JP5232384B2 - Temperature distribution calculation method for ball screw in operation and displacement correction method based on the method - Google Patents

Description

  The present invention focuses on the temperature distribution associated with heat generation in a ball screw in operation that functions as a feed shaft for conveying an article such as a tool (an instrument indispensable for machining), and starts and ends positions of conveyance. The present invention relates to providing a method for correcting the command position.

  The ball screw rotates in a state where it is supported by ball bearings at both ends, thereby transferring a predetermined article by moving a female screw that is screwed at a midway portion.

  Due to the rotation integrated with the ball bearing and screwing with the female screw, frictional heat is generated in the ball screw in operation and is transmitted to each part of the ball screw that is rotating because it is in operation. .

  In addition, the temperature of each article is influenced not only by the heat generated by screwing with the female screw but also by the ambient temperature.

  Thus, the overall length of the ball screw is affected by the temperature distribution of each part, and the command positions such as the transfer start position and end position via the female screw are also changed by the temperature distribution. .

  However, until now, a technique for calculating the temperature distribution at each position for a ball screw in operation corresponding to the passage of a predetermined time and correcting the commanded position based on the temperature distribution has been proposed so far. It has not been.

  Most ball screws are stretched slightly straighter than their original lengths by applying a tensile stress in advance, which causes a certain mechanical deformation.

  And the technique which performs the said correction | amendment considering the relationship with such a mechanical deformation is not proposed until now.

  Incidentally, in Patent Documents 1 and 2, the command position is corrected by the heat generated by the operation of the ball screw, but the temperature measurement at a specific position of the ball screw has been performed all the time, and the temperature at each position has been calculated. The correction is not performed based on the temperature distribution by

On the other hand, Patent Document 3 proposes a method of correcting the amount of heat generation displacement of the main shaft, but does not calculate the heat distribution in the main shaft, but uses the main shaft speed and the main shaft motor load as parameters for measurement. Although only the amount of displacement is calculated, even if such a method is applied to the ball screw, it is impossible to calculate an accurate heat distribution for each part and to realize an accurate correction.
JP 61-168005 A JP-A-6-252596 JP 2002-18677 A

  An object of the present invention is to provide a method of appropriately correcting a command position in each operation time in consideration of a temperature distribution at each position accompanying heat generation in an operation stage in a ball screw.

（０≦ｘ≦ｘ_ｍの範囲）

（ｘ_ｍ≦ｘ≦Ｌの範囲）
但し、
Ｔ：各位置における温度
Ｔ₁：固定端又はその近傍における測定温度
Ｔ₂：移動可能端又はその近傍における測定温度
Ｔ_m：メネジと螺合している位置又はその近傍における測定温度
Ｔ_out：外気の温度
ｘ：各位置の固定端からの距離
ｘ_ｍ：メネジと螺合している位置の固定端からの距離
Ｌ：固定端から移動可能端までの全体の長さ
α²：(ボールネジの周長×表面から外気への熱伝達率)／(ボールネジの断面積×熱伝導率)≒(２×表面から外気への熱伝達率)／(平均半径×熱伝導率)
（２）ボールネジに対し、予め引張応力（テンション）が加えられていない場合において、前記（１）記載の温度分布に基づいてボールネジの各位置における長さの増加量（ΔＬ₁）を下記の数式に立脚したうえでマイクロコンピュータによって算出し、当該長さの増加量の分だけ指定位置の固定端からの距離を小さくすることに基づく稼動中のボールネジにおける変位補正方法、
からなる。

Ｔ₀：ボールネジの稼動前段階における測定温度
β：ボールネジの熱膨張係数 In order to solve the above problems, the basic configuration of the present invention is as follows.
(1) Irradiation is performed by irradiating infrared light to a fixed end coupled to a ball bearing of a ball screw operating as a feed shaft, a movable end or the vicinity thereof, and a position screwed with a female screw or the vicinity thereof. By inputting temperature measurement values based on the reflection to the microcomputer every elapse of a predetermined time, the temperature at each position of the ball screw is based on the following formula or an approximate expression by Taylor expansion for the exponential function part of the formula. in the temperature distribution calculation method in the ball screw running based on that calculated by the microcomputer in response to the input.
Record

(Range of 0 ≦ x ≦ x _m )

