A cylindrical gear micro-modification tolerance expression method based on K chart

Abstract

The application discloses a kind of based on K-shaped chart's cylindrical gear microcosmic modification tolerance expression method, comprising: S1, determine the multiple evaluation positions of the tooth width direction of tooth modification;S2, according to the tooth modification parameter and its tolerance of gear, calculate the tolerance boundary of tooth modification at each evaluation position in the tooth width direction, generate tooth K-shaped chart;S3, determine the multiple evaluation positions of the tooth profile modification in the tooth profile length direction;S4, according to the tooth modification parameter and its tolerance of gear, calculate the tolerance boundary of tooth modification at each evaluation position in the tooth profile length direction, generate tooth K-shaped chart;S5, the tooth K-shaped chart and tooth K-shaped chart are determined by comprehensively described K-shaped chart expression data of gear microcosmic modification.The application constructs the cylindrical gear microcosmic modification tolerance design method based on K-shaped chart's quantifiable calculation and visual expression, solves the technical problems that traditional two-dimensional tolerance marking mode cannot intuitively and accurately represent complex tooth surface modification shape and its allowed tolerance range.

Description

Technical Field

[0001] This invention relates to the field of gear design technology, specifically to a method for expressing the microscopic profile tolerance of cylindrical gears based on K-shaped diagrams. Background Technology

[0002] As a core component of mechanical transmission, the microscopic geometric precision of gears, including tooth profile modification and tooth direction modification, as well as their tolerance design, is a decisive factor directly affecting the key performance characteristics of the transmission system, such as load-bearing capacity, service life, and vibration and noise (NVH). To ensure the meshing quality of gear pairs, traditional techniques generally adopt the method of marking various microscopic geometric tolerances on two-dimensional engineering drawings and defining them by referring to the textual and tabular specifications in standards such as ISO 1328 and AGMA 2000.

[0003] However, with the development of high-precision, high-performance transmission fields such as new energy vehicles, aerospace, and robotics, gear profile design is becoming increasingly complex. Nonlinear profile features such as bulging, tilting, and end edge trimming in the tooth profile and tooth line directions often need to be superimposed. Traditional two-dimensional tables and discrete tolerance annotation methods can no longer meet the requirements for rapid and effective gear evaluation. Existing methods lack intuitiveness and cannot present the overall shape of the micro-geometric errors of the tooth surface and the allowable tolerance range in an integrated and visual way. There is a huge information conversion difference between the design intent and the manufacturing acceptance standards. It is highly dependent on the professional knowledge and experience of engineers and is prone to misinterpretation and misjudgment in the manufacturing and inspection stages, resulting in high communication costs and technical barriers. Secondly, traditional methods have limitations in mathematical representation capabilities. For complex helix angle correction curves, parabolic profiles, and other continuously changing geometric features, they can only be approximated by a limited number of discrete tolerance items. They cannot accurately describe the complete profile shape and tolerance zone of the entire tooth surface or tooth line. This has become a key technical bottleneck restricting the improvement of gear design accuracy and performance.

[0004] Therefore, existing technologies urgently need a new technical solution to address the above problems. Summary of the Invention

[0005] To address the shortcomings of the existing technologies, this invention provides a method for expressing the micro-profile tolerance of cylindrical gears based on K-graphs. By constructing a quantifiable and visually expressible design method for the micro-profile tolerance of cylindrical gears based on K-graphs, this invention solves the technical problem that traditional two-dimensional tolerance annotation methods cannot intuitively, completely, and accurately characterize the complex tooth surface profile shape and its allowable tolerance range.

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0007] A method for expressing the micro-profile tolerance of cylindrical gears based on K-shaped diagrams includes the following steps:

[0008] S1. Determine multiple evaluation positions for tooth profile modification in the tooth width direction;

[0009] S2. Based on the gear's tooth profile micro-modification parameters and their tolerances, calculate the tolerance boundaries of tooth profile modification at each evaluation position in the tooth width direction, and generate a tooth profile K-shape diagram.

[0010] S3. Determine multiple evaluation positions for tooth profile modification in the tooth profile elongation direction;

[0011] S4. Based on the micro-modification parameters and tolerances of the gear tooth profile, calculate the tolerance boundaries of tooth profile modification at each evaluation position in the tooth profile elongation direction, and generate the tooth profile K-shape diagram.

