Rotary ball screw spline set

Abstract

This rotary ball screw spline set provides a solution that reduces localized stress concentration through appropriate load distribution and operational precision. [Solution] The ball spline is provided on a shaft and comprises a spline outer cylinder and a plurality of second balls, the plurality of second balls being provided on the spline outer cylinder and rolling in linear rolling grooves, and there is a second distance from the center of each of the plurality of second balls located in the linear rolling grooves to the center of the shaft, the second distance being longer than the first distance, and the spline outer diameter of the spline outer cylinder is calculated by a predetermined formula.

Description

Technical Field

[0001] The present invention relates to a rotary ball screw spline set, and particularly to a rotary ball screw spline set capable of operating with low inertia.

Background Art

[0002] Currently, rotary ball screw spline sets are widely used in high-precision transmission systems such as robots, CNC machine tools, and automation equipment. Here, in the conventional design method, usually, the overall sizes of the ball nut and the ball spline are adjusted based on empirical rules.

Summary of the Invention

Problems to be Solved by the Invention

[0003] However, with such an adjustment method, non-uniform loads may occur or it may lead to an increase in wear loss, which may affect the product life and accuracy. Considering these problems, in order to ensure the highest motion performance of the rotary ball screw spline set, an optimization method based on mathematical calculations is required to further reduce the volume and weight of the ball nut or the ball spline, and to reduce the moment of inertia generated by the rotation of the rotary ball screw spline set during operation.

Means for Solving the Problems

[0004] In view of the above problems, one aspect of the present invention has the following configuration. A rotary ball screw spline set including a shaft, a ball nut, and a ball spline, wherein the shaft is provided with a spiral screw rolling groove and a linear linear rolling groove on its surface, The ball nut is provided on the shaft and has a plurality of first balls, the plurality of first balls rolling in the screw rolling groove, and there is a first distance from the center of each of the plurality of first balls located in the screw rolling groove to the axis of the shaft. The ball spline is provided on the shaft, and the ball spline comprises a spline outer cylinder and a plurality of second balls, the plurality of second balls being provided on the spline outer cylinder and rolling in the linear rolling groove, There is a second distance between the center of each of the plurality of second balls located in the linear rolling groove and the center of the shaft. The second distance is longer than the first distance, and the spline outer diameter of the spline outer cylinder is calculated by the following formula:

number

number

[0005] Furthermore, in the above embodiment, a may be less than 45°.

[0006] Furthermore, in the above embodiment, the diameter of the first ball may be the same as the diameter of the second ball.

[0007] Furthermore, in the above embodiment, the outer diameter of the ball nut may be equal to the outer diameter of the spline.

[0008] Furthermore, in the above embodiment, the angle of b may be approximately 10° to 15°.

[0009] Furthermore, in the above embodiment, the diameter of X may be thicker than 0.3 millimeters.

[0010] Furthermore, in the above embodiment, the value of Fs may be 5%.

[0011] Furthermore, in the above embodiment, the ball spline further comprises a bearing jacket, The bearing jacket is set on the outer surface of the spline outer cylinder, and a plurality of the second balls are provided between the bearing jacket and the spline outer cylinder, and the outer diameter of the bearing jacket is calculated by the following formula:

number

[0012] Furthermore, in the above embodiment, the inner diameter of the ball spline is calculated by the following formula:

number

[0013] Another aspect of the present invention relates to a rotary ball screw spline set comprising a shaft, a ball nut, and a ball spline, The shaft has a helical screw rolling groove and a linear linear rolling groove provided on its surface. The ball nut is provided on the shaft and has a plurality of first balls. The plurality of first balls roll in the screw rolling groove, and each of the plurality of first balls located in the screw rolling groove has a first distance from the center of the ball to the axis of the shaft. The ball spline is provided on the shaft. The ball spline includes a spline outer cylinder and a plurality of second balls. The plurality of second balls are provided on the spline outer cylinder and roll in the linear rolling groove. Each of the plurality of second balls located in the linear rolling groove has a second distance from the center of the ball to the center of the shaft. The second distance is longer than the first distance, and the spline inner diameter of the spline outer cylinder is calculated by the following formula.

