JP2003035314A - Design method of rolling linear movement guide device and the device designed by the method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a design method of a rolling linear movement guide device for designing crownings formed in rolling body rolling grooves of a slider so as to be made into optimal crowning shapes capable of decreasing ball passing vibration in the rolling linear movement guide device, and the rolling linear movement guide device designed by the method, thus improving moving accuracy of the device. SOLUTION: The design method of the rolling linear movement guide device in which a slider 2 having second rolling body rolling grooves is fitted loosely into a guide rail 1 having a first rolling body rolling grooves 3a, 3b on its outer surface and extending in an axial direction, rolling bodies are mounted between these rolling body rolling grooves and further the crownings are provided at both axial ends of the second rolling body rolling grooves, wherein shapes of the crownings are formed so that stiffness against at least any one direction of a perpendicular direction (a vertical direction), horizontal direction and yawing direction of the slider 2 may be kept roughly constant and besides stiffness against a pitching direction and/or yawing direction of the slider 2 may be kept roughly constant even if the rolling bodies move axially.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for designing a rolling linear motion guide device and a rolling linear motion guide device designed thereby, and more particularly to a technique for improving the motion accuracy of the rolling linear motion guide device.

[0002]

2. Description of the Related Art Rolling linear motion guide devices are widely used to obtain linear motion in various mechanical devices such as robots and machine tools. With the recent demand for miniaturization and high accuracy, rolling linear motion guide devices have been widely used. Further improvement in exercise accuracy is required. One of the factors that lower the motion performance of the rolling linear motion guide device is rolling element passing vibration that causes a periodic displacement component as the rolling element moves. This rolling element passing vibration can be confirmed by measuring the posture (angle) change of the slider of the rolling linear motion guide device when the slider is moved at a constant speed on the guide rail. As an example of rolling element passing vibration in FIG.
The measurement results of the pitching angle displacement with respect to the moving distance of the slider are shown. According to this measurement result, remarkable vibration appears at a wavelength about twice the diameter of the balls or rollers that are rolling elements. Although the change in the angle of the slider due to the vibration passing through the rolling elements is small, it is not negligible at a position where the distance from the slider is large, because it is amplified to a large displacement.

Here, the mechanism by which rolling element passing vibration is generated will be briefly described. Now, consider a rolling linear motion guide device in which a slider 34 having two rows of rolling element rolling grooves 30 and 32 in upper and lower rows moves along a guide rail 36 as shown in FIG. The arrangement of the balls 38 in the two grooves 30, 32 is 1 / the diameter D _w of the balls 38 as shown in FIG.
Assuming that the number of balls is shifted by 2, the number of balls in the upper groove 30 <the number of balls in the lower groove 32. When a preload is applied to the rolling linear motion guide device and an external load does not act, the total ball load of the upper groove 30 = the total ball load of the lower groove 32.
Load per ball> the load per ball in the lower groove 32. That is, the balls in the upper groove 30 are deformed more than the balls in the lower groove 32, and the upper and lower balls 38 are arranged in the same manner (see FIG. 15).
Compared to the state (a), the slider 34 moves downward. When the slider 34 moves by the diameter D _w from this state, the ball 38 moves by D _w / 2, and the state shown in FIG. At this time, the balls 38 are arranged upside down in FIG. 15B, and the slider 34 moves upward.
Therefore, the fluctuations repeatedly appear every distance of twice the ball diameter, which is the main cause of the rolling element passing vibration.

In order to reduce such rolling element passing vibration, the slider 36 of the rolling linear motion guide device is provided with a gently inclined portion called a crowning 40 shown in FIG. By providing the crowning 40, the load on the balls 38 at the end of the slider 34 gradually increases / decreases as the balls move, so that the change in the posture of the slider 34 is alleviated.

[0005]

However, the theoretical study on the optimum shape of the crowning 40 has not been sufficiently conducted, and the magnitude of the rolling element passing vibration changes due to the difference in the crowning shape. It has been known empirically that how to set the crowning shape so as to contribute to improving the motion accuracy of the rolling linear motion guide device has been an issue. Further, as the crowning shape in the conventional rolling linear motion guide device, a single circular arc shape, a single straight slope shape, etc. are mainly used due to the ease of processing, but the design of the shape is mainly based on empirical rules. However, a design method for effectively suppressing rolling element passing vibration has not been used.

The present invention has been made in view of the above situation, and the crowning formed in the rolling element rolling groove of the slider is designed to have an optimum crowning shape capable of reducing the ball passing vibration of the rolling linear motion guide device. An object of the present invention is to provide a method for designing a motion guide device and a rolling linear motion guide device designed by the method, and to improve the motion accuracy of the rolling linear motion guide device.

