Ball screw device

Abstract

By appropriately setting the radial clearance and groove shape, the dynamic friction torque is reduced. [Solution] The ball screw device comprises a screw shaft with a Gothic arch-shaped outer screw groove formed on its outer surface, a nut with a Gothic arch-shaped inner screw groove formed on its inner surface, and a plurality of balls arranged in a track between the outer screw groove and the inner screw groove. The axial direction is parallel to the center line of the screw shaft, and the inner screw groove has a first inner screw groove located on one side of the axial direction from the axial center of the nut, and a second inner screw groove located on the other side of the axial direction. The first and second inner screw grooves are positioned axially offset relative to the outer screw groove so that preload is applied to the balls, and the initial contact angle between the outer screw groove and the ball and the initial contact angle between the inner screw groove and the ball satisfy equation 1. The radial direction is perpendicular to the center line, and the radial clearance in which the nut can move in the radial direction satisfies equations 2 to 4.

Description

[Technical Field]

[0001] This invention relates to a ball screw device. [Background technology]

[0002] Machine tools that require precise positioning, such as machining centers and cylindrical grinding machines, are equipped with a drive system for moving and rotating the table on which the workpiece is placed. The drive system comprises a motor and a ball screw device that converts the rotational motion of the motor's output shaft into linear motion to push or pull one side of the table.

[0003] Such ball screw devices are generally used with preload applied. One method of applying preload is the double-nut preload method. The double-nut preload method has two nuts. A spacer is placed between the two nuts. The spacer causes the thread grooves of the two nuts to be offset axially with respect to the thread groove of the screw shaft, thereby applying preload to the ball. Another method is the spring-type double-nut preload method, which uses an elastic body instead of a spacer. Furthermore, there is an offset preload method that does not use two nuts. In the offset preload method, preload is applied to the ball by offsetting the lead of the thread grooves on the left and right by the amount of preload, with the center of a nut with two or more circulating sections as the boundary. In a ball screw device employing the above preload method, when the ball screw is stationary, the contact points of the ball with the thread groove are one point in the nut's thread groove and one point in the screw shaft's thread groove, for a total of two points.

[0004] On the other hand, when a ball screw device is driven, frictional force acts on the ball from the screw groove. As a result, the ball moves within the cross-section perpendicular to the screw groove, increasing the number of contact points between the ball and the screw groove. In other words, the ball has a total of three contact points with the screw groove, increasing the dynamic friction torque. To address this, the following patent document proposes that when a ball screw device is driven, the ball located on one axial side from the center of the nut makes two contact points, and the ball located on the other axial side makes three contact points.

Prior Art Documents

Patent Documents

[0005]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0006] However, in the above patent documents, since the range of the radial clearance is not shown, it is possible to obtain the ball screw described in the above patent documents by setting the radial clearance large. However, if the radial clearance is large, abnormal noise may occur and the screw efficiency may decrease.

[0007] The present disclosure has been made in view of the above problems, and an object thereof is to provide a ball screw device that appropriately sets the radial clearance and reduces the dynamic frictional torque.

Means for Solving the Problems

[0008] To achieve the above object, a ball screw device according to an aspect of the present disclosure includes a screw shaft having a Gothic arch-shaped outer peripheral screw groove formed on an outer peripheral surface, a nut having a Gothic arch-shaped inner peripheral screw groove formed on an inner peripheral surface, and a plurality of balls arranged in a track between the outer peripheral screw groove and the inner peripheral screw groove. A direction parallel to the center line of the screw shaft is defined as an axial direction. The inner peripheral screw groove has a first inner peripheral screw groove arranged on one side in the axial direction from a central portion in the axial direction of the nut, and a second inner peripheral screw groove arranged on the other side in the axial direction. The first inner peripheral screw groove and the second inner peripheral screw groove are arranged so as to be relatively displaced in the axial direction with respect to the outer peripheral screw groove so that a preload is applied to the balls. An initial contact angle between the outer peripheral screw groove and the ball, and an initial contact angle between the inner peripheral screw groove and the ball, satisfy the following Equation (1). A direction orthogonal to the center line is defined as a radial direction. Further, a radial clearance in which the nut is movable in the radial direction satisfies the following Equations (2) to (4).

