A method for designing profile parameters of a ball screw pair working under extreme temperature conditions

Abstract

This invention discloses a method for designing the profile parameters of a ball screw pair operating under extreme temperature conditions, comprising: initially determining the profile design parameters of the ball screw pair; establishing a mathematical model of the raceway in the normal plane; mapping the raceway profile in the normal plane to the axial plane; performing thermal deformation calculations on the raceway profile and simultaneously on the balls; mapping the profile in the axial plane after thermal deformation to the normal plane; performing circular arc fitting to calculate the raceway profile parameters after thermal deformation; determining whether the clearance value after thermal deformation meets the operating condition requirements; if not, modifying the profile parameters until the operating condition requirements are met; determining whether the contact angle after thermal deformation meets the allowable contact angle requirements; if not, modifying the profile parameters until the allowable contact angle requirements are met; and finally outputting the profile parameters under normal temperature conditions. This invention can solve the problems of short lifespan and unusability of ball screw pairs designed at normal temperature under extreme temperature conditions.

Description

Technical Field

[0001] This invention belongs to the field of mechanical transmission design technology, specifically relating to a method for designing the surface parameters of a ball screw pair operating under extreme temperature conditions. Background Technology

[0002] Screw drives are widely used in traditional mechanical transmission design and selection, and sliding screw drives are often used in complex working conditions. However, sliding screw drives have significant sliding friction resistance between the contact surfaces of the screw threads, resulting in low transmission efficiency, rapid wear, and short service life. They can no longer fully meet the development requirements of modern mechanical transmissions in terms of high speed, high efficiency, and high precision.

[0003] With the development of technology, electric drive technology is increasingly entering extreme temperature conditions, with temperatures exceeding 100°C and dropping to -40°C placing higher demands on lead screws. Traditional sliding screw drives are increasingly proving inadequate, making ball screw pairs, which are better suited to these extreme temperature environments, increasingly necessary for mechanical transmission systems operating under such conditions. A ball screw pair is a transmission element that can bidirectionally convert helical motion into linear motion. Its structure includes a screw shaft, a nut, and balls. The ingenious aspect of the ball screw pair lies in the rolling motion of the balls between the nut and the screw raceway, which significantly improves transmission efficiency compared to sliding. For example, compared to a traditional sliding screw pair, a ball screw pair requires only one-third of the power to achieve the same level of transmission effect. However, unlike sliding screw pairs, the helical transmission between components does not rely on the kinematic pair itself, but rather on an intermediate element (balls) between the screw and the nut, making its design more complex. Especially since the temperatures under these conditions are either too high or too low compared to normal temperatures, thermal expansion and contraction of the components can occur. The raceways of the ball screw and nut are complex curved surfaces. Due to the existence of the lead angle, it is more difficult to predict the dimensional change pattern after the temperature changes. This can cause problems such as jamming or seizing when the temperature changes from room temperature to extreme temperature, or excessive wear, uneven load, or insufficient load-bearing caused by excessive radial clearance or improper contact angle. Ultimately, this leads to a significant reduction in the lifespan of the ball screw pair.

[0004] The problem arises because the ball screw assembly was designed based on its profile parameters at room temperature, without considering thermal deformation. Therefore, it is essential to provide a design method for the profile parameters of ball screw assemblies operating under extreme temperature conditions, based on the principles of thermal deformation. Summary of the Invention

[0005] The purpose of this invention is to provide a method for designing the surface parameters of a ball screw pair that operates under extreme temperature conditions, thereby solving the problem that ball screw pairs designed with raceway surface parameters at room temperature cannot function properly under extreme temperature conditions. This guides the design of ball screw pairs that can operate normally at the corresponding extreme temperatures.

