Method for designing profile parameters of ball screw pair working under limiting temperature working condition

Abstract

The invention discloses a method for designing molded surface parameters of a ball screw pair working under a limiting temperature working condition. The method comprises the following steps: initially determining molded surface design parameters of the ball screw pair; establishing a mathematical model for the raceway in a normal plane; mapping the roller path contour in the normal plane into the shaft plane; carrying out thermal deformation calculation on the raceway profile, and carrying out thermal deformation calculation on the balls at the same time; mapping the contour in the axial plane after thermal deformation into a normal plane; arc fitting is carried out, and raceway profile parameters after thermal deformation are calculated; whether the gap value after thermal deformation meets the working condition requirement or not is judged, and if not, the profile parameters are modified till the working condition requirement is met; whether the contact angle after thermal deformation meets the allowable contact angle requirement or not is judged, and if not, profile parameters are modified till the allowable contact angle requirement is met; and finally, outputting profile parameters in a normal-temperature state. The problems that a ball screw pair designed at the normal temperature is short in service life and cannot be used under the working condition of the limiting temperature can be solved.

Description

Technical Field

[0001] The invention belongs to the technical field of mechanical transmission design, and in particular relates to a method for designing profile parameters of a ball screw pair working under extreme temperature conditions. Background Art

[0002] The use of spiral transmission is very common in the design and selection of traditional mechanical transmission. For complex working conditions, sliding spiral transmission is often used. However, there is a large sliding friction resistance between the contact spiral surfaces of the sliding spiral transmission, so its transmission efficiency is low, wears quickly, and has a short service life. It can no longer fully meet the development requirements of modern mechanical transmission in terms of high speed, high efficiency, and high precision.

[0003] With the development of science and technology, electric drive technology is increasingly entering extreme temperature conditions. High temperatures above 100°C and working conditions below -40°C have put forward higher requirements for screws. Traditional sliding screw transmission is increasingly unable to cope with the situation. Mechanical transmission systems working under such extreme temperature conditions increasingly need ball screw pairs that match the environment. Ball screw pairs are a transmission element that can convert spiral motion into linear motion in both directions. Their structure includes a screw shaft, a nut and a ball. Since the cleverness of the ball screw pair lies in the rolling motion of the ball between the nut and the screw raceway, this mode of motion greatly improves the transmission efficiency compared with sliding. For example, compared with the traditional sliding screw pair, the ball screw pair only needs one-third of the original power to achieve the same level of transmission effect. However, compared with the sliding screw pair, the spiral transmission between components is not achieved by the motion pair itself, but by using an intermediate element (ball) between the screw and the nut. Therefore, its design is more complicated. Especially because the temperature under the above working conditions is either too high or too low compared to normal temperature, it will cause thermal expansion and contraction of the part size. The raceways of the 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. As a result, when the temperature changes from normal temperature to extreme temperature, the ball screw pair may become stuck or jammed, or due to excessive radial clearance and improper contact angle, excessive wear, unbalanced load, insufficient load, etc., which ultimately greatly reduces the life of the ball screw pair.

[0004] The reason for the above problems is that when designing the ball screw pair, the profile parameters are designed according to the normal temperature state. The thermal deformation law is not taken into account. Therefore, it is very necessary to provide a set of design methods for the profile parameters of the ball screw pair working under extreme temperature conditions based on the thermal deformation law. Summary of the invention

[0005] The purpose of the present invention is to provide a method for designing profile parameters of a ball screw pair working under extreme temperature conditions, so as to solve the problem that a ball screw pair designed with raceway profile parameters at normal temperature cannot work normally under extreme temperature conditions. This guides the design of a ball screw pair that can work normally under the corresponding extreme temperature.