[0009]

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[0010]

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[0011]

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[0012]

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[0013] In addition, each symbol in Equation 1 to Equation 4 is as follows. α i : Initial contact angle between the outer thread groove of the screw shaft and the ball α e : Initial contact angle between the inner thread groove of the nut and the ball T r : Radial clearance Dw: Diameter of the ball β: Lead angle of the thread groove (outer thread groove and inner thread groove) R i : Curvature radius of the outer thread groove f i : Groove R ratio of the outer thread groove (R i / Dw) R e : Curvature radius of the inner thread groove f e : Groove R ratio of the inner thread groove (R e / Dw)

[0014] Furthermore, the ball screw device of the present disclosure satisfies the following Equation 5 for the radial clearance, and at rest, there are three contact points between the ball and the outer thread groove and the inner thread groove.

[0015]

Number

[0016] According to the ball screw device of this disclosure, the radial clearance can be properly controlled, and the dynamic friction torque is reduced. [Brief explanation of the drawing]

[0017] [Figure 1] Figure 1 is a cross-sectional view of a ball screw device according to an embodiment. [Figure 2] Figure 2 is a cross-sectional view of a ball screw device according to another embodiment. [Figure 3] Figure 3 is a cross-sectional view of the ball screw device of the embodiment, cut in a direction perpendicular to the track. [Figure 4] Figure 4 is a schematic diagram illustrating radial clearance. [Figure 5] Figure 5 is a cross-sectional view of an embodiment in which the nut is moved radially relative to the screw shaft, and the ball is in four-point contact with the outer and inner screw grooves. [Figure 6] Figure 6 shows the ball contact state during operation of the ball screw device of the embodiment. [Figure 7] Figure 7 is a graph showing the measurement results and friction analysis results for samples 1A, 1B, and 1C. [Figure 8] Figure 8 is a graph showing the measurement results and friction analysis results for samples 2A, 2B, and 2C. [Figure 9] Figure 9 is a graph showing the measurement results for samples 3D, 3E, and 3F, as well as the results from friction analysis. [Figure 10] Figure 10 is a graph showing the measurement results and friction analysis results for samples 4D, 4E, and 4F. [Figure 11] Figure 11 is a cross-sectional view showing the contact state of the first ball in the ball screw device of the embodiment when it is stationary. [Figure 12]Figure 12 is a cross-sectional view of a ball screw device with a larger radial clearance than the ball screw device in Figure 11. [Figure 13] Figure 13 is a cross-sectional view of a ball screw device with a larger radial clearance than the ball screw device in Figure 12. [Figure 14] Figure 14 is a graph showing the measurement results for Example 1. [Figure 15] Figure 15 is a graph showing the measurement results for Example 2. [Modes for carrying out the invention]

[0018] The present invention will now be described in detail with reference to the drawings. However, the present invention is not limited to the embodiments described below. Furthermore, the components in the embodiments below include those easily conceivable by those skilled in the art, those that are substantially identical, and those that fall within the so-called equivalent range. Moreover, the components disclosed in the embodiments below can be combined as appropriate.

[0019] (Embodiment) Figure 1 is a cross-sectional view of a ball screw device according to an embodiment. First, the basic configuration of the ball screw device 1 will be described. As shown in Figure 1, the ball screw device 1 comprises a screw shaft 2, a nut 3 that passes through the screw shaft 2, a plurality of balls 4 arranged between the screw shaft 2 and the nut 3, and two tubes 5. Hereinafter, the direction parallel to the central axis O2 of the screw shaft 2 will be referred to as the axial direction. The direction perpendicular to the central axis O2 will be referred to as the radial direction.

[0020] An outer circumferential thread groove 20 is formed on the outer circumferential surface of the screw shaft 2. An inner circumferential thread groove 30 is formed on the inner circumferential surface of the nut 3. The outer circumferential thread groove 20 and the inner circumferential thread groove 30 are facing each other in the radial direction. The space between the outer circumferential thread groove 20 and the inner circumferential thread groove 30 forms a raceway. A ball 4 is positioned in this raceway. When the ball screw device 1 is driven, the ball 4 moves along the raceway.

[0021] Tube 5 is a cylindrical component fixed to the outer surface of nut 3. Both ends of tube 5 are connected to both ends of the raceway. As a result, ball 4 that has moved from one end of the raceway to the other passes through tube 5 and circulates back to the one end of the raceway. As will be described later, there are two inner circumferential screw grooves 30, a first inner circumferential screw groove 31 and a second inner circumferential screw groove 32, and there are also two raceways. Therefore, two tubes 5 are provided to correspond to each of the raceways.