[0006] The technical solution to achieve the purpose of this invention is as follows:

[0007] A method for designing the surface parameters of a ball screw pair operating under extreme temperature conditions, comprising:

[0008] S1: Initial design parameters for the ball screw assembly: Lead P h ball diameter d b Pitch circle diameter d m Adaptability f v , lead screw outer diameter d 1s , Nut inner diameter d 1n Radial clearance S d Contact angle α of the lead screw raceway s nut raceway contact angle α n ;

[0009] S2: Design the raceway according to the given profile design parameters, and establish a Cartesian coordinate system OX in the axial plane with the projection of the center of the ball onto the central axis of the screw / nut as the origin O. a Y a Z a , set the coordinate system OX a Y a Z a Around X a Rotating the axis counterclockwise by the lead angle λ yields the coordinate system OX in the normal plane. n Y n Z n Establish a coordinate system OX in the normal plane. n Y n Z n Mathematical model of the raceway;

[0010] S3: Map the raceway profile in the normal plane to the axis plane;

[0011] S4: Based on the temperature of the extreme temperature conditions, perform thermal deformation calculation of the raceway profile in the shaft plane, and at the same time perform thermal deformation calculation of the balls.

[0012] S5: Map the contour in the axial plane after thermal deformation to the normal plane;

[0013] S6: Perform circular arc fitting on the raceway data after thermal deformation in the normal plane, and calculate the center coordinates of the left and right circular arc raceways of the screw and nut after thermal deformation, as well as the raceway radius of the screw and the raceway radius of the nut.

[0014] S7: Calculate the raceway profile parameters after thermal deformation based on the raceway arc parameters obtained in step S6 and the data of the ball after thermal deformation obtained in step S4.

[0015] S8: Determine whether the gap value after thermal deformation meets the working condition requirements. If not, proceed to step S1 and modify the radial gap S. d Continue the calculations until the operating conditions are met;

[0016] S9: Determine whether the contact angle after heat deformation meets the allowable contact angle requirement. If not, proceed to step S1 and modify the contact angle α. s α n Continue the calculations until the allowable contact angle requirement is met;

[0017] S10: Outputs the profile parameters of the ball screw assembly under normal temperature conditions.

[0018] The significant advantages of this invention compared to existing technologies are:

[0019] This invention considers the thermal deformation laws of the screw raceway, nut raceway, and ball diameter in a ball screw pair, effectively predicts the changes in various surface parameters of the ball screw pair after temperature changes, guides the optimization design of the surface parameters of the ball screw pair, and thus designs a ball screw pair that can work normally under extreme temperature conditions. Attached Figure Description

[0020] Figure 1 This invention provides a design process for the surface parameters of a ball screw pair operating under extreme temperature conditions.

[0021] Figure 2 This is a schematic diagram of the profile parameters of the double-circular-arc ball screw pair of the present invention;

[0022] Figure 3 A diagram showing the coordinate relationship between the axial plane and the normal plane;

[0023] Figure 4 A schematic diagram of a virtual double arc is shown when a single arc raceway is in contact balance.

[0024] Symbol explanation: 1 Nut; 2 Ball bearing; 3 Lead screw. Detailed Implementation

[0025] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0026] like Figure 1 As shown, this invention provides a method for designing the surface parameters of a ball screw pair operating under extreme temperature conditions, comprising the following steps:

[0027] S1: Initial determination of the surface design parameters of the ball screw pair;

[0028] The raceway dimensions of a ball screw assembly are largely determined by its operating space and required load-bearing capacity, while the main parameters for designing the raceway profile are as follows: Figure 2 As shown. Specific parameters are as follows:

[0029] d m : Pitch circle diameter; d 1n : Nut inner diameter; d 1s : Outer diameter of the lead screw; d b : Ball diameter; P h Lead; α n : Nut raceway contact angle; α s : Contact angle of the lead screw raceway; f v Fit ratio, which is the ratio of raceway radius to ball diameter d. b The ratio is not directly shown in the figure, but is implicitly expressed by the raceway radius; r n : Nut raceway radius; r s : Screw raceway radius; here, r s =r n .

[0030] The figure shows the raceway profile parameters of a ball screw assembly under normal temperature conditions, with no radial clearance. Radial clearance results from the nut's pitch diameter being larger than the screw's pitch diameter. The pitch diameter is, ideally, the diameter of the cylindrical surface enveloping the center of the ball when it contacts the raceway. The specific method for determining the raceway profile parameters includes the following steps:

[0031] S11: Determine the model of the ball screw pair and its lead P based on the performance requirements of the ball screw pair under extreme temperature conditions. h ball diameter d b ;

[0032] S12: Based on the model of the ball screw pair, refine the fixed parameters: pitch circle diameter d m Adaptability f v , lead screw outer diameter d 1s , Nut inner diameter d 1n ; Adaptation ratio f v It is the raceway radius r s r n With ball diameter d b The ratio of .