(Range of x _m ≦ x ≦ L)
However,
T: Temperature at each position T ₁ : Measurement temperature at or near the fixed end T ₂ : Measurement temperature at or near the movable end T _m : Measurement temperature at or near the position screwed with the female screw T _out : Outside air Temperature x: distance from the fixed end at each position x _m : distance from the fixed end at the position screwed with the female screw L: total length from the fixed end to the movable end α ² : (around the ball screw Length x Heat transfer coefficient from surface to outside air / (Ball screw cross section x Thermal conductivity) ≒ (2 x Heat transfer coefficient from surface to outside air) / (Average radius x Heat conductivity)
(2) When a tensile stress is not applied to the ball screw in advance, the amount of increase in length (ΔL ₁ ) at each position of the ball screw based on the temperature distribution described in (1) is expressed by the following formula: A displacement correction method for a ball screw in operation based on a calculation based on a microcomputer and reducing the distance from the fixed end of the specified position by the amount of increase in the length,
Consists of.

T ₀ : Measurement temperature before operation of ball screw β: Thermal expansion coefficient of ball screw

  Based on the basic configuration, in the present invention, the temperature distribution in the ball screw in operation is calculated appropriately and promptly, and the command position such as the transfer start position and end position is fixed due to heat generation. Even if the length from the end increases, it is possible to perform appropriate and prompt correction, and thus it is possible to accurately continue automatic control related to the conveyance of the object.

  The basis of the general formula expressed by [Formula 1] in the basic configuration (1) will be described as follows.

  Factors affecting the temperature T at a specific position where the distance from the fixed end 11 is x include frictional heat generated by the rotation of the ball bearing 3 at the fixed end 11 and the movable end 12 and screwing with the female screw 2. This is a heat transfer from the generated frictional heat along the length direction and heat dissipation by convection caused by a temperature gap with the outside air on the surface of the ball screw 1.

  On the other hand, the temperature change due to heat conduction is expressed by a partial differential equation with a time parameter (t) and a space parameter (x in the case of one dimension, x, y, z in the case of three dimensions). Yes.

  However, in the present invention, since the temperature based on each frictional heat is measured according to the passage of a predetermined time, the change with time of the frictional heat is already set as a known condition, and the elapsed time ( Elucidation by partial differential equations with t) as a parameter is unnecessary.

  That is, it is not necessary to clarify the partial differential equation, and the temperature at the fixed end 11 and the movable end 12 or the vicinity thereof, and the screwing position with or near the female screw 2 is defined as a known boundary condition. In addition, it can be set as an ordinary differential equation using the distance (x) from the fixed end 11 as a parameter.

The heat conductivity of the ball screw 1 is λ, the heat transfer coefficient between the surface of the ball screw 1 and the outside air is h, the temperature of the outside air is T _out , the average cross-sectional area of the ball screw 1 is f, and this corresponds to the cross-sectional area. Assuming that the average circumference is p, as shown in FIG. 1, d ² T / dx ² − (ph / fλ), considering that there is no heat source in the middle other than the frictional heat, as shown in FIG. ) (T-T _out ) = 0 (for example, page 4 of Nobuhiro Seki, “Heat Transfer Engineering” (December 20, 1998, Morikita Publishing Co., Ltd., 1st edition, 15th edition)) General formula (1 · 8)).
When the average radius in the cross-sectional area of the ball screw 1 is r, p / f = 2 / r is established in the ordinary differential equation.

…（ａ）
（０≦ｘ≦ｘ_ｍ）
を得ることができる。 The general solution of the above ordinary differential equation is T = C ₁ · e ^αx + C ₂ · e ^−αx + T _out (where C ₁ and C ₂ are integral constants, where α ² = ph / fλ = 2h / λr), and the screwing position from the fixed end 11 to the female screw 2 (as shown in FIG. 1, the position changes sequentially during operation, but the center position in the length direction from the fixed end 11 In the range (0 ≦ x ≦ x _m ) until the distance is x _m ,
The temperature of the fixed end 11 in the course phase of a predetermined time when the T _1, at x = 0, a T = T _1, the temperature at the screwing position of the female screw 2 at the same time as the T _m In the case of x = x _m , based on the boundary condition that T = T _m ,

... (a)
(0 ≦ x ≦ x _m )
Can be obtained.

…（ｂ）
（ｘ_ｍ≦ｘ≦Ｌ）
を得ることができる。 On the other hand, in the range (x _m ≦ x ≦ L) of the movable end 12 (the entire length of the ball screw 1 is indicated by L) from the position where it is screwed with the female screw 2 or its vicinity. at x = _{x m,} a T = _{T m} at x = L, based on the boundary condition based on a T = T _2,

... (b)
(X _m ≦ x ≦ L)
Can be obtained.