[0022] The internal thread groove 30 of the nut 3 has a first internal thread groove 31 located on one side of the axial direction from the axial center portion 3a of the nut 3, and a second internal thread groove 32 located on the other side of the axial direction. Hereinafter, when viewed from the axial center portion 3a of the nut 3, the direction in which the first internal thread groove 31 is located will be referred to as the first direction X1, and the direction in which the second internal thread groove 32 is located will be referred to as the second direction X2.

[0023] The lead l of the first internal thread groove 31 and the second internal thread groove 32 is the same as the lead of the outer thread groove 20. The axial length w of the central part 3a of the nut 3 is greater than the lead l. Therefore, the first internal thread groove 31 is offset in the first direction X1 relative to the outer thread groove 20. Also, the second internal thread groove 32 is offset in the second direction X2 relative to the outer thread groove 20. As a result, the ball 4 positioned in the first direction X1 relative to the central part 3a of the nut 3 is subjected to a preload F. a0 The force acts upon it. In addition, the ball 4 positioned in the second direction X2 from the central part 3a of the nut 3 is subjected to a preload F. a0 ' is at work.

[0024] Based on the above, when the ball screw device 1 is stationary, the ball 4 basically makes contact with the outer circumference screw groove 20 at one point and with the inner circumference screw groove 30 at one point, for a total of two contact points. However, there are exceptional cases where three contact points occur. The contact state of the ball 4 during operation and the exceptional case of three contact points when stationary will be described later.

[0025] Furthermore, if we denote the size of the virtual circle diameter (Ball Circle Diameter; hereafter abbreviated as BCD) passing through the center of each ball 4 in the orbit as Q, the lead angle β of the orbit can be calculated using the following six equations.

[0026]

number

[0027] Figure 2 is a cross-sectional view of a ball screw device according to another embodiment. Although the ball screw device 1 in this embodiment is an example that employs an offset preload method, the preload type of the ball screw device of this disclosure is not limited to this. For example, the double nut preload method shown in Figure 2 may be employed. Specifically, the double nut type ball screw device 100 comprises a screw shaft 2, two nuts 103 and 104, a plurality of balls 4, and a spacer 6 interposed between the two nuts 103 and 104. The two nuts 103 and 104 and the spacer 6 are tightened in the axial direction to form a single unit.

[0028] Furthermore, this disclosure may also be a spring-type double-nut preloading system using an elastic material such as a disc spring instead of a spacer 6. Also, regarding the direction of the load due to preloading, in this embodiment, the load (tensile preload) is such that the ball 4 positioned in the first direction X1 and the ball 4 positioned in the second direction X2 are separated from each other in the axial direction, starting from the central part 3a of the nut. However, this disclosure may also be a compressive preloading system. Furthermore, the circulation method of the ball 4 in this disclosure is not limited to the tube 5, but may also be an end deflector 7 (see Figure 2) or a spindle (not shown), and is not particularly limited.

[0029] Next, we will explain the details of the outer circumference thread groove 20 and the inner circumference thread groove 30. We will also explain the terminology necessary for the radial clearance, which will be discussed later. Furthermore, the first inner circumference thread groove 31 and the second inner circumference thread groove 32 have the same shape. Therefore, we will explain the first inner circumference thread groove 31 as a representative example, and omit the explanation of the second inner circumference thread groove 32.

[0030] Figure 3 is a cross-sectional view of the ball screw device of the embodiment, cut in a direction perpendicular to the raceway. Note that in Figure 3, no preload is applied (the first inner thread groove 31 is not offset in the first direction X1 relative to the outer thread groove 20).

[0031] As shown in Figure 3, the outer circumferential thread groove 20 of the screw shaft 2 has a Gothic arch shape formed by combining two arcuate surfaces 25. Furthermore, the outer circumferential thread groove 20 is formed symmetrically with respect to a virtual line K extending in the radial direction. Note that the radius of curvature of the arcuate surface 25 of the outer circumferential thread groove 20 is R i This is how it is written. The diameter of ball 4 is denoted as Dw. Therefore, the groove R ratio of the outer screw groove 20 to ball 4 is R i It is written as / Dw.

[0032] The internal thread groove 30 (first internal thread groove 31) of the nut 3 has a Gothic arch shape formed by combining two arcuate surfaces 35. The radius of curvature of the arcuate surface 35 is R e This is how it is written. Therefore, the groove R ratio of the inner thread groove 30 to the ball 4 is R e It is written as / Dw.