[0033] S13: Initially determined changeable parameter: radial clearance S d Contact angle α of the lead screw raceway s nut raceway contact angle α n ;

[0034] S14: Parameter Assignment:

[0035] For the lead screw: the mean diameter is d m The contact angle of the lead screw raceway is α. s The outer diameter is d 1s The raceway radius is r s =d b f v For nuts: the mean diameter is d m +S d The contact angle of the nut raceway is α. n The inner diameter is d 1n The raceway radius is r n =d b f v For ball bearings: diameter d b .

[0036] This method ensures that the performance of the ball screw pair meets the requirements under the corresponding operating conditions. Only the radial clearance S at room temperature is changed. d and contact angle α s α n It does not significantly change performance under extreme temperature conditions, but it can effectively solve problems such as jamming.

[0037] S2: Based on the given profile design parameters, design the raceway and establish a mathematical model of the raceway in the normal plane;

[0038] Given the profile parameters, the raceway can be designed. Raceway design is performed on the normal plane. The normal plane is the plane normal to the helix formed by connecting the centers of the balls, such as... Figure 2 As shown in the right figure. Corresponding to this is the axial plane, which is the plane passing through the centerline of the nut or leadscrew. The angle between the normal plane and the axial plane at the same point is equal to the lead angle λ, as shown... Figure 3 As shown. Mathematical modeling of the raceway in the normal plane involves representing the raceway using mathematical language, such as equations and functions, to facilitate subsequent calculations. The specific steps are as follows:

[0039] S21: Establish a Cartesian coordinate system OX in the axial plane with the projection of the center of the ball onto the central axis of the lead screw / nut as the origin O. a Y a Z a .like Figure 2 As shown, taking the second to last raceway in the top row as an example, the centerline of the lead screw / nut is Z. aAxis, perpendicular to Z a The straight line passing through the center of the ball bearing is X. a The axis, X, points from the origin of the coordinate system to the center of the ball. a The positive direction of the axis. Establish the coordinate system OX. a Y a Z a Around X a Rotating the axis counterclockwise by λ yields the coordinate system OX in the normal plane. n Y n Z n ,like Figure 3 As shown;

[0040] S22: Perform mathematical modeling of the raceway in the normal plane. For a Gothic double-circular-arc raceway profile, the mathematical model of the right raceway of the leadscrew in this coordinate system is:

[0041]

[0042] Where (x,y,z) are the coordinates of a point in this coordinate system. The radius of the pitch circle; Let θ be the radius of the ball bearing; θ is the independent variable of the mathematical model, Θ sr Let θ be the range of values ​​for the right raceway of the leadscrew.

[0043]

[0044] in, Let be the outer radius of the leadscrew.

[0045] The mathematical model of the left raceway of the leadscrew in this coordinate system is:

[0046]

[0047] Where, Θ sl Let θ be the range of values ​​for the left raceway of the leadscrew.

[0048]

[0049] The mathematical model of the right raceway of the nut in this coordinate system is:

[0050]

[0051] in, It is half the mean diameter of the nut; Θ nr Let θ be the range of values ​​for the right raceway of the nut.

[0052]

[0053] in, Let be the inner radius of the nut.

[0054] The mathematical model of the left raceway of the nut in this coordinate system is:

[0055]

[0056] Where, Θ nl Let θ be the range of values ​​for the left raceway of the nut.

[0057]

[0058] This allows the screw raceway and nut raceway in the ball screw pair to be mathematically represented, and the thermal deformation process can be characterized using purely mathematical methods.

