Method and system for finishing gear grinding worm grinding wheel through flexible point of universal diamond roller

Abstract

The invention relates to the technical field of gear grinding machining, and provides a universal method and system for finishing a gear grinding worm grinding wheel through flexible points of a diamond roller. The method comprises the following steps: on the basis of a parameterized mathematical model of a gear tooth surface and a space meshing relationship between a worm grinding wheel and a gear, calculating to obtain a contact point set under a grinding wheel coordinate system; and performing rotary projection processing on the contact points to obtain an axial section profile point set of the worm grinding wheel, and fitting to obtain an axial section profile rz. And an equal residual height method is adopted, so that the diamond roller conducts finishing work on the ith finishing point Pi on the worm grinding wheel based on the rz, and a finishing point sequence P is obtained. And calculating a center coordinate sequence C of the diamond roller according to the P. And the C is converted into a multi-axis movement track instruction of the machine tool to obtain a point finishing track of the diamond roller. According to the method, the worm grinding wheel is trimmed in a point trimming mode, the customization period is shortened, the production cost is reduced, and high-precision trimming of the worm grinding wheels for tooth grinding of different tooth shapes can be achieved.

Description

Technical Field

[0001] This invention relates to the field of gear grinding technology, and in particular to a method and system for dressing worm gear grinding wheels with flexible point dressing using a universal diamond roller. Background Technology

[0002] Gears, as crucial basic transmission components in mechanical equipment, directly impact the performance and reliability of machinery. Worm wheel grinding, a vital process for high-precision gear machining, is widely used in gear manufacturing in the automotive, aerospace, and robotics industries. With the ever-increasing demands on gear transmission performance from industrial development, tooth surface dressing technology has become a key means to improve gear meshing characteristics and reduce vibration and noise. Traditional worm wheel dressing methods often employ shaping dressing or fixed-path dressing, requiring dressing tools (such as diamond rollers) that are typically custom-made according to the target tooth profile. This results in long customization cycles, high costs, and poor adaptability. Especially when performing complex dressings such as tooth profile bulging or tooth direction bulging, existing dressing methods struggle to flexibly and accurately generate the axial profile of the grinding wheel corresponding to the dressed tooth surface, limiting dressing accuracy and processing efficiency. Furthermore, existing dressing processes largely rely on dedicated dressing wheels or complex CNC programs, lacking a universal dressing trajectory planning method that can adapt to different tooth surface dressing requirements. Especially on multi-axis CNC worm gear grinding machines, how to achieve high-precision and high-efficiency point dressing through reasonable trajectory planning remains a technical problem that urgently needs to be solved. Summary of the Invention

[0003] To address the technical problem that existing worm gear dressing methods require customized dressing tools based on the target tooth profile, resulting in poor adaptability, this invention proposes a method and system for dressing grinding worm gears using a universal diamond roller with flexible point dressing.

[0004] In a first aspect, the present invention proposes a method for universal diamond roller flexible point dressing of grinding worm gear grinding wheels, comprising: Based on the gear tooth surface parametric equations and the meshing relationship between the worm grinding wheel and the gear, the coordinates of several contact points between the worm grinding wheel and the gear in the gear coordinate system are calculated. Based on the meshing space coordinate system between the worm grinding wheel and the gear, the coordinates of the contact points are transformed to the grinding wheel coordinate system, and the coordinates of the contact points in the grinding wheel coordinate system are calculated. The worm grinding wheel development angle is calculated based on the parameters of the worm grinding wheel. x The range of values ​​is determined, and contact points are selected within this range. These selected contact points are then subjected to rotational projection to obtain the axial section profile points of the worm wheel. The axial section profile is then obtained after fitting. r z After the blade was applied, the diamond roller was based on... r z Perform the first step on the worm gear grinding wheel i A repair pointP i The repair work was then carried out, followed by the preset residual height. h calculate P i and the next rest point P i+1 line spacing between L i ;pass L i calculate P i+1 The position, until all have been traversed. r z The trim point sequence was then obtained. P .according to P And the roller radius of the diamond roller R Calculate the center coordinate sequence of the diamond roller. C ;Will C The data is converted into multi-axis motion trajectory commands for the machine tool, ultimately resulting in the point trimming trajectory of the diamond roller.

[0005] Secondly, this invention also proposes a system for dressing grinding worm gears using a universal diamond roller with flexible point dressing, which utilizes the method for dressing grinding worm gears using a universal diamond roller with flexible point dressing described in the first aspect. This universal diamond roller with flexible point dressing system includes: a coordinate generation module, a profile fitting module, and a trajectory generation module.