[0033] As shown in Figure 3, in the ball screw device of this embodiment, when no preload is applied, a gap is formed between the outer circumference screw groove 20 and the inner circumference screw groove 30 of the ball 4. In other words, the nut 3 can move relative to the screw shaft 2 in the radial direction. Hereinafter, the gap that allows the nut 3 to move radially relative to the screw shaft 2 will be referred to as the radial gap T r It is called that.

[0034] Figure 4 is a schematic diagram illustrating the radial clearance. Radial clearance T rTo explain in detail, move nut 3 in one radial direction (see arrow A1 in Figure 4). Also, ensure that the inner thread groove 30 and outer thread groove 20 located on the opposite side of the radial direction are in contact with ball 4 (four-point contact state). Next, move nut 3 in the other radial direction (see arrow A2 in Figure 4). Also, ensure that the inner thread groove 30 and outer thread groove 20 located on the side of the radial direction are in contact with ball 4 (four-point contact state). At this time, the amount of radial movement of nut 3 is the radial clearance T. r That is the case.

[0035] Figure 5 is a cross-sectional view of an embodiment in which the nut is moved radially relative to the screw shaft, and the balls make four-point contact with the outer and inner screw grooves. As shown in Figure 5, when the nut 3, which is not preloaded, is moved radially as shown in Figure 4 to make four-point contact, the point where the ball 4 contacts the arcuate surface 25 of the outer screw groove 20 is called the initial contact point 25a. The straight line drawn from the center O4 of the ball 4 to the initial contact point 25a is called the imaginary line K1. The angle between the imaginary line K and the imaginary line K1 is called the initial contact angle α. i It is called that.

[0036] Furthermore, as shown in Figure 5, the point where the ball 4 contacts the arcuate surface 35 of the inner screw groove 30 is referred to as the initial contact point 35a. The straight line drawn from the center O4 of the ball 4 to the initial contact point 35a is referred to as the imaginary line K2. The angle formed by the imaginary line K and the imaginary line K2 is the initial contact angle α. e It is called that.

[0037] Furthermore, in this embodiment, the initial contact angle α i and initial contact angle α e The relationship satisfies the following equation 7.

[0038]

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[0039] Furthermore, if equation 7 is satisfied, the ball 4 on the reverse-acting side, described later, will have a third contact point that makes contact with the outer screw groove 20 (see Figure 6).

[0040] Figure 6 shows the ball contact state during the operation of the ball screw device of the embodiment. Next, the contact state of the balls 4 during the operation of the ball screw device 1 will be described. In the following description, the case in which the nut 3 moves in the second direction X2 (see arrow B1 in Figure 6) due to the rotation of the screw shaft 2 will be used as an example. Note that Figure 6 shows an embodiment in the case of tensile preload.

[0041] Furthermore, the contact state of the balls 4 will be explained separately for the ball 4 on the forward operating side and the ball 4 on the reverse operating side. The ball 4 on the forward operating side is the ball 4 located on the opposite side of the direction in which the nut 3 moves from the central part 3a of the nut 3 (opposite to arrow B1 in Figure 6) (hereinafter referred to as the first ball 41). The ball 4 on the reverse operating side is the ball 4 located on the side of the direction in which the nut 3 moves from the central part 3a of the nut 3 (towards arrow B1 in Figure 6) (hereinafter referred to as the second ball 42).

[0042] As shown in Figure 6, the second ball 42 on the reverse-acting side receives frictional force from the outer circumference screw groove 20 and the second inner circumference screw groove 32. As a result, the second ball 42 is displaced in the direction indicated by arrow B2 in Figure 6. Consequently, the second ball 42 has two contact points with the outer circumference screw groove 20 and one contact point with the second inner circumference screw groove 32, for a total of three contact points.

[0043] Furthermore, the first ball 41 on the forward operating side, like the second ball 42, receives frictional force from the outer circumference screw groove 20 and the first inner circumference screw groove 31, respectively. However, in this embodiment, the radial clearance T r Since this satisfies equations 8 through 10 described later, the number of contact points does not increase. In other words, the first ball 41 has one contact point with the outer circumference screw groove 20 and one contact point with the first inner circumference screw groove 31, for a total of two contact points.