[0006] The technical solution to achieve the purpose of the present invention is:

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

[0008] S1: Preliminary design parameters of the ball screw pair: lead P h , ball diameter d b , pitch circle diameter d m , Adaptation ratio f v , Screw outer diameter d 1s 、Nut inner hole diameter d 1n , radial clearance S d , screw raceway contact angle α 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 on the central axis of the screw / nut as the coordinate origin O a Y a Z a , the coordinate system OX a Y a Z a Around X a The axis rotates counterclockwise by a lead angle λ to obtain the coordinate system OX in the normal plane n Y n Z n , in the normal plane, in the coordinate system OX n Y n Z n Mathematical model of the raceway below;

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

[0011] S4: According to the temperature of the extreme temperature condition, the thermal deformation calculation of the raceway profile is performed in the axial plane, and the thermal deformation calculation of the ball is also performed;

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

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

[0014] S7: Calculate the surface parameters of the raceway after thermal deformation according to the arc parameters of the raceway after thermal deformation in the normal plane obtained in step S6 and the data of the ball after thermal deformation obtained in step S4;

[0015] S8: Determine whether the clearance value after thermal deformation meets the working condition requirements. If not, jump to step S1 to modify the radial clearance S d Continue calculating until the working condition requirements are met;

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

[0017] S10: Output the profile parameters of the ball screw pair at room temperature.

[0018] Compared with the prior art, the present invention has the following significant advantages:

[0019] The present invention takes into account the thermal deformation laws of the screw raceway, nut raceway and ball diameter in the ball screw pair, effectively predicts the changes in various surface parameters of the ball screw pair after the temperature changes, and guides the optimization design of the surface parameters of the ball screw pair, thereby designing a ball screw pair that can work normally under extreme temperature conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 The design process of the profile parameters of the ball screw pair working under the extreme temperature condition of the present invention;

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

[0022] Figure 3 It is the coordinate relationship diagram between the axis plane and the normal plane;

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

[0024] Explanation of symbols: 1 nut; 2 ball; 3 screw. DETAILED DESCRIPTION

[0025] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions 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. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

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

[0027] S1: Preliminary design parameters of the ball screw pair;

[0028] The raceway dimensions of the ball screw pair are basically determined by its working space and the required load-bearing performance, and the main parameters for designing the raceway profile are as follows: Figure 2 The specific parameters are as follows:

[0029] d m : pitch circle diameter; d 1n : nut inner hole diameter; d 1s : outer diameter of the screw; d b : ball diameter; P h : lead; α n : Nut raceway contact angle; α s : screw raceway contact angle; f v : Adaptability ratio, which is the ratio of the raceway radius to the 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 the ball screw pair at room temperature, with no radial clearance. The radial clearance is the result of the nut middle diameter being larger than the screw middle diameter. The so-called middle diameter is the diameter of the cylindrical surface that envelops the ball center when the ball contacts the raceway under ideal conditions. The specific method for determining the raceway profile parameters includes the following steps:

[0031] S11: Determine the model and lead P of the ball screw pair according to the performance requirements of the ball screw pair under the extreme temperature working conditions. h , ball diameter d b ;

[0032] S12: According to the model of ball screw pair, refine the fixed parameters: pitch circle diameter d m , Adaptation ratio f v , Screw outer diameter d 1s 、Nut inner hole diameter d 1n ; Adaptation ratio f v is the raceway radius r s 、r n With ball diameter d b ratio.

[0033] S13: Initially determine the parameters that can be changed: radial clearance S d , screw raceway contact angle α s 、Nut raceway contact angle α n ;

[0034] S14: Parameter assignment:

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

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

[0037] S2: Design the raceway according to the given profile design parameters and establish the mathematical model of the raceway in the normal plane;

[0038] Given the profile parameters, the raceway can be designed. The raceway design is carried out in the normal plane. The so-called normal plane is the normal plane of the spiral line formed by connecting the centers of the balls, such as Figure 2 As shown in the figure on the right. The corresponding one is the axis plane, which is the plane passing through the center axis of the nut or screw. The angle between the normal plane and the axis plane at the same point is equal to the lead angle λ, as shown in Figure 3 As shown. To mathematically model the raceway in the normal plane is to use mathematical language, such as equations and functions, to represent the raceway for better 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 on the central axis of the screw / nut as the coordinate origin O a Y a Z a .like Figure 2 As shown, taking the second to last raceway in the upper row as an example, the center axis of the screw / nut is Z aAxis, perpendicular to Z a The straight line through the center of the ball is X a The direction from the origin to the center of the ball is X a The positive direction of the axis. a Y a Z a Around X a The axis rotates counterclockwise by λ to obtain the coordinate system OX in the normal plane n Y n Z n ,like Figure 3 As shown;

