A method for optimizing profile error of internal thread of wide variable pitch nut and computer storage medium

Abstract

The application discloses a kind of to the profile error optimization method and computer storage medium for wide variable lead nut internal thread, belong to ball screw pair internal thread grinding machine technical field, method includes: step 1, model establishment: the theoretical model of nut internal thread, grinding wheel axial profile model and nut internal thread grinding model are established, based on above-mentioned model, profile error calculation model is presented;Step 2, error analysis: the influence of nut lead, nominal diameter and installation center distance on profile error is analyzed;Step 3, optimization method is presented: for variable lead condition, profile error optimization method is presented and implemented, so that profile error is reduced.By the application, the machining precision can be improved.

Description

Technical Field

[0001] This invention relates to the field of ball screw internal thread grinding technology, and more specifically to a method for optimizing the profile error of the internal thread of a wide variable lead nut and a computer storage medium. Background Technology

[0002] As a key functional component of precision transmission systems, the performance of ball screw assemblies directly affects the accuracy and stability of mechanical equipment. Research on ball screw assemblies in China started relatively late. Although some progress has been made in recent years, there are still shortcomings in the manufacturing processes for high-precision, high-stability products. Particularly in the machining of wide-lead nuts, controlling the profile error is a technical bottleneck. In traditional form grinding methods, the design accuracy of the grinding wheel profile directly determines the machining accuracy of the nut's internal raceways. Therefore, researching how to effectively reduce profile errors and improve machining accuracy is of great significance for enhancing the overall performance of ball screw assemblies.

[0003] Wide variable lead nuts are difficult to machine, especially under variable lead conditions, where the grinding wheel installation angle cannot always be consistent with the helix angle of the nut's internal thread, resulting in increased cross-sectional error.

[0004] Therefore, existing processing methods have significant shortcomings in controlling cross-sectional errors, and a new optimization method is urgently needed to improve processing accuracy. Summary of the Invention

[0005] In view of this, the present invention provides a method for optimizing the profile error of the internal thread of a nut with wide variable lead and a computer storage medium. By establishing an accurate theoretical model and a calculation model, the influence of key parameters on the profile error is systematically analyzed, and effective optimization measures are proposed.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A method for optimizing the profile error of the internal thread of a nut with wide variable lead includes the following steps:

[0008] Step 1: Model Establishment: Establish a theoretical model of the nut's internal thread, an axial profile model of the grinding wheel, and a grinding model of the nut's internal thread. Based on the theoretical model of the nut's internal thread, the axial profile model of the grinding wheel, and the grinding model of the nut's internal thread, construct a profile error calculation model.

[0009] Step 2, Error Analysis: Using the aforementioned cross-section error calculation model, analyze the influence of different parameters on the cross-section error;

[0010] Step 3, Optimization Implementation: Based on the influence of the different parameters on the cross section error, for the variable lead condition, the cross section error is reduced by combining the preset cross section error optimization method.

[0011] Furthermore, the theoretical model is established in the following way:

[0012] Establish the workpiece coordinate system, grinding wheel coordinate system, and normal coordinate system with the nut center, grinding wheel center, and ball center as the origins, respectively;

[0013] Based on the double-circular-arc characteristic of the nut's normal cross section, the theoretical equation for the right raceway is obtained as follows:

[0014]

[0015] Where p is the helical parameter. P h Let λ be the lead of the nut's internal thread, λ be the helix angle, r0 be the nominal radius, and e1 and e2 be the eccentricities of the normal section, with e1 = (rd... b / 2)cosα,e2=(rd b / 2)sinα, where α is the contact angle, d b Where is the diameter of the ball, and μ is the arc angle of the raceway.

[0016] Furthermore, the axial profile model of the grinding wheel is determined by the following formula:

[0017]

[0018] In the formula, X, Y, and Z represent the coordinates of the grinding wheel profile.