[0012] S5. Combining the aforementioned tooth direction K-shape diagram and tooth profile K-shape diagram, determine the K-shape diagram representation data for gear micro-modification.

[0013] As a preferred embodiment, in step S1, the multiple evaluation positions in the tooth width direction include the tooth width start point, the tooth width evaluation start point, the tooth width reference midpoint, the tooth width evaluation end point, and the tooth width end point.

[0014] As a preferred embodiment, step S2, the generation of the tooth-direction K-shape diagram includes the following steps:

[0015] S201. Obtain the gear tooth profile micro-modification parameters and the corresponding tolerances for each parameter;

[0016] S202. Based on the micro-modification parameters of the tooth direction and the tolerances corresponding to each parameter, calculate the modification components at each evaluation position in the tooth width direction.

[0017] S203. For each evaluation position, combine the modification components calculated in step S202 with their corresponding tolerances to determine the upper and lower tolerance boundaries of each modification component, and algebraically superimpose the upper and lower tolerance boundaries of each modification component to obtain the comprehensive tooth modification amount at each evaluation position in the tooth width direction.

[0018] S204. Based on the comprehensive tooth profile modification amount at each evaluation position, the horizontal coordinate of the tooth profile K-shape diagram at each evaluation position is obtained, thus obtaining the gear tooth profile K-shape diagram.

[0019] As a preferred embodiment, in step S202, the modification components at each evaluation position in the tooth width direction include:

[0020] Tooth-to-drum shape modification amount:

[0021] ;

[0022] In the formula, For tooth-to-drum shape modification amount, The amount of the tooth-shaped quadratic parabolic bulge is... This serves as the starting point for the tooth profile modification evaluation. This marks the end point of the tooth profile modification evaluation. The midpoint for tooth profile modification evaluation. For gear tooth width variable, This is the starting point of the tooth width. This is the end point of the tooth width;

[0023] Tooth-direction trimming amount:

[0024] ;

[0025] In the formula, For tooth-shaped edge trimming. This refers to the amount of edge trimming at the starting end of the tooth. This indicates the starting position for edge trimming at the beginning of the tooth direction. This refers to the amount of edge trimming on the tooth flank at the tooth termination point. This is the starting position for edge trimming at the tooth termination end;

[0026] Tooth inclination modification amount:

[0027]

[0028] In the formula, This refers to the amount of tooth profile adjustment by tilting. This is the amount of modification for the gear helix angle.

[0029] As a preferred embodiment, in step S203, the tooth-direction comprehensive modification amount is expressed as:

[0030] ;

[0031] In the formula, This refers to the total profile modification amount along the tooth direction.

[0032] As a preferred embodiment, in step S3, the multiple evaluation positions in the tooth profile elongation direction include the meshing start point, the tooth root trimming start point, the elongation reference midpoint, the tooth tip trimming start point, and the meshing end point.

[0033] As a preferred embodiment, step S4, the generation of the tooth profile K-shape diagram includes the following steps:

[0034] S401. Obtain the micro-modification parameters of the gear tooth profile and the corresponding tolerances of each parameter;

[0035] S402. Based on the micro-modification parameters of the tooth profile and the tolerances corresponding to each parameter, calculate the modification components at each evaluation position in the tooth profile elongation direction.

[0036] S403. For each evaluation position, combine the modification components calculated in step S402 with their corresponding tolerances to determine the upper and lower tolerance boundaries of each modification component, and algebraically superimpose the upper and lower tolerance boundaries of each modification component to obtain the comprehensive tooth profile modification amount at each evaluation position in the tooth profile elongation direction.

[0037] S404. Based on the comprehensive tooth profile modification amount at each evaluation position, the horizontal coordinate of the tooth profile K-shape diagram at each evaluation position is obtained, thus obtaining the gear tooth profile K-shape diagram.