[0040] S22: Mathematical modeling of the raceway in the normal plane. For the Gothic double arc raceway profile, the mathematical model of the right raceway of the screw in this coordinate system is:

[0041]

[0042] Among them, (x, y, z) are the coordinates of the point in this coordinate system. is the pitch circle radius; is the ball radius; θ is the independent variable of the mathematical model, Θ sr is the value range of θ of the right raceway of the screw,

[0043]

[0044] in, is the outer radius of the screw.

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

[0046]

[0047] Among them, Θ sl is the value range of θ of the left raceway of the screw,

[0048]

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

[0050]

[0051] in, Half of the nut's median diameter; Θ nr is the value range of θ of the right raceway of the nut,

[0052]

[0053] in, is the inner radius of the nut.

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

[0055]

[0056] Among them, Θ nl is the value range of θ of the left raceway of the nut,

[0057]

[0058] In this way, the screw raceway and nut raceway in the ball screw pair can be quantified, and the thermal deformation process can be characterized by pure mathematical methods.

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

[0060] Due to the existence of the lead angle, it is not possible to directly perform the differential element method on the raceway for thermal deformation analysis in the normal plane. When performing differential element analysis in the axial plane, it is perpendicular to the central axis of the screw / nut everywhere, so it is very convenient to perform differential element analysis. The specific steps of the normal-axial mapping are as follows:

[0061] S31: Calculate the lead angle λ,

[0062]

[0063] S32: The parameter θ in step S2 is taken at a step length of 0.1°, the raceway is discretized, and after mapping to the normal plane, the raceway is processed by microelement on the normal plane. In order to distinguish, n is used in the upper left corner of the coordinate value to indicate that the coordinate value is the coordinate value of the normal plane, and a is used to indicate that the coordinate value is the coordinate value in the axial plane. That is, the coordinate values ​​in the normal plane are: ( n x,0, n z), the coordinate values ​​in the axial plane are ( a x,0, a z).

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

[0065] And construct the following column vector:

[0066]

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

[0068]

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

[0070]

[0071] S35: Mapping points to the axis plane:

[0072]

[0073] Then the coordinate value of the i-th point mapped to the axis plane is ( a x i ,0, a z i ).

[0074] This method can transform the thermal deformation calculation problem that cannot be directly calculated in the normal plane into the axial plane where thermal deformation calculation is easy.

[0075] S4: According to the temperature of the extreme temperature condition, the thermal deformation calculation of the raceway profile is performed in the axial plane, and the thermal deformation calculation of the ball is also performed;

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

[0077] S41: The temperature T of the screw, nut and ball materials and the corresponding working conditions e , determine their materials at the corresponding temperature T e Thermal expansion coefficient η relative to room temperature T0 = 20°C T Here, the screw, nut and ball are generally made of the same material to facilitate thermal deformation control. However, different materials can also be used. When calculating, pay attention to distinguishing their thermal expansion coefficients;

[0078] S42: Calculate the temperature change from T0 to T e The coordinate values ​​of each data point of the raceway afterwards:

[0079]

[0080] a x iT , a z iT represent the X of the ith 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 ball radius after thermal deformation:

[0082] r bT =[η T(T e -T0)+1]r b (10)

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

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

[0085] S5: Mapping 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 represent the X of the ith 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 surface in the normal plane.

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

[0094] The specific steps are as follows:

[0095] S61: Use the general equation of a circle to represent the arc raceway:

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

[0097] Among them, A, B, C, and D are constant coefficients. Solve the following equation:

[0098]

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

[0100] The meaning of the above equation is: Under the premise of satisfying the constraints g(A,B,C,D), find the solution that makes f p (A,B,C,D) A, B, C, D that obtains the minimum value.

