JP2008168354A - Temperature distribution calculating method in operating ball screw and displacement correction method based on the method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method of suitably correcting a command position in each operating time in due consideration of temperature distribution in each position due to generation of heat in an operating stage, in a ball screw. <P>SOLUTION: According to the temperature distribution calculating method in the ball screw, temperature is measured on both ends of the ball screw 1 and a female screw 2 at intervals of predetermined time, and the temperature distribution of each section unit by integrals of a differential equation based on a time interval (Δt) and a unit section width (Δx) is calculated at intervals of the predetermined time passage by a micro-computer. According to the method of correcting the displacement of a command position in the ball screw, an increment of a distance from a fixed end 11 in each predetermined position is calculated based on the concerned temperature distribution, and when tensile stress is applied at need, in consideration of mechanical deformation amount due to the tensile stress, the distance is corrected to achieve the above problem. <P>COPYRIGHT: (C)2008,JPO&INPIT

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 environmental 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.
Japanese Patent Laid-Open No. 61-16805 JP-A-6-152596 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.

但し、α：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 includes the following (1), (2), and (3).
(1) A temperature measurement value at a fixed end and a moving end coupled to a ball bearing of a ball screw operating as a feed shaft, and a position of a threaded female screw, with a predetermined time interval (Δt) as a unit. Is input to the microcomputer at every elapsed time, the initial temperature (T ₀ ) before the operation of the ball screw and the temperature (T _out ) of the outside air are set as existing numerical requirements, and the time interval (Δt) is used as a unit. The temperature (T _{i, t} ) in each division unit (i-th division unit from the fixed end) divided by the elapsed time and a predetermined unit interval width (Δx) The amount of frictional heat that flows into each section unit along the length of the ball screw, the amount of heat that flows from adjacent section units, and the amount of heat released by convection from each position to the outside air With A temperature distribution calculation method for a ball screw in operation based on calculating a heat distribution of each division unit by a microcomputer using a difference equation based on balance.
(2) A temperature measurement value at the position of the fixed end and the moving end connected to the ball bearing of the ball screw operating as the feed shaft and the screwed screw is expressed in units of a predetermined time interval (Δt). Is input to the microcomputer at every elapsed time, the initial temperature (T ₀ ) before the operation of the ball screw and the temperature (T _out ) of the outside air are set as existing numerical requirements, and the time interval (Δt) is used as a unit. The temperature (T _{i, t} ) in each division unit (i-th division unit from the fixed end) divided by the elapsed time and a predetermined unit interval width (Δx) The amount of frictional heat that flows into each section unit along the length of the ball screw, the amount of heat that flows from the adjacent section units, and the amount of heat released by convection from each position to the outside air , Release A temperature distribution calculation method for a ball screw in operation based on calculating a heat distribution of each division unit by a microcomputer using a difference equation based on a balance with a heat radiation amount due to heat transfer.
(3) When no tensile stress (tension) is applied to the ball screw in advance, the length of the ball screw in each section unit is determined based on the temperature distribution of each section unit described in (1) and (2) above. The amount of increase in the distance from the fixed end (ΔL _1i ) is calculated by the microcomputer based on the following formula, and the distance from the fixed end of the specified division unit is reduced by the amount of the increase in the distance. Displacement correction method for a ball screw in operation based on

Where α is the coefficient of thermal expansion of the 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.

  In general, a temperature change in time and space when a heat source is present in a predetermined object is expressed by a heat conduction equation based on partial differentiation between time and length.

  However, instead of the partial differential equation, it is a conventional means in heat conduction engineering to obtain a temperature change of a predetermined space by a differential equation obtained by dividing the space of the object by a predetermined unit length and unit time.

  The basic method of the present invention is to apply such a differential equation solution along the length direction of the ball screw 1.

The temperature at which the predetermined division unit i (i-th division unit from the fixed end 11) rises during the predetermined time interval (Δt) depends on the amount of heat necessary for the increase in the temperature. Outline,
It can be calculated by the amount of heat transmitted due to friction with the female screw 2 + the amount of heat flowing in from adjacent unit units (i−1 and i + 1 unit units) −the amount of heat dissipated to the outside air.

  However, the amount of heat dissipated to the outside air includes the amount of heat released by convection to the outside air and the amount of heat released by radiant heat transfer to the outside air. However, in the basic configuration (1), only the former is subject to calculation. The latter is not subject to calculation because the degree of contribution is small.