[0019] Furthermore, the grinding model is established through coordinate transformation, including:

[0020] By transforming the coordinate system of the grinding wheel to that of the nut workpiece, and combining the expression for the contact line between the grinding wheel's rotating surface and the nut's internal thread helical surface, the equation for the internal thread helical surface of the nut machined by the grinding wheel is derived. The expression is:

[0021]

[0022] Simultaneously, the coordinate transformation expression for converting the nut workpiece coordinate system to the internal thread normal coordinate system is:

[0023]

[0024] In the formula, R is the grinding wheel radius corresponding to Z in the grinding wheel profile, and Z = f(R) is the mathematical expression for the grinding wheel profile. λ is the angle between the XOY plane and ON, λ is the helix angle, A is the center distance of the grinding wheel installation, Σ is the grinding wheel installation angle, and r0 is the nominal radius;

[0025] By combining the two equations, the normal section expression of the helical surface of the nut's internal thread can be obtained.

[0026] Furthermore, the cross-section error calculation model is constructed through the following steps:

[0027] Point A(z) oi ,x oi Let i be a discrete point on the theoretical cross-section curve, where i = 1, 2, 3...n, and n is the number of discrete points.

[0028] Assume point A′(z) ri′ ,x ri′ Point A on the theoretical cross-section curve lies on the x-axis. n The intersection point of the direction and the inverse cross curve is then found. Let ΔL be the cross-sectional error corresponding to point A, and its length is represented by ΔL.

[0029] Point B(z) ri ,x ri ) and point C(z) ri+1 ,x ri+1 To find the two points on the cross curve adjacent to the intersection point A′, where i = 1, 2, 3...m, and m is the number of discrete points;

[0030] According to point B(z) ri ,x ri ) and point C(z) ri+1 ,x ri+1 The coordinates of the nut's internal thread are used to fit the inverse cross-section curve using a cubic spline curve fitting method, and the magnitude of the cross-section error ΔL is finally obtained.

[0031] ΔL=±|x ri′ -x oi |

[0032] In the formula, point A(z) oi ,x oi Let A'(z) be a discrete point on the theoretical cross-section curve, where i = 1, 2, 3...n, and n is the number of discrete points. ri′ ,x ri′ Point A on the theoretical cross-section curve lies on the x-axis. n The intersection point of the direction and the inverse cross curve is then found. Let be the cross section error corresponding to point A, and let its length be denoted by ΔL, where point B(z) ri ,x ri ) and point C(z) ri+1 ,x ri+1 To find the two points on the cross curve adjacent to the intersection point A′, where i = 1, 2, 3...m, and m is the number of discrete points.

[0033] Furthermore, in step 2, error analysis: using the cross-section error calculation model, the influence of non-lead, nominal diameter, and installation center distance on the cross-section error is analyzed.

[0034] Furthermore, the preset cross-sectional error optimization method includes: adjusting the grinding wheel cross-section and grinding process parameters, and optimizing the grinding wheel mounting angle to make the grinding wheel mounting angle consistent with the helix angle of the nut's internal thread, thereby reducing the cross-sectional error.

[0035] Furthermore, optimization is achieved by integrating a mechanism for Y-axis feed, A-axis deflection, and grinding head mounting. This mechanism includes:

[0036] A base is mounted on the X-axis slide plate, and a Y-axis lead screw guide is installed on the base. A direct-drive lead screw feed system is set on both sides of the base, forming the Y1 axis and Y2 axis, respectively, driving the Y1 axis slide plate and the Y2 axis slide plate to move. A turntable and a spindle slide are installed on both slide plates. A grinding head spindle box is installed on the spindle slide. When the positions of the two axes are controlled synchronously, the turntable, spindle slide, and spindle box are driven to move along the Y-axis. When the Y1 axis is fixed and the Y2 axis is fed, the Y2 axis slide plate will drive the turntable, spindle slide, and spindle box to rotate along the center line formed by the center plane of the electric spindle and the center plane of the Y1 axis lead screw to form the A-axis. At the same time, the rotation center coincides with the grinding wheel center, ensuring that the grinding point position is constant when the installation angle is adjusted.

[0037] A computer storage medium storing a computer program, which, when executed by a processor, implements the steps of a method for optimizing the profile error of the internal thread of a nut with wide variable lead.

