Ball screw pair and reverser for ball screw pair

Abstract

The ball screw pair comprises a lead screw, a nut, a plurality of balls and the returner, the nut is arranged on the lead screw in a sleeving mode, a spiral raceway is formed between the inner surface of the nut and the outer surface of the lead screw, the balls are arranged in the spiral raceway, the returner is arranged on the nut, and the returner is arranged on the nut. A ball return groove is formed in the surface, facing the lead screw, of the reverser, the two ends of the ball return groove communicate with the two adjacent spiral raceways correspondingly, and a ball return curve of the ball return groove is designed based on a heptatic parabola curve. According to the method, the easement curve based on the seven-time parabola type is adopted when the ball return curve of the reverser of the ball screw pair is designed for the first time, the designed ball return curve has no abrupt change value, no sharp points exist at the inlet end and the outlet end of a ball return groove, the dynamic performance of a raceway is improved, and therefore the energy loss of balls is reduced, and the service life of the ball screw pair is prolonged. And the overall transmission efficiency of the ball screw pair is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of ball screws, and in particular relates to a ball screw pair and a return device for the ball screw pair. Background Art

[0002] The ball screw pair is mainly composed of four parts: screw, nut, ball and ball circulation return device. The balls added between the screw and the nut are used to realize the conversion from sliding friction to rolling friction, thereby effectively reducing friction loss and improving transmission efficiency.

[0003] In order to make the balls on the working raceway work in a continuous cycle, the return device is an indispensable part of the internal circulation ball screw pair. Its function is to guide the ball chain advancing in the thread raceway in the reverse direction and climb over the top of the thread teeth along the surface of the screw so that the balls return to the starting thread raceway.

[0004] The ball return groove is a spatial groove on the return device that connects the beginning and end of a section of the threaded raceway on the nut. With the help of this groove, it is ensured that the ball can climb over the top of the thread teeth of the screw and return to the original starting position during the circulation process. When the ball moves along this ball return groove, it can smoothly climb over the top of the thread teeth of the screw. In the process of the ball circulating along the ball return curve groove, the motion trajectory of the ball center with a radius of r is called the ball return groove curve (referred to as the ball return curve). Obviously, the geometric characteristics of this curve and the perfection of the ball return groove structure have a great influence on the working performance of the return device. Therefore, people have been carefully designing this ball return curve.

[0005] If the curve has sharp points, the radius of curvature is too small or the design error is too large, it will seriously affect the smoothness and high-speed performance of the ball movement, which is also an important factor affecting the performance of the internal circulation ball screw pair.

[0006] Therefore, there is a need for a return device for a ball screw pair that can improve the running smoothness and speed of the internal circulation ball screw pair, while significantly reducing the noise, heat generation, and jamming of the product. Summary of the invention

[0007] In view of this, the present invention provides a ball screw pair that can improve the dynamic performance of the raceway, thereby reducing the energy loss of the balls and improving the overall transmission efficiency.

[0008] The second object of the present invention is to provide a return device for the above-mentioned ball screw pair, the return ball curve of the return device has no sharp points, and the acceleration of the ball at the connection point of the curve is uniform, which can ensure that the ball moves smoothly during the movement, with low noise and low heat.

[0009] To achieve the above object, the technical solution adopted by the present invention is:

[0010] A ball screw pair comprises a screw, a nut, a plurality of balls and a return device, wherein the nut is sleeved on the screw, a spiral raceway is formed between the inner surface of the nut and the outer surface of the screw, the plurality of balls are arranged in the spiral raceway, the return device is arranged on the nut, a return ball groove is arranged on the surface of the return device facing the screw, and both ends of the return ball groove are respectively connected to two adjacent spiral raceways.

[0011] The bead return curve of the bead return groove satisfies the seventh-order parabola curve equation shown in formula (I-1):

[0012]

[0013] Alternatively, the bead return curve of the bead return groove satisfies the seventh-order parabola curve equation shown in formula (I-2):

[0014]

[0015] Among them, the coefficients A, B, C, and D in formula (I-1) and formula (I-2) respectively satisfy the equation shown in formula (II):

[0016]

[0017] In formula (I-1), formula (I-2) and formula (II), θ is the parameter angle, the unit is °; ρ is the distance from the center of the ball to the center of the screw, the unit is mm; x F is the horizontal coordinate of point F on the bead return curve, in mm; M, N, P, Q are constants.