Equation

Equation

[0014] Also, in the above aspect, a may be smaller than 45°.

[0015] Furthermore, in the above embodiment, the diameter of the first ball may be the same as the diameter of the second ball.

[0016] Furthermore, in the above embodiment, the angle of b may be approximately 10° to 15°. [Effects of the Invention]

[0017] The spline outer diameter of the spline outer cylinder, as determined by the above formula, corresponds to the shaft diameter and the required load it can withstand. Therefore, by limiting the spline's three-wire height (hs) to be higher than the ball nut's three-wire height, the optimal spline outer diameter can be obtained.

[0018] This ensures that the balls are positioned correctly for load transfer, and proper load distribution and operational precision reduce localized stress concentration. At the same time, because the optimal spline outer diameter can be obtained, the volume of the ball spline can be effectively reduced compared to conventional designs, enabling the entire rotary ball screw spline set to operate with low inertia during operation. Due to its low inertia characteristics, the impact caused by inertia during operation can be improved.

[0019] Furthermore, the inner spline diameter of the spline outer cylinder, as determined by the above formula, corresponds to the shaft diameter and the required load it can withstand. Therefore, by limiting the spline's three-wire height (hs) to be higher than the ball nut's three-wire height, the optimal spline outer diameter can be obtained.

[0020] This ensures that the balls are positioned correctly for load transfer, and proper load distribution and operational precision reduce localized stress concentration. At the same time, because the optimal spline inner diameter can be obtained, the weight of the ball spline can be effectively reduced compared to conventional designs, enabling the entire rotary ball screw spline set to operate with low inertia during operation. Due to its low inertia characteristics, the impact caused by inertia during operation can be improved. [Brief explanation of the drawing]

[0021] [Figure 1] This is a perspective view of a rotary ball screw spline set according to one embodiment of the present invention. [Figure 2] This is a cross-sectional view of a rotary ball screw spline set according to one embodiment of the present invention. [Figure 3] This is a cross-sectional view of a shaft and a second ball according to one embodiment of the present invention. [Figure 4] This is a cross-sectional view of the spline outer cylinder of a ball spline according to one embodiment of the present invention. [Modes for carrying out the invention]

[0022] The explanation will be given with reference to Figures 1 and 2. Figure 1 is a perspective view of a rotary ball screw spline set according to one embodiment of the present invention, and Figure 2 is a cross-sectional view of a rotary ball screw spline set according to one embodiment of the present invention.

[0023] The rotary ball screw spline set 100 of this embodiment comprises a shaft 10, a ball nut 20, and a ball spline 30. The surface of the shaft 10 is provided with a helical screw rolling groove 11 and a linear rolling groove 12.

[0024] The ball nut 20 is provided on the shaft 10 and has a plurality of first balls 21 that roll within the screw rolling groove 11, and the distance from the center of each first ball 21 located within the screw rolling groove 11 to the axis C of the shaft 10 is a first distance d1.

[0025] The ball spline 30 is provided on the shaft 10. The ball spline 30 comprises a spline outer cylinder 31 and a plurality of second balls 32. The plurality of second balls 32 are arranged on the spline outer cylinder 31 and roll in a linear rolling groove 12. There is a second distance d2 from the center of each second ball 32 located in the linear rolling groove 12 to the axis C of the shaft 10, and the second distance d2 is longer than the first distance d1.

[0026] Here, the first distance d1 can be considered as half the height of the three wires of the ball nut 20, and the second distance d2 can be considered as half the height of the three wires of the ball spline 30.

[0027] Here, the three-line height of the ball nut 20 generally refers to the size of the diameter of the circle formed by the path along which the center of the second ball 32 travels, as viewed from the axis C of the shaft 10, when the second ball 32 rolls on the spline outer cylinder 31. Here, the specification of this application uses the length of the part actually referenced (hs is twice the distance from the center of the circle of the second ball 32 to the axis of the spline outer cylinder 31 when the second ball 32 rolling in the straight rolling groove 12 is assembled on the spline outer cylinder 31), but the actual meaning of the three-line height of the ball nut 20 is as described above.