[0007]

In order to achieve the above object, a method of designing a rolling linear motion guide device according to a first aspect of the present invention has an outer surface having a first rolling element rolling groove and an axial direction. A slider having a second rolling element rolling groove facing the first rolling element rolling groove is loosely fitted to a guide rail extending to the first rolling element rolling groove, and the first rolling element rolling groove and the second rolling element. A method of designing a rolling linear motion guide device having a rolling element loaded between the rolling groove and a crowning portion at both axial ends of the second rolling element rolling groove, the shape of the crowning portion being provided. Even if the rolling element between the first rolling element rolling groove and the second rolling element rolling groove moves in the axial direction, the vertical direction (vertical direction) of the slider, the horizontal direction, The rigidity in at least one of the rolling directions is kept substantially constant, and Rigidity against one or both of the pitching direction and the yawing direction of Ida is and sets the shapes each kept substantially constant.

In this method for designing the rolling linear motion guide device,
At least the rigidity of the slider in the vertical direction (vertical direction), the horizontal direction, or the rolling direction is kept substantially constant, and the rigidity of the slider in one or both of the pitching direction and the yawing direction is kept substantially constant. By setting the shape to lean, the first and second
The elastic displacement amount of the rolling element in the rolling element rolling groove is substantially constant regardless of the arrangement position, and the occurrence of rolling element passing vibration when the slider moves can be suppressed. This makes it possible to easily design a rolling linear motion guide device with high motion accuracy.

According to a second aspect of the present invention, there is provided a rolling linear motion guide designing method, wherein the shape of the crowning portion is such that the rolling element between the rolling element rolling grooves is axially rolled with respect to the axial center position of the slider. When the moving bodies are distributed symmetrically, the vertical direction (vertical direction) of the slider in a state in which the rolling elements are arranged at the axial center position and a state in which the rolling elements adjacent to each other in the axial center position are arranged. ) And the rigidity in one or both of the horizontal directions and the rigidity in one or both of the pitching direction and the yawing direction of the slider are
The feature is that each is set so as to be kept substantially constant.

According to the method of designing the rolling linear motion guide device,
Two states in which the number of rolling elements existing in the rolling element rolling groove are different, that is, a state in which the rolling elements are arranged in the axial center position and a state in which the rolling elements adjacent to each other in the axial center position are arranged. On the other hand, by setting the crowning shape in which the rigidity is substantially the same in each state, the displacement amount in the contact angle direction and the displacement amount in the pitching direction during movement of the slider become substantially equal, and ball passing vibration can be reduced.

According to a third aspect of the present invention, there is provided a rolling linear motion guide device designing method, wherein each of a plurality of crowning shape coordinate points having the same rigidity in each of the states is obtained, and an approximate curve is obtained with respect to the plurality of crowning shape coordinate points. It is characterized by setting the crowning shape.

In the method of designing this rolling linear motion guide device,
To calculate the rigidity only for the discrete crowning shape coordinate points by finding the approximate curve for multiple crowning shape coordinate points with the same rigidity and setting the obtained approximate curve to the crowning shape. It is not necessary to calculate the rigidity over the entire crowning portion, the calculation load is reduced, and the crowning shape can be set with necessary and sufficient accuracy.

According to a fourth aspect of the present invention, there is provided a rolling linear motion guide device designing method, wherein the approximate curve passes through at least one of the plurality of crowning shape coordinate points and is different from other crowning shape coordinate points. , Is an approximate curve that passes through its neighborhood.

In the method of designing this rolling linear motion guide device,
By using an approximate curve that passes at least one of the plurality of crowning shape coordinate points and passes the other crowning shape coordinate points in the vicinity thereof, it is possible to obtain a curved shape with less undulation.

According to a fifth aspect of the present invention, in the method for designing a rolling linear motion guide device, the approximated curve is f (x) = a _w x ^w (a _w , w
Is a constant) and is a power function of the type

In the method of designing this rolling linear motion guide device,
By performing the curve approximation using the power function, it is possible to set the curve shape closer to the crowning shape coordinate points as compared with the case of the single arc shape.

The rolling linear motion guide device designing method according to claim 6 is characterized in that the approximate curve is a curve set by combining a plurality of curves.

In the method of designing this rolling linear motion guide device,
By setting the approximate curve by combining a plurality of curves, it is possible to make the curve shape closer to the crowning shape coordinate points and facilitate the processing of the curve shape.

According to a seventh aspect of the present invention, there is provided a method for designing a rolling linear motion guide device, wherein the approximation curve is a curve approximated by the least square method.

