WO2010050281A1 - Motion guide device, and screw device - Google Patents

Abstract

Provided is a motion guide device, which can enlarge the contact area between a roller and a rolling face and can prevent an edge load and a peak contact stress from occurring at the portion where the roller and the rolling face contact each other.  As viewed in a section containing the center line of a roller (3), a rolling face (1b) and a load rolling face (4d) are crowned with a clothoid curve or elliptical curve which has a curvature varied in proportion to the length of the curve and protrudes toward the roller (3).  By forming a crowning shape with a clothoid curve or an elliptical curve, the central portion of the roller (3) in the center line direction can be crown-padded, and the crowned depth can be increased at the end portions of the roller (3) in the center line direction.  Hence, the roller (3) is prevented from causing the edge load, and the contact areas can be retained between the roller (3), and the rolling face (1b) and the load rolling face (4d).

Description

Motion guide device and screw device

The present invention relates to a motion guide device that guides a moving body such as a table in a linear or curved motion, and more particularly to a motion guide device that uses a roller as a rolling element. The present invention also relates to a screw device in which a roller is interposed as a rolling element between a screw shaft and a nut.

2. Description of the Related Art As a motion guide device that guides a moving body to make a linear or curved motion, a motion guide device including a track rail and a moving block that moves along the track rail is known. In order to reduce resistance when the moving block is moved, a large number of rolling elements are interposed between the track rail and the moving block so as to allow rolling motion. The rolling element may be a spherical ball or a cylindrical roller. In a motion guide device using a roller as a rolling element, a cylindrical roller and a flat roller rolling surface are in line contact, and the contact area can be increased. Therefore, a motion guide device using a ball as a rolling element The load capacity can be increased compared to

However, it is known that when the roller and the roller rolling surface are in line contact, peak contact stress, that is, edge load, is generated at the contact portion between the end of the outer peripheral surface of the roller in the center line direction and the roller rolling surface. It has been. When edge loading occurs, premature wear and flaking occur on the outer peripheral surface of the roller and the roller rolling surface. For this reason, various techniques for preventing the occurrence of edge loading have been developed in motion guide devices using rollers.

For example, Patent Document 1 discloses a motion guide device in which both ends in the center line direction of the outer peripheral surface of a roller are crowned. The crowning is formed in a circular arc curve whose diameter gradually decreases toward the end face of the roller when viewed in a cross section including the center line of the roller.

Patent Document 2 discloses a motion guide device in which a full crowning formed of a single circular arc curve is formed on a roller rolling surface of a track rail and a moving block.

Further, Patent Document 3 discloses a motion guide device in which a crowning formed of a logarithmic curve is formed on the roller rolling surface of the track rail and the moving block.

JP 2005-163882 A JP 2008-106873 A JP 2007-211182 A

However, as a result of stress analysis using FEM (Finite Element Method), in the motion guide device described in Patent Document 1 in which arc-shaped crowning is formed at both ends of the roller, It was found that a large contact stress occurred at the boundary with the crowned arc part. It is presumed that the cause is that the shape of the outline of the roller suddenly changes at the joint between the straight line portion and the arc portion. When a large contact stress is generated at the boundary, the roller and the roller rolling surface are prematurely worn and flaking occurs as in the case of edge load.

In the motion guide device described in Patent Document 2 in which a full crowning formed of a single circular arc curve is formed on the roller rolling surface, there is no boundary between the portion subjected to crowning and the portion not subjected to crowning, High contact stress does not occur at the boundary. However, since the contact state between the roller and the roller rolling surface is close to the contact state between the ball and the ball rolling surface, the advantages of using the roller as the rolling element cannot be fully utilized.

In the motion guide apparatus described in Patent Document 3 in which a crowning formed of a logarithmic curve is formed on a roller rolling surface, an extremely complicated logarithm that makes the contact stress acting on the roller and the rolling surface of the roller constant. Since it is necessary to design a curve, there is a problem that it becomes difficult to design and process the crowning. In addition, since the roller contacts the roller rolling surface up to the end of the outer peripheral surface of the roller in the center line direction, there is a problem that an edge load occurs.

Therefore, the present invention can increase the contact area between the roller and the roller rolling surface, and can prevent edge load and peak contact stress from occurring at the portion where the roller and the roller rolling surface are in contact with each other. An object is to provide a motion guide device and a screw device.

The present invention will be described below.
In order to solve the above-described problem, an aspect of the present invention includes a track rail having a roller rolling surface, a load roller rolling surface facing the roller rolling surface of the track rail, and the track rail. A moving block that is assembled so as to be relatively movable, and a plurality of rollers interposed between the roller rolling surface of the track rail and the load roller rolling surface of the moving block so as to be capable of rolling. In at least one of the roller rolling surface, the load roller rolling surface, and the roller, the curvature is proportional to the length of the curve when viewed in a section including the center line of the roller. It is a motion guide device in which the crowning of a convex clothoid curve is formed toward the contacted person.

Another aspect of the present invention includes a track rail having a roller rolling surface and a load roller rolling surface facing the roller rolling surface of the track rail, and is relatively movable with respect to the track rail. A motion guide device comprising: a moving block assembled to the roller rail; and a plurality of rollers interposed between the roller rolling surface of the track rail and the load roller rolling surface of the moving block so as to allow rolling motion. When viewed in a cross-section including the center line of the roller, at least one of the roller rolling surface, the loaded roller rolling surface, and the roller rolling surface and the roller contacting the loaded roller rolling surface, A motion guide device having a long axis in a direction parallel to the center line of the roller and a short axis in a direction perpendicular to the center line of the roller, and a convex elliptic curve crowning is formed toward a contacted partner. A.