[0028] By making the second distance d2 longer than the first distance d1, the height of the three lines of the ball spline 30 becomes longer than the height of the three lines of the ball nut 20. By adjusting the contact angle and position between the ball spline 30 and the shaft 10, the second ball 32 transmits the load at the appropriate position, resulting in appropriate load distribution and movement accuracy, and reducing localized stress concentration. Next, we will explain with reference to Figures 3 and 4. Here, Figure 3 is a cross-sectional view of a shaft and a second ball according to one embodiment of the present invention, and Figure 4 is a cross-sectional view of the spline outer cylinder of a ball spline according to one embodiment of the present invention.

[0029] In this embodiment, the calculation of the spline outer diameter Ds of the spline outer cylinder 31 will be explained using Figures 1 to 4. The spline outer diameter Ds of the spline outer cylinder 31 is calculated using the following formula.

[0030]

number

[0031] Ds is the outer diameter of the spline. When the second ball 32, which rolls within the linear rolling groove 12, is assembled to the spline outer cylinder 31, hs is twice the distance from the center of the circle of the second ball 32 to the axis of the spline outer cylinder 31. a is the angle between the first extension line L1 and the second extension line L2. The first extension line L1 is a hypothetical straight line from the point of contact between the second ball 32 and the straight rolling groove 12 to the center of the circle of the second ball 32. The second extension line L2 is a hypothetical straight line representing the shortest distance from the center of the circle of the second ball 32 to the axis C. b is the machining error angle of the linear rolling groove. φ is the diameter of the second ball 32. Fs is the ball diameter machining error rate. X is the required wall thickness of the spline outer cylinder 31.

[0032] As is clear from Figure 4, the diameter of the outermost ring of the spline outer cylinder 31 is the spline outer diameter Ds.

[0033] Figure 3 shows a cross-sectional view of the shaft 10. The second ball 32, located within the linear rolling groove 12, is indicated by a dotted line. The diameter of the circle indicated by the dashed line in Figure 3 is the value of hs.

[0034] The circle indicated by the dashed line represents the position of the center of the circle of the second ball 32 that rolls within the linear rolling groove 12 assembled in the spline outer cylinder 31.

[0035] Since the linear rolling grooves 12 are provided parallel to the symmetrical upper and lower sides of the shaft 10, the circles shown by the dashed lines also pass through the centers of the circles of the second balls 32 that roll within the upper and lower linear rolling grooves 12, respectively.

[0036] hs is the diameter of the circle represented by the dashed line, and can be considered as the three-line height of the ball spline 30. It is approximately twice the second distance d2, that is, twice the distance from the center of the circle of the second ball 32 to the axis C of the spline outer cylinder 31.

[0037] As can be seen from Figure 3, 'a' refers to an angle (in degrees), which is the angle between the first extension line L1 and the second extension line L2. The first extension line L1 is a hypothetical straight line from the point of contact between the second ball 32 and the straight rolling groove 12 to the center of the circle of the second ball 32. The second extension line L2 is a hypothetical straight line representing the shortest distance from the center of the circle of the second ball 32 to the axis C.

[0038] In this embodiment, the arcuate surface of the linear rolling groove 12 and the arcuate surface of the second ball 32 have different shapes, and the second ball 32 contacts the arcuate surface of the linear rolling groove 12 at two points on the circle, and there are two contact points at this time.

[0039] In Figure 3, only the imaginary straight line from the point of contact between the second ball 32 and the left side of the straight rolling groove 12 to the center of the circle of the second ball 32 is shown, which is the first extension line L1.

[0040] In reality, there is also a contact point to the right of the second ball 32 and the linear rolling groove 12, and the angle between this contact point, the imaginary line of the center of the circle of the second ball 32 and the second extension line L2 is the same as the angle a between the first extension line L1 and the second extension line L2.

[0041] Furthermore, it should be noted that, due to the size and proportions of the drawing in Figure 3, one might visually be misled into believing that the entire arcuate surface of the second ball 32 is in contact with the linear rolling groove 12, but in reality, there are only two contact points.

[0042] Furthermore, when the condition described above is met that the second distance d2 is longer than the first distance d1, and the contact point of the ball spline 30 is set higher than the contact point of the ball nut 20, and the corresponding angle a on the ball nut 20 is set to 45° to simplify calculations, the angle a of the ball spline 30 is often less than 45°.

