Method for predicting loading deformation of linear ball guide rail in multi-ball independent feeding process

Abstract

The invention discloses a linear ball guide rail multi-ball independent feeding process load deformation prediction method, which comprises the following steps: acquiring basic parameters of a linear ball guide rail, determining a class stiffness coefficient according to a Hertz contact theory, and constructing a multi-ball independent load deformation model; measuring characteristic parameters of the guide rail raceway, and establishing a characterization function of the surface topography; substituting the representation function into a multi-ball independent load deformation model to obtain a prediction result of the load deformation of the linear ball guide rail in the feeding process; measuring a vibration signal in the feeding process of the linear ball guide rail under an actual working condition, comparing a prediction result with frequency domain data of the vibration signal under the same working condition, and iteratively updating a representation function of the surface topography of a guide rail raceway and a multi-ball independent load deformation model; and outputting the load deformation prediction model of the linear ball guide rail and the representation function of the raceway surface morphology in the feeding process. By means of the method, high-precision prediction of the loaded deformation of the linear ball guide rail in the feeding process can be achieved.

Description

Technical Field

[0001] The present invention belongs to the field of digital twins of numerically controlled machine tools, and in particular relates to a method for predicting load deformation during the independent feeding process of multiple balls in a linear ball guide. Background Art

[0002] Rolling linear guides are currently widely used in the field of CNC machine tools. Compared with traditional rectangular guides and V-shaped guides, they have many advantages, such as high positioning accuracy, good accuracy retention, and high maintainability. The most unique assembly structure of the raceway and the ball in the rolling linear guide has a direct impact on the processing accuracy and performance of the CNC machine tools, including the raceway surface morphology, the raceway center distance error, and the ball static stiffness characteristics.

[0003] A Chinese patent document with publication number CN105653842A discloses a method for constructing a geometric error model of a rolling guide feed system. First, the contact stiffness of the guide rail is estimated by the equivalent load method. Secondly, a force balance equation of a workbench supported by a slider is established. Thirdly, the geometric deformation relationship of each slider is determined based on the rigidity assumption of the workbench. Supplementary equations are listed based on the physical relationship between deformation and force. Finally, the force-deformation error of the feed system can be solved by combining the equations.

[0004] A Chinese patent document with publication number CN104217080A discloses a model establishment and prediction method for motion error prediction of a rolling linear feed system. The method first analyzes the contact state of the raceway and the ball and the structure of the slider according to the guide rail model, analyzes the relationship between the force and deformation of the ball according to the Hertz theory, and constructs an equivalent nonlinear spring of the ball; constructs a finite element model in the finite element analysis software ANSYS according to the structure of the slider and the linear feed system, and completes the modeling of the prediction model; measures the horizontal and vertical straightness errors of the linear feed system guide rail, fits the measured errors, and constructs an error curve; brings the obtained error curve into the prediction model; applies load to simulate the deadweight and load of the linear feed system; and completes the prediction of the five motion errors of the linear feed system through the finite element analysis software ANSYS.

[0005] At present, the research on load deformation modeling of linear rolling guides is mainly carried out from the perspective of static performance, and there is a lack of research on the dynamic travel process of linear rolling guides. Most of the modeling based on Hertz contact theory in the research assumes that the contact conditions of the balls in the same raceway are the same, ignoring the impact of changes in contact conditions during dynamic feeding and the impact of raceway surface morphology under actual working conditions. This results in low prediction accuracy of load deformation during the feeding process of rolling linear guides and weak dynamic analysis capabilities. Summary of the invention

[0006] Aiming at the deficiencies of the existing technology, the present invention provides a method for predicting the load-bearing deformation during the feeding process of a linear ball guide with multiple independent balls. The contact states of each ball under transient conditions are analyzed independently, a surface topography characterization function is determined and substituted into the load-bearing deformation model of multiple independent balls to predict the load-bearing deformation of the rolling linear guide during the feeding process. By comparing the predicted results with the measured data and iteratively optimizing the characterization function and the load-bearing deformation model in combination with characteristic values such as straightness, surface roughness, and vibration signals, high-precision prediction of the load-bearing deformation is achieved.