[0044] Furthermore, when the nut 3 moves in the first direction X1 due to the rotation of the screw shaft 2, the first ball 41 becomes the ball 4 on the reverse operating side, and the second ball 42 becomes the ball 4 on the forward operating side. In other words, the contact points of the second ball 42 are a total of two.

[0045] Thus, in this embodiment, when the ball screw device 1 is driven, either the first ball 41 or the second ball 42 becomes the ball 4 on the forward operating side, and the number of contact points does not increase. Therefore, the dynamic friction torque is reduced compared to a ball screw device in which all balls 4 (both the first ball 41 and the second ball 42) are in three-point contact when driven.

[0046] Next, the radial clearance T is set so that the ball 4 on the forward operating side makes contact at a total of 2 points, and the ball 4 on the reverse operating side makes contact at a total of 3 points. r This will explain the radial clearance T of this embodiment. r This satisfies each of the following equations, from equation 8 to equation 10.

[0047]

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[0048]

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[0049]

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[0050] Equation 8 shows the radial clearance T when the amount of elastic approach of the ball 4 on the positive operating side to the third contact of the outer screw groove 20 is negative (i.e., there is no contact). r Equation 9 specifies the radial clearance T when the amount of elastic approach of the ball 4 on the positive operating side to the third contact of the inner circumference screw groove 30 is a negative value (i.e., there is no contact). rEquation 10 specifies the radial clearance T when the amount of elastic approach of the ball 4 on the reverse-acting side to the third contact of the outer screw groove 20 is positive (when contact occurs). r It stipulates that...

[0051] Next, we will explain how to derive equation 10 from equation 8. In friction analysis between a ball and a groove, various parameters are intricately related and are generally solved numerically, making it impossible to express the friction and contact state with a simple mathematical formula. Therefore, we performed a parametric study in the friction analysis and derived equation 10 from equation 8 by performing multiple regression analysis from the results of the parametric study. Furthermore, in order to confirm whether the friction analysis used to derive equation 10 from equation 8 is valid in the first place, we conducted the following Test 1.

[0052] (Test 1) In Test 1, multiple ball screw devices were manufactured as samples. Each sample was then driven under predetermined conditions, and the dynamic friction torque was measured. The dynamic friction torque under predetermined conditions was also calculated using friction analysis. The measured dynamic friction torques for each sample were then converted into torque ratios. Similarly, the dynamic friction torques obtained from the friction analysis were converted into torque ratios. The validity of the friction analysis was then confirmed by comparing the torque ratios obtained from the measurements with those obtained from the friction analysis. Details of the torque ratios will be described later.

[0053] Four types of samples (hereinafter referred to as Sample 1, Sample 2, Sample 3, and Sample 4) were prepared. Samples 1 through 4 were designed so that at least one of the following characteristics differed from the other samples: the diameter of the screw shaft, the lead (lead angle), the shape of the outer screw groove, and the shape of the inner screw groove. Table 1 below shows the information for Samples 1 through 4.

[0054] [Table 1]

[0055] Furthermore, regarding sample 1, the radial gap T rThree different samples (hereinafter referred to as Sample 1A, 1B, and 1C) were prepared. Similarly, the radial gap T was also measured for each of Sample 2, Sample 3, and Sample 4. r Samples 2A, 2B, 2C, 3D, 3E, 3F, 4D, 4E, and 4F were prepared, each with different properties.

[0056] Furthermore, for each of the samples 1A, 1B, 1C, 2A, 2B, 2C, 3D, 3E, 3F, 4D, 4E, and 4F, multiple samples with different preload ratios (see the horizontal axis in Figures 7 to 10) were prepared. The preload ratio is the ratio of the preload when the allowable load of sample 1A is set to 1 for samples 1A, 1B, 1C, 2A, 2B, and 2C. For samples 3D, 3E, 3F, 4D, 4E, and 4F, it is the ratio of the preload when the allowable load of sample 3D is set to 1. In addition, six different preload ratios were prepared. Specifically, samples with preload ratios of approximately 0.1, 0.2, 0.3, 0.6, 0.8, and 1.0 were prepared.

[0057] The torque ratio for samples 1A, 1B, and 1C is the ratio when the dynamic friction torque calculated by friction analysis is set to 1 under the conditions of sample 1A and with a preload ratio of 1.0. The torque ratio for samples 2A, 2B, and 2C is the ratio when the dynamic friction torque calculated by friction analysis is set to 1 under the conditions of sample 2A and with a preload ratio of 1.0. The torque ratio for samples 3D, 3E, and 3F is the ratio when the dynamic friction torque calculated by friction analysis is set to 1 under the conditions of sample 3D and with a preload ratio of 1.0. The torque ratio for samples 4D, 4E, and 4F is the ratio when the dynamic friction torque calculated by friction analysis is set to 1 under the conditions of sample 4D and with a preload ratio of 1.0.