[0043] The angle to be adopted is often determined by referring to a table, based on the diameter D of the shaft 10 and the required load of the rotary ball screw spline set 100.

[0044] b is the machining error angle of the straight rolling groove (unit is "°"), and this is because there is a possibility of machining errors when machining the straight rolling groove 12, so an error occurs in the angle a between the first extension line L1 and the second extension line L2.

[0045] When calculating the spline outer diameter Ds, it is necessary to add the machining error angle b of the linear rolling groove.

[0046] Furthermore, depending on the machining method and machining accuracy during processing, this error may occur simultaneously on both sides. Therefore, the machining error angle b of the linear rolling groove defined here refers to the error angle on one side (the left side of the figure), as shown in Figure 3.

[0047] In this embodiment, the preferred range for the machining error angle b of the linear rolling groove is 10° to 15°.

[0048] Machining errors may occur during the manufacturing process of the second ball 32. In order to reduce the spline outer diameter Ds more accurately and effectively while ensuring smooth rolling simply by mounting the second ball 32, the machining error rate Fs of the ball diameter of the second ball 32 should also be considered when calculating the spline outer diameter Ds.

[0049] In this embodiment, the ball diameter machining error rate Fs is 5%, and in other embodiments, the ball diameter machining error rate Fs can be adjusted according to the machining accuracy so that the calculated spline outer diameter Ds better matches the actual requirements.

[0050] When manufacturing and processing the spline outer cylinder 31, it is necessary to form a required wall thickness X of a certain thickness toward the outside of the ball groove where the second ball 32 is provided, in order to meet the required structural strength and conform to the processing tolerances, thereby avoiding any impact on the structural strength.

[0051] The required wall thickness X mentioned above is the minimum wall thickness required based on currently achievable machining tolerances. In this embodiment, the value of the required wall thickness X is greater than 0.3 mm (millimeters).

[0052] To minimize the required spline outer diameter Ds, the size of the spline outer cylinder 31 should be reduced as much as possible, thereby decreasing the overall volume of the ball spline 30 and lowering the inertia during operation. hs must follow the following rules.

[0053]

number

[0054] Here, D is the diameter of shaft 10.

[0055] The spline outer diameter Ds of the spline outer cylinder 31, as determined by the above formula, corresponds to the diameter D of the shaft 10 and the required load that the rotary ball screw spline set 100 can withstand. By limiting the second distance d2 of the ball spline 30 to be longer than the first distance d1, that is, by limiting the height of the three lines of the ball spline 30 to be higher than the height of the three lines of the ball nut 20, the optimal spline outer diameter Ds can be obtained.

[0056] Thus, a ball spline 30 manufactured with an optimal spline outer diameter Ds can effectively reduce the volume of the ball spline 30 compared to conventional splines. This allows the entire rotary ball screw spline set 100 to operate with low inertia during operation, and its low inertia characteristics improve the impact caused by inertia during operation.

[0057] To verify the above effects, inertial analysis was simulated using the spline outer cylinder 31 of Example 1 and the current spline outer cylinder as a comparative example, under the same operating conditions. The results of the relevant analysis data are shown in Table 1 below.

[0058] [Table 1]

[0059] As can be seen from Table 1, if the size of the second ball 32, the diameter D of the shaft 10, and the required load that the rotary ball screw spline set 100 can withstand are all set to the same value, substituting the corresponding condition values ​​into the above formula and calculating the value of the spline outer diameter Ds under condition hs, the spline outer diameter Ds is 3.25 cm.

[0060] The outer diameter Ds of this spline is significantly smaller than the current (comparative example) 3.6 cm. By effectively reducing the outer diameter Ds of the spline and decreasing the overall volume, the weight of the ball spline 30 can also be reduced accordingly.

[0061] The dual effect of volume reduction and weight reduction effectively reduces the inertia of the rotary ball screw spline set 100 during operation. Compared to the rotary ball screw spline set of the comparative example, the rotary ball screw spline set 100 of Example 1 can improve the impact of inertial effects during operation due to its lower inertia characteristics.