[0006] The coordinate generation module is used to calculate the coordinates of several contact points between the worm wheel and the gear in the gear coordinate system based on the gear tooth surface parameter equation and the meshing relationship between the worm wheel and the gear. Based on the meshing space coordinate system between the worm wheel and the gear, it transforms the coordinate system of the contact points to the grinding wheel coordinate system and calculates the coordinates of the contact points in the grinding wheel coordinate system. The profile fitting module is used to calculate the worm wheel generating angle based on the parameters of the worm wheel. x The range of values ​​is determined, and contact points are selected within this range. These selected contact points are then subjected to rotational projection to obtain the axial section profile points of the worm wheel. The axial section profile is then obtained after fitting. r z The trajectory generation module is used after tool setting, based on the diamond roller... r z Perform the first step on the worm gear grinding wheel i A repair point P i The repair work was then carried out, followed by the preset residual height. h calculate P i and the next rest point P i+1 line spacing between L i ;pass Li calculate P i+1 The position, until all have been traversed. r z The trim point sequence was then obtained. P ;according to P And the roller radius of the diamond roller R Calculate the center coordinate sequence of the diamond roller. C ;Will C The data is converted into multi-axis motion trajectory commands for the machine tool, ultimately resulting in the point trimming trajectory of the diamond roller.

[0007] Thirdly, the present invention also provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it implements the steps of the method for general diamond roller flexible point dressing grinding worm wheel as described in the first aspect.

[0008] The beneficial effects of this invention are as follows: This invention uses a point dressing method to dress worm grinding wheels, which can achieve dressing of any grinding wheel profile without the need to customize diamond rollers according to the target tooth profile. This not only reduces the customization cycle and production costs, but also improves the flexibility and dressing accuracy of the grinding wheel dressing process. Attached Figure Description

[0009] 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 some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0010] Figure 1 This is a schematic diagram of the structure of a CNC worm gear grinding machine. Figure 2 Flowchart of a method for dressing a worm gear grinding wheel with flexible points of a general-purpose diamond roller; Figure 3 This is a schematic diagram of a standard involute spiral surface; Figure 4 A schematic diagram showing the spatial meshing coordinate system of the worm gear grinding wheel and the gear. Figure 5 This is a schematic diagram of the parametric surface of a worm gear grinding wheel; Figure 6 This is a schematic diagram of the contact trace on one of the tooth surfaces of a worm gear grinding wheel; Figure 7 This is a diagram of the worm gear tooth profile when the drum-shaped modification amount is 0. Figure 8This is a diagram showing the tooth profile of a worm gear grinding wheel when the drum-shaped trimming amount is 0.1 mm. Figure 9 The diagram shows the tooth profile of the worm gear grinding wheel when the drum-shaped modification amount is 0.35mm. Figure 10 This is a schematic diagram of the dressing coordinate system and point dressing process of the diamond roller; Figure 11 This is a schematic diagram of the dressing point planning for the tooth surface of a worm gear grinding wheel based on the equal residual height method. Detailed Implementation

[0011] The technical solutions in the embodiments of the present invention will be clearly and completely described below. 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.

[0012] It should be noted that when a component is said to be "installed on" another component, it can be directly on the other component or it may be in a component that is centered on it. When a component is said to be "set on" another component, it can be directly set on the other component or it may also be in a component that is centered on it. When a component is said to be "fixed to" another component, it can be directly fixed to the other component or it may also be in a component that is centered on it.

[0013] 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 specification of this invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "or / and" as used herein includes any and all combinations of one or more of the associated listed items.

[0014] In worm gear grinding, diamond rollers are generally used to dress the worm gear. The worm gear is used to dress gears. This invention provides a method for flexible point dressing of grinding worm gears using diamond rollers. Based on the axial profile of the worm gear, the method calculates the trajectory of the diamond roller point dressing. First, a mathematical model of the gear tooth surface is established based on the gear's tooth direction and tooth profile dressing curve. Then, according to the basic principles of coordinate transformation and the meshing equations at the contact points in the basic principle of spatial meshing, the positions of several sets of tooth surface contact points between the worm gear surface and the gear tooth surface, i.e., the contact traces, can be solved. Next, in the worm gear coordinate system, the contact points are rotated and projected onto the axial section plane of the worm gear around its axis, thus obtaining the axial section profile of the worm gear. Finally, based on the equal residual height method, a series of dressing point sequences on the worm gear tooth surface are solved. At this point, the arc center position of the diamond roller can be calculated from the dressing points. Furthermore, based on the movement process of the worm gear dressing machine and the established dressing coordinate system, the center trajectory of the diamond roller in the diamond roller coordinate system, i.e., the point dressing trajectory of the diamond roller, is solved. Each step in the process is described in detail below through examples.

