operation of the friction compensator 13 directly related to the invention of the present application.

The feed drive mechanism has friction forces respectively caused by the first friction source and the second friction source. The friction force caused by the first friction source is the preload of the slider of the linear guide, the preload of the nut part of the ball screw shaft, and the preload of the bearing. The higher the preload, the higher the rigidity as a feed drive mechanism and the greater the friction. The frictional force caused by the second friction source is the sliding resistance of the seals of the oil seal 52 and the movable cover 54 . When the sealing performance is improved, the frictional force becomes larger.

The frictional force changes sharply when the movement direction of the table 3 is reversed. When the movement direction of the table 3 is reversed, that is, when the rotation direction of the ball screw shafts 4A, 4B is reversed. For example, the numerical control device 10 performs arc cutting by performing the arc interpolation motion described above using two orthogonal axes. Sometimes the control system cannot cope with the change in friction. The upper graph of FIG. 1 shows the error between the ideal arc trajectory and the actual trajectory. Portions 71 to 74 surrounded by ellipses are quadrant protrusions. The friction compensator 13 accurately estimates the frictional force when the movement direction of the table 3 is reversed to compensate. Therefore, the numerical controller 10 can reduce the quadrant protrusion as much as possible.

Quadrant protrusions are caused by changes in the friction generated in the feed drive mechanism. The type of quadrant protrusions differs depending on how the ball screw shaft is preloaded. The differences in structure and characteristics of the ball screw shaft preload method are explained. The preloading method of the ball screw shaft includes the oversized ball preloading method and the double nut preloading method.

As shown in FIG. 3 , the feed drive mechanism A of the oversized ball preloading method uses a single nut 35 (hereinafter referred to as the nut 35 ) to apply preloading. The nut 35 is a ball nut. The nut 35 has a ball 37 inside. As shown in FIG. 4 , the ball 37 is always in four-point contact with the nut 35 and the ball screw shaft 34 . The oversized ball preloading method is characterized in that the size of the nut 35 is small and suitable for light loads. Therefore, small machine tools, etc. adopt the oversized ball preloading method.

As shown in FIG. 5 , the feed drive mechanism B of the double nut preloading method has two nuts 45 , 46 . The nuts 45, 46 are ball nuts. A washer 48 is located between the nuts 45 , 46 . As shown in (a), (b) and (c) of FIG. 6 , the ball 47 moves according to the moving direction of the nuts 45 (not shown in FIG. 6 ), 46 . The ball 47 is in two-point contact or three-point contact with the nuts 45, 46 and the ball screw shaft 44, which changes at any time. The hollow arrows in FIG. 6 indicate the direction of rotation of the ball 47 .

For example, as shown in (a) of FIG. 6 , the nut 46 is moving in one direction. The ball 47 is in contact with the nut 46 at one point and with the ball screw shaft 44 at two points, thus making three-point contact. As shown in (b) of FIG. 6 , the nut 46 is in the middle of reversing the moving direction. The ball 47 is in contact with the nut 46 at one point and with the ball screw shaft 44 at one point, thus making two-point contact. Therefore, the friction becomes smaller compared with the three-point contact. As shown in (c) of FIG. 6 , the nut 46 reverses the movement direction and is moving in the opposite direction. The ball 47 is in contact with the nut 46 at two points and with the ball screw shaft 44 at one point, thus making three-point contact. Therefore, the friction becomes larger again. The double nut preload method is characterized by high rigidity. Therefore, large machine tools and the like adopt the double nut preloading method.

Explain the influence of the preload method of the ball screw shaft on the limited protrusion. The error with respect to the ideal trajectory in the case of performing circular interpolation motion using each numerical controller which drives and controls the feed drive mechanisms A and B was investigated.

Figures 7 and 8 are diagrams obtained by amplifying the error between the ideal arc trajectory and the actual trajectory. The feed speed is 3m/min, and the command radius is 25mm. One scale is 5 μm.

The trajectory error is the quadrant protrusion. In the results of Fig. 7 and Fig. 8, quadrant protrusions all occurred around 0°, 90°, 180°, and 270°. The direction of motion of the X axis is reversed at 0° and 180°. The direction of motion of the Y axis is reversed at 90° and 270°. The quadrant protrusions near each reverse position are obtained by the servo system's response to frictional force changes on the arc track. Friction is the force of friction when the direction of motion is reversed.

As shown in FIG. 7 , in the feed drive mechanism A, there is only one quadrant protrusion. Feed drive mechanism A is a super-sized ball preloading method. As shown in FIG. 8 , there are two quadrant protrusions in the feed drive mechanism B. As shown in FIG. Feed drive mechanism B is a double nut preloading method. The reason is as follows. The first quadrant protrusion is the effect of friction when the quadrant changes. The second quadrant protrusion is the effect of increased friction when the contact between the balls and the nut and ball screw shaft changes from two to three points of contact.

The characteristics of the frictional resistance at the time of reverse rotation in the individual ball screw shaft were investigated. 9 and 10 are graphs showing the relationship between the distance from the ball screw shaft to the reverse position and the motor torque [Nm].

As shown in Figure 9, in the oversized ball preload method, the motor torque rises suddenly after the reverse rotation and then becomes constant. As shown in Fig. 10, in the double nut preloading method, the motor torque becomes constant after a slight rise after the reverse rotation, and then becomes constant again after a gentle rise. During the two-point contact period when the ball is lifted from the reverse position, the motor torque increases slightly and then becomes constant. The ball transitions from a state of two-point contact to a state of three-point contact. In the above case, the state of two-point contact and the state of three-point contact are mixed. Therefore, the motor torque rises gently. After that, all balls become three-point contact. Therefore, the motor torque becomes the maximum value and remains constant.