[0007] A method for predicting the load-bearing deformation during the feeding process of a linear ball guide with multiple independent balls, comprising the following steps:

[0008] (1) Obtain the structure and basic parameters of the rolling linear guide, determine the equivalent stiffness coefficient according to Hertz contact theory, and construct a load-bearing deformation model of multiple independent balls;

[0009] (2) Measure the straightness, surface roughness, waviness, and vibration signals of the guideway raceway to determine the surface topography characterization function of the guideway raceway, substitute the characterization function into the load-bearing deformation model of multiple independent balls established in step (1), and obtain the predicted results of the load-bearing deformation varying with displacement during the feeding process;

[0010] (3) Measure the vibration signal of the rolling linear guide during the feeding process under actual working conditions, superimpose and analyze the vibration signals generated by the reciprocating stroke, and compare with the predicted results in step (2). If they match, execute step (4); if not, return to step (2) to adjust the parameters of the characterization function;

[0011] (4) Output the final predicted results of the load-bearing deformation of the rolling linear guide during the feeding process.

[0012] In step (1), it is necessary to obtain the structure of the rolling linear guide, including the number of raceways, the number of balls in the contact state at the same time, and the contact angle of each raceway.

[0013] It is necessary to obtain the basic parameters of the rolling linear guide, including material, radius of curvature, and stiffness coefficient, and calculate the equivalent stiffness coefficient according to the above parameters.

[0014] Determine the equivalent stiffness coefficient according to Hertz contact theory, and the calculation formula is as follows:

[0015]

[0016] In the formula, F is the load borne by a single ball; δ is the elastic deformation of a single ball; n1 and n2 are the Poisson's ratios of the materials of the ball and the groove (slider, guide rail) respectively; E1 and E2 are the elastic moduli of the materials of the ball and the groove respectively; μ is the Hertz coefficient related to stiffness; ∑ρ is the comprehensive curvature of the contact between the ball and the groove;

[0017] Since μ, E1, E2, n1, n2, and ∑ρ are all constants for a specific contact system, the above equation can be simplified to:

[0018]

[0019] where k h describes the relationship between the load F on a single ball and the elastic deformation δ, and is called the stiffness-like coefficient.

[0020] In step (1), the process of constructing the load-deformation model for multiple independent balls is as follows:

[0021] Taking a single raceway pair as the analysis object, since the contact states of all balls are independent, the contact conditions of each ball are independent parameters, including the magnitude of the force on the contact surface and the magnitude of the force-induced deformation.

[0022] Assume that there are n balls in raceway i, and the magnitude of the force on the contact surface of the jth ball is F ij , and the resulting deformation is δ ij , and both the force and the deformation are along the contact angle direction of the raceway pair; let F vi represent the overall contact pressure on raceway i, and we get:

[0023]

[0024] Assume that the contact condition of the jth ball in raceway i has a linear effect on its deformation. Also, given that the slider always maintains a horizontal attitude, and only considering the vertical deformation δ y = ΔZ, then the overall deformation δ i of raceway i is obtained as:

[0025] a1δ i1 + b1 = a2δ i2 + b2 = … = a j δ ij + b j = … = δ i

[0026] For a multi-raceway linear rolling guide system, the system deformation δ y = ΔZ is affected by the combined deformation of all raceways; assuming only a double-raceway system is considered now, then δ y and δ i show a simple linear relationship, that is:

[0027] δ y = δ i sinβ

[0028] Suppose there are n balls in contact in the raceway i at the same time, and the offset contact angle generated by the contact point of the j-th ball and the guide rail raceway is α ij , the deformation generated by the j-th ball is δ ij , under the combined influence of all the balls, the displacement of the raceway i in the direction of the contact angle is δ hi , the displacement of the slider is δ i , the force on the raceway i is F vi , due to the influence of the raceway surface topography, at the same time, the initial contact state Δδ of each ball ij is different, and the following static equations are listed:

[0029]

[0030] In step (2), multiple periodic Fourier series are combined as the characterization function; for a specific linear rolling guide pair, by measuring the waviness, roughness, straightness of the raceway and the vibration signal during the movement process, the parameters of each term in the Fourier series are assigned values to characterize the surface topography characteristics of the guide rail raceway.