[0018] According to some implementation aspects of the present invention, in formula (II), the values ​​of M, N, P, and Q are obtained by formula (III):

[0019]

[0020] Among them, p, q, r, The value of is shown in formula (IV);

[0021]

[0022] In formula (III) and formula (IV), L0 is the basic lead, in mm; d0 is the center circle diameter of the ball of the ball screw pair (ie, the nominal diameter), in mm.

[0023] In some embodiments, the bead return curve represented by formula (I-1) or formula (I-2) is obtained by the following method, which comprises:

[0024] (S1) establishing a three-dimensional coordinate system, the three-dimensional coordinate system comprising an X-axis, a Y-axis and a Z-axis which are perpendicular to each other, wherein the central axis of the spiral raceway is the Y-axis, and establishing a parametric equation of a surface equidistant from the outer surface of the screw, as shown in formula (V);

[0025]

[0026] (S2) establishing a seventh-order parabolic cylinder in the three-dimensional coordinate system, wherein the intersection of the equidistant surface and the seventh-order parabolic cylinder is the bead curve, wherein the parameter equation of the seventh-order parabolic cylinder is as shown in formula (VI);

[0027]

[0028] (S3) The parametric equation shown in formula (V) and the parametric equation shown in formula (VI) are solved simultaneously to obtain the bead return curve shown in formula (I-1) or formula (I-2).

[0029] The horizontal and vertical coordinates of the spiral line and the ball return curve at point F are the same, and the curve OF is the projection of the ball return curve in the XOY plane, wherein the spiral line is a track drawn by the center of the ball when the ball flows along the spiral raceway;

[0030] The determination of coefficients A, B, C, and D includes the following steps:

[0031] (i) Establish the parametric equation of the projection of the helix on the XOY plane as shown in formula (VII);

[0032]

[0033] (ii) According to the intersection and tangency of the bead curve and the spiral line at point F, the values ​​of the bead curve and the spiral line at point F and the first three derivatives are the same, and according to the characteristics of the seventh-order parabola curve, the equation shown in formula (VIII) is obtained;

[0034]

[0035] (III) Solving the equation shown in formula (VIII) to obtain the coefficients A, B, C, and D.

[0036] In some embodiments, a plurality of return devices are arranged on the nut along its axial direction.

[0037] In some embodiments, the plurality of return devices are further distributed along the circumference of the nut so that the force on the entire ball screw pair is uniform.

[0038] In some embodiments, a mounting through hole is provided on the nut at a position corresponding to each of the return devices, and each of the return devices is disposed in each of the mounting through holes in a one-to-one correspondence;

[0039] The ball screw pair also includes a sleeve sleeved on the nut, and the sleeve is used to radially limit the multiple return devices.

[0040] In some embodiments, the outer surface of each reflector is a curved surface.

[0041] In some embodiments, the sleeve and the nut are interference fit, which facilitates installation.

[0042] The second technical solution adopted by the present invention is: a return device for a ball screw pair, the ball screw pair comprising a screw, a nut sleeved on the screw and a plurality of balls, a spiral raceway is formed between the inner surface of the nut and the outer surface of the screw, the plurality of balls are arranged in the spiral raceway, the return device is arranged on the nut, a ball return groove is arranged on the surface of the return device facing the screw, the two ends of the ball return groove are respectively connected to two adjacent spiral raceways, and the ball return curve of the ball return groove satisfies the seventh parabola curve equation shown in formula (I-1) or the seventh parabola curve equation shown in formula (I-2).

[0043] Due to the application of the above technical solution, the present invention has the following advantages compared with the prior art:

[0044] The present invention proposes for the first time that a seventh-order parabola-based transition curve is used when designing the return ball curve of the return device of a ball screw pair. The return ball curve thus designed has no sudden change value and no sharp points at the inlet and outlet ends of the return ball groove, thereby improving the dynamic performance of the raceway, thereby reducing the energy loss of the ball and improving the overall transmission efficiency of the ball screw pair.