[0015] In this embodiment, the method of using a general-purpose diamond roller for flexible point dressing of worm gear grinding wheels is applicable to CNC worm gear grinding machine tools. For example... Figure 1 As shown, this CNC worm gear grinding machine includes 11 CNC axes: linear axes include: grinding wheel radial feed axis X1, grinding wheel tangential feed axis Y1, tool post axial feed axis Z1, nozzle moving axis U1, and outer support moving axis Z2. Rotary axes include: grinding wheel spindle B1, workpiece spindle C1, dressing wheel rotary spindle B2, dressing wheel oscillating axis C2, tool post oscillating axis A1, and automatic loading / unloading workpiece exchange axis C3. The grinding wheel spindle B1 mounts the worm gear grinding tool. The workpiece C1 mounts the gear. The dressing wheel rotary spindle B2 mounts a diamond roller. The multi-axis coupling linkage of CNC motion axes can achieve 11 axes and 5 linkages on this worm gear grinding machine. The point dressing process of the worm gear grinding wheel can be realized by controlling the coordinated movement of the grinding wheel spindle B1, the dressing wheel rotation spindle B2, the grinding wheel radial feed axis X1, the grinding wheel tangential feed axis Y1, and the tool post axial feed axis Z1.

[0016] Please refer to Figure 2 The method for dressing a worm gear grinding wheel with a general-purpose diamond roller flexible point includes the following steps: (1) Establish a mathematical model of the tooth surface of the topological modified gear.

[0017] First, construct the parametric equations of the planar involute of the gear to be machined, such as... Figure 3 As shown, let the radius of its base circle be... r b Involute on the right side of the tooth groove if The starting point is e . oh and x The included angle of the shaft is half the base circle tooth groove angle. s 0. if any point on M The point of tangency between the normal and the base circle is a .Pick For variable parameters, m This represents the development angle of the involute curve of a gear. Based on the properties of the involute curve, Yes = r b m , can be obtained if The expression is: .

[0018] x 0 represents the gear coordinate system if The x-coordinate of any point above, y 0 represents the gear coordinate system if The ordinate of any point above. Then... if Around Figure 3 In z The standard tooth surface equation of a gear is obtained by the helical motion of the shaft. r g,stan ( m , i ): .

[0019] In the formula, i This represents the helix angle of the involute curve of a gear as it rotates about the gear's axis. x Represents the gear coordinate system x Axis coordinates y Represents the gear coordinate system y Axis coordinates β b Let be the base circle helix angle of the gear. Then in... r g,stan ( m , i Overlay tooth profile shaping curves H ( m After that, the equation for the modified tooth profile of the gear is obtained. r g ( m , i Since the tooth profile of the gear is determined solely by the worm gear profile, the trimming trajectory of this invention is only related to the worm gear profile; therefore, tooth profile trimming is introduced. Because tooth profile bulging trimming is a common trimming method, tooth profile bulging trimming is used as an example. Let the initial tooth profile trimming curve be... H ( l )for: H ( l )= λl 2 + h max .

[0020] In the formula, l Indicates curve coefficients, l Involute if arc length, h max This indicates the maximum amount of reshaping. if The polar equation is: .

[0021] In the formula, α express if upward angle m The pressure angle at the location. Furthermore, the integral formula for calculating the arc length of a plane curve is: .

[0022] In the formula, i 0 represents if The angle of expansion at the starting point. if Substituting the polar coordinate equation into the integral formula for calculating the arc length of a plane curve, we can obtain the result. if arc length l : .

[0023] In the formula, α 0 represents if The initial pressure angle. (Based on the teeth) if The midpoint is the reference point for reshaping. α m Let be the pressure angle at the midpoint of the involute. Therefore, the modification amount at any point on the gear tooth profile can be expressed as: .

[0024] Based on the properties of involutes: m = tana , can be obtained from m The tooth profile modification curve is represented. H ( m ): .

[0025] Will H ( m The equation of the gear tooth profile modification surface can be obtained by decomposing along the normal vector direction. r g ( m , i ): .

[0026] (2) Based on the two-parameter envelope method, establish the mathematical model of the worm grinding wheel and solve the coordinates of the contact point in the grinding wheel coordinate system.