Still another aspect of the present invention is a screw shaft having a spiral roller rolling surface on the outer peripheral surface, and a nut having a spiral load roller rolling surface facing the roller rolling surface of the screw shaft, In a screw device comprising a plurality of rollers interposed between the roller rolling surface of the screw shaft and the load roller rolling surface of the nut so as to be capable of rolling motion, in a cross section including a center line of the roller When viewed, at least one of the roller rolling surface, the loaded roller rolling surface, and the roller has a curvature that changes in proportion to the length of the curve, and has a convex clothoid curve that protrudes toward the contact partner. A screw device in which a crowning is formed.

Still another aspect of the present invention is a screw shaft having a spiral roller rolling surface on the outer peripheral surface, and a nut having a spiral load roller rolling surface facing the roller rolling surface of the screw shaft, In a screw device comprising a plurality of rollers interposed between the roller rolling surface of the screw shaft and the load roller rolling surface of the nut so as to be capable of rolling motion, in a cross section including a center line of the roller When viewed, the roller rolling surface, the loaded roller rolling surface, and at least one of the rollers in contact with the roller rolling surface and the loaded roller rolling surface, a direction parallel to the center line of the roller A screw device in which a long axis is a short axis in a direction perpendicular to the center line of the roller, and a convex elliptic curve crowning is formed toward a contact partner.

By forming crownoid curve or elliptic curve crowning, it is possible to increase the crowning depth at the center of the roller in the center line direction, while increasing the crowning depth at the end of the roller in the center line direction. Can do. Therefore, it is possible to secure the contact area between the roller and the roller rolling surface while preventing the edge load from being generated on the roller, and to fully demonstrate the capability of the roller, that is, a motion guide device and a screw device. The load capacity can be increased.

1 is a perspective view (including a partial cross-sectional view) of a motion guide device according to an embodiment of the present invention. Front view of the above exercise plan device (including a partial cross-sectional view) Cross section of roller rolling surface and load roller rolling surface Cross section of roller rolling surface and load roller rolling surface Model diagram of roller in contact with roller rolling surface Comparison diagram of crowning shape formed on roller rolling surface Diagram showing a general plane curve Diagram showing clothoid segment Principle diagram of clothoid interpolation using the tangential method Diagram showing basic clothoid function (fundamental clothoid function) Sectional drawing which shows the other example of a roller rolling surface Sectional view showing another example of track rail The perspective view of the roller screw of other embodiments of the present invention. Perspective view of the roller screw nut Side view showing a roller sandwiched between a screw shaft and a nut Perspective view of screw shaft and circulating member The figure which shows the contact stress which acts on the contact part of a roller and a roller rolling surface ((a) in a figure shows the comparative example 1 where a roller rolling surface is flat, (b) is circular arc crowning on a roller rolling surface. Shows comparative example 2) The figure which shows the contact stress which acts on the contact part of a roller and a roller rolling surface (Comparative example 3 which gave the single circular arc crowning to the roller rolling surface) Graph showing the relationship between crowning depth, maximum surface pressure and elastic approach (for elliptical crowning) Graph showing the relationship between crowning depth, maximum surface pressure, and elastic approach (for clothoid crowning) Graph comparing maximum surface pressure σmax Graph comparing elastic approach amount δ Flow chart for determining optimum shape and calculating allowable load Comparison diagram of crowning shape calculated so that maximum surface pressure of roller σmax = 4000MPa Graph showing contact surface pressure σmax and elastic approach amount δ change when roller load Q is gradually increased Comparison diagram showing surface pressure distribution

DESCRIPTION OF SYMBOLS 1 ... Track rail, 1b ... Roller rolling surface, 2 ... Moving block, 3 ... Roller, 3a ... Outer peripheral surface, 3b ... End surface, 3c ... Chamfer part, 4d ... Load roller rolling surface, 51 ... Screw shaft, 51a ... Roller rolling surface, 52 ... Nut, 52a ... Loaded roller rolling surface, 54 ... Roller

Hereinafter, a motion guide apparatus according to an embodiment of the present invention will be described with reference to the accompanying drawings. FIG. 1 shows a perspective view (including a partial cross-sectional view) of an exercise guide device using a roller as a rolling element, and FIG. 2 shows a front view (including a partial cross-sectional view) of the exercise plan device.

The motion guide device includes a linearly extending track rail 1 and a moving block 2 that is assembled to the track rail 1 through a plurality of rollers 3 as rolling elements.

The track rail 1 has a substantially square cross section. On the left and right side surfaces of the track rail 1, grooves 1a having a substantially V-shaped cross section are formed along the longitudinal direction. As shown in FIG. 2, the groove 1a has a pair of wall surfaces 1b and a bottom surface 1c. The pair of wall surfaces 1b of the groove 1a intersect each other at an angle of 90 degrees. Each of the upper wall surface 1b and the lower wall surface 1b becomes a roller rolling surface 1b on which the roller 3 rolls. For this reason, two roller rolling surfaces 1b are formed on the left and right side surfaces of the track rail 1 in the vertical direction.