[0045] The ball return curve designed by the present invention has no sharp points, which can ensure that the ball moves smoothly during the movement, with low noise and low heat generation. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the embodiments of the present invention. For ordinary technicians in this field, other drawings can also be obtained based on these drawings.

[0047] Figure 1 An exploded view of a ball screw pair according to an embodiment of the present invention;

[0048] Figure 2 It is a schematic diagram of a curve where an equidistant curved surface of a ball screw pair intersects with a seventh-order parabola cylinder according to an embodiment of the present invention;

[0049] Figure 3It is a schematic diagram of the intersection and tangency of the projection curves of the helix line and the return ball curve of the ball screw pair in one embodiment of the present invention on the XOY plane;

[0050] Reference numerals :

[0051] 1. Return device; 2. Lead screw; 3. Nut; 4. Mounting through hole; 5. Sleeve;

[0052] 11. Spiral line projection curve; 12. Seventh-order parabola projection curve; 13. Retroreflector contour projection curve. DETAILED DESCRIPTION

[0053] The return curve of the ball return device currently used in the market is a quintic parabola. However, the quintic parabola design of the return device still has sharp points, and the movement of the ball is not smooth.

[0054] The inventor of the present application proposed to adopt a curve type that is completely different from the existing one and apply it to the design of the return ball curve of the reflector. It was the first time that a gentle curve based on a seventh parabola was used in the design of the return ball curve of the reflector. The return ball curve designed based on this has no sudden change value, no sharp points at the entrance and exit ends of the return ball groove, and the ball moves smoothly during the movement.

[0055] The inventors of this application also found in the research process that the higher the order of the curve type, the more suitable it is: first, when the order of the parabola used exceeds the seventh order, the fourth-order and above derivatives at the entrance and exit of the return bead groove are the same, but the first three derivatives correspond to velocity, acceleration and jerk, respectively, and the fourth-order and above derivatives have lost their clear physical meaning. Therefore, it is meaningless to choose a parabola of the ninth order and above in terms of physics. Second, for return devices with complex shapes, grinding or electrospark machining is usually used, which corresponds to a machining accuracy of about 0.01mm and about 0.02mm, respectively, while the shape difference between the seventh-order parabola and the higher-order parabola is very small, especially for return devices with smaller sizes, the difference between the two is even smaller than the machining error. In other words, it is difficult to distinguish between the seventh-order parabola and the ninth-order and above parabolas in processing.

[0056] The inventors of the present application also discovered during the research process that, for the return bead curve of the reflector, the higher the order of the parabola is, the better it is not, nor can better results be obtained by simply increasing the order. Each time the order is increased, its physical meaning needs to be clarified. For example, the quintic parabola corresponds to acceleration. However, the inventors of the present application discovered that, for the return bead curve of the reflector, the curve obtained by only focusing on acceleration still has the problem of cusps. Furthermore, the inventors of the present application discovered that when studying the return bead curve of the reflector, it is also necessary to pay attention to the concept of the rate of change of acceleration (i.e., jerk). Based on this, the inventors of the present application proposed to use a seventh-order parabola-type relaxation curve and apply it to the design of the return bead curve of the reflector.

[0057] In order to enable those skilled in the art to better understand the technical solutions in the embodiments of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments in the embodiments of the present invention should fall within the scope of protection of the embodiments of the present invention.

[0058] See also Figure 1 The ball screw pair shown includes a screw 2, a nut 3, a plurality of balls and a plurality of returners 1. The nut 3 is sleeved on the screw 2. A spiral raceway is formed between the inner surface of the nut 3 and the outer surface of the screw 2. The plurality of balls are arranged in the spiral raceway. Specifically, a first spiral channel is arranged on the inner surface of the nut 3 along the axial direction of the nut 3 (the length direction of the first spiral channel extends along the axial direction of the nut 3), and a second spiral channel is arranged on the outer surface of the screw 2 along the axial direction of the screw 2 (the length direction of the second spiral channel extends along the axial direction of the screw 2). After the nut 3 is sleeved on the screw 2, the nut 3 and the screw 2 are coaxial, and a spiral raceway is formed between the first spiral channel and the second spiral channel.