Figure 11 and Figure 12 show the relationship between the displacement of the table and the friction torque when the machine tool moves in a small arc. The feed rate is 5mm/min, and the command radius is 0.1mm. Friction is not affected by speed and acceleration in small circular motions.

As shown in Figure 11, in the way of oversized ball preloading, the motor torque presents nonlinear spring characteristics after the direction of motion is reversed. The motor torque becomes an approximately constant value when the displacement increases to a certain extent. The trajectory of the motor torque describes a hysteresis loop. As shown in Figure 12, in the double nut preloading mode, the motor torque changes in a gentle step shape at the position of 0.065 mm after the direction of motion is reversed. The step-like change is the reason why the quadrant protrusions are two. The numerical controller 10 focuses on the friction characteristics of the double nut preload method. The numerical control device 10 can compensate for two quadrant protrusions by estimating the frictional force or frictional torque with high precision.

A detailed structure of the friction compensator 13 and a friction compensation method using the friction compensator 13 will be described with reference to FIG. 13 . The friction compensator 13 includes at least 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, a response delay compensation Section 29. The first friction characteristic estimation unit 26 and the second friction characteristic estimation unit 27 include an absolute value calculation unit and a polarity calculation unit. The absolute value calculation unit calculates the absolute value of the input signal. The polarity calculation unit obtains the polarity of a signal obtained by performing time differential calculation on the input signal.

The host controller inputs the position command signal to the actual position estimation unit 21 . The actual position estimating unit 21 uses a model of the servo control system that performs the feed motion of the table 3 . The actual position estimation part 21 estimates the actual position of the table 3 corresponding to a position command signal, and generates an actual position signal. The actual position estimating unit 21 may be constituted by, for example, a primary lag element or the like. The differentiator 22 is connected to the actual position estimation unit 21 . The differentiator 22 differentiates the actual position signal and outputs the obtained signal 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 whether the sign of the velocity signal is inverted. The sign inversion detection unit 23 outputs a reset signal. The integrator 24 integrates the velocity signal to restore the actual position signal. The integrator 24 clears the integrated value to zero every time the sign inversion detection unit 23 outputs a reset signal. The integrator 24 generates a signal of the displacement from the position at which the table 3 reverses the direction of motion.

The first friction characteristic estimating unit 26 and the second friction characteristic estimating unit 27 are connected to the integrator 24 . The first friction characteristic estimating unit 26 uses approximate expression 1 described later. The first friction characteristic estimating unit 26 obtains the friction torque f ₁ (x′) [N·m]. The friction torque f ₁ increases after reversing from the table. The second friction characteristic estimating unit 27 uses approximate expression 2 described later. The second friction characteristic estimating unit 27 obtains the friction torque f ₂ (x′) [N·m]. The friction torque _f2 increases after the table 3 moves by a predetermined amount after the table 3 reverses. The adder 28 is connected to the first friction characteristic estimating unit 26 and the second friction characteristic estimating unit 27 .

The adder 28 adds f ₁ (x') and f ₂ (x'). The response delay compensator 29 is connected to the output terminal of the adder 28 . The response delay compensator 29 is constituted by an inverse function of the transfer function. The transfer function is obtained by modeling the characteristics from the torque command signal to the torque actually output by the motor 2 . The torque command signal is input to the current control amplifier 15 (see FIG. 2 ). The response delay compensator 29 multiplies the estimated friction torque to generate a friction compensation signal.

Approximate expression 1 of the first friction characteristic estimating unit 26 and approximate expression 2 of the second friction characteristic estimating unit 27 will be described. In this embodiment, various parameters are defined as follows.

f(x') = total friction torque [N m]

・f ₁ (x')＝Increased frictional torque after reversing from the table [N·m]

・f ₂ (x')＝Frictional torque [N·m] increased after the table moves a predetermined amount after the table is reversed

f _c0 ＝ When decomposing the friction torque changed from the reverse rotation of the table to the movement amount after the reverse rotation of the table into two slope components, the friction torque of the first slope component rising from the reverse rotation [N· m]

· a ₀ = rising distance constant of the first slope component above [mm]

· a ₁ = rising distance constant of the above-mentioned second slope component [mm]

・f _c1 ＝The total value of the dynamic friction torque changed from the reverse rotation of the table [N・m]

・f _c2 = The dynamic friction torque caused by the ball screw shaft and a pair of ball nuts increased after the table has been reversed and moved by the above specified amount (Dynamic friction torque when the ball screw shaft and nut are stable (three-point contact) )[N·m]

・a ₂ = Rising distance constant [mm] of the friction torque that increases after the table moves a predetermined amount after the table reverses

·b＝The distance from when the table is reversed to when f ₂ (x') starts to increase [mm]

·x’=displacement of the workbench from the position where the direction of movement is reversed [mm]

sgn = sign function

Let sgn be +1 when dx'/dt>0, 0 when dx'/dt=0, and -1 when dx'/dt<0.

A ₁ , a ₂ , f _c1 , f _c2 , and b are shown in the hysteresis curves when circular interpolation motion is performed in the double nut mode shown in FIG. 16 . The slope of the first slope component is steeper than the slope of the second slope component.