[0101] Formula (14) is solved using the Lagrangian operator method.

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

[0103]

[0104] Compared with the most commonly used The least squares circle fitting method eliminates the influence of the radius and has higher accuracy. The center and radius of the raceway of the normal plane under the extreme working condition can be fitted to calculate the profile parameters of the ball screw pair.

[0105] S7: Calculate the surface parameters of the raceway after thermal deformation according to the arc parameters of the raceway after thermal deformation in the normal plane 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 thermal deformation contact angle:

[0108] Screw raceway thermal deformation contact angle a sT :

[0109]

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

[0111]

[0112] S72: Calculate the thermal deformation median diameter:

[0113] Thermal deformation diameter of the screw d msT :

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

[0115] Thermal deformation diameter of the nut d mnT :

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

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

[0118] S8: Determine whether the clearance value after thermal deformation meets the working condition requirements. If not, jump to step S1 to modify the radial clearance S d Continue calculating until the working condition requirements 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 the extreme temperature condition is [S dTmin ]~[S dTmax ], if [S dTmin ]≤S dT ≤[S dTmax ], then proceed to the next step, otherwise jump to step S1 and optimize S d If S dT <[S dTmin ], increase S d If S dT >[S dTmax ], then reduce S d ;

[0122] Generally speaking, the higher the temperature, the smaller the gap, and the higher the temperature, the more likely it is to get stuck or jammed. This step can effectively avoid problems such as jamming and jamming under extreme temperature conditions.

[0123] S9: Determine whether the contact angle after thermal deformation meets the allowable contact angle requirement. If not, jump to step S1 to modify the contact angle α. s , α n Continue the calculation 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 for the extreme temperature condition is [α Tmin ]~[α Tmax ], if [α Tmin ]≤α T ≤[α Tmax ], then proceed to the next step, otherwise jump to step S1 and optimize α s , α n If α T <[α Tmin ], increase α s , α n ; If α T >[α Tmax ], then reduce α s , α n ;

[0128] It can effectively avoid the problem of excessive wear caused by the increase of contact angle during contact equilibrium under extreme temperature conditions, or the reduction of load-bearing performance due to too small contact angle.

[0129] S10: Output the profile parameters of the ball screw pair at room temperature. This refers to the profile parameters optimized in step S1 after the two 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 , Adaptation ratio f v , Screw outer diameter d 1s 、Nut inner hole diameter d 1n , radial clearance S d , screw raceway contact angle α s 、Nut raceway contact angle α n ;

[0131] The above specific implementation methods are all for Gothic double arc raceways, but single arc raceways are still used in certain specific occasions because of their simple design and processing. Therefore, it is also necessary to establish a design method for the extreme temperature condition parameters of the single arc raceway profile. The specific method is as follows:

[0132] For a single arc raceway profile, such as Figure 4 As shown, the contact state X nThe axis is the symmetry axis, and the raceway on the contact side is treated symmetrically to create a double arc raceway, which is the dotted line part in the figure. The mathematical model of the raceway and subsequent calculations can be carried out according to the above double arc raceway process.

Claims

1. A method for designing profile parameters of a ball screw pair working under extreme temperature conditions, characterized in that: include: S1: Preliminary design parameters of the ball screw pair: lead P h , ball diameter d b , pitch circle diameter d m , Adaptation ratio f v , Screw outer diameter d 1s 、Nut inner hole diameter d 1n , radial clearance S d , screw raceway contact angle α 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 on the central axis of the screw / nut as the coordinate origin O a Y a Z a , the coordinate system OX a Y a Z a Around X a The axis rotates counterclockwise by a lead angle λ to obtain the coordinate system OX in the normal plane n Y n Z n , in the normal plane, in the coordinate system OX n Y n Z n Mathematical model of the raceway below; S3: Map the raceway profile in the normal plane to the axis plane; S4: According to the temperature of the extreme temperature condition, the thermal deformation calculation of the raceway profile is performed in the axial plane, and the thermal deformation calculation of the ball is also performed; S5: Mapping the contour in the axial plane after thermal deformation to the normal plane; S6: Perform arc fitting on the raceway data after thermal deformation in the normal plane, and calculate the center coordinates of the left and right arc raceways of the screw and nut after thermal deformation and the screw raceway radius and nut raceway radius; S7: Calculate the surface parameters of the raceway after thermal deformation according to the arc parameters of the raceway after thermal deformation in the normal plane obtained in step S6 and the data of the ball after thermal deformation obtained in step S4; S8: Determine whether the clearance value after thermal deformation meets the working condition requirements. If not, jump to step S1 to modify the radial clearance S d Continue calculating until the working condition requirements are met; S9: Determine whether the contact angle after thermal deformation meets the allowable contact angle requirement. If not, jump to step S1 to modify the contact angle α. s , α n Continue calculating until the allowable contact angle requirement is met; S10: Output the profile parameters of the ball screw pair at room temperature.