[0038] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a method for optimizing the cross-sectional error of the internal thread of a nut with wide variable lead and a computer storage medium. By establishing an accurate theoretical model and a calculation model, the influence of key parameters on the cross-sectional error is systematically analyzed, and effective optimization measures are proposed. This avoids the obvious deficiencies of the processing method in controlling the cross-sectional error and improves the processing accuracy. Attached Figure Description

[0039] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0040] Figure 1 This is a diagram showing the relationship between several theoretical models involved in this invention.

[0041] Figure 2 This is a schematic diagram showing the coordinates of the nut raceway and the grinding wheel position in the theoretical model of the nut's internal thread in this invention;

[0042] Figure 3 This is a schematic diagram of the axial cross-section of the grinding wheel of the present invention;

[0043] Figure 4 This is a schematic diagram of the method for calculating the cross-section error of the present invention;

[0044] Figure 5 To verify the influence of nut lead on the nut internal thread profile error of this invention, a comparison of normal grinding profiles for different nut leads is shown.

[0045] Figure 6 A diagram showing the designed grinding head mounting device and Y-axis structure;

[0046] Figure 7 This is a comparison of the cross-section error results after optimization according to the method described in this invention;

[0047] Figure 8(a) shows the reduction ratio of the cross-sectional error of the variable lead nut in region a;

[0048] Figure 8(b) shows the reduction ratio of the overall variable lead nut cross-sectional error;

[0049] Figure 9 This is a schematic diagram of the method flow of the present invention. Detailed Implementation

[0050] 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.

[0051] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.

[0052] Example 1:

[0053] See Figure 9 This invention discloses a method for optimizing the profile error of the internal thread of a nut with wide variable lead, the core of which lies in the following steps:

[0054] Step 1: Model Establishment: Establish the theoretical model of the nut internal thread, the grinding wheel axial profile model, and the nut internal thread grinding model. Based on the above models, propose a profile error calculation model.

[0055] Step 2, Error Analysis: Analyze the influence of nut lead, nominal diameter, and installation center distance on the cross-sectional error;

[0056] Step 3: Optimization method proposal: For the variable lead condition, a cross section error optimization method is proposed and implemented to significantly reduce the cross section error;

[0057] Specifically, wide-lead variable-lead ball screw nut refers to a fixed-lead or variable-lead ball screw nut with a wide range of lead variation. Based on the lead and nominal diameter, it can be divided into micro-lead nuts, conventional-lead nuts, and large-lead nuts. Among these, the nominal diameter d0 ≤ 12mm, and the lead P... h Nuts with a lead of ≤3mm are called micro-lead nuts, with a nominal diameter of 16mm ≤ d0 ≤ 100mm and a lead of 4mm ≤ P. h Nuts with a lead of ≤20mm are called standard lead nuts, with a nominal diameter d0 ≥ 16mm and a lead d0 / 2 ≤ P. h Nuts with a lead ≤ d0 are called large lead nuts.

[0058] In a specific embodiment, the theoretical equation for the internal thread of the established theoretical model of the nut's internal thread is as follows:

[0059]

[0060] In one specific embodiment, the axial profile of the grinding wheel in the established grinding wheel axial profile model can be calculated using this formula:

[0061]

[0062] Where p is the helical parameter. P h Let λ be the lead of the nut's internal thread, λ be the helix angle, r0 be the nominal radius, and e1 and e2 be the eccentricities of the normal section, with e1 = (rd... b / 2)cosα,e2=(rd b / 2)sinα, where α is the contact angle, d b Where μ is the diameter of the ball, μ is the raceway arc angle, and θ is a parameter of the thread helix surface.

[0063] In a specific embodiment, the expression for the equation of the helical surface of the nut's internal thread, machined by a grinding wheel, in the established nut internal thread grinding model can be written as:

[0064]

[0065] Simultaneously, the coordinate transformation expression for converting the nut workpiece coordinate system to the internal thread normal coordinate system is:

[0066]

[0067] In the formula, R is the grinding wheel radius corresponding to Z in the grinding wheel profile, and Z = f(R) is the mathematical expression for the grinding wheel profile. λ is the angle between the XOY plane and ON, λ is the helix angle, A is the center distance of the grinding wheel installation, Σ is the grinding wheel installation angle, and r0 is the nominal radius.