Approximate 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){2tanh (|x'|/a ₁ )-1}sgn(dx'/dt)…(1)

In the approximation formula described in Patent Document 1, the tanh functions are one set. The invention combines two sets of tanh functions with different constants. 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 change rapidly during reverse rotation, etc. The first slope is caused by the first friction factor. The second friction factor is an oil seal or the like which changes slowly compared with the first friction factor. The second slope component is caused by a second friction factor.

Approximate formula 2 is as follows.

·f ₂ (x')＝f _c2 {tanh((|x'|-b)/a ₂ )-1/2}sgn(dx'/dt)...(2)

When |x'|-b<0, f ₂ (x')=-f _c2 /2·sgn(dx'/dt).

The formula (2) is used to cope with the friction of the double nut preloading method. The friction of the double nut preload method increases after the nuts are reversed and moved a specified amount.

Using the formulas (1) and (2), approximate formula 3 of the total friction torque f(x') is the following formula.

f(x')=f ₁ (x')+f ₂ (x')...(3)

In approximate formulas 1 and 2, the exp function can also be used instead of the tanh function. Approximate expressions 1 and 2 can also be expressed as follows, for example. Appropriate values for a ₀ , a ₁ in formula (4) and a ₂ in formula (5) are selected relative to a ₀ , a ₁ in formula (1) and a 2 in formula ₍₂ ). Therefore, equations (4) (5) can draw substantially the same curves as equations (1) (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).

It is also possible to use the cos function to express Approximate Expression 2 as follows. In approximate expression 2, the rise becomes gentle around |x'|-b=0. Approximate formula 2 can draw a curve closer to the measured data.

f ₂ (x')＝-f _c2 /2cos{{(|x'|-b)/a ₂ }π}sgn(dx'/dt)...(6)

When |x'|-b<0 or |x'|-ba 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 the conventional friction compensation method. Case 2 is the case where circular interpolation motion is performed using only approximate formula 1 of the present invention. Case 3 is a case where circular interpolation motion is performed using equation (1) as approximate equation 1 and equation (2) as approximate equation 2 according to the present invention. Case 4 is a case where circular interpolation motion is performed using equation (4) as approximate equation 1 and equation (5) as approximate equation 2 according to the present invention. Case 5 is a case where circular interpolation motion is performed using equation (1) as approximate equation 1 and equation (6) as approximate equation 2 according to the present invention. Case 1 refers to the approximate formula described in Japanese Patent Application Laid-Open No. 2008-210273, and only uses the first term of formula (1) described in the present invention, that is, f _c0 {tanh(|x'|/a ₀ )-1/2 }sgn(dx'/dt) as an approximation with the same meaning. Cases 1 to 5 perform circular interpolation motion with a feed rate of 5mm/min and a command radius of 0.1mm. The results obtained by comparing the relationship between table displacement and motor torque with actual measurement data are as follows.

In Cases 1 and 2, the definitions of the parameters of the approximation expressions used by the first friction characteristic estimating unit 26 and the second friction characteristic estimating unit 27 of the friction compensator 13 are also the same as the definitions above.

The results of Case 1 will be described with reference to FIG. 14 . In FIG. 14 , actual measured values are indicated by thick lines, and values calculated by the approximate formula are indicated by thin lines. The parameter is selected to be the value that best approximates the rising characteristic of the measured data after inversion. In this example, f _c0 =0.9, a ₀ =0.0025. As shown in FIG. 14 , the value of the approximate expression of the motor torque agrees with the slope of the increase amount 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 the second-stage rise occurs at about 70 μm after the reversal. The approximate expression is a constant value, so it does not match the measured value. The reason is as follows: the conventional approximation formula of Patent Document 1 can only cope with the single characteristic of rapid friction change after reverse rotation caused by the linear guide or the like. Therefore, the conventional approximate formula cannot correct the friction characteristics of oil seals and the like and the friction characteristics of the double nut preload method. Friction characteristics of oil seals etc. change slowly after reverse rotation. The friction characteristic of the double nut preload method increases after the nut moves a specified distance after reverse rotation.

As shown in FIG. 14 and FIG. 15 , there is a difference in the torque value immediately before reverse rotation between the actual measured value and the result of the approximate expression in cases 1 and 2. The actual torque command is the sum of the output of the speed controller 12 and the output of the approximate expression. Control is performed so that the torque command matches the value of the actual measurement value. The speed controller 12 outputs, for example, about -0.175 N·m before inversion at -100 μm. The actual torque command is the value obtained by shifting the approximate formula downward by 0.175N·m. Therefore, the approximate expression agrees with the actual measurement value at the rising portion of the friction torque after inversion.

The results of Case 2 will be described with reference to FIG. 15 . Case 2 only uses the formula (1) of the present invention. Also in FIG. 15 , actual measured values are indicated by thick lines, and values calculated by the approximate formula are indicated by thin lines. The parameter is selected to be the value that best approximates the rising characteristic of the first stage after inversion of the measured data. In this example, f _c0 =0.9, a ₀ =0.0025, f _c1 =0.625, a ₁ =0.031. As shown in Fig. 15, a combination of two sets of tanh functions is used to approximate the change in friction after inversion. In the first stage of friction increase from after inversion to 60 μm, the measured values agree with the approximate formula. In the second stage of friction increase, the measured values do not agree with the approximate formula. Therefore, although case 2 can cope with slow reverse torque characteristics such as oil seals, it cannot cope with the increase in friction in the two stages of the double nut preloading method.