The moving block 2 includes a horizontal portion 2a facing the upper surface of the track rail 1 and sleeve portions 2b extending downward from the left and right sides of the horizontal portion 2a and facing the left and right side surfaces of the track rail 1. As shown in FIG. 2, upper and lower two load roller rolling surfaces 4 d are formed on the sleeve portion 2 b of the moving block 2. The load roller rolling surface 4d of the moving block 2 and the roller rolling surface 1b of the track rail 1 constitute a load region of the roller circulation path. The sleeve 2b of the moving block 2 is provided with two upper and lower roller escape passages 7 in parallel with the load roller rolling surface 4d at a predetermined interval. This roller escape passage 7 constitutes a no-load region of the roller circulation path. Further, the sleeve portion 2b is provided with a U-shaped direction change path 8 for connecting the both ends of the load roller rolling surface 4d and the roller escape passage 7 and circulating the roller 3. The direction change path 8 is three-dimensionally crossed between the upper loaded roller rolling surface 4d and the lower roller escape passage 7 and between the lower loaded roller rolling surface 4d and the upper roller escape passage 7. Connecting. These loaded roller rolling surfaces 4d, the pair of direction changing paths 8, and the roller escape passage 7 constitute an annular roller circulation path. Each roller circulation path is formed in one plane, and the roller 3 circulates two-dimensionally in each roller circulation path. The plane on which one roller circulation path is located is orthogonal to the plane on which the other roller circulation path is located. One roller circulation path is arranged on the inner peripheral side of the other roller circulation path.

A protruding portion 4 c is formed on the sleeve portion 2 b of the moving block 2 and has a shape matched to the groove 1 a provided on the side surface of the track rail 1. Two protruding roller rolling surfaces 4d as load rolling element rolling portions corresponding to the roller rolling surface 1b are formed on the protruding portion 4c. The load roller rolling surface 4d is provided in total on the top and bottom of the left and right sleeve portions 2b of the moving block 2 in a total of four. In this embodiment, the roller rolling surface 1b and the load roller rolling surface 4d are formed in a total of four strips, two on each side, but the number of strips can be set variously depending on the type of motion guide device. Can do.

In the moving block 2, resin circulation path molded bodies 11, 12, 13, and 14 are incorporated. The circulation path molded bodies 11, 12, 13, and 14 extend along both side edges of the load roller rolling surface 4d, and when the moving block 2 is removed from the track rail 1, the roller 3 from the load roller rolling surface 4d. The holding member 11, 12, 13 that prevents falling off and the escape passage constituting member 14 that returns the roller 3 are configured.

FIG. 3 shows a sectional view of the loaded roller rolling surface 4d and the roller rolling surface 1b. A large number of rollers 3 that roll while receiving a load are interposed between the load roller rolling surface 4d and the roller rolling surface 1b facing each other. The holding members 11, 12, and 13 prevent the roller 3 from moving in the center line direction. That is, the holding members 11, 12, and 13 are formed with guide surfaces 41 that can contact the end surface of the roller 3 in the center line direction. The distance L + ΔL between the pair of guide surfaces 41 is set slightly longer than the length L of the roller 3 in the center line direction so that a clearance ΔL is generated. Each of the pair of guide surfaces 41 is formed with guide grooves 11a, 12a, and 13a for guiding a pair of connecting belts of the roller retainer 10 to be described later.

As shown in FIG. 2, the escape passage constituting member 14 is formed in a pipe shape, and has a guide hole 20 that matches the shape of the roller 3 inside, and a guide groove 20 a that guides the connecting belt of the roller retainer 10. Have As shown in FIG. 1, the rollers 3 are chained like a chain by a roller retainer 10. One roller retainer is accommodated in each of the four rows of roller circulation paths.

FIG. 4 shows the cross-sectional shapes of the roller rolling surface 1b and the loaded roller rolling surface 4d when viewed in a cross-section including the center line of the roller 3. On the roller rolling surface 1b and the loaded roller rolling surface 4d, a convex clothoid curve or an elliptic curve crowning is formed toward the roller 3 which is a contact partner. The roller 3 includes a cylindrical outer peripheral surface 3a, a pair of end surfaces 3b in the direction of the center line of the roller 3, and an arc-shaped chamfered portion 3c formed at an angle between the outer peripheral surface 3a and the end surface 3b.

Note that the same effect can be obtained by crowning the outer peripheral surface 3a of the roller 3 instead of the roller rolling surface 1b and the loaded roller rolling surface 4d. However, it is not suitable for mass production to process the crowning one by one on the large number of rollers 3. If the roller rolling surface 1b and the loaded roller rolling surface 4d are ground using a grindstone having a predetermined crowning shape, the roller rolling surface 1b and the loaded roller rolling surface 4d can be easily crowned.

FIG. 5 shows a model diagram of the roller 3 in contact with the roller rolling surface 1b. In the description of the crowning formed on the roller rolling surface 1b, an xy coordinate system is used in which the contour line of the roller 3 is the x-axis and the y-axis is in the direction perpendicular to the contour line. The crowning depth is represented by the y-axis value of the roller rolling surface 1b. The crowning is formed in line symmetry with respect to the y axis passing through the central portion O of the roller 3 in the center line direction, so that the origin is set at the central portion O of the roller 3 in the center line direction.

Fig. 6 shows a comparison of three types of crowning shapes under the same load. In this figure, the crowning shapes of the arc curve, elliptic curve, and clothoid curve are compared. The contour line of the roller 3 is indicated by the x axis, and the direction orthogonal to the x axis is indicated by the y axis. The clothoid curve and elliptic curve are closer to the x-axis origin than the arc curve (ie, the center of the roller), the tangential direction is closer to the horizontal direction, and away from the x-axis origin (ie, the end of the roller). Has a characteristic that the tangential direction inclines sharply from the horizontal direction. Therefore, the crowning meat can be piled up in the vicinity of the center portion of the roller 3 in the center line direction (shaded area in the figure), while the crowning depth λε can be increased at the end portion of the roller 3 in the center line direction. .