[0031] In step (2), the prediction of the deformation under load during the feeding process is completed by a program written in a computer language, and the calculation process includes matrix operations and function operations.

[0032] In step (3), the vibration signal of the rolling linear guide during the feeding process under actual working conditions is completed by a special test bench, and the test bench includes a displacement sensor, a vibration sensor, a level and a single-axis rolling linear guide as the measurement object.

[0033] In step (3), the vibration signal of the rolling linear guide during the reciprocating process within the stroke range under the same working state is measured repeatedly; by superimposing the reciprocating signal and noise filtering, the vibration signal generated by the influence of the raceway surface topography characteristics is retained, and compared with the frequency domain data of the predicted result of the deformation under load, the frequency and phase of different orders of the characterization function are adjusted, and repeated prediction and comparison are carried out until the frequency difference and the maximum phase error between the predicted result and the measured result under actual working conditions are less than 10% of the minimum period.

[0034] Taking the same stroke direction as the positive direction and the opposite stroke direction as the negative direction, the vibration signals generated by the reciprocating strokes are superimposed to eliminate the influence of the systematic error caused by the inconsistent reciprocating motion directions, and whether to filter is selected according to the actual situation, and finally the vibration signal generated under the influence of the raceway surface topography characteristics is retained.

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] The present invention predicts the load deformation of a rolling linear guide during the feeding process by independently analyzing the contact state of each ball under transient conditions and combining with the characterization function of the surface topography of the guideway raceway. The straightness, roughness of the guideway, and the vibration signal of the actual working condition are measured as characteristic values, and the characterization function and the load deformation model are iteratively optimized to achieve high-precision prediction of the load deformation of the rolling linear guide during the feeding process. Description of the Drawings

[0037] Figure 1 It is a flowchart of a method for predicting the load deformation of a linear ball guide with multiple independent balls during the feeding process according to an embodiment of the present invention.

[0038] Figure 2 It is a simplified mechanical model of the overall force situation of a linear rolling guide system according to an embodiment of the present invention.

[0039] Figure 3 It is the contact state of a single rolling element in the raceway pair according to an embodiment of the present invention.

[0040] Figure 4 It is an equivalent model of independent contact of balls according to an embodiment of the present invention.

[0041] Figure 5 It is an equivalent model of a single raceway pair according to an embodiment of the present invention.

[0042] Figure 6 、 Figure 7 It is a demonstration of the analysis result of a multi-ball independent model according to an embodiment of the present invention.

[0043] Figure 8 It is a demonstration of the predicted result of the load deformation of a linear ball guide during the feeding process according to an embodiment of the present invention. Detailed Embodiment

[0044] The present invention will be further described in detail below with reference to the drawings and embodiments. It should be noted that the following embodiments are intended to facilitate the understanding of the present invention and do not limit it in any way.

[0045] As Figure 1 shown, a method for predicting the load deformation of a linear ball guide with multiple independent balls during the feeding process includes the following steps:

[0046] Step 1, obtain the basic parameters of the rolling linear guide and determine the stiffness coefficient of the same kind according to the Hertz contact theory.

[0047] Step 2, establish a multi-ball independent model according to the structure of the rolling linear guide.

[0048] Step 3, measure the straightness, surface roughness, etc. of the guideway raceway as characteristic values to determine the initial characterization function of the surface topography of the guideway raceway.

[0049] Step 4: Substitute the raceway topography characterization function into the load deformation model of the linear motion rolling guide to obtain the initial prediction result of the load deformation during the feeding process.