The result of using approximate formula 3 of the present invention will be described. Fig. 16 shows the case where both approximate formula 1 and approximate formula 2 use the tanh function in case 3. Fig. 17 shows the case where the exp function is used in both approximate formula 1 and approximate formula 2 in case 4. FIG. 18 shows the case of using equation (1) as approximate equation 1 and using the cos function of equation (6) as approximate equation 2 in case 5. The actual measured value is shown by a thick line, and the value calculated by the approximate formula is shown by a thin line. In the cases 3 to 5, the parameter selection is the value that can best approximate the actual measurement data as a whole. 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. 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. 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. As shown in FIG. 16 and FIG. 17 , the value of the approximate expression 3 of the present invention of the motor torque agrees with the first-stage rise of the actual measurement value, and also agrees with the second-stage rise. Approximate formula 3 should deal with the friction increase of the first time and the second time. Therefore, cases 3 and 4 can cope with the friction increase in the two stages of the double nut preloading method.

The difference between the approximate formulas of cases 3 and 4 is that changing the values of a ₀ , a ₁ , and a ₂ results in approximately the same curves. Therefore, the result obtained by using Approximate Expression 3 by using a combination of Approximate Expression 1 as Expression (1) and Approximate Expression 2 as Expression (5) is also a calculation result that closely approximates the actual measurement value. The result obtained by using Approximate Expression 3 by using a combination of Approximate Expression 1 as Expression (4) and Approximate Expression 2 as Expression (2) is also a calculation result that closely approximates the actual measurement value.

As shown in Figure 18, Case 5 uses the cos function in the second stage of frictional rise. Therefore, the rise is smoother than in cases 3 and 4, and is a value closer to the actual measurement value. The calculation result obtained by using the approximation formula 3 by using the approximation formula 1 as the formula (4) and the approximation formula 2 as the formula (6) is also a calculation result that closely approximates the actual measurement value similarly to the case 5.

In order to investigate the reduction effect of quadrant projections in Cases 2 and 3, the error between the ideal arc trajectory and the actual trajectory was investigated. The actual trajectory shown in FIG. 19 is a circular trajectory when the feed rate is set to 6 m/min and the command radius is set to 50 mm. Case 6 is a comparative example. Case 6 is a case where no friction compensation is performed at all. In FIG. 19 , case 2 is shown by a long dashed line, case 3 is shown by a solid line, and case 6 is shown by a short dashed line.

In Case 6 two quadrant protrusions were produced. The two quadrant projections are characteristic of the double nut preload method. In case 2 one of the two quadrant protrusions disappeared. The second remains. In Case 2, friction compensation is performed using only the approximate formula 1 that only deals with the first stage. The approximate formula that only deals with reverse rotation can deal with the oversized ball preload method, but cannot deal with the double nut preload method. Therefore, it is impossible to eliminate the quadrant protrusion only by dealing with the approximate expression after inversion, and thus good machining accuracy cannot be obtained.

In Case 3, the quadrant protrusions basically disappeared. Case 3 uses the approximate formula 3 of the present invention to perform friction compensation. The reason is as follows: By using the approximate expressions 1 and 2, it is possible to estimate with high accuracy either of the frictional forces generated in two stages after the shaft inversion. Therefore, the numerical control device 10 can support both the feed drive mechanism of the oversized ball preload method and the feed drive mechanism of the double nut preload method. The numerical control device 10 can also support machine tools with complex reverse friction characteristics. Therefore, the numerical control device 10 can effectively improve the machining accuracy of the workpiece.

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

As described above, the numerical control device 10 and the friction compensation method of this embodiment can not only support the feed drive mechanism of the oversized ball preloading method, but also fully support the feed driving mechanism of the double nut preloading method. In the double nut preload method, the balls make two-point or three-point contact with the nut and the ball screw shaft depending on the direction of movement of the nut. In the double nut preload method, the ball screw shaft reverses to generate the first quadrant projection, and the second quadrant projection occurs when the table 3 moves further by a predetermined amount. Previous friction compensation methods only supported oversized ball preloading. Conventional friction compensation methods cannot eliminate the second quadrant protrusion unique to the double nut preload method. In the present embodiment, two approximation expressions are used, and in the case of the double nut preloading method, it is possible to estimate with high accuracy the increase in frictional force generated in two stages. The protrusion in the first quadrant is caused by the frictional properties after inversion. The friction characteristics after inversion include a sharp change in friction characteristics after inversion and a gradual change in friction characteristics after inversion. An example of the former is the change in friction characteristics caused by linear guides. An example of the latter is a change in friction characteristics caused by an oil seal on the motor shaft. In the present embodiment, two approximate expressions can be used in consideration of two kinds of friction characteristics. In this embodiment, not only the protrusion in the first quadrant can be eliminated, but also the protrusion in the second quadrant, which cannot be eliminated conventionally, can be reliably eliminated. This embodiment can also effectively eliminate the quadrant protrusion in the double nut preload mode and with an oil seal. This embodiment can reliably improve machining accuracy.

The present invention is not limited to the above-described embodiments, and various changes can be made. For example, in the friction compensator 13 of the above-described embodiment, the first friction characteristic estimating 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 approximate expression 2. The friction compensator 13 adds f ₁ (x′) and f ₂ (x′) using approximate expression 3 to calculate the total friction torque f(x′). The friction compensator 13 adds the total friction torque f(x') to the torque.