である。 Here, when ρ is the density (kg / m ³ ) of the ball screw 1, c is the specific heat (J / kgK) of the ball screw 1, and V is the volume of each division unit, FIG. as shown in b), a between segmental unit i is from time t at time t + Delta] t, the amount of heat required to raise the temperature T _i, from _t the temperature T _i, in _{t + Delta] t} is

It is.

が成立する。 On the other hand, the total a thermal resistance between the frictional heating surface and the ball screw 1 R ₁ (K / W), the thermal resistance between the frictional heating surface and the female screw 2 R ₂ (K / W), which is generated per unit time by friction The amount of heat is Q (W), of which the amount of heat transmitted to the ball screw 1 side per unit time is Q ₁ (W), the amount of heat transmitted to the female screw 2 side per unit time is Q ₂ (W), and the friction the temperature at the surface and T _B, when the temperature of the internal thread 2 side was T _mn is

Is established.

を得ることができる。 If it erased the temperature T _B in the friction surface,

Can be obtained.

Thus, the amount of frictional heat (Q) generated per unit time can be obtained by the following relational expression based on actual measurement recommended by the ball screw manufacturer.
Q = 0.12πnqf (n)
However,
n: Ball screw rotation speed (rpm)
f (n): a linear approximate expression of f (n) = cn + d with the ball screw rotation speed n as a variable, where c and d are coefficients obtained by experiment q: coefficient related to frictional heat obtained by measurement Female thread 2 The amount of heat transferred to the unit of division i by friction with the unit unit i per unit time is equal to the above Q _{1. As a result} , the amount of heat per unit time transmitted to the unit of division i by friction with the female screw 2 is as follows:
Q ₁ = {0.12πnqf (n) + (T _mn −T _{i, t} ) / R ₂ } / (1 + R ₁ / R ₂ )
Can be obtained.

である。 When _AD is the sectional area of the sectional unit (actually, the average sectional area of the ball screw: m ² ) and λ is the thermal conductivity (W / mK) of the ball screw 1, it is adjacent to the sectional unit i. The amount of heat flowing from the division units i-1 and i + 1 is

It is.

When A ₀ is the surface area (m ² ) of each division unit i and h is the heat transfer coefficient (W / m ² K) from the surface of the division unit to the outside air, the heat release obtained by convection to the outside air is , A ₀ h (T _{i, t} −T _out ).

前記（２）の基本構成は、前記（１）の基本構成に区分単位から外気への放射伝熱による熱放射量を加味している点において相違している。 Therefore, in the embodiment of the basic configuration (1), the following general formula can be derived.

The basic configuration (2) is different from the basic configuration (1) in that the amount of heat radiation due to radiant heat transfer from the division unit to the outside air is added.

  The amount of radiation due to such radiant heat transfer is ignored when the ball screw 1 reaches a relatively high temperature due to heat generation (actually, when it reaches 70 ° C. or higher) and when the surface area of the ball screw 1 is large. Since it is not possible, the basic configuration (2) is effective in such a case.

…(ｂ)
基本構成（１）に立脚している（ａ）の差分方程式及び基本構成（２）に立脚している（ｂ）の差分方程式の解法は、何れも同一であるので、後者を順次解法するプロセスについて説明する。 Therefore, based on the basic configuration (2), the differential equation that is actually adopted is that epsilon is the emissivity of the division unit and σ is the Stefan-Boltzmann constant (about 5.67 × 10 ⁻⁸ W / m ² K ⁴ ). In this case, it is expressed by the following difference equation.

... (b)
Since the difference equations of (a) based on the basic configuration (1) and the difference equations of (b) based on the basic configuration (2) are the same, the latter is sequentially solved. Will be described.

In the initial stage (t = 0) when the ball screw 1 starts to rotate,
T _{i, t} = T _{i-1, t} = T _{i + 1} = T _out
With the time interval Δt as a unit, the temperatures T _{0, t} , T _{N + 1, t} , and T _mn at the end of the ball screw 1 can be obtained by actual measurement as time elapses, and Q _{1 of} the first term on the right side of the equation (b) can also be calculated every time based on the time interval Δt by the equation [Equation 4].