[0050] Step 5: Measure the vibration signal of the linear motion rolling guide during the feeding process within the stroke range under the working condition, superimpose and analyze the vibration signals generated by the reciprocating stroke, and compare with the prediction result. If they do not match, optimize the characterization function and iterate until the frequencies match. Figure 2 It is a simplified mechanical model of the overall force condition of the linear rolling guide system. Assume that there are 4 rows of grooves in the guide system, and the number of balls participating in contact in each row of grooves is the same (both are n), then the force states between the balls above and below the guide are the same. The contact pressure between a single ball above and the groove is represented by F v1 and the contact pressure between a single ball below and the groove is represented by F v2 . Figure 1 where Z1 and Z2 are the coordinate positions of the center of gravity of the slider and the rail respectively, F v is the normal load received by the guide system, and β is the contact angle.

[0051] In Step 1, according to the Hertz contact theory, the relationship between the local contact force F received by a single ball and the elastic deformation δ can be expressed as:

[0052]

[0053] F / N is the local contact force received by a single ball; δ / mm is the elastic deformation of a single ball; n1 and n2 are the Poisson's ratios of the materials of the ball and the groove (slider, rail) respectively; E1 / GPa and E2 / GPa are the elastic moduli of the materials of the ball and the groove (slider, rail) respectively; μ is the Hertz coefficient related to the stiffness; ∑ρ / mm -1 is the comprehensive curvature of the contact between the ball and the groove. Among them, μ, E1, E2, n1, n2, and ∑ρ are all constants for a specific contact system, so the above formula can be simplified as:

[0054]

[0055] Here, k h describes the relationship between the load F received by a single ball and the deformation δ, and can be called the stiffness-like coefficient.

[0056] Assume that each ball is always in a compressed state under the external load, and under the action of the external load F v , the relative deformation generated by the guide system can be represented by ΔZ, then we can get:

[0057] F v +2nF v2 sinβ=2nF v1sinβ

[0058] δ y =ΔZ = Z1 - Z2

[0059]

[0060]

[0061] where δ1 and δ2 are the elastic deformations generated by a single ball under the action of the contact pressures F v1 、F v2 . Since the stress states between the upper and lower balls are the same, the corresponding deformations are also the same respectively.

[0062] In addition, during the assembly process of the guide rail system, a pre-tightening force is usually applied. Assuming that under the action of the pre-tightening force, the normal pressure generated on the contact surface by a single ball is F0, and the initial deformation generated by the pre-tightening force is δ0, the Hertz contact theory is also satisfied between the two, that is:

[0063]

[0064] Assuming that the initial deformation amounts of all the upper and lower balls are the same, all being δ0, then under the action of the load F v , it can be obtained that:

[0065]

[0066] F v1 = f(F v , F0)

[0067]

[0068] Figure 3 is the contact state of a single rolling element in the raceway pair. In the ideal state, the raceway surfaces of the slider and the guide rail are both cylindrical surfaces or elliptical cylindrical surfaces, and are approximately linear guide rails in the feed direction section cut along the contact point. In the actual state, the raceway surface is not an invariable straight line, but a wavy curve.

[0069] Figure 4 is the equivalent model of independent ball contact. The ball can be equivalent to a deflected non-linear spring. Among them, F vi is the load uniformly distributed on the i-th row of raceways of the slider, F ij is the normal load borne by the j-th ball in the i-th row of raceways; α ij is the deflected contact angle generated due to the deflection of the contact point, Δδ ij is the initial deformation amount in the deformation direction generated by the deflection of the contact point; Q ij is the force on the ball in the deformation direction.

[0070] Assume that the deformation of the j-th ball in the i-th column is δ ij , ignoring the influence of the horizontal force on the ball, F vj equals the sum of the normal loads F ij borne by all the balls in the contact state.