[0027] In this step, since the meshing of the worm wheel and gear follows the basic principle of spatial meshing of a helical surface, the data calculation between the gear and the worm wheel is performed through coordinate transformation between different spatial coordinate systems. Furthermore, the meshing relationship between the worm wheel and gear involves not only rotation but also a composite motion along the workpiece and grinding wheel axes. Therefore, it is essential to first establish a fitting spatial coordinate system for the meshing of the worm wheel and the workpiece gear. For example... Figure 4 As shown, since the worm wheel grinds a gear, the two tooth surfaces are in point contact. The positions of the contact points satisfy the spatial meshing equation. By solving the meshing equation using the least squares method, we can obtain several sets of tooth surface contact points, and thus a series of contact traces between the worm wheel and the gear tooth surfaces. Specifically, the meshing equation for the contact points between the gear and the worm wheel is: .

[0028] In the formula, n The normal vector of the tooth surface at the contact point. v 12 The relative velocity between the gear and the worm gear grinding wheel surfaces at the contact point. r 1 represents the position vector from the contact point to the rotating axis of the worm grinding wheel. r 2 represents the position vector from the contact point to the gear's rotation axis. w 1 represents the angular velocity of the worm grinding wheel. w 2 represents the angular velocity of the gear. v 01 The speed at which the worm wheel moves along its axis. v 02 Let be the speed at which the gear moves along its axis. From the relationship of continuous displacement generation in gear grinding, the given independent motion parameters are: w 1. v 01 , v 02 .but w 2 can be expressed as: .

[0029] In the formula, i 'for v 01 and w A transmission ratio of 2 indicates the additional rotation angle of the gear when the worm gear wheel moves one unit length axially. This occurs when the grinding wheel shaft moves axially by one lead of 2. πp At time 1, the additional rotation angle of the gear is 2.πz 1 / z 2, therefore the transmission ratio is i '=- i 21 / p 1. i 21 for w 1 and w The transmission ratio is 2. i ''for v 02 and w A transmission ratio of 2 indicates the additional rotation angle of the gear itself per unit axial movement. When the worm wheel moves 2 units along the gear's axis... πp 2, meaning with one lead, the additional rotation angle of the gear is 2. π Therefore, the transmission ratio is i ''=2 π / 2 πp 2 = 1 / p 2. p 1 represents the helical parameters of the worm gear grinding wheel. p 2 represents the helical parameter of the gear.

[0030] Based on the above independent motion parameters and meshing relationships, the meshing equation is established as follows: .

[0031] In the formula, This represents the rotation angle of a gear, and can be expressed as: In the form of. U 1. U 2. V 1. V 2. W 1. W 2 are functions relating to the tooth surface equation and coordinate transformation parameters, respectively. For specific calculation methods of these functions, please refer to "Principles of Gear Meshing" by Wu Xutang. ∈(- π , π Substituting this into the meshing equation, we get m , i Then will m , i Substitution r g ( m , i The coordinates of the contact point are obtained from the input. The process is then iterated through. This yields the coordinates of multiple contact points. These contact points form the contact trace between the gear and the worm wheel. The obtained contact point coordinates are currently in the gear coordinate system and need to be converted to the grinding wheel coordinate system. (Refer to...) Figure 4First, determine the gear coordinate system. S g To the grinding wheel coordinate system S w Coordinate transformation matrix between M wg : .

[0032] In the formula, i w The rotation angle of the worm gear grinding wheel. i g For the rotation angle of the gear, A The center distance between the gear and the worm wheel. l w This represents the axial movement distance of the worm gear grinding wheel. l g This represents the axial movement distance of the gear. According to... M wg Transform the contact point coordinates in the gear coordinate system to the contact point coordinates in the grinding wheel coordinate system.

[0033] (3) Calculate the axial section profile of the worm grinding wheel. r z .

[0034] When the gear is a helical gear, the tooth profile of the helical gear is directly obtained from the profile of the worm grinding wheel when dressing it with a worm grinding wheel, and the tooth profile dressing curve is determined by the tooth profile shape of the worm grinding wheel. When dressing a worm grinding wheel with a diamond roller, the axes of the diamond roller and the worm grinding wheel are in the same horizontal plane. Therefore, it can be understood that the dressing trajectory of the diamond roller dressing the worm grinding wheel in this horizontal section is the tooth profile of the worm grinding wheel across the axial section. Furthermore, since the diamond roller used for point dressing of the worm grinding wheel is a general-purpose diamond roller with an outer arc, it maintains point contact throughout the dressing process, hence the name "point dressing." Because the dressing trajectory of the diamond roller is the horizontal axial section of the worm grinding wheel, when dressing a worm grinding wheel with a general-purpose diamond roller, it is necessary to calculate the axial section tooth profile shape of the worm grinding wheel. (The axial section profile of the worm grinding wheel is then described.) r z The solution process is as follows: To screen redundant contact points in the grinding wheel coordinate system: First, based on the involute curve of the end section of the worm grinding wheel and the base circle radius of the worm grinding wheel... r w The relationship determines the generating angle of the worm grinding wheel. x The range of values ​​for: .