[0059] S3: Map the raceway profile in the normal plane to the axis plane;

[0060] Because of the lead angle, it's impossible to directly perform infinitesimal element analysis on the raceway for thermal deformation within the normal plane. However, when performing infinitesimal element analysis within the axial plane, which is perpendicular to the central axis of the leadscrew / nut, it's much easier to perform the analysis. The specific steps for normal-axis mapping are as follows:

[0061] S31: Calculate the lead angle λ.

[0062]

[0063] S32: The parameter θ from step S2 is set to values ​​with a step size of 0.1°. The raceway is discretized and mapped to the normal plane. Then, the raceway is processed into infinitesimal elements in the normal plane. To distinguish them, 'n' is used in the upper left corner of the coordinate value to indicate that the coordinate value is in the normal plane, and 'a' is used to indicate that the coordinate value is in the axis plane. That is, the coordinate values ​​in the normal plane are all: ( n x,0, n z), the coordinate values ​​in the axis plane are all ( a x,0, a z).

[0064] The coordinates of the i-th point on the plane raceway are calculated according to formulas (1), (2), (3), and (4). n x i ,0, n z i ), where the subscript i represents the sequence number, which is a positive integer.

[0065] And it is constructed into the following column vector:

[0066]

[0067] S33: Calculate the travel angle τ of the i-th point. i :

[0068]

[0069] S34: Construct the normal-axis mapping matrix for each point:

[0070]

[0071] S35: Map each point to the axis plane:

[0072]

[0073] The coordinates of the i-th point mapped to the axis plane are ( a x i ,0, a z i ).

[0074] This method can transform the problem of calculating thermal deformation, which cannot be directly calculated in the normal plane, to the axial plane, where thermal deformation calculation is easier.

[0075] S4: Based on the temperature of the extreme temperature conditions, perform thermal deformation calculation of the raceway profile in the shaft plane, and at the same time perform thermal deformation calculation of the balls.

[0076] The lead screw / nut is divided into a series of very short cylinders, and the calculation is performed according to the thermal deformation law of cylinders. The specific steps are as follows:

[0077] S41: The materials of the lead screw, nut, and balls, and the corresponding operating temperature T. e Determine the materials of these materials at the corresponding temperature T. e The coefficient of thermal expansion η relative to room temperature T0 = 20℃ T Here, the lead screw, nut, and ball bearings are generally made of the same material to facilitate control of thermal deformation. However, different materials can also be used; when performing calculations, it is important to distinguish their coefficients of thermal expansion.

[0078] S42: Calculate the temperature change from T0 to T e The coordinates of each data point on the raceway are as follows:

[0079]

[0080] a x iT , a z iT X represents the i-th point of the raceway in the axial plane after thermal deformation. a Axis and Z a The coordinate values ​​of the axis.

[0081] S43: Calculate the radius of the ball after thermal deformation:

[0082] r bT =[η T(T e -T0)+1]r b (10)

[0083] r bT It is the radius value of the ball after thermal deformation.

[0084] This method can obtain the deformation law of the raceway in the axial plane.

[0085] S5: Map the contour in the axial plane after thermal deformation to the normal plane;

[0086] The specific steps are as follows:

[0087] S51: Construct the axis-normal mapping matrix for each point on the raceway:

[0088]

[0089] S52: Map each point to the normal plane:

[0090]

[0091] n x iT , n z iT Let X represent the i-th point of the raceway in the normal plane after thermal deformation. n Axis and Z n The coordinate values ​​of the axis.

[0092] This method can obtain the thermal deformation law of the raceway profile in the normal plane.

[0093] S6: Perform circular arc fitting on the raceway data after thermal deformation in the normal plane;

[0094] The specific steps are as follows:

[0095] S61: Representing the circular raceway using the general equation of a circle:

[0096] A(z 2 +x 2 )+Bz+Cx+D=0 (13)

[0097] Where A, B, C, and D are the coefficients of the constant term. Solve the following equation:

[0098]

[0099] Where f p (A,B,C,D) is a function with independent variables A, B, C, and D, m is the total number of points on a raceway, and g(A,B,C,D) is a constraint function. n x iT ,n z iT Let X represent the i-th point of the raceway in the normal plane after thermal deformation. n Axis and Z n The coordinate values ​​of the axis.