[0068] By combining the two equations, the normal section expression of the helical surface of the nut's internal thread can be obtained.

[0069] In one specific embodiment, a method for calculating the cross-section error is given through a cross-section error calculation model. Point A(z) oi ,x oi Let A'(z) be a discrete point on the theoretical cross-section curve, where i = 1, 2, 3...n (n is the number of discrete points). ri′ ,x ri′ Point A on the theoretical cross-section curve lies on the x-axis. n The intersection point of the direction and the inverse cross curve is then found. Let be the cutoff error corresponding to point A, and let its length be denoted by ΔL. Where, point B(z... ri ,x ri ) and point C(z) ri+1 ,x ri+1 Let A be two points adjacent to the intersection point A′ on the inverse cross-section curve, where i = 1, 2, 3...m (m is the number of discrete points). Based on the coordinates of points B and C, a cubic spline curve fitting method can be used to fit the inverse cross-section curve, and finally the magnitude of the nut internal thread cross-section error ΔL can be obtained.

[0070] ΔL=±|x ri′ -x oi |

[0071] Specifically, the cross section error calculation model can systematically analyze the specific impact of different parameters on the cross section error.

[0072] In one specific embodiment, the optimization method of the present invention reduces the profile error by adjusting the grinding wheel mounting angle to match the helix angle of the nut's internal thread.

[0073] Specifically, this invention proposes a mechanism that integrates Y-axis feed, A-axis deflection, and grinding head mounting, enabling automatic adjustment of the grinding wheel mounting angle and further improving machining accuracy.

[0074] Specifically, the method is applicable to both constant lead and variable lead nuts of various leads.

[0075] Specifically, this invention proposes a mechanism integrating Y-axis feed, A-axis deflection, and grinding head mounting. The mechanism includes a base mounted on an X-axis slide plate, on which components such as the Y-axis lead screw and guide rail are mounted. A direct-drive lead screw feed system, designated as Y1 and Y2 axes, is set on both sides of the base, driving the Y1 and Y2 axis slide plates respectively. A turntable and a spindle slide are mounted on both slide plates, with the grinding head spindle box mounted on the spindle slide. When the positions of the two axes are synchronously controlled, the turntable, spindle slide, and spindle box move along the Y-axis. When the Y1 axis is fixed and the Y2 axis is feeding, the Y2 axis slide plate drives the turntable, spindle slide, and spindle box to rotate along the centerline formed by the center plane of the electric spindle and the center plane of the Y1 axis lead screw, forming the A-axis. Simultaneously, the rotation center coincides with the grinding wheel center.

[0076] On the other hand, a computer storage medium is proposed, on which a computer program is stored, which, when executed by a processor, implements the steps of a method for optimizing the profile error of the internal thread of a wide variable lead nut.

[0077] Example 2:

[0078] Please see Figure 1 This invention provides a method for optimizing the profile error of the internal thread of a nut with a wide variable lead, specifically including the following steps:

[0079] Step 1: Model Establishment: Establish the theoretical model of the nut internal thread, the grinding wheel axial profile model, and the nut internal thread grinding model. Based on the above models, propose a profile error calculation model.

[0080] Step 2, Error Analysis: Analyze the influence of nut lead, nominal diameter, and installation center distance on the cross-sectional error;

[0081] Step 3: Optimization method proposal: For the variable lead condition, a cross section error optimization method is proposed and implemented to reduce the cross section error by at least 37.2%.

[0082] Please see Figure 2 Based on the fact that the intersection of the raceway of the nut's internal thread and the normal plane at any point on the arc is an eccentric double circular arc, a workpiece coordinate system o-xyz is established with the nut's center as the origin, a grinding wheel coordinate system O-XYZ is established with the grinding wheel's center as the origin, and an internal thread normal coordinate system o is established with the ball's center as the origin. n -x n y n z n Since the normal section of the nut is a double circular arc and the left and right raceways are symmetrical, the following uses the right raceway as an example to solve the theoretical equation of the nut's internal thread. The specific equation is as follows:

[0083]

[0084] Where p is the helical parameter. P h Let λ be the lead of the nut's internal thread, λ be the helix angle, r0 be the nominal radius, and e1 and e2 be the eccentricities of the normal section, with e1 = (rd... b / 2)cosα,e2=(rd b / 2)sinα, where α is the contact angle, d b Where is the diameter of the ball, and μ is the arc angle of the raceway.