[0071]

[0072] Figure 5 The equivalent model of a single raceway pair. Taking a single raceway pair as the analysis object, since the contact states of all the balls are independent, the contact conditions of each ball are independent parameters, including the magnitude of the force on the contact surface and the magnitude of the force deformation. Assume that there are n balls in the i-th raceway, and the magnitude of the force on the contact surface of the j-th ball is F ij , and the resulting deformation is δ ij , and both the force and the deformation are along the contact angle direction of the raceway pair. Let F vi represent the overall contact pressure received by the i-th raceway, and it can be obtained that:

[0073]

[0074] Assume that the contact condition of the j-th ball in the i-th raceway has a linear influence on its deformation. At the same time, it is known that the slider always maintains a horizontal posture, and only the vertical deformation δ y =ΔZ is considered. Then the overall deformation δ i of the i-th raceway can be obtained as:

[0075] a1δ i1 +b1 = a2δ i2 +b2 =... = a j δ ij +b j =... = δ i

[0076] For a multi-raceway linear rolling guide system, the system deformation δ y =ΔZ is affected by the comprehensive influence of the deformations of all the raceways. Assume that only a double-raceway system is considered now, then δ y and δ i show a simple linear relationship, that is:

[0077] δ y =δ i sinβ

[0078] where δ i is the in the above formula, that is, the deformation amount generated by a single raceway. Since only a double-raceway system is considered, there is only one raceway on one side, so it is the deformation amount of a single raceway.

[0079] Assume that at the same moment, there are n balls in contact in the j-th ball within the i-th raceway, and the offset contact angle generated by the contact point between the j-th ball and the guide raceway is α ij , and the deformation generated by the j-th ball is δ ij . Under the combined influence of all the balls, the displacement of the i-th raceway in the contact angle direction is δ hi , the displacement of the slider is δ i , and the force on the i-th raceway is F vi . The following static equations can be listed:

[0080]

[0081] By solving the static equations, the force F on the corresponding i-th raceway can be obtained vi . Under the condition of, the displacement δ of the i-th raceway in the contact angle direction hi .

[0082] In the above model of equivalent contact with a non-linear spring, the contact state of the balls is equivalent to that of non-linear springs, but the different initial lengths of each spring are not considered. Due to the influence of the raceway surface topography, at the same moment, the initial contact state Δδ of each ball ij is different, and the above formula is corrected as follows:

[0083]

[0084] When the external load received by the slider is less than the critical load, the balls in the upper and lower raceways are both under pressure, and the deformation in the vertical direction remains the same; when the external load is greater than the critical load, only the upper raceway is under pressure.

[0085] Among them, since the two-side raceways of the slider and the guide are regarded as symmetrically distributed, so F v1 = F v2 = F v / (2 * csoα p ), where α p is the contact angle between the deformed slider raceway and the guide raceway under the load condition, and the initial contact angle is α0 = 45°.

[0086] α pi = arctan(a p sinα0 / (a p cosα0 + δ pci + δ pri ))

[0087] α p can be calculated from the above formula. Among them, a p is the distance between the curvature centers of the slider raceway and the guide raceway, which is called the raceway center distance. δpci and δ pri are respectively the slider side deformation and the guide rail side deformation of the corresponding raceway i under the load condition. The relative deformation ΔZ of the reference guide rail system is also the geometric error δ of the slider, y as shown in the following formula:

[0088] δ y = δ hi *sinα p

[0089] In step 3, a periodic Fourier series is used as the characterization function of the guide rail raceway surface topography. Under the contact conditions that conform to the Hertz contact theory, the errors caused by the surface topography of the guide rail raceway mainly come from the manufacturing errors of the guide rail raceway surface and the deformation errors generated during the assembly of the guide rail. The guide rail raceway is usually formed by milling or turning, and the surface roughness is ensured by grinding. Therefore, it can be characterized by a Fourier series with a relatively high frequency and a relatively small wavelength. The assembly process of the guide rail often uses multiple sets of bolts and nuts to complete. The pre-tightening force of the bolts and nuts will cause the guide rail to deform at each assembly hole position, thus having a regular impact on the overall surface topography. Considering that the number of bolts and nuts is limited and there is a certain spacing between each set of bolts and nuts, it can be characterized by a Fourier series with a relatively small frequency and a relatively long wavelength. Assuming that the direction along the guide rail raceway is the Z direction, the characterization function can be described by the following formula:

[0090]

[0091] where a1, a2 are constants, a 1n , b 1n , a 2n , b 2n are the amplitudes of the Fourier series corresponding to each frequency, n represents the order of the Fourier series. Generally, n = 1, and more orders are required for more complex topographies. T represents the wavelength (or period) of the Fourier series. For a specific linear rolling guide pair, the determination of the above parameters requires measuring the waviness, roughness, straightness of the raceway and the vibration signals during the movement process.