[0035] In the formula, r wa The radius of the tooth tip circle of the worm gear grinding wheel is... Figure 5 The radius of the base circle at point A. r wf The radius of the root circle of the worm gear grinding wheel is... Figure 5 The radius of the base circle at point B. x max for x The upper limit, x min for x The lower limit. Then filter out. x lie in[ x min , x max The contact points within the interval are used as the contact points that constitute the axial section profile, and these contact points are divided into contact point clouds of the left tooth surface of the worm grinding wheel according to their different locations. r wl Contact point cloud of the right tooth surface r wr .Will r wl , r wr The axial section profile points of the worm grinding wheel are obtained by rotating and projecting them onto the axial section plane of the worm grinding wheel. r d : .

[0036] .

[0037] .

[0038] In the formula, Mzi For the projection matrix, x i for r wl , r wr Upper i The contact points in the grinding wheel coordinate system x Axis coordinates y i for r wl , r wr Upper i The contact points in the grinding wheel coordinate system y Axis coordinates z i for r wl , r wr Upper i The contact points in the grinding wheel coordinate system z Axis coordinates for r wl , r wr The rotation angle of the contact point projected onto the axial section of the worm wheel. p w These are the helical parameters of the worm gear grinding wheel. For example... Figure 6 As shown, the final calculations for the left and right tooth surfaces of the worm grinding wheel are... r d The axial section profile is obtained by performing a quadratic fitting. r z It should be noted that the worm grinding wheel shaft section profile corresponding to different tooth profile camber modification amounts should be calculated and compared separately, such as... Figure 7 (Drum-shaped shaping amount is 0) Figure 8 (The drum-shaped trimming amount is 0.1mm) Figure 9 As shown in the figure (with a drum-shaped modification amount of 0.35mm), it can be seen from the figure that the worm grinding wheel tooth profile corresponding to the standard involute tooth profile of the gear is approximately a straight line. When the drum-shaped modification amount of the gear is 0.1mm and 0.35mm, the corresponding worm grinding wheel shaft section profile produces a significant change in curvature, and the size of the curvature is directly proportional to the modification amount.

[0039] (4) Calculate the point trimming trajectory of the diamond roller.

[0040] The dressing process of a CNC worm gear grinding machine is mainly achieved through the coordinated movements of the grinding wheel spindle B1, the dressing wheel rotation spindle B2, the grinding wheel radial feed axis X1, the grinding wheel tangential feed axis Y1, and the tool post axial feed axis Z1. Therefore, based on the motion relationship of the diamond roller dressing worm gear grinding wheel, a spatial coordinate system for diamond roller dressing worm gear grinding wheel is established. Figure 10 As shown, the axial section profile obtained by the above steps r z The worm grinding wheel is dressed using a universal diamond roller with an outer arc. During the dressing process, the diamond roller maintains a set rotation speed around B2, while the worm grinding wheel maintains a set rotation speed around B1 and performs feed motions along the X1 and Y1 directions. The specific point dressing process is as follows: First, the dressing point on the left / right tooth surface of a single end of the worm grinding wheel is located through tool setting. Then, the worm grinding wheel is reciprocated along the Y1 direction. Each reciprocating motion completes the dressing work at that point. Then, one feed along the X1 and Y1 directions moves the worm grinding wheel to the next dressing point. Again, the reciprocating feed along the Y1 direction gradually dresses the tooth profile of the left / right tooth surface of a single end of the worm grinding wheel. This process is repeated for each end of the grinding wheel, thus dressing the left and right tooth surfaces sequentially. During this process, the diamond roller is based on... rz Perform the first step on the worm gear grinding wheel i A repair point P i The repair work was then carried out, followed by the preset residual height. h calculate P i and the next rest point P i+1 line spacing between L i .pass L i calculate P i+1 The position, until all have been traversed. r z The trim point sequence was then obtained. P This repair point P i The solution can be obtained based on the method of equal residual height. For example... Figure 11 As shown, the equal residual height method includes: Determine the residual height after trimming h and the radius of the diamond roller R .Should h This represents the maximum un-trimmed height between two adjacent dressing points, and its upper limit threshold can be set according to the grinding accuracy requirements of the gear to be machined. Next, the dressing points are calculated. P i Local radius of curvature R b，i and P i x-axis x i The second derivative: f ''( x i ), to judge P i Geometric features of the surface at: when R b，i If the surface approaches infinity, then its geometric characteristics are determined to be planar; when... f ''( x i If ) < 0, then the geometric feature of the surface is determined to be a convex surface; when f ''( x i If ) > 0, then the surface geometry is determined to be a concave surface. The corresponding row spacing is then determined based on the surface geometry. L i : When trimming the plane, determine L i for: .