[0085] Please see Figure 3 Based on the principle of helical surface machining, when a grinding wheel is grinding the internal thread of a nut, at any instant of relative motion, there is always a tangent contact line between the grinding wheel and the raceway to be machined. The machining motion is equivalent to the rotational surface and the helical surface moving along themselves. Therefore, when the contact line rotates around the axis of the grinding wheel, the equation of the rotational surface of the grinding wheel is obtained, as shown in the following formula:

[0086] zn x +An y cotΣ+(A-x+pcotΣ)n z =0

[0087] Where, n x n y n z The three normal vectors of the internal thread equation of the screw can be used to calculate the axial profile of the grinding wheel in the axial profile model of the grinding wheel in this invention.

[0088]

[0089] X, Y, Z represent the coordinates of the grinding wheel profile, specifically XYZ coordinates in the grinding wheel coordinate system O.

[0090] Given the cross-section of the grinding wheel, the normal cross-section of the helical surface to be machined can be determined analytically. By transforming the coordinate system of the grinding wheel and the coordinate system of the nut workpiece, and combining the expression of the contact line between the grinding wheel's rotating surface and the helical surface of the nut's internal thread, the expression for the equation of the helical surface of the nut's internal thread machined by the grinding wheel can be derived:

[0091]

[0092] Simultaneously, the coordinate transformation expression for converting the nut workpiece coordinate system to the internal thread normal coordinate system is:

[0093]

[0094] By combining the two equations, the normal section expression of the helical surface of the nut's internal thread can be obtained.

[0095] Please see Figure 4In the cross-sectional error calculation model of this invention, the cross-sectional error of the nut's internal thread can be understood as composed of the cross-sectional errors of a series of discrete points between the theoretical cross-section and the ground cross-section of the nut's internal thread. Since the number and position of discrete points between the theoretical cross-section and the inverse cross-section cannot be completely one-to-one, a method for calculating the cross-sectional error is given. Point A(z) oi ,x oi Let A'(z) be a discrete point on the theoretical cross-section curve, where i = 1, 2, 3...n (n is the number of discrete points). ri′ ,x ri′ Point A on the theoretical cross-section curve lies on the x-axis. n The intersection point of the direction and the inverse cross curve is then found. Let be the cutoff error corresponding to point A, and let its length be denoted by ΔL. Where, point B(z... ri ,x ri ) and point C(z) ri+1 ,x ri+1 Let A be two points adjacent to the intersection point A′ on the inverse cross-section curve, where i = 1, 2, 3...m (m is the number of discrete points). Based on the coordinates of points B and C, a cubic spline curve fitting method can be used to fit the inverse cross-section curve, and finally the magnitude of the nut internal thread cross-section error ΔL can be obtained.

[0096] ΔL=±|x ri′ -x oi |

[0097] In the formula, point A(z) oi ,x oi Let A'(z) be a discrete point on the theoretical cross-section curve, where i = 1, 2, 3...n, and n is the number of discrete points. ri′ ,x ri′ Point A on the theoretical cross-section curve lies on the x-axis. n The intersection point of the direction and the inverse cross curve is then found. Let be the cross section error corresponding to point A, and let its length be denoted by ΔL, where point B(z) ri ,x ri ) and point C(z) ri+1 ,x ri+1 Let A' be two points adjacent to the intersection point A' on the inverse cut curve, where i = 1, 2, 3...m, and m is the number of discrete points. Since the coordinates of point A' may not exist on the inverse cut curve, it is necessary to solve for them based on the coordinates of points B and C to obtain the specific coordinates of point A'.