…(ｂ)'
前記(ｂ)'式のうち、Ｔ_0,2Δt及びＴ_0,Δt、Ｔ_ｍｎは何れも実測によって判明している以上、前記(ｂ)'式から、Ｔ_1,Δtを得ることが可能となる（尚、前記(ｂ)'式において、（ｂ）式のＴ_i-1,tに対応する部分は、端部の外側であることから、Ｔ_outによって代置している。）。 Specifically, T _0,0 = T _{N + 1,0} = T _out at the end, but T _{0, Δt} , T _{N + 1, Δt} , T _mn after the time interval Δt has elapsed. Is obtained by actual measurement and input to the microcomputer, and therefore, for the end T _{0, Δt} and its adjacent T _{1, Δt} , the following differential equation is obtained from the equation (b). It will be established.

... (b) '
Among the expressions (b) ′, T _0,2Δt and T _{0, Δt} , T _mn are all found by actual measurement, so that T _{1, Δt} can be obtained from the expression (b) ′. (In the equation (b) ′, the portion corresponding to T _{i−1, t} in the equation (b) is outside the end portion, and is replaced by T _out ).

From T _0,3Δt and T _0,2Δt at the next end, T _1,2Δt can be calculated in the same manner as in the equation (b) ′.

Similarly, since the measured values of T _0,2Δt , T _0,3Δt and each T _mn at the stage when the unit time intervals 2Δt and 3Δt have elapsed are _known , similarly to the equation (b) ′, T _{1 , 3Δt} can be calculated.

…(ｂ)”
前記(ｂ)”式においては、Ｔ_2,Δt以外は全て、既知の数値であることから、Ｔ_2,Δtを算定することが可能となる。 Thus, by determining T _1,2Δt and T _{1, Δt} , the following T _{0, Δt} , T _1,2Δt , and T _{2, Δt} are expressed as follows based on the above equation (b) ′. The formula is established.

... (b) "
In the expression (b) ”, all except T _{2, Δt} are known numerical values, so that T _{2, Δt} can be calculated.

On the other hand, T _1,3Δt can be calculated in the same manner as in the equation (b) ′. _Therefore , T _2,2Δt can also be calculated in the same manner as in the equation (b) ″.

The temperature T _{i, t} of the division unit i according to the above (b) ′, (b) ″, etc. is the temperature for each elapsed time of the fixed end 11 for the division unit located between the fixed end 11 and the female screw 2. Although it is assumed that T _{0, t} is a known actual measurement value, the temperature T _{N +} at the movable end 12 can be obtained even when the division unit i is located between the female screw 2 and the movable end 12. If it is assumed that _{1, t} is a known actual measurement value, it will not be explained again that T _{i, t} can be calculated similarly.

In this way, the time (t = s · Δx, for the division unit i in the difference equation of the above-mentioned formula (b) sequentially for each position by the time interval Δt and the unit interval width Δx. However, it is possible to calculate T _{i, t} when s is an arbitrary positive integer).

Thus, in the basic configurations (1) and (2), instead of the complicated method of elucidating the partial differential equation in the ball screw 1, the measured temperature values at the fixed end 11 or the movable end 12 and the female screw 2 are obtained. By inputting to the computer every time when a predetermined time interval Δt has elapsed, the temperature T _{i, t} in an arbitrary division unit i is calculated for the elapsed time with the time interval Δt as a unit by a relatively simple difference equation. It has technical features in the possible points.

したがって、このような固定端１１からの距離の増加量ΔＬ_1iに基づいて、基本構成（３）においては、当該距離の増加量（ΔＬ_1i）だけ指定位置に該当している区分単位の固定端１１からの距離を小さくすることに基づく変位の補正を実現している。 When the temperature T _{i, t} in each division unit i is calculated based on the basic configurations (1) and (2), the difference ΔT _{i, t} = T _{i, t} −T from the initial temperature T ₀ is calculated. _{As a} matter of course, ₀ is calculated. Therefore, when the thermal expansion coefficient is α, the increase in distance from the fixed end 11 (ΔL _1i ) can be calculated as follows.

Therefore, based on the increase amount ΔL _1i of the distance from the fixed end 11, in the basic configuration (3), the fixed end of the segment unit corresponding to the designated position by the increase amount of the distance (ΔL _1i ). Displacement correction based on reducing the distance from 11 is realized.