For example, the friction compensator disclosed in Japanese Patent Laid-Open No. 210273 may be modified so as to conform to the object of the present invention. The friction compensator can compensate the friction force increased in two stages by using two approximation formulas 5, 6 different from the above-mentioned embodiment. The structure and operation of the friction compensator 106 will be described. The friction compensator 106 is a modified example of the friction compensator 13 .

The structure of the friction compensator 106 will be described with reference to FIG. 20 . Part of the structure of the friction compensator 106 is the same as that of the friction compensator 13 shown in FIG. 13 . 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 estimating unit 56 and a fourth friction characteristic estimating unit 57 . The third friction characteristic estimating section 56 is used in place of the first friction characteristic estimating section 26 . The fourth friction characteristic estimating section 57 is used instead of the second friction characteristic estimating section 27 . The third friction characteristic estimating unit 56 and the fourth friction characteristic estimating unit 57 respectively calculate differential values using approximate expressions 5 and 6 described later. The multiplier 59 and the integrator 60 are provided between the adder 28 and the response delay compensator 29 .

The adder 28 adds the respective differential values calculated by the third friction characteristic estimating unit 56 and the fourth friction characteristic estimating unit 57 and outputs it 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. An integrator 60 is connected to the output of the multiplier 59 . The integrator 60 performs a time integration operation on the rate of change calculated by the multiplier 59 . The response delay compensator 29 is connected to the output terminal of the integrator 60 .

The response delay compensator 29 is constituted by an inverse function of the transfer function. The transfer function is obtained by modeling the characteristics from the torque command signal to the torque actually output by the motor 2 . The torque command signal is input to the current control amplifier 15 (see FIG. 2 ). The response delay compensator 29 multiplies the integrated value output from the integrator 60 to generate a friction compensation signal.

Approximate expressions 5 and 6 will be described. The third friction characteristic estimating unit 56 and the fourth friction characteristic estimating unit 57 use approximate expressions 5 and 6. The definitions of various parameters in this modified example are the same as those defined in the approximate expressions 1 and 2 above.

Approximate formulas 5 and 6 are obtained by differentiating approximate formulas 1 and 2 with x'. Approximate formula 5 is formula (7) obtained after differential operation of formula (1) with 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)

Approximate formula 6 is formula (8) obtained after differential operation of formula (2) with x'.

·df ₂ /dx'＝f _c2 /a ₂ {1-tanh ² {(|x'|-b)/a ₂ }}...(8)

When |x'|-b<0, df ₂ /dx'=0.

The difference in effect between the case where friction compensation was performed by the friction compensator 13 of the above-described embodiment and the case where friction compensation was performed by the friction compensator 106 of this modified example was investigated. The former method is compensation method 1, and the latter method is compensation method 2. In FIG. 21, the data of compensation method 1 is shown by thin lines, and the data of compensation method 2 is shown by thick lines.

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

As described above, when the control method of Japanese Patent Laid-Open No. 210273 is changed to perform the same compensation as the present invention, the same effect can be obtained at non-high speed. The mode of the present invention is a mode in which calculation is performed using a friction estimation expression expressed simply as a function of the reverse distance, and the torque command is added to the torque command. The present invention can perform friction compensation from a low-speed region to a high-speed region with high precision, and the present invention is superior to conventional methods.

In the above embodiment, the formula (1) used in the approximation formula 1 is a combination of two sets of tanh functions. Equation (4) is a combination of two groups of exp functions. A combination of the first term being the tanh function and the second term being the exp function, and a combination of the first term being the exp function and the second term being the tanh function can also obtain the same effect.

In the above-mentioned embodiment, the first term of the approximation formula 1 is to use the tanh function or the exp function to approximate the sharp friction change after the reversal. The sharp friction change after the reversal becomes a constant value immediately after the sharp rise. Therefore, the first term of approximate formula 1 can also be approximated using a ramp function or a step function.

In the above-mentioned embodiment, the table 3 is used as a moving body. The moving body may also be a mechanism that supports a main shaft for gripping a tool. Secure the workbench in advance. The mechanism can also be composed of a spindle head and a column. The spindle head is supported rotatably around the spindle. The column supports the spindle head in such a manner that the spindle head can move up and down or back and forth.

Case 7 is constructed using equation (1) as approximate equation 1 and equation (5) as approximate equation 2. Case 8 is constructed using equation (4) as approximate equation 1 and equation (2) as approximate equation 2.

In Case 7, 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. 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. FIG. 23 is a diagram of case 7. FIG. FIG. 24 is a diagram of Case 8. FIG.

In the present invention, any one of the two formulas of formula (1) and (4) can be used as approximate formula 1, and the three formulas of formula (2), (5) and (6) can be used Any one of the formulas is used as approximate formula 2. Therefore, six methods can be combined.

The above embodiment uses the feed mechanism of the double nut preloading method. The present invention can also obtain the same effect for the feed mechanism of the offset preloading method. The feed mechanism of the offset preload method integrates a pair of nuts and washers into one nut. The present invention can also obtain the same result in the feed mechanism of the offset preloading method.