[0058] Figure 7 shows the measurement results and friction analysis results for samples 1A, 1B, and 1C. Figure 8 shows the measurement results and friction analysis results for samples 2A, 2B, and 2C. Figure 9 shows the measurement results and friction analysis results for samples 3D, 3E, and 3F. Figure 10 shows the measurement results and friction analysis results for samples 4D, 4E, and 4F.

[0059] As shown in Figures 7 to 10, the difference between the torque ratio obtained by measurement and the torque ratio obtained by friction analysis fell within ±20%. Therefore, it was found that the friction analysis was highly accurate. Thus, it can be said that the friction analysis allows for the accurate analysis of the dynamic friction torque of the ball screw device 1. In other words, the results obtained by the friction analysis reflect both the contact state between the ball 4 on the forward operating side and the screw groove, and the contact state between the ball 4 on the reverse operating side and the screw groove, and were found to be highly reliable.

[0060] (Parametric study, multiple regression analysis) Next, we will explain the parametric study mentioned above. As shown in Table 2 below, a total of 69,498 different conditions were prepared for the parametric study.

[0061] [Table 2]

[0062] Based on the results of the parametric study, factors influencing the dynamic friction torque were identified, and multiple regression analysis was performed to derive equation 13 from the regression equation 11 shown below. Specifically, for the ball 4 on the forward operating side, equation 11 was derived by performing multiple regression analysis on the amount of elastic approach of the outer circumference screw groove 20 to the third contact point. Equation 12 was derived by performing multiple regression analysis on the amount of elastic approach of the inner circumference screw groove 30 to the third contact point for the ball 4 on the forward operating side. Equation 13 was derived by performing multiple regression analysis on the amount of elastic approach of the outer circumference screw groove 20 to the third contact point for the ball 4 on the reverse operating side.

[0063]

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[0064]

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[0065]

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[0066] Here, on the forward operating side, ball 4 makes contact at a total of two points. In other words, the condition for a third contact not to occur is that equations 11 and 12 have negative values. On the reverse operating side, the condition for ball 4 to make contact at a total of three points is that equation 13 has a positive value. For these reasons, we derive 0 > equation 11, 0 > equation 12, and 0 < equation 13.

[0067] Then, from equations 0 > equation 11, 0 > equation 12, and 0 < equation 13, we get radial gap T r By moving it to the left side, equation 10 can be obtained from equation 8. However, if the right side of equation 9 becomes a negative value from equation 8, the radial gap T r Regardless, this indicates that ball 4 does not contact the third contact point. In other words, if the right-hand side of equation 9 becomes a negative value from equation 8, then equation 9 will hold true from equation 8. Also, if the right-hand side of equation 10 becomes a negative value, then the radial clearance T r Regardless of the value of , this shows that ball 4 will not make contact with the third contact point. In other words, if the right-hand side of equation 10 is a negative value, equation 10 will not hold true.

[0068] In addition, radial gap T r If equation 10 is satisfied (when the ball 4 on the reverse-acting side contacts the outer screw groove 20), a third contact point does not physically occur between the ball 4 and the inner screw groove 30. For this reason, the amount of elastic approach of the inner screw groove 30 to the third contact point with respect to the ball 4 on the reverse-acting side has not been derived (regression analysis).

[0069] Next, the contact state of the balls 4 when the ball screw device 1 of this embodiment is stationary will be described with reference to Figures 11 to 13. In this embodiment, when the ball screw device is stationary, the radial clearance T rDepending on the size of the contact points, the ball may make two-point or three-point contact. The following explains the cases where the ball makes two-point contact and three-point contact.

[0070] When stationary, no kinetic friction force acts from the screw groove, and the first ball 41 and the second ball 42 are in the same contact state, without distinction between the forward operating side and the reverse operating side. Therefore, the following explanation will use the first ball 41 side.