In the method of designing this rolling linear motion guide device,
By performing the curve approximation by the least squares method, it is possible to approximate a curve having a small residual from the crowning shape coordinate points.

A rolling linear motion guide device according to an eighth aspect comprises a slider having a crowning shape set by using the method for designing the linear motion guide device according to any one of the first to seventh aspects. It is characterized by being

In this rolling linear motion guide device, by providing a slider having a crowning shape set by the above-described rolling linear motion guide design method, ball passing vibration is reduced, motion accuracy is improved, and highly precise rolling linear motion is achieved. It can be a guide device.

[0023]

BEST MODE FOR CARRYING OUT THE INVENTION Preferred embodiments of a rolling linear motion guide designing method according to the present invention and a rolling linear motion guide device designed thereby will be described in detail with reference to the drawings. FIG. 1 is a perspective view showing a schematic configuration of a rolling linear motion guide device according to the present invention, and FIG. 2 is A-A of FIG.
FIG. Rolling linear motion guide device 100 of the present embodiment
Is a rolling element rolling groove (first rolling element rolling groove) 3a on the outer surface,
It has a guide rail 1 having 3b and extending in the X-axis direction, and a slider 2 mounted over the guide rail 1. The guide rail 1 is, as shown in FIGS. 1 and 2,
One rolling element rolling groove 3a, which is a groove formed continuously in the X-axis direction at the ridgeline where the upper surface 1a and both side surfaces 1b of the guide rail 1 intersect and the cross section of which is a substantially arcuate shape, and the guide rail 1
The other rolling element rolling groove 3b having a substantially semicircular cross section is formed at a substantially central position on both side surfaces 1b.

The slider 2 has a slider body 2a.
And the end caps 2b attached to both ends thereof, and the slider body 2a is formed on the inner surface of both sleeves 4 so as to face the rolling element rolling grooves 3a and 3b of the guide rail 1 (second rolling element rolling groove). Rolling element rolling groove) of 5a, 5b,
The rolling element return path (not shown) penetrates the thick portion of the sleeve in the X-axis direction. The end cap 2b has a curved path (not shown) that communicates the rolling element rolling grooves 5a and 5b of the slider body 2a with the rolling element return path parallel to the rolling grooves 5a and 5b. A rolling element circulation circuit is formed by the rolling element return path and the curved paths at both ends. A large number of rolling elements 6 made of, for example, steel balls are filled in the rolling element circulation circuit. Thereafter, the rolling element rolling grooves 3a and 5a are in the upper rolling path 7, and the rolling element rolling grooves 3b and 5b are in the lower rolling path 8.
Will be referred to as appropriate.

The rolling linear motion guide device 100 having the above structure is
When the slider 2 moves on the guide rail 1 fixed to the base, the rolling element 6 rolls in the upper rolling path 7 and the lower rolling path 8 and moves at a lower speed than the slider 2 in the moving direction of the slider 2. , And makes a U-turn on the curved path on the one end side to move while rolling on the rolling element return path in the opposite direction to the slider movement direction, and makes another U-turn on the curved path on the other end side to make an upper rolling path. 7 and the circulation such as returning to the lower rolling path 8 is repeated.

Next, the rolling element rolling groove 5 of the slider body 2a
The crowning shape designing method for determining the optimum crowning shape formed in a and 5b will be described in detail. FIG. 3 is a conceptual arrow view of the B-B cross section with respect to the contact angle direction m of the rolling element rolling grooves 3a and 5a, in which (a) shows the balls 6 symmetrically with respect to the axial center O of the slider body 2a. The state in which the balls 6 are distributed and arranged, (b) shows the state in which the balls 6 are arranged such that the balls are located directly below the axial center O of the slider body 2a. In the figure, L ₁ is the axial length of the slider body 2a, s is the distance between adjacent balls 6, and n is L ₁ when the ball 6 is arranged at the axial center O of the slider body 2a.
It represents the number of balls 6 present inside. Although the crowning shape in the drawing shows the crowning amount in an exaggerated manner, the actual balls 6 are in contact with the rolling element rolling grooves. In addition, the rolling linear motion guide device of the present embodiment shows an example having four rows of rolling element rolling paths, but here, in order to simplify the calculation, two rolling elements that are the upper rolling paths 7 are provided. The moving body rolling groove 3a,
The same balls are arranged in 3a and 5a, 5a, and the two rolling element rolling paths 3b, 3b and 5b, 5b serving as the lower rolling path 8 are formed.
Consider the same ball arrangement inside.