The following explains how to calculate clothoid curves and elliptic curves. First, the clothoid curve will be described. Clothoid curve, also known as Cornu'sClothspiral, is a curve whose curvature changes in proportion to the length of the curve. As described above, the crowning is formed symmetrically with respect to the y-axis. For this reason, in calculating the crowning of the clothoid curve, only one of the right clothoid curve and the left clothoid curve with respect to the y-axis need be obtained.

<Clothoid curve>
As shown in FIG. 7, generally, a plane curve can be expressed by the following integral formula.

ここで、Ｐは曲線上の点の位置ベクトル，Ｐ₀は始点の位置ベクトル，ｓはＰ₀からＰまでの曲線の長さ，φは接線方向角(rad)，ｊ＝√(-１)は虚数単位である。ｙ軸を虚軸に取るものとする。クロソイド曲線は方向φが長さｓの２次式で表わされる次式の曲線である。

Here, P is the position vector of the point on the curve, P ₀ is the position vector of the starting point, s is the length of the curve from P ₀ to P, φ is the tangential angle (rad), j = √ (−1) Is an imaginary unit. The y axis is taken as the imaginary axis. The clothoid curve is a curve of the following equation represented by a quadratic equation in which the direction φ is length s.

　φをsで微分したものが曲率c_v，その逆数が曲率半径ρである。曲率c_vを再びsで微分すると、曲率の変化率が得られる。これを縮率と呼び、c_uで表わす。クロソイド曲線の場合には、

Differentiating φ with respect to s is the curvature c _v , and its inverse is the curvature radius ρ. Differentiating with curvature c _v again s, the rate of change of curvature are obtained. This is called the reduction ratio and is represented by c _u . For clothoid curves,

となる。縮率c_uの一定な曲線がすなわちクロソイドである。

It becomes. A constant curve with a reduction ratio c _u is a clothoid.

One clothoid segment, that is, a finite partial clothoid curve, can be represented by four parameters: h, c ₀ , c ₁ , c ₂ . Where h is the length of the clothoid segment (mm), c ₀ is the initial direction (rad), c ₁ is the initial curvature (rad / mm), and c ₂ is half the reduction rate (rad / mm ² ) .

If this is the case, since c ₁ and c ₂ include the dimension of length, it is difficult to use due to the influence of the scale, so this is transformed as follows.

First, the dimensionless displacement S is defined.

At the start point s = 0, S = 0, and at the end point s = h, S = 1. At this time, the equations (1) to (4) become the following equations.

　終点P1におけるφの値をφ₁とすると、

When the value of phi at the end P1 and phi _1,

となる（図８参照）。すなわち、φ₀は初期方向（=C₀）,φ_vは長さhの曲線が初期曲率を持つ円弧であるときの接線角の増分（これを円弧増分と名付ける）,φ_uはこれにさらにクロソイド分が加わることによる接線角の増分（これをクロソイド増分と名付ける）である。

(See FIG. 8). That is, φ ₀ is the initial direction (= C ₀ ), φ _v is the increment of the tangent angle when the curve of length h is an arc with an initial curvature (this is called the arc increment), φ _u is It is the tangential angle increment due to the addition of the clothoid (this is termed the clothoid increment).

As described above, one clothoid segment can be represented by four parameters, that is, h, φ ₀ , φ _v , and φ _u . Here, only h is related to the size of the figure, and the other three are not related to the size, but only to the shape of the curve. A clothoid curve can be drawn by setting the above four parameters.

<Clothoid interpolation>
Given two points P ₀ (x ₀ , y ₀ ) and P ₁ (x ₁ , y ₁ ), consider a clothoid segment passing through these two points. Since the clothoid segment has four parameter degrees of freedom, two conditions can be satisfied in addition to the x increment (x ₁ -x ₀ ) and the y increment (y ₁ -y ₀ ). As the remaining two conditions, a tangential direction φ _{0 at the} start point and a tangential direction φ ₁ at the end point are given. That is, given the coordinates of two points P ₀ (x ₀ , y ₀ ), P ₁ (x ₁ , y ₁ ) and the tangential directions φ ₀ , φ _{1 of the} two points, a clothoid segment is obtained from these four conditions. FIG. 9 shows the principle of interpolation.

Thus, when φ ₀ and φ ₁ are given,

である。すなわち、φ_vとφ_uの和は既知である。

It is. That is, the sum of φ _v and φ _u is known.

Here, the formula for obtaining the end point coordinate P1 is transformed as follows.

とおくと、

After all,

 
　となる。式(14)は単位長さのクロソイドを示す基本式である。λ(=l/h)を弦弧比、Ψを視野角と名付ける（図９参照）。φ_vとφ_uが定まれば式(14)によりλとΨが求まるが、今の場合、式(11)によりφ_vとφ_uの和は既知なので、φ_vとφ_uのどちらか一方を与えることによって、λ及びΨが変化する。この関係の一例を示したのが図１０である。

It becomes. Formula (14) is a basic formula showing a unit length clothoid. Let λ (= l / h) be the string arc ratio and Ψ be the viewing angle (see FIG. 9). If φ _v and φ _u are determined, λ and Ψ can be obtained from equation (14). However, in this case, the sum of φ _v and φ _u is already known from equation (11), so either φ _v or φ _u can be obtained. To change λ and ψ. An example of this relationship is shown in FIG.