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

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

4. The method for designing profile parameters of a ball screw pair working under extreme temperature conditions according to claim 1, characterized in that: The thermal deformation calculation of the raceway profile is carried out by the following formula: a x iT , a z iT represent the X of the ith point of the raceway in the axial plane after thermal deformation a Axis and Z a Axis coordinate value, η T is the temperature T of the material of the screw, nut and ball under the corresponding working conditions e The thermal expansion coefficient relative to room temperature T0 is ( a x i ,0, a z i ) is the coordinate value of the i-th point mapped to the axis plane.

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

6. The method for designing profile parameters of a ball screw pair working 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 represent the X of the ith point of the raceway in the normal plane after thermal deformation n Axis and Z n The coordinate value of the axis, τ i is the travel angle of the i-th point, λ is the lead angle, a x iT , a z iT represent the X of the ith 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 profile parameters of a ball screw pair working under extreme temperature conditions according to claim 1, characterized in that: The center coordinates of the left and right arc raceways of the screw and nut after thermal deformation and the screw raceway radius and nut raceway radius are: Among them (z cT ,x cT ) is the center coordinate of the left and right arc raceways of the screw and nut after thermal deformation, r sT is the radius of the left and right arc raceways of the screw after thermal deformation, r nT is the radius of the left and right arc raceways of the nut after thermal deformation, A, B, C, D are the coefficients of the general equation of the circle, and are solved by the following formula: where f p (A,B,C,D) is a function whose independent variables are A, B, C, and D. m is the total number of points on a raceway. g(A,B,C,D) is a constraint function. n x iT , n z iT represent the X of the ith 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 profile parameters of a ball screw pair working under extreme temperature conditions according to claim 7, characterized in that: The raceway profile parameters after thermal deformation calculation include: Screw raceway thermal deformation contact angle a sT : Nut raceway thermal deformation contact angle α nT : Thermal deformation diameter of the screw d msT : d msT =2(x cT |-(r sT -r bT )cosα sT ) Thermal deformation diameter of the nut d mnT : d mnT =2(x cT |+(r nT -r bT )cosα nT ) where r bT It is the ball radius value after thermal deformation.

9. The method for designing profile parameters of a ball screw pair working under extreme temperature conditions according to claim 8, characterized in that: Radial clearance value S after thermal deformation dT for: S dT =d mnT -d msT Assume that the allowable clearance under the extreme temperature condition is [S dTmin ]~[S dTmax ], if the gap value S after thermal deformation dT Satisfy dTmin ]≤S dT ≤[S dTmax ], then proceed to the next step, otherwise jump to step S1 and optimize S d :If S dT <[S dTmin ], increase S d If S dT >[S dTmax ], then reduce S d .

10. The method for designing profile parameters of a ball screw pair working under extreme temperature conditions according to claim 8, characterized in that: Contact angle α at contact equilibrium after thermal deformation T for: Assume that the allowable contact angle under the extreme temperature condition is [α Tmin ]~[α Tmax ], if [α Tmin ]≤α T ≤[α Tmax ], then proceed to the next step, otherwise jump to step S1 and optimize α s , α n :If α T <[α Tmin ], increase α s , α n ; If α T >[α Tmax ], then reduce α s , α n .

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