[0092] In step 4, the guide rail raceway surface topography characterization function is substituted into the multi-ball independent model to obtain the predicted results of the load deformation of the rolling linear guide within the stroke range.

[0093] In step 5, for a specific linear rolling guide, measure and process its vibration signals, compare them with the predicted results of the load deformation of the rolling linear guide obtained in step 4 within the stroke, observe the differences in their characteristics, optimize the characterization function by changing the parameters of the guide rail raceway surface topography characterization function, repeatedly substitute it into the multi-ball independent model, and repeatedly compare it with the measured vibration signals, and iterate this process.

[0094] Under the same working condition, the vibration signal of the rolling linear guide during reciprocating motion within the stroke range is measured repeatedly while keeping the load unchanged. Taking the same stroke direction as the positive direction, the reciprocating signals are superimposed to eliminate the influence of some systematic errors. Filtering is selected according to the actual situation, and the vibration signal caused by the influence of the raceway surface topography is retained. This signal is compared with the frequency-domain data of the predicted results of the load-induced deformation, and the frequencies and phases of different orders of the characterization function are adjusted. Then, repeated prediction and comparison are carried out, and the iteration continues until the frequency difference and the maximum phase error between the predicted result and the measured result under the actual working condition are both less than 10% of the minimum period. At this time, the value of the predicted result of the load-induced deformation of the linear ball guide is the accurate prediction of the load-induced deformation under the actual working condition. The final predicted result is output, that is, the load-induced deformation under different loads can be accurately predicted within the stroke range. The iterative raceway topography characterization function can also be used as a virtual mapping of the guideway raceway surface, which solves the difficulty of measuring the raceway topography by instruments under actual working conditions to a certain extent.

[0095] Figure 6 、 Figure 7 This is a demonstration of the analysis results of the multi-ball independent model in the embodiment of the present invention. In the load-induced deformation model of multi-ball independence, at the same moment and under the same working condition, each ball in the raceway is analyzed independently. Affected by the raceway topography of the guideway, each ball has a different contact state and undergoes different load-induced deformations.

[0096] Figure 8 This is a demonstration of the predicted results of the load-induced deformation of the linear ball guide during the feeding process in the embodiment of the present invention. Within the stroke range, as the slider feeds, the positions of the contacting guideway raceways are different, the raceway surface topographies are also different, the contact states of the balls change, and finally the load-induced deformation of the linear ball guide changes.

[0097] The above embodiments have described the technical solutions and beneficial effects of the present invention in detail. It should be understood that the above are only specific embodiments of the present invention and are not used to limit the present invention. Any modification, supplement, and equivalent replacement made within the scope of the principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for predicting the load deformation during the feeding process of a linear ball guide with multiple independent balls, characterized in that, It includes the following steps: (1) Obtain the structure and basic parameters of the rolling linear guideway, determine the equivalent stiffness coefficient according to Hertz contact theory, and construct a load-bearing deformation model for multiple independent balls; (2) Measure the straightness, surface roughness, waviness and vibration signals of the guideway raceway to determine the characterization function of the surface topography of the guideway raceway, and substitute the characterization function into the load-bearing deformation model for multiple independent balls established in step (1) to obtain the predicted results of load-bearing deformation varying with displacement during the feeding process; (3) Measure the vibration signals of the rolling linear guideway during the feeding process under actual working conditions, superimpose and analyze the vibration signals generated during the reciprocating stroke, and compare with the predicted results in step (2). If they match, execute step (4); if not, return to step (2) to adjust the parameters of the characterization function; (4) Output the final predicted results of the load-bearing deformation of the rolling linear guideway during the feeding process.