In FIG. 10, φ ₀ = 0, φ _v + φ _u = 60 °, and φ _v = −180 ° to + 180 °, giving 30 ° stepwise φ _v and showing a unit length clothoid curve. It was. From FIG. 10, the approximate tendency of λ and Ψ can be known.

  If Ψ is now considered to be a function of φ _v,

Obtaining the root of this function by giving the desired value of Ψ can be easily performed by a normal root search method.

In summary, when P ₀ , P ₁ , φ ₀ , and φ ₁ are given, the procedure for obtaining the four parameters of clothoid is as follows.
(1) φ ₀ is given.
(2) φ _v and the sum of φ _u is obtained.
(3) Search for φ _v (or φ _u ) such that the value of the viewing angle Ψ matches the given value. φ _u (or φ _v ) is obtained from the sum.
(4) h is determined from the given l and the value of λ calculated using the determined values of φ _v and φ _u .

The clothoid curve and clothoid interpolation are also described in Japanese Patent Laid-Open Nos. 6-168822, 6-259567, and 2000-82152 proposed by the applicant.

With the above clothoid interpolation, the coordinates P ₀ of the starting point, the coordinates P ₁ of the end point, tangential phi ₀ of the starting point, it is possible to obtain the clothoid curve tangentially phi ₁ of the end point. In this embodiment, as shown in FIG. 6, roller rolling is performed by giving a coordinate (0, 0) of the origin O as the start point coordinate P _{0 and a} predetermined crowning depth λε as the end point coordinate P _1. The coordinates (x _ε , λ _ε ) of the end of the surface 1b are given. Then, 0 ° (horizontal direction) is given as the tangent direction φ _{0 at the} start point, and a predetermined angle φ ₁ is given as the tangential direction φ _{1 at the} end point. This makes it possible to calculate the right clothoid curve with respect to the y-axis. The left clothoid curve with respect to the y-axis is formed symmetrically with respect to the right clothoid curve. The two clothoid curves have a continuous coordinate, tangential direction, and curvature at the origin O.

Here, an arbitrary clothoid curve can be drawn by arbitrarily setting the crowning depth λε and the tangential direction φ ₁ at the end of the roller rolling surface 1b. After drawing the clothoid curve, stress analysis using FEM is performed, and the roller rolling surface at the point b in the center line direction end of the roller 3 and the maximum surface pressure σmax at the contact portion between the roller 3 and the roller rolling surface 1b. Check for contact with 1b. Usually, a basic static load rating (allowable load) is determined based on a load that is an allowable surface pressure defined by the ISO standard. The load is changed (increased), the maximum surface pressure σmax becomes the allowable surface pressure of ISO, the point b of the roller 3 is not in contact with the roller rolling surface 1b, and the roller 3 and the roller rolling surface 1b It can be said that the shape when the distance from the contact position to point b is as close to 0 as possible is the optimal clothoid curve. However, there is no clothoid curve in the current ISO standard roller rolling surface shape. Only 4600 MPa is defined for the contact between the ball and the planar ball rolling surface, 4200 MPa is defined for the contact between the ball and the R-groove shaped ball rolling surface, and 4000 MPa is defined for the contact between the roller and the planar roller rolling surface. It is. Based on these, in the case of contact between the current roller and the roller rolling surface 1b of the clothoid curve, a range of about 4000 to 4200 MPa is considered appropriate.

As shown in FIG. 5, the maximum surface pressure σmax is the maximum pressure generated at the contact portion when a predetermined load Q (for example, Q = 2540N) is applied to the roller 3. The elastic approaching amount δ is an amount by which the roller 3 and the roller rolling surface 1b approach when an allowable load Q is applied to the roller 3. If the maximum surface pressure σmax is reduced under the same load, the contact area is large, and the elastic approach amount δ is also small. When obtaining the optimum shape based on the above, the elastic approach amount δ is also calculated for confirmation. However, when the maximum surface pressure σmax reaches the allowable surface pressure, it is a necessary condition for obtaining the optimum condition that the point b of the roller does not contact the roller rolling surface 1b.

In order to check that the point b of the roller does not contact the roller rolling surface 1b, it is also necessary to calculate the contact length Leff _{TED / CPA} , which is the length of the contact portion between the roller rolling surface 1b and the roller 3. . If the contact length Leff _{TED / CPA} is less than the length L1 in the direction of the center line of the outer peripheral surface 3a of the roller 3, the point b of the roller 3 will not contact the roller rolling surface 1b. Conversely, if the contact length LeffTED / CPA is equal to or greater than the length L1 in the direction of the center line of the outer peripheral surface 3a of the roller 3, the point b of the roller 3 comes into contact with the roller rolling surface 1b and an edge load occurs.

Next, the elliptic curve crowning will be described. As shown in FIG. 6, in the case of elliptic curve crowning, the major axis of the ellipse is taken in the x-axis direction parallel to the center line of the roller 3, and the minor axis of the ellipse is taken in the y-axis direction perpendicular to the center line of the roller 3. Take. Unlike the clothoid curve, the position where the crowning depth λε moves in the y-axis direction from the contact position (origin O) between the roller 3 and the roller rolling surface 1b is taken as the origin of the y-axis. Then, the elliptic curve is expressed by the following equation.

 
　ここで、λε：ローラ転走面１ｂの端部のクラウニング深さ，Ｘε：原点からのローラ転走面１ｂのｘ軸方向の長さ

Where λε is the crowning depth at the end of the roller rolling surface 1b, and Xε is the length in the x-axis direction of the roller rolling surface 1b from the origin.