[0062] Furthermore, if the above conditions are met, the diameters of the first ball 21 and the second ball 32 can be made the same to ensure consistency in the movement of all balls in the rotary ball screw spline set 100 and to avoid additional friction and stress caused by balls of different diameters.

[0063] Furthermore, after determining the spline outer diameter Ds based on the formula and conditions described above, the nut outer diameter of the ball nut 20 can be made equal to the spline outer diameter Ds.

[0064] This makes post-installation planning more convenient for the entire rotary ball screw spline set 100, eliminating the need to individually design, manufacture, and assemble parts corresponding to both the nut outer diameter of the ball nut 20 and the spline outer diameter Ds of the ball spline 30.

[0065] As can be seen from Figures 1 and 2, in this embodiment, the ball spline 30 further includes a bearing jacket 33 set on the outer surface of the spline outer cylinder 31, and a plurality of second balls 32 are provided between the bearing jacket 33 and the spline outer cylinder 31.

[0066] Since the bearing jacket 33 is attached to the spline outer cylinder 31 and the two are assembled via a plurality of second balls 32, the outer diameter Rs of the bearing jacket 33 is calculated by the following formula in order to ensure that the bearing jacket 33 also has an optimal outer diameter Rs.

[0067]

number

[0068] Rs is the outer diameter of the jacket.

[0069] As can be seen in Figure 2, the outer diameter Rs of the jacket refers to the diameter of the bearing jacket 33. The bearing jacket 33 is fitted into the spline outer cylinder 31, and the second ball 32 is sandwiched between them.

[0070] Therefore, the jacket outer diameter Rs is calculated based on the spline outer diameter Ds, increasing the diameter φ of the second ball 32 outwards, and also taking into account the machining error rate Fs of the ball diameter of the second ball 32.

[0071] Furthermore, by referring to the spline outer cylinder 31 and adding the same required wall thickness X to the outside, the above-mentioned formula for calculating the jacket outer diameter Rs can be obtained. Since the jacket outer diameter Rs is obtained in accordance with the spline outer diameter Ds of the spline outer cylinder 31, the volume of the jacket outer diameter Rs can also be effectively reduced, saving the material required to manufacture the bearing jacket 33 and effectively lowering manufacturing costs.

[0072] In addition to the above method of calculating the spline outer diameter Ds to effectively reduce the volume of the spline outer cylinder 31 and reduce the inertia of the rotary ball screw spline set 100, the spline inner diameter ds of the ball spline 30 can also be further calculated by the following formula.

[0073]

number

[0074] ds is the inner diameter of the spline. The spline inner diameter ds is the diameter of the inner circle of the ball spline 30. The spline inner diameter ds calculated using the formula described above is the optimal spline inner diameter ds obtained assuming it matches the spline outer diameter Ds. By calculating the optimal spline inner diameter ds, the overall weight of the ball spline 30 can be further reduced, and the inertia of the rotary ball screw spline set 100 can be reduced.

[0075] Similarly, to verify the effect of simultaneously changing the spline outer diameter Ds and spline inner diameter ds as described above, inertial analysis was performed by simulating the spline outer cylinder 31 of Example 2 and a conventional spline outer cylinder as a comparative example under the same operating conditions. The results of the relevant analysis data are shown in Table 2 below.

[0076] [Table 2]

[0077] As can be seen from Table 2, under the condition that the size of the second ball 32, the diameter D of the shaft 10, and the required load that the rotary ball screw spline set 100 can withstand are all set to the same value, substituting the corresponding condition values ​​into the above formula, the values ​​of the spline outer diameter Ds and spline inner diameter ds that satisfy the condition hs can be calculated, and the spline outer diameter Ds is 3.25 cm and the spline inner diameter ds is 1.7 cm.

[0078] In addition to the spline outer diameter Ds being significantly shorter than the current (i.e., comparative example) 3.6 cm, the spline inner diameter ds is longer than the current (i.e., comparative example) 1.61 cm. Changing both the spline outer diameter Ds and the spline inner diameter ds further reduces the overall volume, and the weight of the ball spline 30 is reduced accordingly.