[0038] As a preferred embodiment, in step S402, the modification components at each evaluation position in the tooth profile elongation direction include:

[0039] Tooth-shaped and drum-shaped trimming amount:

[0040] ;

[0041] In the formula, For tooth-shaped and drum-shaped shaping, The amount of the tooth-shaped quadratic parabolic drum shape, This serves as the starting point for tooth profile modification evaluation. This marks the end point of the tooth profile modification evaluation. The midpoint for tooth profile modification evaluation. For the position variable of the gear tooth profile;

[0042] Tooth profile trimming amount:

[0043] ;

[0044] In the formula, For tooth profile trimming. For the edge trimming of the tooth tip. This marks the starting point for edge trimming at the tooth tip. To measure the edge of the tooth root. This marks the starting point for tooth root trimming;

[0045] Tooth profile tilt modification amount:

[0046] ;

[0047] In the formula, This refers to the amount of tooth profile tilt modification. This is the amount of gear pressure angle modification.

[0048] As a preferred embodiment, in step S403, the total tooth profile modification amount is expressed as follows:

[0049] ;

[0050] In the formula, This refers to the overall profile modification amount.

[0051] As a preferred option, in step S5, the tooth direction K-shape diagram and the tooth profile K-shape diagram are integrated to generate K-shape diagram representation data for gear micro-modification.

[0052] Compared with the prior art, the present invention has the following technical effects:

[0053] 1. Traditional tolerance representation methods relying on two-dimensional drawings and numerical tables require personnel with extremely high professional skills in spatial imagination and data correlation, which can easily lead to misunderstandings and misjudgments between design, process, and inspection departments. The K-shaped diagram generated by the method of this invention compresses and projects the complex three-dimensional geometry of the tooth surface and its allowable error range into a two-dimensional planar diagram. Its horizontal axis corresponds to the modification amount, and the vertical axis corresponds to the tooth width or extension position. By establishing the mapping relationship between the micro-geometric parameters of the tooth surface and the tolerance domain, different modification amounts and allowable deviation ranges of tooth profile and tooth direction are expressed in a K-shaped diagram. This breaks through the discreteness and static limitations of traditional tolerance annotation and enables the visual analysis of the coupling relationship of micro-parameters. This helps relevant personnel to quickly and accurately determine whether the micro-geometry of the gear tooth surface is up to standard.

[0054] 2. Traditional discrete tolerances struggle to accurately describe continuous shaping features such as parabolic bulges and linear inclinations. This invention's method establishes a mathematical model to calculate the theoretical shaping and tolerance boundaries at any point along the entire evaluation path. This structured K-shaped diagram data representation provides a structured tolerance data interface for CAE simulation and CAM machining, significantly improving the collaborative efficiency of the entire gear design-manufacturing-inspection process, while simultaneously promoting the intelligent and efficient development of gear manufacturing. Attached Figure Description

[0055] To make the objectives, technical solutions, and advantages of the invention clearer, the invention will now be described in further detail with reference to the accompanying drawings, wherein:

[0056] Figure 1 This is a flowchart of a method for expressing the microscopic profile tolerance of cylindrical gears based on a K-shaped diagram, as disclosed in this invention.

[0057] Figure 2 This is a schematic diagram of tooth profile modification in an embodiment of the present invention;

[0058] Figure 3 This is a schematic diagram of tooth profile modification in an embodiment of the present invention;

[0059] Figure 4 This is a schematic diagram showing the tolerance representation of the gear tooth profile micro-modification K-shape diagram in an embodiment of the present invention;

[0060] Figure 5 This is a schematic diagram showing the tolerance representation of the gear tooth profile micro-modification K-shape in an embodiment of the present invention. Detailed Implementation

[0061] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but only to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0062] The present invention will now be described in further detail with reference to the accompanying drawings.

[0063] Traditional gear micro-parameter tolerance annotation often uses two-dimensional engineering drawings combined with text and table specifications from standards such as ISO 1328 or AGMA 2000. Its drawback is that geometric errors are expressed in tables and numbers after being decomposed by multiple two-dimensional projections, lacking an intuitive representation of the overall tooth surface. This can easily lead to misinterpretation and misjudgment in the manufacturing and inspection stages, and requires a high level of professional knowledge from engineers, increasing the technical threshold and communication costs. In addition, traditional discrete tolerance parameters cannot accurately and completely describe complex continuous shaping features such as helical drum shapes and parabolic edge trimmings. This makes advanced CAE simulation analysis lack accurate input boundaries, and precision CNC machining also lacks continuous path guidance beyond the point of view, seriously hindering the gear industry's transformation and upgrading towards digital and intelligent manufacturing. To address the aforementioned problems and shortcomings, this invention proposes a method for expressing the micro-modification tolerance of cylindrical gears based on a K-shaped diagram. The core of this method is not simply graphical representation, but rather the construction of a mathematical model to calculate and synthesize various modification quantities (bulging, inclination, edge modification) and their tolerances of tooth profile and tooth direction into a tolerance boundary line that continuously varies along the tooth width or span direction, ultimately generating an intuitive K-shaped diagram.