[0041] When trimming convex surfaces, determine L i for: .

[0042] When trimming concave surfaces, determine L i for: .

[0043] The highest point of the tooth surface on the axial profile of the worm grinding wheel is selected as the first dressing point. P 1, which can be written as P 1 = ( x 1, z 1). For a known current trim point P 1. Its line spacing L 1. Decide on the next rest stop P x-coordinate of 2 x 2: x 2= x 1+ L 1. Due to r z It consists of a series of profile points, and the tooth profile is modified using a drum-shaped modification. P The ordinate of 2 can be obtained from the fitting relationship between its abscissa and axial ordinate: z = f ( x The fitting formula needs to be fitted according to the specific shaping curve; different shapings require different fitting methods, which will not be elaborated on here. Continuing with... P Starting from point 2, repeat the steps of curvature calculation, line spacing determination, and residual height verification until the entire range is traversed. r z Region. Through this point-by-point process, all the final adjustment points are obtained { P 1. P 2、…、 P i ...} constitute a trim point sequence P Furthermore, in determining the next adjustment point... P i+1 After that, it can be calculated P i and P i+1 The actual residual height between h i : .

[0044] If | h i - h| < threshold, then it means h i Meet the requirements and retain P i+1 Conversely, it can be based on h i Adjustment L i Perform iterative calculations, for example, if h i If it exceeds the upper limit expected value, L i Reduce the step size by one (for example, the step size could be 0.005 mm). If h i If the value is less than the lower expected value, increase the step size by one, until | h i - h | < threshold. At this point, the residual height method can solve for the required trimming points.

[0045] At this time, according to P And the roller radius of the diamond roller R The center coordinate sequence of the diamond roller can then be calculated. C Specifically, based on the repair points P i The normal direction can be used to calculate the center coordinates of the diamond roller at the corresponding position. C i Its expression is: .

[0046] The calculation formula is as follows: .

[0047] In the formula, x i for P i The x-coordinate. Traverse all trim points { P 1. P 2、…、 P i After 、, …}, the corresponding { C 1. C 2、…、 C i The sequence of center coordinates of the diamond roller is composed of 、, …} C Finally, C The data is converted into multi-axis motion trajectory commands for the machine tool to obtain the point trimming trajectory of the diamond roller.

[0048] In another embodiment, a system for flexible point dressing of grinding worm gears using a universal diamond roller is proposed, which utilizes the aforementioned method for flexible point dressing of grinding worm gears using a universal diamond roller. This universal diamond roller flexible point dressing system includes: a coordinate generation module, a profile fitting module, and a trajectory generation module. The coordinate generation module calculates the coordinates of several contact points between the worm gear and the gear in the gear coordinate system based on the gear tooth surface parameter equation and the meshing relationship between the worm gear and the gear. Based on the meshing space coordinate system between the worm gear and the gear, the coordinate system of the contact points is transformed to the grinding wheel coordinate system, and the coordinates of the contact points in the grinding wheel coordinate system are calculated. The profile fitting module calculates the worm gear generating angle based on the parameters of the worm gear. x The range of values ​​is determined, and contact points are selected within this range. These selected contact points are then subjected to rotational projection to obtain the axial section profile points of the worm wheel. The axial section profile is then obtained after fitting. r z The trajectory generation module is used after tool setting, based on the diamond roller... r z Perform the first step on the worm gear grinding wheel i A repair point P i The repair work was then carried out, followed by the preset residual height. h calculate P i and the next rest point P i+1 line spacing between L i .pass L i calculate P i+1 The position, until all have been traversed. r z The trim point sequence was then obtained. P .according to P And the roller radius of the diamond roller R Calculate the center coordinate sequence of the diamond roller. C .Will C The data is converted into multi-axis motion trajectory commands for the machine tool, ultimately resulting in the point trimming trajectory of the diamond roller.