[0079] The dual effect of volume reduction and weight reduction more effectively reduces the inertia of the rotary ball screw spline set 100 during operation. Compared to the rotary ball screw spline set of the comparative example, the rotary ball screw spline set 100 of Example 2 has lower inertia characteristics, thus improving the impact of inertia during operation.

[0080] From the above explanation, it can be seen that the inertia of the rotary ball screw spline set 100 during operation can be reduced by reducing the volume and weight of the ball spline 30. In the above-described embodiment 1, the spline outer diameter Ds was changed, but in embodiment 2, both the spline outer diameter Ds and the spline inner diameter ds are changed.

[0081] However, in other embodiments, the volume and weight of the ball spline 30 can be reduced simply by changing the spline inner diameter ds, thereby achieving the effect of reducing the inertia of the rotary ball screw spline set 100 during operation.

[0082] In the structure of the rotary ball screw spline set 100 described above, in Embodiment 3, the second distance d2 is set to be longer than the first distance d1, a is set to be less than 45°, the diameter of the first ball 21 is the same as the diameter φ of the second ball 32, and the angle of b is approximately 10° to 15°. Next, the spline inner diameter ds is calculated using the formula described later.

[0083]

number

[0084] ds is the inner diameter of the spline. It is important to note that when calculating the spline diameter ds as described above, hs must also follow the following rules.

[0085]

number

[0086] D is the diameter of shaft 10. a is the angle between the first extension line L1 and the second extension line L2, where the first extension line L1 is a hypothetical straight line from the point of contact between the second ball 32 and the straight rolling groove 12 to the center of the circle of the second ball 32, and the second extension line L2 is a hypothetical straight line representing the shortest distance from the center of the second ball 32 to the axis C. b is the machining error angle of the linear rolling groove.

[0087] To verify the above effects, inertia analysis was performed by simulating the spline outer cylinder 31 of Example 3 with a conventional spline outer cylinder as a comparative example under the same operating conditions. The results of the relevant analysis data are shown in Table 3 below.

[0088] [Table 3]

[0089] As can be seen from Table 3, under conditions where the size of the second ball 32, the diameter D of the shaft 10, the required load that the rotary ball screw spline set 100 can withstand, and the spline outer diameter Ds are all set to the same value, substituting the corresponding condition values ​​into the above formula and calculating the spline inner diameter ds value that satisfies the condition hs, it can be seen that the spline inner diameter ds is 1.7 cm.

[0090] The spline inner diameter ds will be slightly longer than the current (comparative example) 1.61 cm. When the spline inner diameter ds is slightly longer, the thickness of all walls of the ball spline 30 can be slightly reduced, and the weight of the ball spline 30 can be reduced accordingly. The reduced weight also reduces the inertia of the rotary ball screw spline set 100 during operation. Compared to the rotary ball screw spline set of the comparative example, the rotary ball screw spline set 100 of Example 3 has lower inertia characteristics, which improves the impact of inertia during operation.

[0091] The present invention is as shown in the embodiments described above, but these embodiments do not limit the technical scope of the invention. Anyone skilled in the art can make some changes and modifications without departing from the spirit and scope of the invention, and the technical scope of the invention shall be interpreted in accordance with the claims. [Explanation of Symbols]

[0092] 100 Rotary Ball Screw Spline Set 10 shafts 11 Screw rolling grooves 12. Straight rolling grooves 20 Ball Nuts 21 First ball 30 Ball Splines 31 Splined outer cylinder 32. Second ball 33 Bearing Jacket a b. Machining error angle of linear rolling groove C axis center d1 First distance d2 Second distance D shaft diameter Ds spline outer diameter ds spline inner diameter When a second ball rolling in a straight rolling groove is assembled on the spline outer cylinder, the distance from the center of the second ball to the axis of the spline outer cylinder is twice the distance from the center of the second ball to the axis of the spline outer cylinder. L1 First Extension Line L2 Second Extension Line Rs Jacket Outer Diameter X Required wall thickness φ diameter