[0100] The above equation means: given the constraint g(A,B,C,D), find the equation that makes f... p (A,B,C,D) where A, B, C, and D are the minimum values.

[0101] Equation (14) is solved using the Lagrange operator method.

[0102] S62: Calculate the center coordinates (z) of the left and right arc raceways of the lead screw and nut after thermal deformation. cT ,x cT ) and screw raceway radius r sT Nut raceway radius r nT :

[0103]

[0104] Compared to the most commonly used in the industry The least squares circle fitting method eliminates the influence of the radius, resulting in higher accuracy. By fitting the center and radius of the raceway on the normal plane under extreme conditions, the profile parameters of the ball screw pair can be calculated.

[0105] S7: Calculate the raceway profile parameters after thermal deformation based on the raceway arc parameters obtained in step S6 and the data of the ball after thermal deformation obtained in step S4.

[0106] The specific steps are as follows:

[0107] S71: Calculate the thermal deformation contact angle:

[0108] Lead screw raceway thermal deformation contact angle α sT :

[0109]

[0110] Nut raceway thermal deformation contact angle α nT :

[0111]

[0112] S72: Calculate the mean diameter for heat deformation:

[0113] The mean diameter d of the lead screw under thermal deformation msT :

[0114] d msT =2(|x cT |-(rsT -r bT cosα sT (18)

[0115] The mean diameter d of the nut under heat deformation mnT :

[0116] d mnT =2(|x cT |+(r nT -r bT cosα nT (19)

[0117] After calculating the raceway profile parameters, we can determine the contact state of the ball screw pair under extreme operating conditions and whether it is stuck.

[0118] S8: Determine whether the gap value after thermal deformation meets the working condition requirements. If not, proceed to step S1 and modify the radial gap S. d Continue the calculations until the operating conditions are met;

[0119] S81: Calculate the gap value S after thermal deformation. dT :

[0120] S dT =d mnT -d msT (20)

[0121] S82: Determine if the allowable clearance under extreme temperature conditions is [S dTmin ]~[S dTmax If [S] dTmin ]≤S dT ≤[S dTmax If the result is positive, proceed to the next step; otherwise, go to step S1 and optimize S. d If S dT <[S dTmin Increase S d If S dT >[S dTmax If S decreases, then S decreases. d ;

[0122] Generally, the higher the temperature, the smaller the gap, and high temperatures often lead to jamming or seizing. This step effectively avoids jamming or seizing problems under extreme temperature conditions.

[0123] S9: Determine whether the contact angle after heat deformation meets the allowable contact angle requirement. If not, proceed to step S1 and modify the contact angle α. s α n Continue the calculations until the allowable contact angle requirement is met.

[0124] The specific steps are as follows:

[0125] S91: Calculate the contact angle α at contact equilibrium after thermal deformation. T :

[0126]

[0127] S92: Determine if the allowable contact angle under extreme temperature conditions is [α]. Tmin ]~[α Tmax If [α] Tmin ]≤α T ≤[α Tmax If the result is positive, proceed to the next step; otherwise, go to step S1 to optimize α. s α n If α T <[α Tmin Increase α s α n If α T >[α Tmax If α is reduced, then α will decrease. s α n ;

[0128] This effectively avoids excessive wear caused by an increased contact angle during contact equilibrium under extreme temperature conditions, or reduced load-bearing capacity due to an excessively small contact angle.

[0129] S10: Output the profile parameters of the ball screw assembly under normal temperature conditions. This refers to the optimized profile parameters in step S1 after the judgments in steps S8 and S9.

[0130] The specific parameters are as follows: Lead P h ball diameter d b Pitch circle diameter d m Adaptability f v , lead screw outer diameter d 1s , Nut inner diameter d 1n Radial clearance S d Contact angle α of the lead screw raceway s nut raceway contact angle α n ;

[0131] The above-described specific implementation methods all describe Gothic double-circular-arc raceways. However, single-circular-arc raceways are still used in certain specific applications due to their simple design and manufacturing. Therefore, it is also necessary to establish a design method for the extreme temperature operating parameters of single-circular-arc raceway profiles. The specific method is as follows:

[0132] For a single circular arc raceway profile, such as Figure 4 As shown, X in the contact state nUsing the axis of symmetry, the raceway on the contacting side is treated symmetrically to create a virtual double-circular-arc raceway, as shown by the dashed line in the diagram. The mathematical model of the raceway and subsequent calculations can then be performed following the process described above for a double-circular-arc raceway.