An arbitrary elliptic curve can be drawn by arbitrarily setting the crowning depth λε at the end of the roller rolling surface 1b. After drawing the elliptic curve, the stress analysis using FEM is performed as in the case of the clothoid curve, the maximum surface pressure σmax and the contact length Leff _{TED / CPA} are calculated, and the optimal shape of the elliptic curve is obtained.

As described above, by forming a clothoid curve or an elliptic curve crowning on the roller rolling surface 1b, it is possible to fill the crowning meat at the center in the centerline direction of the roller 3, while the centerline of the roller 3 The crowning depth at the end in the direction can be increased. Therefore, it is possible to secure a contact area between the roller 3 and the roller rolling surface 1b while preventing the edge load from occurring on the roller 3. Therefore, it is possible to ensure the contact area between the roller 3 and the roller rolling surface 1b while preventing the edge load from being generated on the roller 3, and to fully demonstrate the capability of the roller 3, that is, the rolling element. As a result, the load capacity of the motion guide device using the roller 3 can be increased.

Further, by forming a clothoid curve or a single elliptic curve on the entire portion where the roller 3 and the roller rolling surface 1b and the loaded roller rolling surface 4d are in contact, peak contact stress is generated at the contact portion. Can be prevented. The same applies even if the roller 3 changes its relative position with respect to the roller rolling surface 1b and the load roller rolling surface 4d due to misalignment.

FIG. 11 shows an example in which a linear straight portion 1b1 is formed at the center of the roller rolling surface 1b, and a clothoid curve crowning 1b2 continuous to the straight portion 1b1 is formed on both sides of the linear portion 1b1. At the connection point C1 between the straight portion 1b1 and the crowning 1b2, the tangential direction and the curvature of the straight portion 1b1 and the crowning 1b2 are continuous. By forming a crowned curve crown 1b2 in which the tangential direction and curvature continuously change in the straight line portion 1b1, it is possible to smoothly change the contour shape of the roller rolling surface 1b, and the roller 3 and the roller rolling surface. It is possible to prevent the peak contact stress from being generated at the portion where the contact with 1b occurs.

Note that the present invention is not limited to the above-described embodiment, and can be applied to other embodiments without departing from the scope of the present invention. As described above, the roller rolling surface and the load roller rolling surface may be flattened and crowned. You may crown only either a roller rolling surface or a load roller rolling surface. You may crown all of a roller, a roller rolling surface, and a load roller rolling surface. In this case, a predetermined crowning depth may be taken between the roller, the roller rolling surface, and the load roller rolling surface.

Further, as shown in FIG. 12, the present invention can also be applied to a DF type motion guide device in which left and right protrusions of the track rail 1 are sandwiched between upper and lower rollers 3. Further, the present invention is also applicable to a roller spline using a roller as a rolling element, or a roller screw having a roller interposed between a roller rolling surface of a screw shaft and a load roller rolling surface of a nut so as to allow rolling motion. be able to.

FIG. 13 shows a perspective view of the roller screw. The roller screw includes a screw shaft 51 having a spiral roller rolling surface 51a formed on the outer peripheral surface, and a nut having a spiral load roller rolling surface 52a facing the roller rolling surface 51a on the inner peripheral surface. 52.

The screw shaft 51 is formed by cutting and grinding or rolling a spiral roller rolling surface 51a having a predetermined lead on the outer peripheral surface of a steel bar such as carbon steel, chrome steel, or stainless steel. . The roller rolling surface 51a has a V-shaped cross section and an opening angle of about 90 degrees (see FIG. 15). In this embodiment, two roller rolling surfaces 51 a are formed on the outer peripheral surface of the screw shaft 51. A plurality of rollers 54 are arranged in parallel on each of the two roller rolling surfaces 51a. Of course, the number of roller screws is appropriately determined depending on the application of the roller screw, such as one, two or three.

FIG. 14 is a perspective view of the nut 52. The nut 52 is formed by cutting and grinding or rolling a spiral load roller rolling surface 52a having a predetermined lead on the inner peripheral surface of a cylinder such as carbon steel, chrome steel, or stainless steel. is there. The load roller rolling surface 52a has a V-shaped cross section and an opening angle of about 90 degrees. A flange 52b for attaching the nut 52 to the mating part is formed at the end of the outer periphery of the nut 52 in the axial direction.

FIG. 15 shows the roller 54 sandwiched between the roller rolling surface 51 a of the screw shaft 51 and the loaded roller rolling surface 52 a of the nut 52. The roller 54 is cylindrical and has substantially the same diameter and length. The shape of the roller 54 viewed from the side surface is close to a square. The roller 54 includes a cylindrical outer peripheral surface 54c, a pair of spherical end surfaces 54a having a constant curvature radius R, and a chamfered portion 54d formed between the outer peripheral surface 54c and the end surface 54a.

The outer peripheral surface 54 c of the roller 54 is in contact with the roller rolling surface 51 a of the screw shaft 51 and the load roller rolling surface 52 a of the nut 52. When viewed in a cross section including the center line 54b of the roller 54, the roller rolling surface 51a and the loaded roller rolling surface 52a of the nut 52 have a clothoid curve or an elliptic curve that is convex toward the roller 54 that is the contact partner. Crowning is formed.