  In the present invention, it is assumed that the temperature at the fixed end 11 and the movable end 12 is measured every time in units of the time interval Δt, but the measurement is performed on the fixed end 11 and the movable end 12. The temperature of the fixed part of the ball bearing is measured, and the temperature of the rotating fixed end 11 and movable end 12 is calculated by multiplying the measured value by a predetermined correction coefficient obtained by a prior experiment. Yes.

The displacement correction method of the basic configuration (3) reflects the temperature distribution of each division unit as in the basic configuration (1) and (2), so the accurate distance displacement (ΔL _1i ) is calculated. This enables extremely accurate and appropriate correction.

  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.

In Example 1, when a tensile stress (tension) is applied to the ball screw 1 in advance, the increase in the overall length caused by the heat generated by the method of claim 5 (the total number of division units is calculated). When N, ΔL _1N in the formula of claim 5 is compared with the increase in the overall length based on the tensile stress (ΔL ′), and the former exceeds the latter (ΔL _1N > ΔL ′ In the case), based on the following general formula, the amount of increase in the distance from the fixed end 11 (ΔL _2i ) is calculated by the microcomputer, and the distance from the fixed end 11 of the designated division unit is increased in the distance. A displacement correction method for the ball screw 1 in operation based on reducing it by the amount (ΔL _2i ) is employed.
ΔL _2i = ΔL _1i −i · ΔL ′ / N
Note that i · ΔL ′ / N in the second term on the right-hand side of the length increase amount (ΔL ₂ ) is the distance from the fixed end 11 and the total length ( It originates from the experience side that it is roughly proportional to the ratio (i / N) to L).

  The correction method when a tensile stress (tension) is applied to the ball screw 1 is not limited to the above method, and there are other correction methods.

但し、

（ΔＴ_k,t＞ΔＴの場合）

（ΔＴ_k,t≦ΔＴの場合）
上記補正方法は、発熱による全体の距離の増加量（ΔＬ_1Ｎ）と引張応力による距離の増加量（ΔＬ’）とを対比している訳ではない以上、前者が後者よりも大きい場合についても、固定端１１からの距離の増加量ΔＬ_2ｉが算定される場合があるが、特に前者と後者との差が大きくない場合には、実際の補正に格別の支障が生じている訳ではない。 That is, in Example 1, as another correction method, when a tensile stress (tension) is applied to the ball screw 1 in advance, a temperature change (ΔT) corresponding to the tensile stress is used as the tensile stress. The total increase in length (ΔL ′) is calculated by dividing by the quantity (αL) obtained by multiplying the thermal expansion coefficient (α) and the overall length (L) (ΔT = ΔL ′ / ( αL)), the temperature increment (ΔT _i = T _{i, t} −T ₀ ) in each division unit is compared with the temperature change (ΔT) corresponding to the tensile stress, and the former is larger than the latter (ΔT). _In accordance with the following general formula that depends on whether or not _i > ΔT), the amount of increase in distance (ΔL _2i ) from the fixed end 11 in a predetermined section unit is calculated by the microcomputer, and the specified position is fixed. The distance from the end 11 is the amount of increase in the distance (ΔL _{2 i} ) The displacement correction method for the ball screw 1 in operation based on making it smaller is also adopted.

However,

(When ΔT _{k, t} > ΔT)

(When ΔT _{k, t} ≦ ΔT)
The above correction method does not compare the total distance increase due to heat generation (ΔL _1N ) and the distance increase due to tensile stress (ΔL ′), so that the former is larger than the latter. In some cases, the increase amount ΔL _2i of the distance from the fixed end 11 may be calculated. However, particularly when the difference between the former and the latter is not large, the actual correction does not cause any particular trouble.

  As described above, in the first embodiment, it is possible to execute a very appropriate correction command in the ball screw 1 to which a tensile stress (tension) is applied in advance.

  When a tensile stress (tension) is applied to the ball screw 1 as in the first embodiment, the mechanical device supporting the ball screw 1 via the fixed end 11 is deformed due to the tensile stress. In some cases, the position of the fixed end 11 may be displaced in the length direction on the pulled side.

In such a case, as in the first embodiment, when the amount of displacement is set to a while taking into account the comparison with the total length increase (ΔL ′) based on the tensile stress (tension), FIG. 1, since the position of the ball screw 1 has moved by a as a whole, the actual position is reduced by [a / Δx], so the position of i is actually set to i− [a / It is essential to perform a correction such as Δx].
(However, [] is a so-called Gaussian symbol, [a / Δx] represents the integer part of the numerical value by a / Δx, and i is expressed as N + [a / Δx] can be selected.)