According to Hertz's elastic contact theory, the vertical rolling element load Q _j of the ball 6 with the number _j is given by the equation (1).

[Equation 1] Here, K is the Hertzian nonlinear spring constant, and δ _j is the elastic deformation amount between the ball of number j and the rolling element rolling groove surface with respect to the contact angle direction m shown in FIG. 3 (a) and 3 (b)
The elastic deformation amount δ _{j at} is given by equation (2).

[Equation 2]

In the equation (2), δ ₀ is the oversize amount of the ball and corresponds to the interference. C _j represents the crowning amount, and C _j ≧ 0. When δ _j <0, δ _j = 0. From the equations (1) and (2), the vertical rigidity k _j caused by the elastic deformation between the ball number j and the rolling element rolling groove surface is as shown in the equation (3).

[Equation 3]

When the slider body tilts by a small angle θ (see FIG. 1) in the pitching direction around the axial center O, the reaction moment M _j generated by the ball with the number _j is given by the equation (4).

[Equation 4] Here, x _j is the X-axis coordinate of the ball with the number j. (4) the slope direction stiffness k around point O by a ball number j from equation _jθ
Is as in equation (5).

[Equation 5]

As shown in FIG. 3A, the slider body 2a
In the state in which the balls are distributed with respect to the center O in the axis direction of n, there are n-1 balls within the range of L ₁ . Figure 3
In the arrangement of balls in (a), the sum of vertical rigidity k _A and the sum of tilt rigidity k due to the balls existing within the range of L _1
Aθ is given as follows.

[Equation 6]

Here, x _Aj is a number j when balls are arranged symmetrically with respect to the axial center O of the slider body.
It is the X-axis coordinate of the ball. Now, the number 1 shown in FIG.
And the crowning amount at the ball position of number n-1 is C _a
If the crowning amount is 0 at other ball positions, the crowning portions 10a, 10 at both ends of the slider body are
Balls numbered 1 and n-1 are arranged in b. At this time, the above equations (6) and (7) can be expressed as follows.

[Equation 7]

On the other hand, as shown in FIG. 3B, in the arrangement in which the balls are located directly below the axial center O of the slider body 2a, n balls exist within the range of L ₁ . In the arrangement of the ball is shown in FIG. 3 (b), the sum of the vertical stiffness by balls present in the range of L ₁ k _B, and the sum k inclination direction stiffness
_Bθ is given as follows.

[Equation 8]

Here, x _Bj is the X-axis coordinate of the ball with the number j when the ball is located right below the axial center O of the slider body 2a. Now, let us say that the crowning amount at the ball positions of the numbers 1 and n shown in FIG. 3B is C _b , the crowning amount at the ball positions of the numbers 2 and n-1 is C _c , and the crowning amounts at other ball positions. Is 0
Then, the numbers 1 and 2 are provided on the left crowning portion 10a and the number n is provided on the right crowning portion 10b.
-1 and n balls are placed. At this time, the expressions (10) and (11) can be expressed as follows.

[Equation 9]

By the way, when a constant external load is applied in the vertical direction, if k _a = k _B (14) holds, the vertical movement amount of the slider body shown in FIGS. 3 (a) and 3 (b) becomes equal. . When a constant external moment acts in the pitching direction, k _Aθ = k _Bθ (15)

If the following is true, the inclination amounts of the slider body 2a shown in FIGS. 3 (a) and 3 (b) become equal. Therefore, (1
If the equations (4) and (15) are established at the same time, the vertical movement amount and the inclination amount of the slider body 2a in the ball arrangement shown in FIG. 3 (a) become the slider body 2a in the ball arrangement shown in FIG.
Becomes equal to the amount of vertical movement and the amount of inclination. This allows
When the expressions (14) and (15) are satisfied at the same time, it can be expected that the amplitude of the ball passing vibration is attenuated as compared with the case where the expressions are not satisfied. As described above, the method for designing the crowning shape according to the present invention makes the rigidity in the vertical direction and the rigidity in the pitching direction match in the state of FIG. 3A and the state of FIG. It is characterized by significantly reducing the occurrence of passing vibration. here,
In equations (14) and (15), (8), (9), (1
By substituting the expressions (2) and (13) for rearranging, the following expression is obtained as a condition for reducing the ball passing vibration.