Claims

1. A method for designing the surface parameters of a ball screw pair operating under extreme temperature conditions, characterized in that, include: S1: Initial design parameters for the ball screw assembly: Lead P h ball diameter d b Pitch circle diameter d m Adaptability f v , lead screw outer diameter d 1s , Nut inner diameter d 1n Radial clearance S d Contact angle α of the lead screw raceway s nut raceway contact angle α n ; S2: Design the raceway according to the given profile design parameters, and establish a Cartesian coordinate system OX in the axial plane with the projection of the center of the ball onto the central axis of the screw / nut as the origin O. a Y a Z a , set the coordinate system OX a Y a Z a Around X a Rotating the axis counterclockwise by the lead angle λ yields the coordinate system OX in the normal plane. n Y n Z n Establish a coordinate system OX in the normal plane. n Y n Z n Mathematical model of the raceway; S3: Map the raceway profile in the normal plane to the axis plane; S4: Based on the temperature of the extreme temperature conditions, perform thermal deformation calculation of the raceway profile in the shaft plane, and at the same time perform thermal deformation calculation of the balls. S5: Map the contour in the axial plane after thermal deformation to the normal plane; S6: Perform circular arc fitting on the raceway data after thermal deformation in the normal plane, and calculate the center coordinates of the left and right circular arc raceways of the screw and nut after thermal deformation, as well as the raceway radius of the screw and the raceway radius of the nut. S7: Calculate the raceway profile parameters after thermal deformation based on the raceway arc parameters obtained in step S6 and the data of the ball after thermal deformation obtained in step S4. S8: Determine whether the gap value after thermal deformation meets the working condition requirements. If not, proceed to step S1 and modify the radial gap S. d Continue the calculations until the operating conditions are met; S9: Determine whether the contact angle after heat deformation meets the allowable contact angle requirement. If not, proceed to step S1 and modify the contact angle α. s α n Continue the calculations until the allowable contact angle requirement is met; S10: Outputs the profile parameters of the ball screw assembly under normal temperature conditions.

2. The method for designing the surface parameters of a ball screw pair operating under extreme temperature conditions according to claim 1, characterized in that, The mathematical model of the raceway includes: The right raceway of the leadscrew is in coordinate system OX n Y n Z n The mathematical model below is: The left raceway of the leadscrew is in coordinate system OX n Y n Z n The mathematical model below is: The right raceway of the nut in coordinate system OX n Y n Z n The mathematical model below is: The left raceway of the nut is in coordinate system OX n Y n Z n The mathematical model below is: Where (x, y, z) is the coordinate system OX n Y n Z n The coordinates of the point below; r m r is the radius of the pitch circle. b r is the radius of the ball bearing. s r is the radius of the lead screw raceway. n r is the nut raceway radius. mn Let θ be half the pitch diameter of the nut, and let θ be the independent variable of the mathematical model. sr The range of values ​​for θ on the right raceway of the leadscrew, Θ sl The range of values ​​for θ on the left raceway of the leadscrew, Θ nr For the range of values ​​of θ on the right raceway of the nut, Θ nl Let θ be the range of values ​​for the left raceway of the nut; sr Θ sl Θ nr and Θ nl The upper and lower limits are solved by the following system of equations: Where r 1s Let r be the outer radius of the leadscrew. 1n Let be the inner radius of the nut.