との積、即ち、αＬは、必ずしも小さな数値という訳ではない。通常、Ｌ＝１〜３（ｍ）の範囲内にあり、平均半径ｒは、０．０１〜０．０３（ｍ）の範囲内にある場合が多いが、例えばＬ＝２（ｍ）であり、ｒ＝０．０２（ｍ）の場合において、表面と外気との熱伝達率ｈ≒２（Ｗ／ｍ²Ｋ）とし、λ≒１６（Ｗ／ｍＫ）とした場合、α≒３．５４であり、αＬ≒７．１である。 In the general solution including the exponential function according to (a) and (b), the length L of the ball screw 1 is set, and

, Ie, αL is not necessarily a small number. Usually, L is in the range of 1 to 3 (m), and the average radius r is often in the range of 0.01 to 0.03 (m). For example, L = 2 (m). When r = 0.02 (m), the heat transfer coefficient between the surface and the outside air is h≈2 (W / m ² K), and when λ≈16 (W / mK), α≈3.54 And αL≈7.1.

When Taylor expansion is applied to the exponential function part of the equations (a) and (b), an odd-order polynomial appears, but when the exponential function is 7 at the maximum, the Taylor expansion is made 31-dimensional. When calculated up to ³³ 33/33! Is a numerical value that is clearly smaller than 1 / 10,000 and is still in such a state after the 35th dimension. Therefore, in the exponential function part of the equations (a) and (b), the approximation is quite good. The formula can be obtained.
Of course, the orders adopted in the approximate expression based on the Taylor expansion are the specific values of the ball screw length width (L), the radius (r), the heat transfer coefficient with the outside air (h), and the thermal conductivity (λ) and It may be set appropriately according to the required accuracy.

は、事前に、熱伝達率（ｈ）及び熱伝導率（λ）を測定することによって予め設定することもできるが、現実にボールネジ１を稼動させたうえで、赤外線温度測定器などによって、所定の温度分布を測定したうえで、前記一般解（ａ）、（ｂ）との対比、又は２次以上の近似によって得られた近似式との対比に基づいて直接αの数値として算出することも可能である。 Constants that are inevitably subject to calculation in the temperature distribution by the general solutions (a) and (b) and the temperature distribution by the second-order approximation or higher.

Can be set in advance by measuring the heat transfer coefficient (h) and the thermal conductivity (λ) in advance, but after the ball screw 1 is actually operated, it is determined by an infrared temperature measuring instrument or the like. It is also possible to calculate directly as a numerical value of α based on the comparison with the general solutions (a) and (b) or the comparison with the approximate expression obtained by the approximation of the second order or higher. Is possible.

As a method of measuring the temperature at both ends and the screwed positions with the female screw 2 and in the vicinity thereof,
A method of directly measuring temperature by irradiating infrared light to both ends rotated by an infrared temperature measuring device and a screwed portion of a female screw, and reflecting the infrared rays.

Is adopted .

  When the infrared temperature measuring instrument (2) is used, it is difficult to directly measure the screwing positions of both ends and the female screw 2. Therefore, the temperature measurement is performed at a position in the vicinity of these positions. become.

  Reflecting such a situation, in the basic configuration (1), not only the screwing positions of the both ends of the ball screw 1 and the female screw 2 but also the positions in the vicinity thereof are selected as the target of the part for temperature measurement. It is possible.

  The basic configuration (2) is based on the temperature distribution of the basic configuration (1), and the amount of increase in length due to heat generation at each position is calculated by a microcomputer.

このように、ボールネジ１の稼動段階において、前記基本構成（１）の如き正確な温度分布を速やかに算定した後、前記基本構成（２）に基づいて、各位置の長さの増加量を算定した場合には、ボールネジ１を解した搬送開始位置及び終了位置などの指令位置に対し、前記増加した長さ分だけ、固定端１１からの距離を小さくするような指令を発することによって、正確な変位の補正を行うことが可能となる。 That is, when the temperature at a predetermined position where the distance from the fixed end 11 is x is T, the thermal expansion coefficient is β, and the initial temperature before operation of the ball screw 1 is T ₀ , the length at the predetermined position is The amount of increase (ΔL ₁ ) is expressed by the following integral formula.