[Equation 10]

In equation (16), δ ₀ , x _Aj , x _Bj ,
When n is given as a design parameter and the crowning amount C _a is temporarily set to _a predetermined value, the set crowning amount C a
C _b for _a, C _c is determined. Here, as shown in the dimension of the crowning shape in FIG. 4, C _a , C _b , and C _c are
x _{A 1} , x _B1 , x _B2 (or x _{A (n-1)} , x _Bn , x _{B (n-1)} )
The amount of crowning in. In addition, x in FIG.
The position of = ± x _s represents the coordinates of the intersection of the straight line portion of the rolling element rolling groove of the slider body 2a and the crowning portions 10a and 10b. That is, when x = ± x _s , the crowning amount is 0.
Becomes

As described above, in the crowning portion 10a (left side in the figure) of the slider body 2a, as shown in the enlarged view of the C portion of FIG. 4 in FIG. 5, P _L0 (−x _s , 0), P _L1 (x _A1 ，
C _a ), P _L2 (x _B1 , C _b ), P _L3 (x _B2 , C _c ), four crowning shape coordinate points satisfy the condition (16) which is a conditional expression for reducing the ball passing vibration. Become. Further, at the crowning portion 10b (right side in the figure) of the slider body 2a, as shown in the enlarged view of section D of FIG.
_R0 (x _s , 0), P _R1 (x _{A (n-1)} , C _a ), P _R2 (x _Bn ,
The four crowning shape coordinate points of C _b ), P _R3 (x _{B (n-1)} , C _c ) satisfy the equation (16).

In this embodiment, the slider body 2a
With respect to the crowning at both ends, the above-mentioned crowning shape coordinate points are curve-approximated by a power function to formulate the crowning shape. Note that the coordinates of the points satisfying the equation (16), because they depend on the setting value of the crowning amount C _a, seek other crowning amount C _b and C _c by a crowning amount C _a is small change in the amount, these It is obtained by curve approximation using a power function. With such a method, the crowning shape coordinate points of the crowning shape are obtained using the crowning amount C _a as a parameter, and the crowning amount C _j when curve approximation is performed using a power function is (1
It is expressed by the equation 7).

[0039]

[Equation 11] Here, a _w and w are constants of a power function, which are constants calculated when a curve is approximated by a method such as the least square method. By optimally determining these constants a _w and w, it becomes possible to effectively reduce the ball passing vibration. Note that the curve approximation method may be any method other than the least-squares method as long as it is an approximation method that can reduce the residual.

FIG. 7 shows the crowning shape coordinate points P _L0 , P _L1 , P _L2 , P _L3 and P _R0 , P determined by the above method.
It is a figure which shows the result of curve-approximating with _R1 , P _R2 , and P _{R3 by} a power function, and the result of curve-approximating to a single circular arc shape.
The crowning shape coordinate points P _L0 , P _L1 , P _L2 , P _L3
Has the same crowning amount as each of the crowning shape coordinate points P _R0 , P _R1 , P _R2 and P _R3 , the total number of crowning shape coordinate points indicated by black circles in the figure is four.
If these crowning shape coordinate points are directly connected as they are, a smooth shape is not obtained, and it becomes difficult to process the actual crowning. Therefore, the curve approximation is performed by using the equation (17) so as to pass through the four crowning shape coordinate points, but the arrangement of the crowning shape coordinate points in this case causes a large swell in the approximation result. Therefore, P _L0 (P _R0 )
For the crowning shape coordinate point of P _L1 (P
_R1 ), P _L2 (P _R2 ) and P _L3 (P _R3 ) were subjected to curve approximation under the condition that they passed through the vicinity of the crowning shape coordinate points. The result is the curve shown by the solid line in the figure.
In addition, the conventional single arc shape (radius R = 110
The crowning shape of 0 mm) is also shown by a dotted line. In this way, by performing curve approximation using a power function, the total amount of deviation from the crowning shape coordinate points can be made smaller than in the case of curve approximation in a single arc shape.

Next, a change in the attitude of the slider when the slider moves will be described. The slider body 2a is shown in FIG.
When the robot moves in the vertical direction by z _a and changes the attitude in the pitching direction by θ, the ball with the number j in the rolling element rolling groove 3a of the upper rolling path 7 and the rolling element rolling groove 3b of the lower rolling path 8 The elastic deformations δ _Uj and δ _{Lj of} are given by the following equation.

[Equation 12] Here, x _Uj and x _Lj are the X-axis coordinates of the ball with the number j in the upper rolling path 7 and the lower rolling path 8, respectively, and are given by the following equations.