[0059] Depend on Figure 1 It can be seen that a plurality of mounting holes 4 are provided in the axial direction of the nut 3, each mounting hole 4 passes through the inner and outer surfaces of the nut 3, and a returner 1 is installed in each mounting hole 4. The surface of the returner 1 facing the screw 2 is provided with a return ball groove, and the two ends of the return ball groove are respectively connected with two adjacent spiral raceways, so that a lead of ball circulation rolling is formed between the two adjacent spiral raceways and the return ball groove of a returner 1. When the ball screw pair is working, each circle of balls passes through the guide of the return ball groove on the returner 1 and crosses the surface of the screw 2 to form a cycle.

[0060] In order to ensure that the force on the nut 3 is uniform, the plurality of mounting through holes 4 are also evenly arranged along the circumferential direction of the nut 3 .

[0061] See also Figure 1The outer surface of each returner 1 is an arc-shaped surface. In some embodiments, the curvature of the outer surface of the returner 1 is consistent with the curvature of the outer surface of the nut 3. The ball screw pair also includes a sleeve 5 that is interference-fitted on the outer surface of the nut 3 to radially limit the returner 1, and the sleeve 5 can reduce the overflow of grease from the mounting through hole 4 and can isolate noise.

[0062] The return ball curve of the return device 1 is a three-dimensional space curve, the corresponding vector value function is differentiable, and its derivative is continuous. In the embodiment of the present invention, the return ball curve of the return device 1 is designed to satisfy the seventh-order parabolic curve equation. The structure is ingenious and the design is reasonable. The return ball curve has no sharp points, which can ensure that the ball moves smoothly during the movement, with low noise and low heat.

[0063] The following describes a design method for a bead-returning curve that satisfies a seventh-order parabolic curve equation, including the following steps:

[0064] (1) Figure 2 As shown, a three-dimensional coordinate system is established, which includes an X-axis, a Y-axis and a Z-axis that are perpendicular to each other. The central axis of the spiral raceway is taken as the Y-axis, and a parametric equation of a surface equidistant from the outer surface of the screw is established, as shown in formula (V).

[0065]

[0066] Among them, θ and y are dependent variables, θ represents the parameter angle, the unit is °, and ρ is the distance from the center of the ball to the center of the screw, the unit is mm, the value of ρ is equal to half of the sum of the inner diameter of the thread of the ball screw pair and the diameter of the ball. The former is also the diameter of the imaginary cylindrical surface that coincides with the bottom of the external thread. Since the center of the ball is on a curved surface equidistant from the outer surface of the screw, ρ is a constant;

[0067] (2) Figure 2 As shown, a seventh-order parabola cylinder is established in the three-dimensional coordinate system. The intersection of the equidistant surface and the seventh-order parabola cylinder is the bead curve, as shown in Figure 3 As shown, curve OF is the projection of half of the beading curve in the XOY plane, and the origin O is its symmetric point. Therefore, when calculating the coordinates of the beading curve, only the OF curve needs to be calculated, and the other half symmetrical to it can reverse the signs of the obtained coordinates x and y. Among them, the parametric equation of the seventh parabola cylinder is shown in formula (VI);

[0068]

[0069] (3) The parametric equation shown in formula (V) and the parametric equation shown in formula (VI) are solved simultaneously to obtain the parametric equation of the bead return curve as shown in formula (I-1);

[0070]

[0071] For the convenience of design and application, the horizontal coordinate x is taken as the parameter variable, and the parametric equation of the bead curve can also be written as shown in formula (I-2);

[0072]

[0073] (4) Determine the values ​​of coefficients A, B, C, and D. The values ​​of A, B, C, and D are determined by the boundary conditions, such as Figure 3 As shown, curve 11 is a spiral line projection curve, curve 12 is a seventh-order parabola projection curve, and curve 13 is a return device profile projection curve;

[0074] (41) The parametric equation for the projection of the helix on the XOY plane is established as shown in formula (VII), where the helix is ​​a trajectory drawn by the center of the ball when the ball flows along the spiral raceway;

[0075]

[0076] Among them, d0 represents the center circle diameter of the ball of the ball screw pair (i.e. the nominal diameter), the unit is mm; L0 represents the basic lead, the unit is mm.