[0049] In another embodiment, a computer-readable storage medium is also provided. This computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the above-described method for general-purpose diamond roller flexible point dressing grinding worm gear grinding wheel. This computer-readable storage medium may include, but is not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof.

[0050] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0051] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A method for dressing a worm gear grinding wheel with a universal diamond roller flexible point dressing, characterized in that, It includes: Based on the gear tooth surface parameter equation and the meshing relationship between the worm grinding wheel and the gear, the coordinates of several contact points between the worm grinding wheel and the gear in the gear coordinate system are calculated. Based on the meshing spatial coordinate system between the worm gear and the gear, the coordinate system of the contact point is transformed to the grinding wheel coordinate system, and the coordinates of the contact point in the grinding wheel coordinate system are calculated. Calculation of worm wheel development angle based on worm wheel parameters ξ The range of values ​​is determined, and contact points are selected within this range. These selected contact points are then subjected to rotational projection to obtain the axial section profile points of the worm wheel. The axial section profile is then obtained after fitting. r z ; After the blade was applied, the diamond roller was based on r z Perform the first step on the worm gear grinding wheel i A repair point P i The repair work was then carried out, followed by the preset residual height. h calculate P i and the next rest point P i+1 line spacing between L i ;pass L i calculate P i+1 The position, until all have been traversed r z The trim point sequence was then obtained. P ; according to P And the roller radius of the diamond roller R Calculate the center coordinate sequence of the diamond roller. C ;Will C The data is converted into multi-axis motion trajectory commands for the machine tool, ultimately resulting in the point trimming trajectory of the diamond roller.

2. The method for dressing a worm gear grinding wheel with a universal diamond roller flexible point according to claim 1, characterized in that, Methods for obtaining the coordinates of several contact points include: First, construct the standard tooth surface equation based on the parameters of the gear to be machined. r g,stan ( μ , θ ): ； In the formula, μ Indicates the development angle of the involute of a gear. θ This represents the helix angle of the involute curve of a gear as it rotates about the gear's axis. x Represents the gear coordinate system x Axis coordinates y Represents the gear coordinate system y Axis coordinates r b Let be the base circle radius of the gear. σ 0 represents the half-angle of the base circle tooth groove of the gear. β b The base circle helix angle of the gear; exist r g,stan ( μ , θ Overlay tooth profile shaping curves H ( μ After that, the equation for the modified tooth profile of the gear is obtained. r g ( μ , θ ); The meshing equation is established based on the meshing relationship at the contact point between the worm gear and the gear: ； In the formula, U 1. U 2. V 1. V 2. W 1. W 2 are functions relating to the tooth surface equation and coordinate transformation parameters, respectively; Indicates the rotation angle of the gear, and ; Substituting into the meshing equation, we get μ , θ ;Will μ , θ Substitution r g ( μ , θ The coordinates of the contact point are obtained from the input; the process is iterated through. This yields the coordinates of multiple contact points; these multiple contact points form a contact trace.

3. The method for dressing a worm gear grinding wheel with a universal diamond roller flexible point dressing according to claim 2, characterized in that, Methods for selecting contact points that constitute the axial section profile include: Determine the gear coordinate system S g To the grinding wheel coordinate system S w Coordinate transformation matrix between M wg : ； in, θ w The rotation angle of the worm gear grinding wheel. θ g For the rotation angle of the gear, A The center distance between the gear and the worm wheel. λ w This represents the axial movement distance of the worm gear grinding wheel. λ g This represents the axial movement distance of the gear; according to M wg Transform the contact point coordinates in the gear coordinate system to the contact point coordinates in the grinding wheel coordinate system; Based on the involute curve of the end section of the worm grinding wheel and the base circle radius of the worm grinding wheel r w The relationship determines the generating angle of the worm grinding wheel. ξ The range of values ​​for: ； In the formula, r wa Let be the addendum circle radius of the worm gear grinding wheel. r wf Let be the radius of the root circle of the worm gear grinding wheel. ξ max for ξ The upper limit, ξ min for ξ The lower limit; Filter out ξ lie in[ ξ min , ξ max The contact points within the interval are used as the contact points that constitute the axial section profile.