2. The method for predicting the load deformation during the feeding process of multiple independent balls in a linear ball guide according to claim 1, characterized in that, In step (1), it is necessary to obtain the structure of the rolling linear guideway, including the number of raceways, the number of balls in contact at the same time, and the contact angle of each raceway.

3. The method for predicting the load deformation during the feeding process of multiple independent balls of a linear ball guide according to claim 1, characterized in that, In step (1), it is necessary to obtain the basic parameters of the rolling linear guideway, including material, radius of curvature, and stiffness coefficient, and calculate the equivalent stiffness coefficient according to the above parameters.

4. The method for predicting the load deformation during the feeding process of multiple independent balls in a linear ball guide according to claim 1, characterized in that, In step (1), the process of constructing a load-bearing deformation model for multiple independent balls is as follows: Taking a single raceway pair as the analysis object, since the contact states of all balls are independent, the contact conditions of each ball are independent parameters, including the magnitude of the force on the contact surface and the magnitude of the force deformation; Assume that there are n balls in the raceway i, and the force on the contact surface of the j-th ball is F ij , and the resulting deformation is δ ij , and both the force and the deformation are along the contact angle direction of the raceway pair; let F vi represent the overall contact pressure received by the raceway i, and it can be obtained that: Assume that the contact condition of the j-th ball in the i-th raceway has a linear effect on its deformation. At the same time, it is known that the slider always maintains a horizontal attitude, and only the vertical deformation δ of the system is considered. y = ΔZ, then the overall deformation δ of the i-th raceway can be obtained. i : a1δ i1 +b1 = a2δ i2 +b2 = … = a j δ ij +b j = … = δ i For a multi-raceway linear rolling guide system, the system deformation δ y = ΔZ is affected by the combined deformation of all raceways; assuming only a double-raceway system is considered now, then δ y and δ i show a simple linear relationship, that is: δ y = δ i sinβ Suppose there are a total of n balls in contact in raceway i at the same time, and the offset contact angle generated by the contact point of the jth ball and the guide raceway is α ij , the deformation generated by the jth ball is δ ij , under the combined influence of all the balls, the displacement of raceway i in the contact angle direction is δ hi , the displacement of the slider is δ i , raceway i is subjected to a force F vi , due to the influence of the raceway surface topography, at the same time, the initial contact state Δδ of each ball ij is different, and the following static equations are listed: where k h describes the relationship between the load F on a single ball and the elastic deformation δ, and is called the stiffness-like coefficient.

5. The method for predicting the load deformation during the feeding process of multiple independent balls in a linear ball guide according to claim 1, characterized in that In step (2), a combination of multiple periodic Fourier series is used as the characterization function; for a specific linear rolling guideway pair, by measuring the waviness, roughness, straightness of the raceway and the vibration signals during the movement process, the parameters of the Fourier series are assigned to characterize the surface topography characteristics of the guideway raceway.

6. The method for predicting the load deformation during the feeding process of multiple independent balls in a linear ball guide according to claim 1, characterized in that In step (2), the prediction of the load-bearing deformation during the feeding process is completed by a program written in a computer language, and the calculation process includes matrix operations and function operations.

7. The method for predicting the load deformation during the feeding process of multiple independent balls of a linear ball guide according to claim 1, characterized in that In step (3), the vibration signals of the rolling linear guideway during the feeding process under actual working conditions are completed using a special test bench, which includes a displacement sensor, a vibration sensor, a level gauge, and a single-axis rolling linear guideway as the measurement object.

8. The method for predicting the load deformation during the feeding process of multiple independent balls in a linear ball guide according to claim 1, characterized in that In step (3), repeatedly measure the vibration signals of the rolling linear guideway during the reciprocating process within the stroke range under the same working state for multiple times; by superimposing the reciprocating signals and filtering the noise, retain the vibration signals generated by the influence of the surface topography characteristics of the raceway, compare with the frequency-domain data of the predicted results of the load-bearing deformation, adjust the frequencies and phases of different orders of the characterization function, and repeatedly predict and compare until the frequency difference and the maximum phase error between the predicted results and the measured results under actual working conditions are both less than 10% of the period.

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