[0077] (42) The spiral line and the bead curve intersect and are tangent at point F. The values ​​of the two at point F and the first three derivatives are the same. According to the characteristics of the seventh-order parabola curve, the equation shown in formula (VIII) is obtained;

[0078]

[0079] Among them, p, q, r, The value of is shown in formula (IV);

[0080]

[0081] (43) Solving and simplifying the equation shown in formula (VIII), we obtain coefficients A, B, C, and D, as shown in the equation shown in formula (II);

[0082]

[0083] Wherein, M, N, P, and Q are constants, and their values ​​are shown in formula (III);

[0084]

[0085] In the actual processing of the return device, when calculating the spatial curve of the entire return ball groove, x is used as the variable and a calculation program is written on the computer to obtain the coordinate value of the curve. The coordinate value is input into the CNC milling machine to process an internal circulation return device based on the seventh parabola.

[0086] When studying the return ball curve of the return device, the inventors of the present application found that the first two derivatives at the intersection of the spiral line and the return ball curve are the same, which can ensure that the acceleration of the ball is the same when entering and leaving the return ball groove. However, the third-order derivatives at the intersection are different, that is, the rate of change of acceleration (also known as jerk) is different, which will affect the smoothness of the movement and increase the risk of damage to mechanical components. Therefore, the inventors of the present application paid attention to the concept of the rate of change of acceleration (that is, jerk). Based on this, the inventors of the present application proposed to use a seventh-order parabolic relaxation curve and apply it to the design of the return ball curve of the return device. The third-order derivative at the intersection of the spiral line and the return ball curve is the same, that is, the rate of change of acceleration (that is, jerk) is the same, and the return ball curve designed in this way has no sudden change value, and there are no sharp points at the entrance and exit ends of the return ball groove, so that the dynamic performance of the raceway is improved, thereby reducing the energy loss of the ball and improving the overall transmission efficiency of the ball screw pair.

[0087] The following explains the principle that the bead-returning curve based on the seventh-order parabola design of the present invention has advantages over the existing curves:

[0088] First, changes in acceleration will cause changes in force. A sudden change in jerk means that the rate of change of acceleration changes suddenly. In a mechanical system, according to Newton's second law F=m×a, changes in acceleration will cause changes in force. When the jerk changes suddenly, the rate of change of force will also change suddenly. Taking the ball return process as an example, the ball is subjected to the reaction force of the ball return groove to its gravity, thereby changing the rolling direction and returning from one spiral raceway to another. The magnitude and direction of the reaction force have a direct impact on the ball. The sudden change in jerk will cause the reaction force to change dramatically in a short period of time. The sudden force change at the junction of the entrance and exit is also called the force cusp. This sudden increase or decrease in force can easily exceed the limit that the ball material can withstand, leading to the initiation of fatigue cracks, thereby reducing the fatigue life of the ball.

[0089] Secondly, sudden changes in jerkiness can cause vibrations in the mechanical system. When the rate of change of acceleration changes suddenly, the system will be subjected to a momentary shock, which will excite the natural frequency of the mechanical system and thus generate vibrations. For example, during the rotation of the ball, sudden changes in jerkiness can cause vibrations in the ball screw pair. This vibration will not only affect the performance and life of the ball screw pair, but will also generate loud noises, often accompanied by local heating. When this vibration happens to be in the resonant frequency range, it can even have unpredictable destructive consequences.

[0090] The return ball curve of the return device designed by adopting the above design method has no sharp points, which can ensure that the ball moves smoothly during the movement, with low noise and low heat.

[0091] The ball return curve of the return device designed by the above-mentioned design method of the embodiment of the present invention has no sudden change value, so that the dynamic performance of the raceway is improved, thereby reducing the energy loss of the ball and improving the overall transmission efficiency.

[0092] The return ball curve of the return device designed by the above design method has no sharp points, uniform ball acceleration, and no sudden change value, which can ensure that the ball moves smoothly during the movement, with low noise and low heat.