[0064] Specifically, such as Figures 1 to 3 As shown in this embodiment, the method for expressing the micro-profile tolerance of cylindrical gears based on K-shaped diagrams includes the following steps:

[0065] S1. Determine multiple evaluation positions for tooth profile modification in the tooth width direction;

[0066] In this embodiment, a tooth profile modification plane coordinate system is established. The tooth profile modification is defined in the unfolded plane of the measuring cylinder. The tooth width direction is used as the vertical coordinate and the tooth profile modification amount is used as the horizontal coordinate, thereby determining the reference point position and vertical coordinate value for evaluating the tooth profile modification along the tooth width direction in the K-shape diagram.

[0067] Specifically, to quantitatively evaluate the profile modification and tolerance in the gear tooth direction, a series of key evaluation points need to be defined on the tooth width. These points typically include, but are not limited to, the tooth width starting point V. st Tooth width evaluation starting point V e1 Reference midpoint V for tooth width m Tooth width evaluation termination point V e2 Tooth width endpoint V end ,in:

[0068] Tooth width starting point V st That is, the tooth-direction starting point, which is the point where the measuring probe first contacts the tooth line length direction according to the specified measurement direction of the gear, and its ordinate value is 0;

[0069] Starting point for tooth width evaluation V e1 The point at the first end of the range of tooth helix measurements specified in ISO 1328-2013 has a ordinate value of min(mn, 5%*B), where mn is the gear module and B is the tooth width.

[0070] The reference midpoint of the tooth width is the midpoint of the gear tooth width, and its ordinate value is (V). st +V end ) / 2;

[0071] Tooth width evaluation termination point V e2 The point at the second end of the range of values ​​for the toothed helix as specified in ISO 1328-2013 has a ordinate value of V. e2 =BV e1 ;

[0072] Tooth width end point V end The tooth-direction final measurement point is the point where the measuring probe last contacts the tooth line length direction according to the specified measurement direction of the gear, and its ordinate value is B.

[0073] It should be noted that the evaluation locations listed above (such as V) st V e1 V m V e2 V end This is merely an exemplary embodiment for implementing the method. Those skilled in the art will understand that, in order to obtain a more accurate and smoother K-shaped boundary curve, a greater number of evaluation location points can be obtained within the aforementioned evaluation interval, thereby generating a smoother K-shaped diagram that more accurately characterizes the micro-geometry of the gear tooth surface.

[0074] S2. Based on the gear's tooth profile micro-modification parameters and their tolerances, calculate the tolerance boundaries of tooth profile modification at each evaluation position in the tooth width direction, and generate a tooth profile K-shape diagram.

[0075] In this embodiment, the generation of the tooth-direction K-shape diagram includes the following steps:

[0076] S201. Obtain the gear tooth profile micro-modification parameters and the corresponding tolerances for each parameter;

[0077] In practical implementation, the micro-parameters of the gear design mainly include the tooth direction secondary parabolic bulge, the tooth flank trimming amount at the tooth direction starting end, the tooth flank trimming amount at the tooth direction ending end, and the gear helix angle trimming amount. This trimming tolerance can be found in existing standards such as ISO1328 (or existing DIN standards), or it can be provided by the engineering.

[0078] S202. Based on the micro-modification parameters of the tooth direction and the tolerances corresponding to each parameter, calculate the modification components at each evaluation position in the tooth width direction.