[0098] For details, see Figure 4Based on the coordinates of points B and C, the inverse cutoff curve can be fitted using a cubic spline curve fitting method. The equation of the fitted inverse cutoff curve can be expressed as:

[0099] z = a(xx) ri ) 3 +b(xx ri ) 2 +c(xx ri )+d (1)

[0100] In the formula, a, b, c, and d are the coefficients of the cubic spline fitting curve, and their specific values ​​are related to the coordinate values ​​of points B and C.

[0101] Let the z-coordinate of point A′ be... oi′ The z-coordinate of point A on the theoretical cross section curve is equal to the z-coordinate of point A. oi , i.e. z oi′ =z oi Substituting the coordinates into equation (1), we can obtain the specific coordinates of point A′.

[0102] Given point A(z) oi ,x oi ) and point A′(z ri′ ,x ri′ After determining the coordinates of the nut, the magnitude of the internal thread profile error ΔL can be obtained, i.e.:

[0103]

[0104] Because z oi′ =z oi Therefore, equation (2) can be simplified to:

[0105] ΔL=±|x ri′ -x oi | (3)

[0106] In this context, "+" indicates that the inverse cross section curve is above the theoretical cross section curve, meaning that the inverse cross section curve is larger than the theoretical cross section curve, while "-" indicates that the inverse cross section curve is below the theoretical cross section curve, meaning that the inverse cross section curve is smaller than the theoretical cross section curve.

[0107] The cross-sectional error calculation model provided by equation (3) can be used to determine the cross-sectional error of the nut's internal thread normal cross-section at different discrete points. By analyzing and calculating the determined cross-sectional error, the maximum cross-sectional error ΔL can be obtained. max Minimum error ΔL min Average error These three indicators are used to evaluate the cross-sectional error of the normal section of the nut's internal thread.

[0108] Please see Figure 5This invention has verified the effects of nut lead, nominal nut diameter, and installation center distance on the nut internal thread profile error. Only a comparison of the normal grinding profiles for different nut leads is shown here. The final conclusions are as follows: as the nut lead increases, the profile error increases; as the nominal nut diameter increases, the profile error increases; and as the installation center distance increases, the profile error decreases.

[0109] Please see Figure 6 To achieve the optimized method of this invention, a mechanism integrating Y-axis feed, A-axis deflection, and grinding head mounting is designed. The mechanism includes a base mounted on an X-axis slide, on which components such as the Y-axis lead screw and guide rail are installed. A direct-drive lead screw feed system, designated as Y1 and Y2 axes, is set on both sides of the base, driving the Y1 and Y2 axis slides respectively. A turntable and a spindle slide are mounted on both slides, with the grinding head spindle box mounted on the spindle slide. When the positions of the two axes are synchronously controlled, the turntable, spindle slide, and spindle box move along the Y-axis. When the Y1 axis is fixed and the Y2 axis is feeding, the Y2 axis slide drives the turntable, spindle slide, and spindle box to rotate along the centerline formed by the center plane of the electric spindle and the center plane of the Y1 axis lead screw, forming the A-axis. Simultaneously, the rotation center coincides with the grinding wheel center. This device allows for the automatic measurement and offset of the large lead grinding rod mounting position in an internal thread grinding machine, enabling the grinding wheel to automatically offset by a certain angle to meet the nut lead angle requirements.

[0110] Specifically, as shown in Table 1, the X-axis of the machine tool is responsible for the feed motion of the grinding head, with a total stroke of 300mm. The roller linear guide pair serves as the guiding element, and the Rexroth MLP140 linear motor assembly is used as the driving element. The Heidenhain LS-195S linear grating ruler is used as the feedback element, thus forming a fully closed-loop position control system. The X-axis guide rail adopts the MR55 specification, and three V3-level heavy preload sliders are arranged on each side according to the size of the slide plate to obtain the maximum rigidity and damping, which can suppress grinding vibration to the greatest extent. The guide rail pair adopts centralized lubrication. In order to minimize the impact of oil mist generated during grinding on the components, the X-axis slide adopts a fully enclosed structural design. The motor, grating ruler and other components are separated from the processing area by the outer protective cover and the end bellows armor protective covers, further improving the reliability of the machine tool. At the same time, other electrical pipelines installed on the upper part of the X-axis slide plate pass through the slide plate and are led out by a fully enclosed cable chain to avoid the corrosion and aging of the cables.