FIG. 16 shows the positional relationship between the circulation member 53 attached to the nut 52 and the screw shaft 51. Two sets of circulation members 53 are provided to circulate the rollers 54 that move on the two roller rolling surfaces 51a. The circulation member 53 includes a circulation pipe 58 that is inserted into a through-hole extending in the axial direction of the nut 52, and a pair of direction change path constituting members 62 that are attached to end portions in the axial direction of the circulation pipe 58. The circulation member 53 is formed with a no-load return path that connects one end and the other end of the load roller rolling path 56. The no-load return passage is formed in the circulation pipe 58, and extends straightly in parallel with the center line of the nut 52, and is connected to both ends of the straight passage and is a curve formed in the pair of direction change path constituent members 62. And a pair of direction change paths. The roller 54 that has rolled to one end of the load roller rolling path 56 is guided into the direction changing path of the circulation member 53, passes through the straight path, and then returns to the other end of the load roller rolling path 56 from the remaining direction changing path. It is.

As shown in FIG. 17, when the roller 3 having a diameter of 4.0 mm, a total length of 7.0 mm, and a length of the outer peripheral surface of the center line of 6.4 mm is used and the length of the roller rolling surface 1 b is 9 mm, Stress was analyzed. For the FEM analysis of contact stress, general-purpose contact problem analysis software that extended Hertz's contact theory was used. As shown in FIG. 17A, first, as Comparative Example 1, the contact stress when the roller 3 is brought into contact with a flat roller rolling surface 1b that is not crowned and a load Q is applied to the roller 3 is shown. Analyzed. As shown in the lower part of FIG. 17A, it was found that an excessive edge load occurs at the end of the roller.

Further, as shown in FIG. 17 (b), as Comparative Example 2, the contact stress when arc-shaped crowning R1 was applied to both ends of the roller rolling surface 1b was analyzed. By applying crowning R1 as shown in the lower part of FIG. 17B, no edge load occurs at the end of the roller. However, it has been found that peak contact stress is generated at the connection portion C1 between the straight portion L2 and the crowning R1. It is presumed that the cause is that the shape of the contour of the roller rolling surface 1b changes abruptly at the connecting portion between the straight line portion L2 and the crowning R1.

Next, as shown in FIG. 18, as Comparative Example 3, a single arc-shaped crowning was applied to the roller rolling surface 1b, and the contact stress was analyzed. The radius of curvature R of the crowning was set so that the b point of the roller did not contact the roller rolling surface. As shown in the graph on the right side of FIG. 18, a smooth stress distribution in which no peak contact stress was generated at the contact portion between the roller 3 and the roller rolling surface 1b was obtained. However, if the roller rolling surface 1b is formed in a single arc shape, the stress distribution is the same as that of the motion guide device using a ball as a rolling element. No matter how the radius of curvature R of the crowning is set, there is a limit to bring the maximum surface pressure σmax close to the allowable surface pressure.

As shown in FIG. 6, the roller rolling surface 1 b was crowned with an elliptic curve, the maximum surface pressure σmax and the elastic approach amount δ were calculated, and compared with the arcuate curve crowning. In obtaining the optimal shape of the elliptic curve, the crowning depth λε in FIG. 6 was variously changed, and the presence or absence of contact at the b point of the roller was examined. The results are shown in Table 1.

FIG. 19 is a graph of the results in Table 1. It was found that the maximum surface pressure σmax and the elastic approach amount δ can be most suppressed in the range where there is no contact at the point b when the crowning depth λε is 0.04176 mm.

The optimal shape of the clothoid curve was obtained as well as the elliptic curve. As shown in Table 2, the crowning depth λε was variously changed, and the maximum surface pressure σmax, the elastic approach amount δ, and the contact length Leff _{TED / CPA} were calculated.

FIG. 20 is a graph of the results in Table 2. It was found that the maximum surface pressure σmax and the elastic approach amount δ can be most suppressed in the range where there is no contact at the point b when the crowning depth λε is 0.03023 mm.

Arc curved shape Table 3 shows the results of comparing the crowning depth lambda _Ipushironbi in crowning depth λε and point b of the elliptic curve and a clothoid curve. FIG. 6 depicts these curves at this time.

21 and 22 are graphs comparing the maximum surface pressure σmax and the elastic approach amount δ when using an arc curve, an elliptic curve, and a clothoid curve. It was found that the elliptical curve can suppress the maximum surface pressure σmax and the elastic approach amount δ more than the arc curve, and the clothoid curve can suppress the maximum surface pressure σmax and the elastic approaching amount δ more than the elliptic curve.

Next, the inventor calculated the allowable load of the roller when the maximum surface pressure of the roller σmax = 4000 MPa (ISO standard) on the full crowning rolling surface of the arc curve, the elliptic curve, and the clothoid curve. In each crowning shape, when the allowable load is applied, there is no contact at the connection point b between the straight portion and the corner portion of the roller, and the contact length L _eff = 6.4 mm is a shape that can load the largest allowable load. Satisfying the condition.

FIG. 23 shows a flowchart for determining the optimum shape and calculating the allowable load. First, a roller load Q _{0 at} which σ = 4000 MPa with respect to a flat roller rolling surface is derived by the Hertz equation and set as an initial value (S1). Next, contact analysis (TED / CPA) when the roller load Q ₀ is applied is performed, and the crowning depth λε and the contact surface pressure σ _N at that time are calculated as the contact length L _eff = 6.4 mm. (S2). Since full crowning is applied, the crowning shape can be determined by determining an arbitrary crowning depth λε. The crowning shape obtained in S2 is a shape that can avoid stress concentration at point b of the roller end with respect to a given roller load. Next, it is determined whether or not the contact surface pressure σ _N calculated in S2 is 4000 MPa (S3). If σ _N = 4000 MPa, the maximum value of the allowable load has been obtained, and the analysis is completed. Otherwise, the roller load is changed and the procedure of S2 is repeated. The roller load Q _{N + 1} of the next step is set to Q _{N + 1} = Q _N / 2 when the number of calculations N <3 (S4). When N ≧ 3, the relationship between the contact surface pressure σ and the roller load Q is linearly approximated by the first and second calculation results, and the roller load Q when σ = 4000 MPa becomes Take the way.