Claims (7)

1. a numerical control device, possesses: feed mechanism, and it has ballscrew shaft and the ball nut of fit on this ballscrew shaft, for the moving body being fixed on this ball nut is moved; Motor, it is rotated driving to above-mentioned ballscrew shaft; Position detecting mechanism, its detection utilizes the position of the moving body that above-mentioned motor moves; Speed generating unit, the consistent speed command of position command that its generation makes the position of the detected moving body of this position detecting mechanism generate with control part; Speed detecting mechanism, it detects the speed of above-mentioned motor; Torque generating unit, the consistent torque instruction of speed command that its generation makes the detected speed of above-mentioned speed detecting mechanism generate with above-mentioned speed generating unit; Friction estimator, it estimates the friction force or the friction torque that after the sense of rotation reversion of above-mentioned motor, produce; And correction unit, friction force or friction torque that it estimates according to above-mentioned friction estimator are proofreaied and correct above-mentioned torque instruction,

Wherein, above-mentioned ball nut is made up of a pair of ball nut with multiple balls,

This numerical control device also possesses:

Actual position estimation portion, it estimates the physical location of the above-mentioned moving body corresponding with above-mentioned position command; And

Calculating part, its physical location estimating according to above-mentioned actual position estimation portion calculates the displacement after the moving direction reversion of above-mentioned moving body,

The first friction estimator, it estimates the friction force being caused by above-mentioned feed mechanism or the friction torque of increase from the moving direction reversion of above-mentioned moving body by the displacement that calculates taking above-mentioned calculating part as the approximate expression of variable; And

The second friction estimator, it has moved after ormal weight the friction force or the friction torque that increase due to above-mentioned ballscrew shaft and a pair of ball nut by the displacement that calculates taking above-mentioned calculating part above-mentioned moving body after the approximate expression of variable is estimated the moving direction reversion of above-mentioned moving body

Afore mentioned rules amount is that after the moving direction reversion of above-mentioned moving body, above-mentioned moving body moves in above-mentioned multiple ball distance when at least one ball contacts with above-mentioned a pair of ball nut and 3 of above-mentioned ballscrew shafts,

Above-mentioned friction estimator is carried out additive operation to above-mentioned the first friction estimator and above-mentioned the second friction estimator friction force or friction torque of estimating respectively.

2. numerical control device according to claim 1, is characterized in that,

If the amount of movement that the friction force changing from the moving direction reversion of above-mentioned moving body or friction torque are reversed after moving direction with respect to above-mentioned moving body resolves into the second slope composition that the first slope composition and slope are less than this first slope composition, and the displacement from moving direction backward position of above-mentioned moving body is made as to x ', friction force or the friction torque of the rising from reversion of above-mentioned the first slope composition are made as to f _c0, the rising distance constant of above-mentioned the first slope composition is made as to a ₀, the rising distance constant of above-mentioned the second slope composition is made as to a ₁, the kinetic force of friction changing from the moving direction reversion of above-mentioned moving body or the total value of kinetic friction torque are made as to f _c1, be made as f by having moved the kinetic force of friction being caused by ballscrew shaft and a pair of ball nut or the kinetic friction torque that increase after afore mentioned rules amount after the moving direction reversion of above-mentioned moving body _c2, afore mentioned rules amount is made as to b, be made as a by moved the friction force that increases after afore mentioned rules amount b or the rising distance constant of friction torque from the moving direction reversion of above-mentioned moving body ₂, sign function is made as to sgn, the above-mentioned approximate expression f of above-mentioned the first friction estimator ₁the above-mentioned approximate expression f of (x '), above-mentioned the second friction estimator ₂(x ') be

$f_1\left(x^{\&prime;}\right)=f_{c0}(\tanh \left(\frac{\left|x^{\&prime;}\right|}{a_0}\right)-\frac{1}{2})\mathrm{sgn}\left(\frac{{\mathrm{dx}}^{\&prime;}}{\mathrm{dt}}\right)+(f_{c1}+\frac{f_{c2}}{2}-\frac{f_{c0}}{2})(2\tanh \left(\frac{\left|x^{\&prime;}\right|}{a_1}\right)-1)\mathrm{sgn}\left(\frac{{\mathrm{dx}}^{\&prime;}}{\mathrm{dt}}\right)$

$f_2\left(x^{\&prime;}\right)=f_{c2}(\tanh \left(\frac{\left|x^{\&prime;}\right|-b}{a_2}\right)-\frac{1}{2})\mathrm{sgn}\left(\frac{{\mathrm{dx}}^{\&prime;}}{\mathrm{dt}}\right)$

$\left|x^{\&prime;}\right|-b<0\&DoubleRightArrow;f_2\left(x^{\&prime;}\right)=-\frac{f_{c2}}{2}\mathrm{sgn}\left(\frac{{\mathrm{dx}}^{\&prime;}}{\mathrm{dt}}\right).$

3. numerical control device according to claim 1, is characterized in that,

If the amount of movement that the friction force changing from the moving direction reversion of above-mentioned moving body or friction torque are reversed after moving direction with respect to above-mentioned moving body resolves into the second slope composition that the first slope composition and slope are less than this first slope composition, and the displacement from moving direction backward position of above-mentioned moving body is made as to x ', friction force or the friction torque of the rising from reversion of above-mentioned the first slope composition are made as to f _c0, the rising distance constant of above-mentioned the first slope composition is made as to a ₀, the rising distance constant of above-mentioned the second slope composition is made as to a ₁, the kinetic force of friction changing from the moving direction reversion of above-mentioned moving body or the total value of kinetic friction torque are made as to f _c1, be made as f by having moved the kinetic force of friction being caused by ballscrew shaft and a pair of ball nut or the kinetic friction torque that increase after afore mentioned rules amount after the moving direction reversion of above-mentioned moving body _c2, afore mentioned rules amount is made as to b, be made as a by moved the friction force that increases after afore mentioned rules amount b or the rising distance constant of friction torque from the moving direction reversion of above-mentioned moving body ₂, sign function is made as to sgn, the above-mentioned approximate expression f of above-mentioned the first friction estimator ₁the above-mentioned approximate expression f of (x '), above-mentioned the second friction estimator ₂(x ') be