3. The method for designing the surface parameters of a ball screw pair operating under extreme temperature conditions according to claim 1, characterized in that, The raceway profile in the normal plane is mapped to the axial plane using the following formula: in( a x i ,0, a z i ) represents the coordinates of the i-th point mapped to the axis plane. n x i ,0, n z i ) represents the coordinates of the i-th point on the normal plane raceway, τ i τ is the travel angle at the i-th point, λ is the lead angle; i It can be calculated using the following formula:

4. The method for designing the surface parameters of a ball screw pair operating under extreme temperature conditions according to claim 1, characterized in that, The thermal deformation of the raceway profile is calculated using the following formula: a x iT , a z iT X represents the i-th point of the raceway in the axial plane after thermal deformation. a Axis and Z a The coordinate values ​​of the axis, η T It refers to the temperature T of the materials of the lead screw, nut, and balls under the corresponding operating conditions. e The coefficient of thermal expansion relative to room temperature T0, ( a x i ,0, a z i ) represents the coordinates of the i-th point mapped to the axis plane.

5. The method for designing the surface parameters of a ball screw pair operating under extreme temperature conditions according to claim 4, characterized in that, The following thermal deformation calculations were performed on the ball bearings: r bT =[η T (T e -T0)+1]r b r bT It is the radius value of the ball after thermal deformation.

6. The method for designing the surface parameters of a ball screw pair operating under extreme temperature conditions according to claim 1, characterized in that, The contour in the axial plane after thermal deformation is mapped to the normal plane by the following formula: n x iT , n z iT Let X represent the i-th point of the raceway in the normal plane after thermal deformation. n Axis and Z n The coordinate values ​​of the axis, τ i Let λ be the travel angle at the i-th point, and λ be the lead angle. a x iT , a z iT X represents the i-th point of the raceway in the axial plane after thermal deformation. a Axis and Z a The coordinate values ​​of the axis.

7. The method for designing the surface parameters of a ball screw pair operating under extreme temperature conditions according to claim 1, characterized in that, The coordinates of the centers of the left and right arc raceways of the lead screw and nut after heat deformation, and the radii of the lead screw raceway and the nut raceway are as follows: Among them (z) cT ,x cT (r) represents the coordinates of the center of the left and right arc raceways of the lead screw and nut after thermal deformation. sT r represents the radius of the left and right arc raceways of the leadscrew after heat deformation. nT Let A, B, C, and D be the radii of the left and right arc raceways of the nut after heat deformation, and A, B, C, and D be the coefficients of the general equation of a circle. The solution is obtained using the following formula: Where f p (A,B,C,D) is a function with independent variables A, B, C, and D, m is the total number of points on a raceway, and g(A,B,C,D) is a constraint function. n x iT , n z iT Let X represent the i-th point of the raceway in the normal plane after thermal deformation. n Axis and Z n The coordinate values ​​of the axis.

8. The method for designing the surface parameters of a ball screw pair operating under extreme temperature conditions according to claim 7, characterized in that, The calculation of the raceway profile parameters after thermal deformation includes: Lead screw raceway thermal deformation contact angle α sT : Nut raceway thermal deformation contact angle α nT : The mean diameter d of the lead screw under thermal deformation msT : d msT =2(x cT |-(r sT -r bT )cosα sT ) The mean diameter d of the nut under heat deformation mnT : d mnT =2(x cT |+(r nT -r bT )cosα nT ) Where r bT It is the radius value of the ball after thermal deformation.

9. The method for designing the surface parameters of a ball screw pair operating under extreme temperature conditions according to claim 8, characterized in that, Radial clearance value S after heat deformation dT for: S dT =d mnT -d msT Let the allowable clearance under extreme temperature conditions be [S]. dTmin ]~[S dTmax If the gap value S after heat deformation dT Satisfy [S] dTmin ]≤S dT ≤[S dTmax If the result is positive, proceed to the next step; otherwise, go to step S1 and optimize S. d If S dT <[S dTmin Increase S d If S dT >[S dTmax If S decreases, then S decreases. d .

10. The method for designing the surface parameters of a ball screw pair operating under extreme temperature conditions according to claim 8, characterized in that, Contact angle α at contact equilibrium after heat deformation T for: Let the allowable contact angle under extreme temperature conditions be [α]. Tmin ]~[α Tmax If [α] Tmin ]≤α T ≤[α Tmax If the result is positive, proceed to the next step; otherwise, go to step S1 to optimize α. s α n If α T <[α Tmin Increase α s α n If α T >[α Tmax If α is reduced, then α will decrease. s α n .

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