ボールネジ１において、引張応力（テンション）が加えられることによって機械的変形が生じた場合の補正方法は、前記方法のみに限定される訳ではなく、他の補正方法も存在する。 That is, in Example 2, the position of the fixed end 11 is displaced by the displacement amount a in the length direction on the side where the tension is applied to the ball screw 1 in advance because tensile stress is applied in advance. In the case, the increase in the total length due to heat generation (in the mathematical formula of claim 5, the increase in distance from the fixed end 11 (ΔL _1N ) and the tensile stress when the total number of division units is N. If the former exceeds the latter (when ΔL _1N > ΔL ′), the fixed length of the predetermined division unit is fixed based on the following general formula. Displacement correction in the ball screw during operation based on calculating the increase amount (ΔL _3i ) of the distance from the end by the microcomputer and reducing the distance from the fixed end 11 at the specified position by the increase amount (ΔL _3i ) of the distance. Adopt the method That.

In the ball screw 1, the correction method in the case where mechanical deformation is caused by applying a tensile stress (tension) is not limited to the above method, and other correction methods exist.

但し、

（ΔＴ_k,t＞ΔＴの場合）

（ΔＴ_k,t≦ΔＴの場合）
（但し、〔 〕は、所謂ガウス記号であって、〔ａ／Δｘ〕は、ａ／Δｘによる数値のうちの整数部分を表しており、かつｉは、〔ａ／Δｘ〕から、Ｎ＋〔ａ／Δｘ〕の数値を選択することができる。
上記補正方法もまた、発熱による全体の距離の増加量（ΔＬ_1Ｎ）が引張応力による距離の増加量（ΔＬ’）とを対比している訳ではない以上、前者が後者よりも大きい場合についても、固定端１１からの距離の増加量ΔＬ_2ｉが算定される場合があるが、特に前者と後者との差が大きくない場合には、実際の補正に格別の支障が生じている訳ではない。 That is, in the second embodiment, as another correction method,
When the position of the fixed end 11 is displaced by a displacement amount a in the length direction due to a tensile stress (tension) being applied to the ball screw 1 in advance, a temperature change corresponding to the tensile stress ( ΔT) is calculated by dividing the increase in overall length (ΔL ′) based on the tensile stress by the quantity (αL) obtained by multiplying the thermal expansion coefficient (α) by the overall length (L). (ΔT = ΔL ′ / (αL)), and the temperature increment (ΔT _i = T _{i, t} −T ₀ ) in each segment unit is compared with the temperature change (ΔT) corresponding to the tensile stress, In accordance with the following general formula that depends on whether or not the former is greater than the latter (ΔT _i > ΔT), the amount of increase in the distance (ΔL _3i ) from the fixed end 11 in a predetermined section unit is determined by the microcomputer. Calculated from the fixed end 11 of the specified position. The release may be employed a displacement correction method of the ball screw running based to minimize the increase of the distance ([Delta] L _3i).

However,

(When ΔT _{k, t} > ΔT)

(When ΔT _{k, t} ≦ ΔT)
(However, [] is a so-called Gaussian symbol, [a / Δx] represents the integer part of the numerical value by a / Δx, and i is expressed as N + [a / Δx] can be selected.
Also in the above correction method, the amount of increase in the total distance due to heat generation (ΔL _1N ) does not compare with the amount of increase in distance due to tensile stress (ΔL ′), so that the former is larger than the latter. In some cases, the increase amount ΔL _2i of the distance from the fixed end 11 may be calculated. However, particularly when the difference between the former and the latter is not large, there is no particular problem in actual correction.

  As described above, in the second embodiment, it is possible to execute a very appropriate correction command even for the female screw 2 in which mechanical deformation has occurred due to tensile stress (tension).

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

BRIEF DESCRIPTION OF THE DRAWINGS It is a side view explaining the basic principle of this invention, (a) has shown the condition at the time t of both ends, female thread, and each division unit, (b) has shown the situation of time t + (DELTA) t about both ends and female thread. Is shown. The white arrow in the horizontal direction indicates that the female screw can move in both directions.