$f_1\left(x^{\&prime;}\right)=f_{c0}(\frac{1}{2}-\exp \frac{-\left|x^{\&prime;}\right|}{a_0})\mathrm{sgn}\left(\frac{{\mathrm{dx}}^{\&prime;}}{\mathrm{dt}}\right)+(f_{c1}+\frac{f_{c2}}{2}-\frac{f_{c0}}{2})(1-2\exp \frac{-\left|x^{\&prime;}\right|}{a_1})\mathrm{sgn}\left(\frac{{\mathrm{dx}}^{\&prime;}}{\mathrm{dt}}\right)$

$f_2\left(x^{\&prime;}\right)=f_{c2}(\frac{1}{2}-\exp \frac{-\left(\right|x^{\&prime;}|-b)}{a_2})\mathrm{sgn}\left(\frac{{\mathrm{dx}}^{\&prime;}}{\mathrm{dt}}\right)$

$\left|x^{\&prime;}\right|-b<0\&DoubleRightArrow;f_2\left(x^{\&prime;}\right)=-\frac{f_{c2}}{2}\mathrm{sgn}\left(\frac{{\mathrm{dx}}^{\&prime;}}{\mathrm{dt}}\right).$

4. numerical control device according to claim 1, is characterized in that,

If the amount of movement that the friction force changing from the moving direction reversion of above-mentioned moving body or friction torque are reversed after moving direction with respect to above-mentioned moving body resolves into the second slope composition that the first slope composition and slope are less than this first slope composition, and the displacement from moving direction backward position of above-mentioned moving body is made as to x ', friction force or the friction torque of the rising from reversion of above-mentioned the first slope composition are made as to f _c0, the rising distance constant of above-mentioned the first slope composition is made as to a ₀, the rising distance constant of above-mentioned the second slope composition is made as to a ₁, the kinetic force of friction changing from the moving direction reversion of above-mentioned moving body or the total value of kinetic friction torque are made as to f _c1, be made as f by having moved the kinetic force of friction being caused by ballscrew shaft and a pair of ball nut or the kinetic friction torque that increase after afore mentioned rules amount after the moving direction reversion of above-mentioned moving body _c2, afore mentioned rules amount is made as to b, be made as a by moved the friction force that increases after afore mentioned rules amount b or the rising distance constant of friction torque from the moving direction reversion of above-mentioned moving body ₂, sign function is made as to sgn, the above-mentioned approximate expression f of above-mentioned the first friction estimator ₁the above-mentioned approximate expression f of (x '), above-mentioned the second friction estimator ₂(x ') be

$f_1\left(x^{\&prime;}\right)=f_{c0}(\tanh \left(\frac{\left|x^{\&prime;}\right|}{a_0}\right)-\frac{1}{2})\mathrm{sgn}\left(\frac{{\mathrm{dx}}^{\&prime;}}{\mathrm{dt}}\right)+(f_{c1}+\frac{f_{c2}}{2}-\frac{f_{c0}}{2})(2\tanh \left(\frac{\left|x^{\&prime;}\right|}{a_1}\right)-1)\mathrm{sgn}\left(\frac{{\mathrm{dx}}^{\&prime;}}{\mathrm{dt}}\right)$

$f_2\left(x^{\&prime;}\right)=f_{c2}(\frac{1}{2}-\exp \frac{-\left(\right|x^{\&prime;}|-b)}{a_2})\mathrm{sgn}\left(\frac{{\mathrm{dx}}^{\&prime;}}{\mathrm{dt}}\right)$

$\left|x^{\&prime;}\right|-b<0\&DoubleRightArrow;f_2\left(x^{\&prime;}\right)=-\frac{f_{c2}}{2}\mathrm{sgn}\left(\frac{{\mathrm{dx}}^{\&prime;}}{\mathrm{dt}}\right).$

5. numerical control device according to claim 1, is characterized in that,

If the amount of movement that the friction force changing from the moving direction reversion of above-mentioned moving body or friction torque are reversed after moving direction with respect to above-mentioned moving body resolves into the second slope composition that the first slope composition and slope are less than this first slope composition, and the displacement from moving direction backward position of above-mentioned moving body is made as to x ', friction force or the friction torque of the rising from reversion of above-mentioned the first slope composition are made as to f _c0, the rising distance constant of above-mentioned the first slope composition is made as to a ₀, the rising distance constant of above-mentioned the second slope composition is made as to a ₁, the kinetic force of friction changing from the moving direction reversion of above-mentioned moving body or the total value of kinetic friction torque are made as to f _c1, be made as f by having moved the kinetic force of friction being caused by ballscrew shaft and a pair of ball nut or the kinetic friction torque that increase after afore mentioned rules amount after the moving direction reversion of above-mentioned moving body _c2, afore mentioned rules amount is made as to b, be made as a by moved the friction force that increases after afore mentioned rules amount b or the rising distance constant of friction torque from the moving direction reversion of above-mentioned moving body ₂, sign function is made as to sgn, the above-mentioned approximate expression f of above-mentioned the first friction estimator ₁the above-mentioned approximate expression f of (x '), above-mentioned the second friction estimator ₂(x ') be