[Equation 13]

Where x_U1Is the number on the upper rolling path 7
It is the X-axis coordinate of the ball of 1, and a (0 ≦ a <1.0) is the initial
Positions of upper rolling path 7 and lower rolling path 8 in the state
It is a constant indicating the relationship, and the upper rolling path 7 and the lower rolling path 8
When the position of the ball deviates by 1/2 of the ball diameter, a = 0.5
Become. In the above equation (18), δ_Uj<0, δ _Lj
When <0, δ_Uj= 0, δ_Lj= 0. (1)
From the formula, the number j in the upper rolling path 7 and the lower rolling path 8
Vertical ball rolling element load Q_Uj, Q_LjIs given by equation (20)
It

[Equation 14]

The vertical load F _z of the slider body and the moment M _{p in the} pitching direction are given by equation (21).

[Equation 15] Here, n _U and n _L are the numbers of balls in the load range of the upper rolling path 7 and the lower rolling path 8, respectively. With F _z = 0 and M _p = 0, the equation (21) is summarized as follows.

[Equation 16]

Thus, the equations (18) and (20),
It is possible to calculate the attitude change z _{a of the} slider and the angle θ in the pitching direction using the equation (21). That is,
Numerical calculation is performed to calculate z _a and θ such that the expression (22) holds. Further, by calculating Z _a and θ using the moving distance of the ball as a parameter, the relationship between the moving distance of the ball and the posture change can be obtained.

Here, FIG. 8 is a diagram showing the results of the simulation of the ball passing vibration by the above-described power function curved line and the single arc-shaped crowning,
(A) shows the vertical displacement of the slider with respect to the moving distance of the ball, and (b) shows the pitching angle displacement of the slider with respect to the moving distance of the ball. Here, the moving distance of the ball is the moving distance of the ball moving in the rolling element rolling groove when the slider moves on the guide rail. In addition, here, the crowning length L _{c is set} to 6.4 mm, and the constant a indicating the positional relationship of the balls in the upper rolling path 7 and the lower rolling path 8 in the equation (19) is calculated as 0.5. ing.

According to FIG. 8 (a), the curve-shaped crowning by the power function has a smaller vertical displacement than the single arc-shaped crowning, and the generation of the vertical ball passing vibration is reduced. I understand that Also, FIG.
According to (b), the single arc-shaped crowning periodically generates a large amplitude pitching angle displacement.
Curved crowning with a power function produces little pitching angular displacement. In this way, the occurrence of ball passing vibration in the pitching direction is greatly reduced.

As described above, according to the method for designing the rolling linear motion guide device of the present invention, the position of the ball filled in the rolling element rolling groove formed in the guide rail 1 and the slider 2 is determined by the slider. Even when the rolling element rolling groove is moved differently for each of the two rolling elements, the ball passing vibration of the rolling element 6 can be reduced, and the slider 2
It is possible to easily determine a crowning shape that can reduce the change in the posture. As a result, the motion accuracy of the rolling linear motion guide can be improved, and the rolling linear motion guide device applicable to a portion requiring high accuracy can be stably supplied while suppressing the design cost. Further, since the rigidity is calculated only for the discrete crowning shape coordinate points, it is not necessary to calculate the rigidity for the entire crowning portion, and the crowning shape can be set with necessary and sufficient accuracy while reducing the calculation load.

Now, the results obtained by simulating the ball passing vibration while changing various conditions such as the size of the crowning shape will be described. FIG. 9 is a diagram showing the result of calculating the amplitude of the ball passing vibration when the constant a is changed,
(A) shows the vertical displacement, and (b) shows the amplitude of the pitching angle displacement for a curved crowning with a power function and a single arc crowning, respectively. The crowning length L _c in this case is 6.4 mm.

According to this figure, when there is no positional deviation of the balls on the upper rolling path 7 and the lower rolling path a = 0 and 1, the amplitude becomes 0 and the positional deviation becomes maximum a = 0. Amplitude tends to increase near 0.5. In the curve-shaped crowning using a power function, the maximum vertical amplitude appearing near a = 0.5 is suppressed to be smaller than that in the single arc-shaped crowning, and especially for the amplitude of pitching angle displacement,
Is greatly reduced over the entire area of. For this reason,
The crowning shape that approximates a curve using a power function can reduce the amplitude of the ball passing vibration more than the case of the single arc shape, and has less influence on the positional deviation of the ball.

FIG. 10 shows the results of calculation of the amplitude of the ball passing vibration when the crowning length L _c is changed. (A) shows the vertical displacement and (b) shows the pitching angle displacement. , And the curve-shaped crowning with a power function and the single-arc-shaped crowning, respectively. The constant a in this case is 0.5. According to this figure, the curve-shaped crowning with a power function has a smaller overall amplitude than the single arc-shaped crowning, and the use of a power function reduces the amplitude of the ball passing vibration. It has an advantage. Further, when the length L _c of the crowning shape by the power function is 6 mm, the amplitude of the vertical displacement is the lowest.