Thus, in the operation stage of the ball screw 1, after calculating the accurate temperature distribution as in the basic configuration (1), the amount of increase in the length of each position is calculated based on the basic configuration (2). In such a case, an accurate command can be obtained by issuing a command to reduce the distance from the fixed end 11 by the increased length with respect to the command position such as the transfer start position and the end position after the ball screw 1 is disassembled. It becomes possible to correct the displacement.

  Hereinafter, it demonstrates according to an Example.

  In most cases, the ball screw 1 is applied with a tensile stress (tension) from the pre-operation stage in order to maintain a straight state, and is set to be longer than the original length.

Reflecting this situation, in a normal embodiment, the length increase amount (ΔL ′) due to the tensile stress applied to the ball screw 1 and the overall length increase amount due to heat generation (ΔL ′) In the integral formula, ΔL ₁ ) when x = L is compared, and when the former is greater than the latter, it is attributed to the fact that the length does not increase due to heat generation. There is no need to make a special correction for the command position.

  On the contrary, when the former exceeds the latter, the command position of the feed axis of the machine tool is corrected.

即ち、実施例１においては、予め引張応力（テンション）が加えられた場合において、極めて適切な補正指令を実行することが可能となる。 In Example 1, when a tensile stress (tension) is applied to the ball screw 1 in advance, the total length increase (ΔL ′) based on the tensile stress is obtained by the method of claim 4. When the latter exceeds the former (the amount of increase ΔL ₁ in the case where x = L in the general formula of claim 4) In the case of x = L where ΔL ₁ > ΔL ′), the amount of increase in length (ΔL ₂ ) is calculated by a microcomputer based on the following general formula, and the distance from the fixed end 11 at the specified position The displacement correction method for the ball screw 1 in operation based on reducing the length by the amount of increase (ΔL ₂ ) is employed.

That is, in the first embodiment, it is possible to execute a very appropriate correction command when a tensile stress (tension) is applied in advance.

Note that x · ΔL ′ / L in the second term on the right side of the length increase amount (ΔL ₂ ) is the distance from the fixed end 11 and the total length (the length of the length increase due to the tensile stress at each position). It is derived from the rule of thumb that it is roughly proportional to the ratio (x / L) to L).

  When a tensile stress (tension) is applied to the ball screw 1 as in the first embodiment, the mechanical device holding the ball screw 1 via the fixed end 11 is deformed due to the tensile stress, The fixed end 11 may be displaced in the length direction where the tensile stress is applied.

  In such a case, as in Example 1, when considering the comparison with the increase in the overall length based on the tensile stress (tension) (ΔL ′) and at the same time the displacement amount is a, Even if the position of x is measured, the distance from the actual fixed end 11 is small by a, and therefore, a formula substituted with x−a is substituted for x in the formulas (a) and (b). It is essential to correct by

（但し、前記積分式において、積分の上限値であるｘは、最大値として、Ｌ＋ａまで選択することができる。）
このような実施例２においては、引張応力（テンション）を原因として、機械的変形が生じた場合においても、極めて適切な補正指令を実行することが可能となる。 That is, in Example 2, in the case where the length is increased based on mechanical deformation rather than the original length due to the fact that tensile stress (tension) has been applied to the ball screw 1 in advance, Increase in overall length due to heat generation (increment amount ΔL ₁ when x = L in the integral equation of ΔL ₁ ) and increase in overall length based on tensile stress (ΔL When the former exceeds the latter (when ΔL ₁ > ΔL ′ when x = L), the amount of increase in length (ΔL ₃ ) is microscopically based on the following general formula: A displacement correction method for the ball screw 1 in operation is employed, which is calculated by a computer and is based on reducing the distance from the fixed end 11 at the designated position by the increase amount (ΔL ₃ ) of the length.

(However, in the integration formula, x, which is the upper limit value of integration, can be selected up to L + a as the maximum value.)
In the second embodiment, it is possible to execute a very appropriate correction command even when mechanical deformation occurs due to tensile stress (tension).

The reason for adopting the ratio of x / L is the same as in the case of Example 1, and ΔL ″ which is the degree of mechanical deformation is the original length by removing the tensile stress (tension) once. It can be calculated by comparison with (L ₀ ).

  The present invention can be used in various industrial fields in which an article is moved by a ball screw.

It is a side view explaining the basic principle of the present invention according to an embodiment. The white line arrow indicates the moving direction of the female screw, and the black line arrow indicates that the movable end can move in the length direction.