[0093] It should also be noted that the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features.

[0094] In the description of the present invention, it is necessary to understand that the orientations or positional relationships indicated by terms such as “radial”, “axial”, “bottom”, “inner” and “outer” are based on the orientations or positional relationships shown in the accompanying drawings and are only for the convenience of describing the present invention and simplifying the description. They do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention.

[0095] In addition, in the description of the present invention, unless otherwise specified and limited, it should be noted that the terms "installed", "connected" and "connected" should be understood in a broad sense. For example, it can be a mechanical connection or an electrical connection, or it can be the internal connection of two components. It can be a direct connection or an indirect connection through an intermediate medium. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to the specific circumstances.

[0096] The above implementation methods are only used to illustrate the embodiments of the present invention, and are not limitations of the embodiments of the present invention. Ordinary technicians in the relevant technical field may make various changes and modifications without departing from the spirit and scope of the embodiments of the present invention. Therefore, all equivalent technical solutions also belong to the scope of the embodiments of the present invention. The patent protection scope of the embodiments of the present invention should be defined by the claims.

Claims

1. A ball screw pair, comprising a screw (2), a nut (3), a plurality of balls and a return device (1), wherein the nut (3) is sleeved on the screw (2), a spiral raceway is formed between the inner surface of the nut (3) and the outer surface of the screw (2), the plurality of balls are arranged in the spiral raceway, the return device (1) is arranged on the nut (3), a surface of the return device (1) facing the screw (2) is provided with a return ball groove, the two ends of the return ball groove are respectively connected to two adjacent spiral raceways, and the characteristics are: The bead return curve of the bead return groove satisfies the seventh-order parabola curve equation shown in formula (I-1): Alternatively, the bead return curve of the bead return groove satisfies the seventh-order parabola curve equation shown in formula (I-2): Among them, the coefficients A, B, C, and D in formula (I-1) and formula (I-2) respectively satisfy the equation shown in formula (II): In formula (I-1), formula (I-2) and formula (II), θ is the parameter angle, the unit is °; ρ is the distance from the center of the ball to the center of the screw, the unit is mm; x F is the horizontal coordinate of point F on the bead return curve, in mm; M, N, P, Q are constants.

2. The ball screw pair according to claim 1, characterized in that: In the formula (II), the values ​​of M, N, P, and Q are obtained from the formula (III): Among them, p, q, r, The value of is shown in formula (IV); In formula (III) and formula (IV), L0 is the basic lead, in mm; d0 is the center circle diameter of the ball of the ball screw pair, in mm.

3. The ball screw pair according to claim 1, characterized in that: The bead return curve represented by formula (I-1) or formula (I-2) is obtained by the following method, which comprises: (S1) establishing a three-dimensional coordinate system, the three-dimensional coordinate system comprising an X-axis, a Y-axis and a Z-axis which are perpendicular to each other, wherein the central axis of the spiral raceway is the Y-axis, and establishing a parametric equation of a surface equidistant from the outer surface of the screw as shown in formula (V); (S2) establishing a seventh-order parabolic cylinder in the three-dimensional coordinate system, wherein the intersection of the equidistant surface and the seventh-order parabolic cylinder is the bead curve, wherein the parameter equation of the seventh-order parabolic cylinder is as shown in formula (VI); (S3) The parametric equation shown in formula (V) and the parametric equation shown in formula (VI) are solved simultaneously to obtain the bead return curve shown in formula (I-1) or formula (I-2).

4. The ball screw pair according to claim 1 or 3, characterized in that: The horizontal and vertical coordinates of the spiral line and the ball return curve at point F are the same, and the curve OF is the projection of the ball return curve in the XOY plane, wherein the spiral line is a track drawn by the center of the ball when the ball flows along the spiral raceway; The determination of coefficients A, B, C, and D includes the following steps: (i) Establish the parametric equation of the projection of the helix on the XOY plane as shown in formula (VII); (ii) According to the intersection and tangency of the bead curve and the spiral line at point F, the values ​​of the bead curve and the spiral line at point F and the first three derivatives are the same, and according to the characteristics of the seventh-order parabola curve, the equation shown in formula (VIII) is obtained; (III) Solving the equation shown in formula (VIII) to obtain the coefficients A, B, C, and D.