[0111] The grinding head mounting device is installed on the X-axis slide plate and is used to perform functions such as grinding head clamping, grinding angle adjustment, and Z-axis grinding position adjustment. It mainly includes components such as the spindle box, turntable, slide plate, and base. The spindle box is used to install the grinding electric spindle and adopts a clamping outer diameter structure to ensure the installation accuracy of the electric spindle. The spindle box is mounted on the turntable via a dovetail groove and can be manually adjusted and locked along the Z-axis of the machine tool to match the requirements of grinding rods of different lengths. The turntable is mounted on the slide plate and is driven by an indexing screw, allowing it to rotate a certain angle around the center of the annular groove. The rotation center is also the center of the dressing roller, ensuring that the axial direction of the electric spindle is consistent with the lead angle of the nut being machined. The turntable is mounted on the slide plate, which is connected to the slide plate via a precision dovetail structure. Manual adjustment of the slide plate in the Y-axis of the machine tool is achieved through a lifting screw, mainly used for the application of eccentric grinding rods when machining nuts with large lead angles.

[0112] Table 1. Parameters of Grinding Head Mounting Device

[0113]

[0114]

[0115] Please see Figure 7 After optimization using the method of this invention, the cross-sectional error generated by the optimized grinding method for the variable lead nut in region b is larger than that generated by interference grinding, but both are within the range of 0.0016 mm. In region a, the cross-sectional error generated by the optimized grinding method shows a significant decreasing trend compared to the cross-sectional error generated by interference grinding, with the overall level within 0.0016 mm, and maintaining a uniform level with the cross-sectional error in region b. Overall, the cross-sectional error generated by interference grinding is more uniform.

[0116] Specifically, based on the principle of helical surface machining, this invention establishes a theoretical model of the nut's internal thread, a grinding wheel axial profile model, and a nut internal thread grinding model. Building upon this, it innovatively proposes a calculation model for reducing profile error, see [link to relevant documentation]. Figures 8(a)-8(b) To reduce the cross-sectional error of variable lead nuts, the influence of three key parameters—nut lead, nominal diameter, and installation center distance—on the cross-sectional error was systematically analyzed. Secondly, addressing the cross-sectional error problem under variable lead conditions, the installation structure of the grinding wheel and grinding head on the internal thread grinding machine was optimized, and the installation angle was adjusted to match the helix angle of the nut's internal thread, resulting in a 37.2% reduction in cross-sectional error. This invention not only significantly improves the transmission accuracy of ball screw pairs but also provides an effective solution for high-precision thread grinding through innovative improvements to the grinding machine structure, possessing significant engineering application value.