FIG. 24 shows the crowning shape calculated so that the maximum surface pressure of the roller σmax = 4000 MPa. The crowning depth λε increases in the order of arc, ellipse, and clothoid, but the depth λεb at point b decreases in the order of arc, ellipse, and clothoid.

The table compares the allowable loads for each crowning shape. It can be seen that the allowable load increases in the order of arc, ellipse, and clothoid. In each crowning shape, the contact surface pressure σmax = 4000 MPa and the contact length L _eff = 6.4 mm are set.

FIG. 25 shows changes in the contact surface pressure σmax and the elastic approach amount δ when the roller load Q is gradually increased. In particular, when the crowning is a clothoid curve, the contact surface pressure σmax and the elastic approach amount δ can be reduced.

FIG. 26 shows the surface pressure distribution when the contact surface pressure σmax = 4000 MPa in each crowning shape shown in FIG. In the case of arc crowning, the surface pressure distribution at the contact portion is also close to a spherical surface. In the case of an elliptical crowning, the surface pressure distribution is more bulging than an arc crowning. In the case of clothoid crowning, the surface pressure distribution is further swelled. The allowable load increases due to the swelling of the surface pressure distribution.

This specification is based on Japanese Patent Application No. 2008-278911 filed on Oct. 29, 2008. All this content is included here.

Claims (9)

A track rail having a roller rolling surface, a load roller rolling surface facing the roller rolling surface of the track rail, and a moving block assembled to be movable relative to the track rail; In a motion guide device comprising: a plurality of rollers interposed between the roller rolling surface of the track rail and the load roller rolling surface of the moving block so as to allow rolling motion;
When viewed in a cross section including the center line of the roller, the curvature changes in proportion to the length of the curve and contacts at least one of the roller rolling surface, the load roller rolling surface, and the roller. A motion guide device in which crowning of convex clothoid curve is formed toward the opponent. 2. The crowning of the clothoid curve is formed on the roller rolling surface, the load roller rolling surface, and the entire portion of the roller that contacts at least one of the opponents. The motion guide apparatus described. The roller rolling surface, the load roller rolling surface, and at least one contour line of the roller include a linear straight portion, and the crowning continuous to the straight portion,
The motion guide device according to claim 1, wherein a tangential direction and a curvature of the linear portion and the crowning are continuous at a connection point between the linear portion and the crowning. A track rail having a roller rolling surface, a load roller rolling surface facing the roller rolling surface of the track rail, and a moving block assembled to be movable relative to the track rail; In a motion guide device comprising: a plurality of rollers interposed between the roller rolling surface of the track rail and the load roller rolling surface of the moving block so as to allow rolling motion;
When viewed in a cross-section including the center line of the roller, at least one of the roller rolling surface, the loaded roller rolling surface, and the roller rolling surface and the roller contacting the loaded roller rolling surface, A motion guide device having a major axis in a direction parallel to a center line of the roller and a minor axis in a direction orthogonal to the center line of the roller, and a convex elliptic curve crowning is formed toward a contact partner. 5. A single elliptic curve crowning is formed on the entire surface of at least one of the roller rolling surface, the load roller rolling surface, and the roller that contacts the counterpart. The motion guide device according to 1. 6. The motion guide device according to claim 1, wherein the crowning is formed on the roller rolling surface and the load roller rolling surface. The roller includes a cylindrical outer peripheral surface, a pair of end surfaces in the direction of the center line, and a chamfered portion formed at a corner of the outer peripheral surface and the end surface,
When the maximum surface pressure defined by the ISO standard is applied to the roller, the length of the roller rolling surface and the load roller rolling surface in contact with the roller is the length of the outer peripheral surface of the roller. The motion guide apparatus according to claim 6, wherein the crowning is formed so as to be less than a length in a direction of a center line. A screw shaft having a spiral roller rolling surface on the outer peripheral surface;
A nut having a spiral load roller rolling surface facing the roller rolling surface of the screw shaft;
A screw device comprising: a plurality of rollers interposed between the roller rolling surface of the screw shaft and the load roller rolling surface of the nut so as to allow rolling motion;
When viewed in a cross section including the center line of the roller, the curvature changes in proportion to the length of the curve and contacts at least one of the roller rolling surface, the load roller rolling surface, and the roller. Screw device in which crowning of convex clothoid curve is formed toward the other party. A screw shaft having a spiral roller rolling surface on the outer peripheral surface;
A nut having a spiral load roller rolling surface facing the roller rolling surface of the screw shaft;
In a screw device comprising: a plurality of rollers interposed between the roller rolling surface of the screw shaft and the load roller rolling surface of the nut so as to allow rolling motion;
When viewed in a cross-section including the center line of the roller, at least one of the roller rolling surface, the loaded roller rolling surface, and the roller rolling surface and the roller contacting the loaded roller rolling surface, A screw device having a long axis in a direction parallel to a center line of the roller and a short axis in a direction perpendicular to the center line of the roller, and a convex elliptic curve crowning is formed toward a contact partner.

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