[0071] Figure 11 is a cross-sectional view showing the contact state of the first ball in the ball screw device of the embodiment when stationary. Note that the ball screw device shown in Figure 11 has a radial clearance T r This diagram shows the case where the pressure is set to a small value and the first ball 41 is in contact with the third contact point. For the sake of explanation, the contact point between the first ball 41 and the outer screw groove 20 when stationary is referred to as the actual contact point 26, and the contact point between the first ball 41 and the inner screw groove 30 is referred to as the actual contact point 36. Furthermore, the line drawn from the center O4 of the ball 4 to the actual contact point 26 is referred to as the imaginary line K5, and the line drawn from the center O4 of the ball 4 to the actual contact point 36 is referred to as the imaginary line K6. The line segment L is the line connecting the actual contact points 26 and 36.

[0072] As shown in Figure 11, the center O4 of the first ball 41 is displaced toward the third contact point (actual contact point 26) of the screw shaft 2, and the first ball 41 is in contact with the outer screw groove 20 at two points. In other words, the first ball 41 is supported at three points. At this time, the actual contact angle α is formed by the imaginary line K and the imaginary line K5. iA The initial contact angle α i This is the same. Here, the line segment L shown in Figure 11 does not pass through the center O4 of the first ball 41. Therefore, the line segment L shown in Figure 11 is shorter than the line segment L shown in Figures 12 and 13.

[0073] Figure 12 is a cross-sectional view of a ball screw device with a larger radial clearance than the ball screw device in Figure 11. As shown in Figure 12, the radial clearance T rIncreasing the value causes the line segment L to pass through the center O4 of the ball. In this state, the first ball 41 is supported at the two points (actual contact points 26 and 36) at both ends of the line segment L. In other words, the first ball 41 is in contact with the third contact point (actual contact point 26) of the screw shaft 2, but the ball load is zero.

[0074] Figure 13 is a cross-sectional view of a ball screw device with a larger radial clearance than the ball screw device in Figure 12. As shown in Figure 13, the radial clearance T r If the angle is increased further, the first ball 41 will not contact the third contact point (actual contact point 26) of the outer screw groove 20. Also, the line segment L passes through the center O4 of the ball. And the actual contact angle α iA =α eA >Initial contact angle α i This is the result.

[0075] Here, the radial clearance shown in Figure 12 is T. CN If you look closely, this radial gap T CN The formula for calculating this is given by the following 14 equations based on the geometric conditions.

[0076]

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[0077] Furthermore, as shown in Figures 11 to 13, the radial clearance T r <T CN In this case, the ball makes contact at three points when stationary. In other words, radial gap T r The ball will have three points of contact when stationary if it satisfies the following equation 15.

[0078]

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[0079] The radial gap T that satisfies equations 8 through 10 above is... rBy setting it, the reduction of dynamic frictional torque can be achieved. By satisfying Equation (15), a three-point contact state is achieved at rest, and risks such as improvement of stability and oscillation can be reduced.

[0080] (Example 1) Next, examples will be described. In Example 1, the values of the initial contact angle and the like of Samples 2A, 2B, and 2C were substituted into Equations (8) to (10) and calculated. The calculation results are shown below.

[0081] Equation (8) ··· Tr > 0.021 (mm) Equation (9) ··· Tr > -0.132 (mm) Equation (10) ··· Tr < 0.173 (mm)

[0082] From the above results, the radial clearance T r is specified as 0.021 (mm) < Tr < 0.173 (mm). Therefore, among Samples 2A, 2B, and 2C, Samples 2B and 2C satisfied the above conditions, while Sample 2A did not.

[0083] Next, the dynamic frictional torques of Samples 2A, 2B, and 2C were measured, and the torque ratios were calculated. Also, in order to determine the torque ratios of Samples 2A, 2B, and 2C, the dynamic frictional torque of a conventional ball screw device was measured. The torque ratios of Samples 2A, 2B, and 2C and the conventional example are ratios when the torque of the conventional example is set to 1. Hereinafter, the respective torque ratios are shown in FIG. 14.

[0084] FIG. 14 is a diagram (graph) showing the measurement results of Example 1. As shown in FIG. 14, for Samples 2B and 2C in which the radial clearance T r is included in the range indicated by Equations (8) to (10), it was found that the torque ratio is smaller than that of the conventional example and the dynamic frictional torque is reduced. On the other hand, for Sample 2A in which the radial clearance T r is not included in the range indicated by Equations (8) to (10), it was found that the torque ratio is higher than that of the conventional example and the dynamic frictional torque is increased.