$f_1\left(x^{\&prime;}\right)=f_{c0}(\frac{1}{2}-\exp \frac{-\left|x^{\&prime;}\right|}{a_0})\mathrm{sgn}\left(\frac{{\mathrm{dx}}^{\&prime;}}{\mathrm{dt}}\right)+(f_{c1}+\frac{f_{c2}}{2}-\frac{f_{c0}}{2})(1-2\exp \frac{-\left|x^{\&prime;}\right|}{a_1})\mathrm{sgn}\left(\frac{{\mathrm{dx}}^{\&prime;}}{\mathrm{dt}}\right)$

$f_2\left(x^{\&prime;}\right)=f_{c2}(\tanh \left(\frac{\left|x^{\&prime;}\right|-b}{a_2}\right)-\frac{1}{2})\mathrm{sgn}\left(\frac{{\mathrm{dx}}^{\&prime;}}{\mathrm{dt}}\right)$

$\left|x^{\&prime;}\right|-b<0\&DoubleRightArrow;f_2\left(x^{\&prime;}\right)=-\frac{f_{c2}}{2}\mathrm{sgn}\left(\frac{{\mathrm{dx}}^{\&prime;}}{\mathrm{dt}}\right).$

6. numerical control device according to claim 1, is characterized in that,

If the displacement from moving direction backward position of above-mentioned moving body is made as to x ', be made as f by having moved the kinetic force of friction being caused by ballscrew shaft and a pair of ball nut or the kinetic friction torque that increase after afore mentioned rules amount after the moving direction reversion of above-mentioned moving body _c2, afore mentioned rules amount is made as to b, be made as a by moved the friction force that increases after afore mentioned rules amount b or the rising distance constant of friction torque from the moving direction reversion of above-mentioned moving body ₂, sign function is made as to sgn, the above-mentioned approximate expression f of above-mentioned the second friction estimator ₂(x ') be

$f_2\left(x^{\&prime;}\right)=-\frac{f_{c2}}{2}\cos \left(\frac{\left|x^{\&prime;}\right|-b}{a_2}\mathrm{\&pi;}\right)\mathrm{sgn}\left(\frac{{\mathrm{dx}}^{\&prime;}}{\mathrm{dt}}\right)$

$\left|x^{\&prime;}\right|-b<0\mathrm{or}\left|x^{\&prime;}\right|-b-a_2>0\&DoubleRightArrow;f_2\left(x^{\&prime;}\right)=-\frac{f_{c2}}{2}\mathrm{sgn}\left(\frac{{\mathrm{dx}}^{\&prime;}}{\mathrm{dt}}\right).$

7. a friciton compensation method, comprise the following operation of being undertaken by the numerical control device that possesses feed mechanism, motor and position detecting mechanism: speed generates operation, generate the consistent speed command of position command that the position of the detected moving body of above-mentioned position detecting mechanism is generated with control part; Speed detects operation, detects the speed of above-mentioned motor; Torque generates operation, generates and makes above-mentioned speed detect the consistent torque instruction of speed command that the detected speed of operation generates with above-mentioned speed generation operation; Operation is estimated in friction, estimates the friction force or the friction torque that after the sense of rotation reversion of above-mentioned motor, produce; And correcting process, the friction force or the friction torque that estimate according to above-mentioned friction estimation operation are proofreaied and correct above-mentioned torque instruction, wherein, above-mentioned feed mechanism has ballscrew shaft and the ball nut of fit on this ballscrew shaft, for the moving body being fixed on this ball nut is moved, above-mentioned motor is rotated driving to above-mentioned ballscrew shaft, and above-mentioned position detecting mechanism detects the position that utilizes the moving body that above-mentioned motor moves

Wherein, above-mentioned ball nut is made up of a pair of ball nut with multiple balls,

This friciton compensation method also comprises:

Actual position estimation operation, it estimates the physical location of the above-mentioned moving body corresponding with above-mentioned position command; And

Calculation process, its physical location estimating according to above-mentioned actual position estimation operation calculates the displacement after the moving direction reversion of above-mentioned moving body,

Operation is estimated in the first friction, estimates the friction force being caused by above-mentioned feed mechanism or the friction torque of increase from the moving direction reversion of above-mentioned moving body by the displacement that calculates taking above-mentioned calculation process as the approximate expression of variable; And

Operation is estimated in the second friction, the friction force or the friction torque that increase due to above-mentioned ballscrew shaft and a pair of ball nut have been moved after ormal weight by the displacement that calculates taking above-mentioned calculation process above-mentioned moving body after the approximate expression of variable is estimated the moving direction reversion of above-mentioned moving body

Afore mentioned rules amount is that after the moving direction reversion of above-mentioned moving body, above-mentioned moving body moves in above-mentioned multiple ball distance when at least one ball contacts with above-mentioned a pair of ball nut and 3 of above-mentioned ballscrew shafts,

Estimate in operation in above-mentioned friction, above-mentioned the first friction is estimated to operation and above-mentioned the second friction estimate that friction force or friction torque that operation estimates respectively carry out additive operation.