[0117] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0118] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for optimizing the profile error of the internal thread of a nut with wide variable lead, characterized in that, Includes the following steps: Step 1: Model Establishment: Establish a theoretical model of the nut's internal thread, an axial profile model of the grinding wheel, and a grinding model of the nut's internal thread. Based on the theoretical model of the nut's internal thread, the axial profile model of the grinding wheel, and the grinding model of the nut's internal thread, construct a profile error calculation model. Step 2, Error Analysis: Using the aforementioned cross-section error calculation model, analyze the influence of different parameters on the cross-section error; Step 3, Optimization Implementation: Based on the influence of the different parameters on the cross section error, for the variable lead condition, the cross section error is reduced by combining the preset cross section error optimization method; The grinding model is established through coordinate transformation, including: By transforming the coordinate system of the grinding wheel to that of the nut workpiece, and combining the expression for the contact line between the grinding wheel's rotating surface and the nut's internal thread helical surface, the equation for the internal thread helical surface of the nut machined by the grinding wheel is derived. The expression is: Simultaneously, the coordinate transformation expression for converting the nut workpiece coordinate system to the internal thread normal coordinate system is: In the formula, For the cross-section of the grinding wheel and The corresponding grinding wheel radius, The mathematical expression for the profile of the grinding wheel. for plane and The included angle, The helix angle, The center distance for grinding wheel installation. Install the angle for the grinding wheel. The nominal radius; By combining the two equations, the normal section shape of the helical surface of the nut's internal thread can be obtained; The cross-section error calculation model is constructed through the following steps: Point Let be a discrete point on the theoretical cross section curve, where where n is the number of discrete points; Assumption point Point A on the theoretical cross-section curve lies on the coordinate axis. The intersection point of the direction and the inverse cross curve is then found. The cross section error at point A is represented by the length denoted by . express; Point and points To find the intersection point on the cross curve Two adjacent points, where, m is the number of discrete points; According to the point and points The coordinates are used to fit the inverse section curve using a cubic spline curve fitting method, and finally the section error of the nut's internal thread is obtained. Size: In the formula, point Let be a discrete point on the theoretical cross section curve, where n is the number of discrete points, assuming points Point A on the theoretical cross-section curve lies on the coordinate axis. The intersection point of the direction and the inverse cross curve is then found. The cross section error at point A is represented by the length denoted by . This indicates that, among them, points and points To find the intersection point on the cross curve Two adjacent points, where, , m The number of discrete points.

2. The method for optimizing the profile error of the internal thread of a nut with wide variable lead according to claim 1, characterized in that, The theoretical model is established in the following way: Establish the workpiece coordinate system, grinding wheel coordinate system, and normal coordinate system with the nut center, grinding wheel center, and ball center as the origins, respectively; Based on the double-circular-arc characteristics of the nut's normal cross section, the theoretical equation for the right raceway is obtained as follows: in, For the helical parameters, , For the lead of the nut's internal thread, The helix angle, Nominal radius, eccentricity , The eccentricity of the normal section and , , Contact angle, The diameter of the ball is [missing information]. The arc angle of the raceway.

3. The method for optimizing the profile error of the internal thread of a nut with wide variable lead according to claim 1, characterized in that, The axial cross-sectional model of the grinding wheel is determined by the following formula: In the formula, X, Y, and Z represent the coordinates of the grinding wheel profile.

4. The method for optimizing the profile error of the internal thread of a nut with wide variable lead according to claim 1, characterized in that, Step 2, Error Analysis: Using the cross-section error calculation model, analyze the influence of non-lead, nominal diameter and installation center distance on the cross-section error.

5. The method for optimizing the profile error of the internal thread of a nut with wide variable lead according to claim 1, characterized in that, The preset method for optimizing the profile error includes: adjusting the profile of the grinding wheel and the grinding process parameters, and optimizing the grinding wheel mounting angle to make the grinding wheel mounting angle consistent with the helix angle of the nut's internal thread, thereby reducing the profile error.

6. The method for optimizing the profile error of the internal thread of a nut with wide variable lead according to claim 5, characterized in that, Optimization is achieved through a mechanism that integrates Y-axis feed, A-axis deflection, and grinding head mounting. This mechanism includes: A base is mounted on the X-axis slide plate, and a Y-axis lead screw guide is installed on the base. A direct-drive lead screw feed system is set on both sides of the base, forming the Y1 axis and Y2 axis, respectively, driving the Y1 axis slide plate and the Y2 axis slide plate to move. A turntable and a spindle slide are installed on both slide plates. A grinding head spindle box is installed on the spindle slide. When the positions of the two axes are controlled synchronously, the turntable, spindle slide, and spindle box are driven to move along the Y-axis. When the Y1 axis is fixed and the Y2 axis is fed, the Y2 axis slide plate will drive the turntable, spindle slide, and spindle box to rotate along the center line formed by the center plane of the electric spindle and the center plane of the Y1 axis lead screw to form the A-axis. At the same time, the rotation center coincides with the grinding wheel center, ensuring that the grinding point position is constant when the installation angle is adjusted.

7. A computer storage medium, characterized in that, The computer storage medium stores a computer program, which, when executed by a processor, implements the steps of a method for optimizing the profile error of the internal thread of a wide-lead nut as described in any one of claims 1 to 6.

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