[0085] Also, when the initial contact angles of Samples 2A, 2B, and 2C are substituted into Equation (15), Tr < 0.098 mm was calculated. Therefore, Samples 2B and 2C that satisfy this condition are in three-point contact when the ball screw device is stationary.

[0086] (Example 2) In Example 2, the values of the contact angles of Samples 4D, 4E, and 4F were substituted into Equations (8) to (10) and calculated. The calculation results are as follows.

[0087] Equation (8) ··· Tr > 0.018 (mm) Equation (9) ··· Tr > -0.070 (mm) Equation (10) ··· Tr < 0.219 (mm)

[0088] From the above results, the range of the radial clearance T r was specified as 0.018 (mm) < Tr < 0.219 (mm). Therefore, among Samples 4D, 4E, and 4F, Samples 4E and 4F satisfied the above conditions, while Sample 4D did not.

[0089] Next, the dynamic friction torques of Samples 4D, 4E, and 4F were measured, and the torque ratios were calculated. Also, in order to determine the torque ratios of 4D, 4E, and 4F, the dynamic friction torque of a conventional ball screw device was measured. The torque ratios of 4D, 4E, and 4F and the conventional example are the ratios when the torque of the conventional example is set to 1. Hereinafter, the respective torque ratios are shown in FIG. 15.

[0090] FIG. 15 is a diagram (graph) showing the measurement results of Example 2. As shown in FIG. 15, Samples 4E and 4F in which the radial clearance T r is included in the range shown by Equations (8) to (10) were found to have a smaller torque proportion and a reduced dynamic friction torque than the conventional example. On the other hand, it was found that Sample 4D in which the radial clearance T r is not included in the range shown by Equations (8) to (10) has a higher torque ratio and an increased dynamic friction torque than the conventional example.

[0091] Furthermore, substituting the initial contact angles of 4D, 4E, and 4F into equation 15, we calculated that Tr < 0.090 mm. Therefore, samples 4E and 4F, which satisfy this condition, have three-point contact when the ball screw device is stationary. [Explanation of Symbols]

[0092] 1. Ball screw device 2 Screw shaft 3 nuts 3a central part 4 balls 5 tubes 20 Outer circumference thread grooves 30 Internal thread groove 31 First internal thread groove 32 Second internal thread groove 41 First Ball 42. Second ball α i ...Initial contact angle between the screw shaft and the ball α e ...Initial contact angle between the nut and the ball T r ...Radial gap Dw... Ball diameter β... Lead angle of screw grooves (outer and inner screw grooves) R i ...radius of curvature of the outer thread groove f i ...Outer thread groove radius (R) i / Dw) R e ...radius of curvature of the internal thread groove f e ...R ratio of the groove radius of the internal thread groove (R e / Dw)

Claims

1. A screw shaft having a Gothic arch-shaped outer thread groove formed on its outer surface, A nut having a Gothic arch-shaped internal thread groove formed on its inner surface, A plurality of balls arranged in the raceway between the outer circumference screw groove and the inner circumference screw groove, Equipped with, The direction parallel to the center line of the screw shaft is defined as the axial direction. The internal thread groove comprises a first internal thread groove located in one axial direction from the axial center of the nut, and a second internal thread groove located in the other axial direction. The first inner circumferential screw groove and the second inner circumferential screw groove are positioned offset in the axial direction relative to the outer circumferential screw groove so that preload is applied to the ball. The initial contact angle between the outer circumferential screw groove and the ball, and the initial contact angle between the inner circumferential screw groove and the ball satisfy the following equation 1. The direction perpendicular to the aforementioned center line is defined as the radial direction. The radial clearance in which the nut can move in the radial direction satisfies equations 2 through 4 below. Ball screw device. [Math 1] [Math 2] [Math 3] [Math 4] α ｉ : Initial contact angle between the screw shaft and the ball α ｅ : Initial contact angle between the nut and the ball T ｒ : Radial gap Dw: Ball diameter β: Lead angle of screw grooves (outer and inner screw grooves) R ｉ : Radius of curvature of the outer thread groove f ｉ : Outer circumference screw groove groove R ratio (R ｉ / Dw) R ｅ : Radius of curvature of the internal thread groove f ｅ : Groove R ratio of the inner circumferential thread groove (R ｅ / Dw)

2. The radial clearance satisfies the following equation 5, When stationary, the ball has three contact points with the outer circumference screw groove and the inner circumference screw groove. The ball screw device according to claim 1. [Math 5]

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