Explanation of symbols

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

Claims (9)

Elapsed time in units of a predetermined time interval (Δt) for temperature measurement values at the fixed end and the moving end connected to the ball bearing of the ball screw operating as the feed shaft and the screwed screw Each time, the initial temperature (T ₀ ) before the operation of the ball screw and the temperature of the outside air (T _out ) are set as existing numerical requirements, and the elapsed time in units of the time interval (Δt) The temperature (T _{i, t} ) in each division unit (i-th division unit from the fixed end) divided by a predetermined unit interval width (Δx) is used for the degree of temperature rising at each time interval and the movement of the female screw. Based on the balance between the amount of frictional heat flowing into each section unit along the length direction of the ball screw, the amount of heat flowing from adjacent section units, and the amount of heat released by convection from each position to the outside air A temperature distribution calculation method for a ball screw in operation based on calculating a heat distribution of each division unit by a microcomputer using a difference equation based on the system. 2. The temperature distribution calculation method for a ball screw in operation according to claim 1, wherein the difference equation is as follows.
Record

However,
T _{i, t} : temperature of the i-th element at time t (K)
T _{i, t + Δt} : temperature of the i-th element at time t + Δt (K)
A ₀ : Surface area of division unit (heat radiation area to outside air) (m ² )
A _D : sectional area of section unit (heat conduction area between elements) (m ² )
λ: Thermal conductivity of ball screw (W / mK)
ρ: Ball screw density (kg / m ³ )
c: Ball screw specific heat (J / kgK)
V: Ball screw element volume (m ³ )
h: Heat transfer coefficient from the surface of the division unit to the outside air (W / m ² K)
T _mn : female screw temperature (K)
R ₁ : Thermal resistance between the frictional heating surface and the ball screw element (K / W)
R ₂ : Thermal resistance between the frictional heating surface and the female screw (K / W)
Q ₁ : Of the amount of frictional heat generated per unit time by the movement of the female screw, the amount of heat (W) transmitted to the ball screw,

In the above equation, f (n) is a linear approximate expression of f (n) = cn + d with the ball screw rotation speed n as a variable, c and d are constants obtained by experiments, and q is an actual measurement. Is a coefficient related to the frictional heat obtained by. Elapsed time in units of a predetermined time interval (Δt) for temperature measurement values at the fixed end and the moving end connected to the ball bearing of the ball screw operating as the feed shaft and the screwed screw Each time, the initial temperature (T ₀ ) before the operation of the ball screw and the temperature of the outside air (T _out ) are set as existing numerical requirements, and the elapsed time in units of the time interval (Δt) The temperature (T _{i, t} ) in each division unit (i-th division unit from the fixed end) divided by a predetermined unit interval width (Δx) is used for the degree of temperature rising at each time interval and the movement of the female screw. On the basis of the length direction of the ball screw, the amount of frictional heat flowing into each section unit, the amount of heat flowing from the adjacent section unit, the amount of heat radiated by the convection from each position to the outside air, and the radiation transmission heat Calculation method of temperature distribution in ball screw during operation based on calculating heat distribution of each division unit by microcomputer using difference equation based on balance with heat radiation by. 4. The temperature distribution calculating method for a ball screw in operation according to claim 3, wherein the difference equation is as follows.
Record

However,
T _{i, t} : temperature of the i-th element at time t (K)
T _{i, t + Δt} : temperature of the i-th element at time t + Δt (K)
A ₀ : Surface area of division unit (heat radiation area to outside air) (m ² )
A _D : sectional area of section unit (heat conduction area between elements) (m ² )
λ: Thermal conductivity of ball screw (W / mK)
ρ: Ball screw density (kg / m ³ )
c: Ball screw specific heat (J / kgK)
V: Ball screw element volume (m ³ )
h: Heat transfer coefficient from the surface of the division unit to the outside air (W / m ² K)
ε: Emissivity of section unit surface σ: Stefan-Boltzmann constant (5.67 × 10 ^-8 W / m ² K ⁴ )
T _mn : female screw temperature (K)
R ₁ : Thermal resistance between the frictional heating surface and the ball screw element (K / W)
R ₂ : Thermal resistance between the frictional heating surface and the female screw (K / W)
Q ₁ : Of the amount of frictional heat generated per unit time by the movement of the female screw, the amount of heat (W) transmitted to the ball screw,