[0079] In practice, based on the micro-modification parameters of the tooth direction, the modification components at each evaluation location are calculated using the corresponding mathematical model. The modification separation includes the tooth direction bulging modification amount, the tooth direction edge modification amount, and the tooth direction tilting modification amount. The specific mathematical model is as follows:

[0080] The equation for the crowning modification within the tooth profile evaluation range is as follows:

[0081] ;

[0082] In the formula, For tooth-to-drum shape modification amount, The amount of the tooth-shaped quadratic parabolic bulge is... This serves as the starting point for the tooth profile modification evaluation. This marks the end point of the tooth profile modification evaluation. The midpoint for tooth profile modification evaluation. For gear tooth width variable, This is the starting point of the tooth width. This is the end point of the tooth width;

[0083] The equation for the quadratic parabolic tooth flank trimming at the tooth tip is as follows:

[0084] ;

[0085] In the formula, For tooth-shaped edge trimming. This refers to the amount of edge trimming at the starting end of the tooth. This indicates the starting position for edge trimming at the beginning of the tooth direction. This refers to the amount of edge trimming on the tooth flank at the tooth termination point. This is the starting position for edge trimming at the tooth termination end;

[0086] The inclination modification equation for the tooth direction evaluation range is as follows:

[0087]

[0088] In the formula, This refers to the amount of tooth profile adjustment by tilting. This is the amount of modification for the gear helix angle.

[0089] S203. For each evaluation position, combine the modification components calculated in step S202 with their corresponding tolerances to determine the upper and lower tolerance boundaries of each modification component, and algebraically superimpose the upper and lower tolerance boundaries of each modification component to obtain the comprehensive tooth modification amount at each evaluation position in the tooth width direction.

[0090] In practical implementation, the modified components, i.e., the abscissa values, of different evaluation points in the tooth direction obtained above are calculated. That is, the upper and lower tolerance boundaries of each evaluation position and each modified component are algebraically superimposed to obtain the upper and lower abscissas of the tooth direction modification amount at that position. Thus, the expression equation for its comprehensive tooth direction modification amount is obtained as follows:

[0091] ;

[0092] In the formula, This refers to the total profile modification amount along the tooth direction.

[0093] S204. Based on the tooth profile modification amount at each evaluation position, the horizontal coordinate (i.e., tooth profile modification amount) of the tooth profile K-shape diagram at each evaluation position is obtained, thus obtaining the gear tooth profile K-shape diagram.

[0094] S3. Determine multiple evaluation positions for tooth profile modification in the tooth profile elongation direction;

[0095] In this embodiment, similar to the tooth profile evaluation, to evaluate the profile modification and tolerance in the tooth profile direction, a series of evaluation position points need to be defined on the effective meshing section of the tooth profile. Specifically, a tooth profile modification plane coordinate system is established. The tooth profile modification is defined along the tooth profile curve on the measurement end face. The length of the measured gear tooth profile is used as the vertical axis, and the tooth profile modification amount is used as the horizontal axis. The reference point position and vertical axis value of the tooth profile modification evaluation in the length direction in the K-shape diagram are determined, i.e., the length.

[0096] Specifically, the multiple evaluation locations along the tooth profile elongation direction include, but are not limited to: the engagement initiation point, the root trimming initiation point, the elongation reference midpoint, the tip trimming initiation point, and the engagement termination point, wherein:

[0097] The starting point of engagement, its ordinate value It is equal to the expansion of the point at the root of the gear where it meshes with the effective tip circle of the mating gear. ;

[0098] The starting point for tooth root trimming is the starting position of the tooth root trimming, with coordinate values... Equal to the span corresponding to that position ;

[0099] The starting point for tooth tip trimming is the starting position of the trimming process at the top of the gear, with coordinate values... Equal to the span corresponding to that position ;

[0100] The meshing termination point is the effective addendum circle of the gear, with coordinate values... Equal to the expansion at the effective tip circle ;

[0101] The midpoint of the extended length reference is the midpoint of the extended length between the gear meshing start point and meshing end point, with coordinate values... equal .

[0102] It should be noted that the evaluation locations listed above are only one exemplary embodiment of this method. Those skilled in the art will understand that, in order to obtain a more accurate and smoother K-shaped boundary curve, a greater number of evaluation locations can be obtained within the above evaluation interval, thereby generating a smoother K-shaped diagram and more accurately characterizing the micro-geometry of the gear tooth surface.