Explanation of symbols

1 Ball screw 11 Fixed end 12 Movable end 2 Female screw 3 Ball bearing

Claims (8)

Infrared light is irradiated to the fixed end and movable end connected to the ball bearing of the ball screw operating as the feed shaft, or the vicinity thereof, and the position screwed to the female screw or the vicinity thereof, and reflection to the irradiation is performed. By inputting the temperature measurement value based on the microcomputer every time the predetermined time elapses, the temperature at each position of the ball screw is based on the following mathematical expression or an approximate expression by Taylor expansion for the exponential function part of the mathematical expression. temperature distribution calculating method in the ball screw running based on that calculated by the microcomputer in response to the input.
Record

(Range of 0 ≦ x ≦ x _m )

(Range of x _m ≦ x ≦ L)
However,
T: Temperature at each position T ₁ : Measurement temperature at or near the fixed end T ₂ : Measurement temperature at or near the movable end T _m : Measurement temperature at or near the position screwed with the female screw T _out : Outside air Temperature x: distance from the fixed end at each position x _m : distance from the fixed end at the position screwed with the female screw L: total length from the fixed end to the movable end α ² : (average of the ball screw Perimeter x heat transfer coefficient from surface to outside air / (average cross section of ball screw x heat conductivity) = (2 x heat transfer coefficient from surface to outside air) / (average radius x heat conductivity)   In a ball screw having a length in a range of 1 m to 3 m and a radius in a range of 0.01 m to 0.03 m, an approximate expression by Taylor expansion up to 31 dimensions is adopted for x and (L−x). The method of calculating a temperature distribution during operation of the ball screw according to claim 1. When a tensile stress (tension) is not previously applied to the ball screw, the amount of increase in length (ΔL ₁ ) at each position of the ball screw is based on the following formula based on the temperature distribution according to claim 1 or 2. In addition, a displacement correction method for a ball screw in operation based on calculation by a microcomputer and reducing the distance from the fixed end of the designated position by the amount of increase in the length.

T ₀ : Measurement temperature before operation of ball screw β: Thermal expansion coefficient of ball screw When a tensile stress (tension) is previously applied to the ball screw, the increase in the overall length caused by the heat generated by the method of claim 3 (in the general formula of claim 3, x = When the amount of increase in length ΔL ₁ ) is compared with the amount of increase in overall length (ΔL ′) based on the tensile stress, the former exceeds the latter (x = L) In the case of ΔL ₁ > ΔL ′), the amount of increase in length (ΔL ₂ ) is calculated by a microcomputer based on the following general formula, and the distance from the fixed end of the designated position is determined as the amount of increase in the length ( A displacement correction method for a ball screw in operation based on making it smaller by ΔL ₂ ).

Caused by heat generation when the position of the fixed end is displaced by a distance a in the length direction where the tensile force is applied due to the fact that a tensile stress is applied to the ball screw in advance. The total length increase amount (in the general formula of claim 3, the length increase amount ΔL ₁ when x = L) and the total length increase amount based on the tensile stress (ΔL ′) In contrast, when the former exceeds the latter (when ΔL ₁ > ΔL ′ when x = L), the amount of increase in length (ΔL ₃ ) is calculated by a microcomputer based on the following general formula. A displacement correction method for a ball screw in operation based on reducing the distance from the fixed end of the designated position by an increase amount (ΔL ₃ ) of the length.

(However, in the integration formula, x, which is the upper limit value of integration, can be selected up to L + a as the maximum value.)   At each end of the ball screw, the temperature of the fixed portion of the bearing that supports the ball screw is measured, and the temperature at the fixed end and the movable end of the rotating ball screw or the vicinity thereof is determined in advance by experiments. The temperature distribution calculating method for the ball screw according to claim 1, wherein the temperature of the end of the ball screw is calculated by multiplying the correction coefficient of the temperature. The temperature (T _m ) at or near the position where the ball screw is screwed with the female screw is calculated by multiplying the measured value of the female screw temperature by a predetermined correction coefficient found by a prior experiment. The temperature distribution calculation method for the ball screw according to claim 1 or 2.   3. The temperature distribution calculating method for a ball screw according to claim 1, wherein a temperature at a position where the both ends of the ball screw and the female screw are engaged, or a temperature in the vicinity of the position is measured by an infrared reflection thermometer.

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