5. The ball screw pair according to claim 1, characterized in that: A plurality of return devices (1) are arranged on the nut (3) along its axial direction.

6. The ball screw pair according to claim 5, characterized in that: The multiple return devices (1) are also distributed along the circumference of the nut (3).

7. The ball screw pair according to claim 5, characterized in that: The nut (3) is provided with a mounting through hole (4) at a position corresponding to each of the return devices (1), and each of the return devices (1) is arranged in a one-to-one correspondence in each of the mounting through holes (4); The ball screw pair further comprises a sleeve (5) sleeved on the nut (3), and the sleeve (5) is used to radially limit the plurality of return devices (1).

8. The ball screw pair according to claim 7, characterized in that: The outer surface of each return device (1) is an arc-shaped surface; and / or the sleeve (5) and the nut (3) are interference fit.

9. A return device for a ball screw pair, the ball screw pair comprising a screw (2), a nut (3) sleeved on the screw (2) and a plurality of balls, a spiral raceway is formed between the inner surface of the nut (3) and the outer surface of the screw (2), the plurality of balls are arranged in the spiral raceway, the return device (1) is arranged on the nut (3), a surface of the return device (1) facing the screw (2) is provided with a return ball groove, the two ends of the return ball groove are respectively connected to two adjacent spiral raceways, and the characteristics are: The bead return curve of the bead return groove satisfies the seventh-order parabola curve equation shown in formula (I-1): Alternatively, the bead return curve of the bead return groove satisfies the seventh-order parabola curve equation shown in formula (I-2): Among them, the coefficients A, B, C, and D in formula (I-1) and formula (I-2) respectively satisfy the equation shown in formula (II): In formula (I-1), formula (I-2) and formula (II), θ is the parameter angle, the unit is °; ρ is the distance from the center of the ball to the center of the screw, the unit is mm; x F is the horizontal coordinate of point F on the bead return curve, in mm; M, N, P, Q are constants.

10. The return device for a ball screw pair according to claim 9, characterized in that: In the formula (II), the values ​​of M, N, P, and Q are obtained from the formula (III): Among them, p, q, r, The value of is shown in formula (IV); In formula (III) and formula (IV), L0 is the basic lead, in mm; d0 is the center circle diameter of the ball of the ball screw pair, in mm.

11. The return device for a ball screw pair according to claim 9, characterized in that: The bead return curve represented by formula (I-1) or formula (I-2) is obtained by the following method, which comprises: (S1) establishing a three-dimensional coordinate system, the three-dimensional coordinate system comprising an X-axis, a Y-axis and a Z-axis which are perpendicular to each other, wherein the central axis of the spiral raceway is the Y-axis, and establishing a parametric equation of a surface equidistant from the outer surface of the screw, as shown in formula (V); (S2) establishing a seventh-order parabolic cylinder in the three-dimensional coordinate system, wherein the intersection of the equidistant surface and the seventh-order parabolic cylinder is the bead curve, wherein the parameter equation of the seventh-order parabolic cylinder is as shown in formula (VI); (S3) The parametric equation shown in formula (V) and the parametric equation shown in formula (VI) are solved simultaneously to obtain the bead return curve shown in formula (I-1) or formula (I-2).

12. The return device for a ball screw pair according to claim 9 or 11, characterized in that: The horizontal and vertical coordinates of the spiral line and the ball return curve at point F are the same, and the curve OF is the projection of the ball return curve in the XOY plane, wherein the spiral line is a track drawn by the center of the ball when the ball flows along the spiral raceway; The determination of coefficients A, B, C, and D includes the following steps: (i) Establish the parametric equation of the projection of the helix on the XOY plane as shown in formula (VII); (ii) According to the intersection and tangency of the bead curve and the spiral line at point F, the values ​​of the bead curve and the spiral line at point F and the first three derivatives are the same, and according to the characteristics of the seventh-order parabola curve, the equation shown in formula (VIII) is obtained; (III) Solving the equation shown in formula (VIII) to obtain the coefficients A, B, C, and D.

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