FIG. 11 shows a result obtained by simulating the ball passing vibration in the same manner as in FIG. 8 with the crowning length L _c being 6.0 mm where the amplitude of vertical displacement is the minimum and the constant a being 0.5. It is a figure. According to this figure
Vertical method displacement for curved crowning with a power function is greatly reduced, and pitching angle displacement is also small.By designing this crowning shape, a rolling linear motion guide device with extremely small ball passing vibration can be obtained. To be

Next, a second embodiment of the method of designing the rolling linear motion guide device according to the present invention will be described. In the designing method of the present embodiment, when the crowning shape coordinate points of the crowning shape described above are subjected to curve approximation, an approximate curve is set by combining a plurality of curves. FIG. 12 shows a crowning shape formed by an arc having three different radii and center positions. That is, the crowning shape is formed by three types of arcs from the end of the slider body along the X-axis direction to the distance L _c . The intermediate points P _RO1 (x _R1 , H ₁ ) and P _RO2 (x _R2 , H ₂ ) that are the boundaries of the arcs are set arbitrarily.

First, between the crowning shape coordinate point P _R0 and the intermediate point P _RO1 , the central position O ₀ (L ₁ / 2-L _c ,
R ₀ is formed by an arc of a radius R ₀ of), the radius R between the intermediate point P _RO1 to the intermediate point P _RO2 the center position _{O 1 (x O1, H R1} )
It is formed by a circular arc of ₁ and is formed by a circular arc of radius R _{2 at} the center position O ₂ (x _O2 , H _R2 ) between the intermediate point P _RO2 and the extreme point P _RO3 .

FIG. 13 shows an example of forming a crowning shape by combining three different arcs. According to this, by continuously connecting three different types of arcs, it is possible to obtain a curve shape that substantially matches the curve approximated by the above-described power function, and further reduce the deviation with respect to the four crowning shape coordinate points. Can be set. Therefore, it is possible to make the crowning shape closer to the crowning shape coordinate point which is the optimum position for preventing the ball passing vibration,
Vibration and posture change during slide movement can be greatly reduced.
Further, even when the crowning shape is machined, the machining program can be easily generated and machining can be performed by the NC machining machine or the like by setting the circular arc shape.

Although an example in which three different arcs are combined is shown here, an arbitrary number of arcs can be combined as necessary. By determining the crowning shape using a plurality of arcs in this way, a more appropriate crowning shape can be obtained according to the positional relationship of the crowning shape coordinate points.

In each of the above-described embodiments, the rolling linear motion guide device using balls is used for explanation, but the present invention is not limited to this, and the rolling linear motion guide device using other rolling elements such as rollers is used. Also, even with a linear motion guide device of a type in which a separator is inserted between balls, the crowning shape can be determined by the same design method. In each of the above embodiments, the case where the number of balls included in the crowning portion is two on one side and the number of balls included on one side is one,
Even if the number of balls is other than this, the crowning shape can be determined by the same method. In the above embodiment, the crowning shape is determined by considering the rigidity in the vertical direction and the pitching direction. However, instead of the vertical direction, the horizontal direction or rolling direction (rotational direction around the Z axis), pitching direction Instead, yawing direction (width of guide rail)
The stiffness can be used and the crowning shape can be determined in a similar manner.

[0057]

As described in detail above, according to the method for designing the rolling linear motion guide device of the present invention, at least one of the vertical direction (vertical direction), the horizontal direction, and the rolling direction of the slider is provided. By setting the shape such that the rigidity is kept substantially constant and the rigidity with respect to one or both of the pitching direction and the yawing direction of the slider is kept substantially constant, the inside of the first and second rolling element rolling grooves The amount of elastic displacement generated in the rolling element is substantially constant regardless of the position where the rolling element is arranged, and the generation of vibrations passing through the rolling element when the slider moves can be suppressed. This makes it possible to easily design a rolling linear motion guide device with high motion accuracy. By setting the crowning shape according to the method of designing the rolling linear motion guide device, it becomes possible to easily design the rolling linear motion guide device with high motion accuracy.

[Brief description of drawings]

FIG. 1 is a perspective view showing a schematic configuration of a rolling linear motion guide device according to the present invention.

FIG. 2 is a sectional view taken along line AA of FIG.

FIG. 3 is a conceptual arrow view of a BB cross section of a rolling element rolling groove.

FIG. 4 is a diagram showing dimensions of a crowning shape.

5 is an enlarged view of portion C in FIG.

6 is an enlarged view of part D in FIG.

FIG. 7 is a diagram showing a result of curve approximation of a power function and a result of curve approximation to a single arc shape for each crowning shape coordinate point.