Claims

1. A rotary ball screw spline set comprising a shaft, a ball nut, and a ball spline, The shaft has a helical screw rolling groove and a linear rolling groove on its surface. The ball nut is provided on the shaft and has a plurality of first balls, the plurality of first balls rolling in the screw rolling groove, and there is a first distance from the center of each of the plurality of first balls located in the screw rolling groove to the axis of the shaft. The ball spline is provided on the shaft, and the ball spline comprises a spline outer cylinder and a plurality of second balls, the plurality of second balls being provided on the spline outer cylinder and rolling in the linear rolling groove, There is a second distance between the center of each of the plurality of second balls located in the linear rolling groove and the center of the shaft. The second distance is longer than the first distance, and the outer diameter of the spline outer cylinder is calculated by the following formula: [Number 13] Ds is the outer diameter of the spline, hs is twice the distance from the center of the circle of the second ball to the axis of the spline outer cylinder when the second ball that rolls in the linear rolling groove is assembled on the spline outer cylinder. a is the angle between the first extension line and the second extension line, The first extension line is a virtual straight line from the point of contact between the second ball and the linear rolling groove to the center of the second ball. The second extension line is a virtual straight line representing the shortest distance from the center of the circle of the second ball to the axis. b is the machining error angle of the linear rolling groove, φ is the diameter of the second ball, Fs is the ball diameter machining error rate, X is the required wall thickness of the spline outer cylinder, HS must follow the following rules: [Number 14] A rotary ball screw spline set characterized in that D is the diameter of the shaft.

2. The rotary ball screw spline set according to claim 1, characterized in that a is less than 45°.

3. The rotary ball screw spline set according to claim 1, characterized in that the diameter of the first ball is the same as the diameter of the second ball.

4. The rotary ball screw spline set according to claim 1, characterized in that the outer diameter of the ball nut is equal to the outer diameter of the spline.

5. The rotary ball screw spline set according to claim 1, characterized in that the angle of b is approximately 10° to 15°.

6. The rotary ball screw spline set according to claim 1, characterized in that the diameter of X is thicker than 0.3 millimeters.

7. The rotary ball screw spline set according to claim 1, characterized in that the value of Fs is 5%.

8. The aforementioned ball spline further comprises a bearing jacket, The bearing jacket is set on the outer surface of the spline outer cylinder, and a plurality of the second balls are provided between the bearing jacket and the spline outer cylinder, and the outer diameter of the bearing jacket is calculated by the following formula: [Number 15] The rotary ball screw spline set according to claim 1, characterized in that Rs is the outer diameter of the jacket.

9. The inner diameter of the ball spline is calculated by the following formula: [Number 16] The rotary ball screw spline set according to claim 1, characterized in that ds is the inner diameter of the spline.

10. In a rotary ball screw spline set comprising a shaft, a ball nut, and a ball spline, The shaft has a helical screw rolling groove and a linear rolling groove on its surface. The ball nut is provided on the shaft and has a plurality of first balls, the plurality of first balls rolling in the screw rolling groove, and there is a first distance from the center of each of the plurality of first balls located in the screw rolling groove to the axis of the shaft. The ball spline is provided on the shaft, and the ball spline comprises a spline outer cylinder and a plurality of second balls, the plurality of second balls being provided on the spline outer cylinder and rolling in the linear rolling groove, There is a second distance between the center of each of the plurality of second balls located in the linear rolling groove and the center of the shaft. The second distance is longer than the first distance, and the inner diameter of the spline of the spline outer cylinder is calculated by the following formula: 【Number 17】 ds is the inner diameter of the spline, When the second balls that roll in the linear rolling grooves are assembled on the spline outer cylinder, hs is twice the distance from the center of the circle of the second ball to the axis of the spline outer cylinder. φ is the diameter of the second ball, HS must follow the following rules: [Number 18] D is the diameter of the shaft, a is the angle between the first extension line and the second extension line, The first extension line is a virtual straight line from the point of contact between the second ball and the linear rolling groove to the center of the second ball. The second extension line is a virtual straight line representing the shortest distance from the center of the circle of the second ball to the axis. A rotary ball screw spline set characterized in that b is the machining error angle of the linear rolling groove.

11. The rotary ball screw spline set according to claim 10, characterized in that a is less than 45°.

12. The rotary ball screw spline set according to claim 10, characterized in that the diameter of the first ball is the same as the diameter of the second ball.

13. The rotary ball screw spline set according to claim 10, characterized in that the angle of b is approximately 10° to 15°.

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