4. The method for dressing a worm gear grinding wheel with a universal diamond roller flexible point according to claim 1, characterized in that, Obtain the axial section profile r z The methods include: Based on the equation for tooth profile modification and tooth surface r g ( μ , θ Calculate the contact point cloud on the left tooth surface of the worm gear grinding wheel respectively. r wl Contact point cloud of the right tooth surface r wr ; Will r wl , r wr The axial section profile points of the worm grinding wheel are obtained by rotating and projecting them onto the axial section plane of the worm grinding wheel. r d : ； ； ； In the formula, Mzi For the projection matrix, x i for r wl , r wr Upper i The contact points in the grinding wheel coordinate system x Axis coordinates y i for r wl , r wr Upper i The contact points in the grinding wheel coordinate system y Axis coordinates z i for r wl , r wr Upper i The contact points in the grinding wheel coordinate system z Axis coordinates for r wl , r wr The rotation angle of the contact point projected onto the axial section of the worm wheel. p w The helical parameters of the worm gear grinding wheel; right r d The axial section profile is obtained by performing a quadratic fitting. r z .

5. The method for dressing a worm gear grinding wheel with a universal diamond roller flexible point according to claim 1, characterized in that, Determine the repair point P i The methods include: Calculate trim points P i Local radius of curvature R b，i and P i x-axis x i The second derivative: f ''( x i ), and use this to judge P i The surface geometry features at the location; determine the corresponding row spacing based on the surface geometry features. L i ; according to L i Determine the next trim point P i+1 The horizontal axis coordinate in the grinding wheel coordinate system; based on P i+1 x-axis fitting P i+1 Axial coordinates in the grinding wheel coordinate system; Among them, the highest point of the tooth surface on the axial tooth profile of the worm grinding wheel is selected as the first dressing point. P 1.

6. The method for dressing a worm gear grinding wheel with a universal diamond roller flexible point according to claim 5, characterized in that, judge P i Methods for defining surface geometry at a given location include: when R b，i If the surface approaches infinity, then the geometric characteristics of the surface are determined to be planar. when f ''( x i If ) < 0, then the geometric feature of the surface is determined to be a convex surface; when f ''( x i If ) > 0, then the geometric feature of the surface is determined to be a concave surface; When trimming the plane, determine L i for: ； When trimming convex surfaces, determine L i for: ； When trimming concave surfaces, determine L i for: ； In the formula, R The outer radius of the diamond roller is... h The residual height between preset trim points.

7. The method for dressing a worm gear grinding wheel with a universal diamond roller flexible point according to claim 6, characterized in that, Determine the next adjustment point P i+1 Then, calculate P i and P i+1 The actual residual height between h i : ； If | h i - h If | < threshold, then retain P i+1 Conversely, according to h i Adjustment L i Perform iterative calculations until | h i - h | < threshold.

8. The method for dressing a worm gear grinding wheel with a universal diamond roller flexible point according to claim 1, characterized in that, Obtain the center coordinate sequence C The methods include: according to P i Calculate the center coordinates of the diamond roller at the corresponding position in the normal direction. C i : ； R The outer radius of the diamond roller is given; after traversing all the trimming points, the center coordinate sequence of the diamond roller is obtained. C .

9. A system for general-purpose diamond roller flexible point dressing grinding worm gear grinding wheels, characterized in that, The method uses a universal diamond roller flexible point dressing system for dressing a grinding worm gear as described in any one of claims 1 to 8; the universal diamond roller flexible point dressing system includes: The coordinate generation module is used to calculate the coordinates of several contact points between the worm wheel and the gear in the gear coordinate system based on the gear tooth surface parameter equation and the meshing relationship between the worm wheel and the gear; based on the meshing space coordinate system between the worm wheel and the gear, the coordinate system of the contact points is transformed to the grinding wheel coordinate system, and the coordinates of the contact points in the grinding wheel coordinate system are calculated. The profile fitting module is used to calculate the generating angle of the worm grinding wheel based on its parameters. ξ The range of values ​​is determined, and contact points are selected within this range. These selected contact points are then subjected to rotational projection to obtain the axial section profile points of the worm wheel. The axial section profile is then obtained after fitting. r z ; The trajectory generation module is used to generate the diamond roller based on the tool setting process. r z Perform the first step on the worm gear grinding wheel i A repair point P i The repair work was then carried out, followed by the preset residual height. h calculate P i and the next rest point P i+1 line spacing between L i ;pass L i calculate P i+1 The position, until all have been traversed r z The trim point sequence was then obtained. P ;according to P And the roller radius of the diamond roller R Calculate the center coordinate sequence of the diamond roller. C ;Will C The data is converted into multi-axis motion trajectory commands for the machine tool, ultimately resulting in the point trimming trajectory of the diamond roller.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the method for general diamond roller flexible point dressing of a grinding worm wheel as described in any one of claims 1 to 8.

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