In the above equation, f (n) is a linear approximate expression of f (n) = cn + d with the ball screw rotation speed n as a variable, c and d are constants obtained by experiments, and q is an actual measurement. Is a coefficient related to the frictional heat obtained by. When a tensile stress (tension) is not applied to the ball screw in advance, the fixed end of the length of each ball screw unit according to the temperature distribution of each unit of claim 1, 2, 3, 4 The amount of increase in distance (ΔL _1i ) is calculated by the microcomputer based on the following formula, and the distance from the fixed end of the specified division unit is reduced by the amount of increase in the distance. Displacement correction method for ball screw in operation based on

Where α is the coefficient of thermal expansion of the ball screw When a tensile stress (tension) is applied to the ball screw in advance, the increase in the overall length caused by the heat generated by the method of claim 5 (when the total number of division units is N, claim) (ΔL _1N ) in Formula 5 and the increase in the overall length based on the tensile stress (ΔL ′) are compared, and when the former exceeds the latter (when ΔL _1N > ΔL ′), the following general Based on the formula, the amount of increase in the distance from the fixed end (ΔL _2i ) is calculated by the microcomputer, and the distance from the fixed end of the designated division unit is reduced by the amount of increase in the distance (ΔL _2i ). Displacement correction method for ball screw in operation based on
ΔL _2i = ΔL _1i −i · ΔL ′ / N When a tensile stress (tension) is applied to the ball screw in advance, the temperature change (ΔT) corresponding to the tensile stress is calculated as the total length increase (ΔL ′) based on the tensile stress. Calculated by dividing the expansion coefficient (α) by the total length (L) by the quantity (αL) (ΔT = ΔL ′ / (αL)), and the temperature increment (ΔT _i ) in each division unit = T _{i, t} −T ₀ ) and the temperature change (ΔT) corresponding to the tensile stress, and the following depends on whether the former is larger than the latter (ΔT _i > ΔT) In accordance with the general formula, the amount of increase in the distance from the fixed end (ΔL _2i ) in a predetermined segment unit is calculated by the microcomputer, and the distance from the fixed end of the designated position is the amount of increase in the distance (ΔL _2i ). Bolnet in operation based on making it smaller Displacement correction method in.

However,

(When ΔT _{k, t} > ΔT)

(When ΔT _{k, t} ≦ ΔT) When the tensile force (tension) is applied to the ball screw in advance, when the position of the fixed end is displaced by the displacement amount a in the length direction on the pulled side, the entire cause caused by heat generation Amount of increase in length (In the formula of claim 5, when the total number of division units is N, the amount of increase in distance from the fixed end (ΔL _1N ) and the amount of increase in the total length based on tensile stress (ΔL ′ ), And when the former exceeds the latter (when ΔL _1N > ΔL ′), based on the following general formula, the amount of increase in the distance from the fixed end of the predetermined segment unit (ΔL _3i ) Is calculated by the microcomputer, and the displacement correction method for the ball screw in operation is based on reducing the distance from the fixed end of the designated position by the increase amount (ΔL _3i ) of the distance.

(However, [] is a so-called Gaussian symbol, [a / Δx] represents the integer part of the numerical value by a / Δx, and i is expressed as N + [a / Δx] can be selected.) A temperature change corresponding to the tensile stress (ΔT) when the position of the fixed end is displaced by a displacement amount a in the length direction because a tensile stress (tension) is previously applied to the ball screw. Is calculated by dividing the increase in overall length (ΔL ′) based on the tensile stress by the quantity (αL) obtained by multiplying the thermal expansion coefficient (α) by the overall length (L) ( ΔT = ΔL ′ / (αL)), a temperature increase in each division unit (ΔT _i = T _{i, t} −T ₀ ) and a temperature change corresponding to the tensile stress (ΔT) are compared. In accordance with the following general formula which depends on whether or not the latter is larger (ΔT _i > ΔT), the microcomputer increases the amount of increase in distance from the fixed end (ΔL _3i ) by a microcomputer. , The distance from the fixed end of the specified position Increment ([Delta] L _3i) by a displacement correction method of the ball screw running based on reducing.

However,

(When ΔT _{k, t} > ΔT)

(When ΔT _{k, t} ≦ ΔT)
(However, [] is a so-called Gaussian symbol, [a / Δx] represents the integer part of the numerical value by a / Δx, and i is expressed as N + [a / Δx] can be selected.)

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