FIG. 8 is a diagram showing a result obtained by simulating a ball passing vibration due to a crown shape of a single arc shape and a curved shape using a power function.

FIG. 9 is a diagram showing a result of calculating the amplitude of the ball passing vibration when the constant a is changed.

FIG. 10 is a diagram showing a result of calculating the amplitude of the ball passing vibration when the crowning length is changed.

FIG. 11 is a diagram showing results of ball passing vibrations obtained by simulation.

FIG. 12 is a diagram showing a crowning shape formed by an arc having three different radii and center positions.

FIG. 13 is a diagram showing an example in which three different arcs are combined to form a crowning shape.

FIG. 14 is a diagram showing measurement results of pitching angle displacement with respect to a moving distance of a slider.

FIG. 15 is a diagram showing a rolling linear motion guide device having upper and lower two rows of ball grooves.

FIG. 16 is a diagram showing a crowning shape of a slider.

[Explanation of symbols]

1 guide rail 2 sliders 3a, 3b rolling element rolling grooves 5a, 5b rolling element rolling groove 6 balls (rolling elements) 10a, 10b crowning portion 100 rolling linear motion guide device P _L0 , P _L1 , P _L2 , P _L3 , P _R0 , P _R1 , P _R2 , P _R3 Crowning shape coordinate points

   ─────────────────────────────────────────────────── ─── Continued front page    (72) Inventor Hiroyuki Ota             1603-1 Kamitomioka Town, Nagaoka City, Niigata Prefecture Nagaoka Technology             Faculty of Engineering, University of Science (72) Inventor Kenta Nakano             1603-1 Kamitomioka Town, Nagaoka City, Niigata Prefecture Nagaoka Technology             Faculty of Engineering, University of Science (72) Inventor Soichiro Kato             78 Toba-cho, Maebashi-shi, Gunma Nippon Seiko Co., Ltd.             In the company (72) Inventor Jun Matsumoto             78 Toba-cho, Maebashi-shi, Gunma Nippon Seiko Co., Ltd.             In the company F term (reference) 3J104 AA22 BA11 DA13 EA01 EA06

Claims (8)

[Claims] 1. A slider having an outer surface having a first rolling element rolling groove and an axially extending guide rail having a second rolling element rolling groove facing the first rolling element rolling groove. Is loosely fitted, a rolling element is loaded between the first rolling element rolling groove and the second rolling element rolling groove, and at the both axial ends of the second rolling element rolling groove. A method of designing a rolling linear motion guide device having a crowning portion, wherein the shape of the crowning portion is such that a rolling element between the first rolling element rolling groove and the second rolling element rolling groove is Even if the slider moves in the axial direction, the rigidity of the slider in at least one of the vertical direction (vertical direction), the horizontal direction, and the rolling direction is kept substantially constant, and one of the pitching direction and the yawing direction of the slider is maintained. Or, a shape in which the rigidity for both is kept approximately constant Setting method of designing a linear motion rolling guide device characterized by the. 2. The shape of the crowning portion is such that when the rolling elements between the rolling element rolling grooves are distributed symmetrically in the axial direction with respect to the axial center position of the slider, the axial center Rigidity of the slider with respect to one or both of a vertical direction (vertical direction) and a horizontal direction in a state in which the rolling elements are arranged at positions, and between the rolling elements adjacent to each other in the axial center position, 2. The method of designing a rolling linear motion guide device according to claim 1, wherein the rigidity of the slider in one of the pitching direction and the yawing direction or both is set so as to be kept substantially constant. 3. A crowning shape is obtained by obtaining a plurality of crowning shape coordinate points having the same rigidity in each of the states and obtaining approximate curves for the plurality of crowning shape coordinate points. 2. The method for designing the rolling linear motion guide device described in 2. 4. The approximated curve is an approximated curve that passes through at least one of the plurality of crowning-shaped coordinate points and passes in the vicinity of other crowning-shaped coordinate points. The method for designing the rolling linear motion guide device according to claim 3. 5. The approximated curve is f (x) = a _w x ^w (a
5. A method of designing a rolling linear motion guide device according to claim 3 or 4, wherein _w and w are power functions of a constant type. 6. The rolling linear motion guide designing method according to claim 3, wherein the approximate curve is a curve set by combining a plurality of curves. 7. The method of designing a rolling linear motion guide device according to claim 3, wherein the approximate curve is a curve approximated by a least squares method. 8. A slider having a crowning shape set by using the method for designing a rolling linear motion guide device according to any one of claims 1 to 7. Rolling linear motion guide device.