[0103] S4. Based on the micro-modification parameters and tolerances of the gear tooth profile, calculate the tolerance boundaries of tooth profile modification at each evaluation position in the tooth profile elongation direction, and generate the tooth profile K-shape diagram.

[0104] In this embodiment, the generation of the tooth profile K-shape diagram includes the following steps:

[0105] S401. Obtain the micro-modification parameters of the gear tooth profile and the corresponding tolerances of each parameter;

[0106] In practice, the micro-modification parameters of gear tooth profile mainly include the amount of secondary parabolic bulge, the amount of tooth tip modification, the amount of tooth root modification, and the amount of gear pressure angle modification. These tooth profile tolerances can be found in existing standards such as ISO1328 (or existing DIN standards) or can be provided by the engineering team.

[0107] S402. Based on the micro-modification parameters of the tooth profile and the tolerances corresponding to each parameter, calculate the modification components at each evaluation position in the tooth profile elongation direction.

[0108] In practice, based on the above parameters, the corresponding mathematical model is used to calculate the shaping components at each evaluation location. These shaping components include tooth profile bulge shaping amount, tooth profile edge shaping amount, and tooth profile inclination shaping amount. The specific mathematical model is as follows:

[0109] The equation for the drum-shaped modification within the tooth profile evaluation range is as follows:

[0110] ;

[0111] In the formula, For tooth-shaped and drum-shaped shaping, The amount of the tooth-shaped quadratic parabolic drum shape, This serves as the starting point for tooth profile modification evaluation. This marks the end point of the tooth profile modification evaluation. The midpoint for tooth profile modification evaluation. For the position variable of the gear tooth profile;

[0112] The tooth tip is edged using a quadratic parabolic curve, and the tooth root is edged using a quadratic parabolic curve. The equations are as follows:

[0113] ;

[0114] In the formula, For tooth profile modification amount, For the edge trimming of the tooth tip. This marks the starting point for edge trimming at the tooth tip. To measure the edge of the tooth root. This marks the starting point for trimming the tooth root.

[0115] The inclination modification equation for the tooth profile evaluation range is as follows:

[0116] ;

[0117] In the formula, This refers to the amount of tooth profile tilt modification. This is the amount of gear pressure angle modification.

[0118] S403. For each evaluation position, combine the modification components calculated in step S402 with their corresponding tolerances to determine the upper and lower tolerance boundaries of each modification component, and algebraically superimpose the upper and lower tolerance boundaries of each modification component to obtain the comprehensive tooth profile modification amount at each evaluation position in the tooth profile elongation direction.

[0119] In practical implementation, the total tooth profile modification amount is expressed as follows:

[0120] ;

[0121] In the formula, This refers to the overall profile modification amount.

[0122] S404. Based on the comprehensive tooth profile modification amount at each evaluation position, the horizontal coordinate of the tooth profile K-shape diagram at each evaluation position is obtained, thus obtaining the gear tooth profile K-shape diagram.

[0123] S5. Combining the aforementioned tooth direction K-shape diagram and tooth profile K-shape diagram, determine the K-shape diagram representation data for gear micro-modification.

[0124] In practice, the tooth profile K-shape diagram and the tooth shape K-shape diagram are integrated to generate K-shape diagram representation data for gear micro-modification.

[0125] In this embodiment, the tooth-direction K-shaped diagram and the tooth profile K-shaped diagram completely define the micro-geometry of a single tooth surface of the gear and its allowable manufacturing error range from the tooth line direction and tooth profile direction, respectively. This embodiment integrates the two to form a structured K-shaped diagram representation data. This data not only includes the coordinates of all the evaluation position points, theoretical modification amounts, and upper and lower tolerance boundary values, but also the parameter basis and calculation logic for generating this data. This data is a complete digital representation of the gear's micro-geometric quality, which can be directly used to guide manufacturing processes, serve as a testing and judgment standard for gear measurement centers, or be input into CAE software for performance simulation analysis, thereby connecting the data chain of design, manufacturing, testing, and simulation.

[0126] To better illustrate the effectiveness of the proposed K-shaped diagram-based method for expressing the micro-profile tolerance of cylindrical gears, the following examples will be used to illustrate this.

[0127] This embodiment takes the main reduction gear pair of an automotive transmission as an example. The macroscopic parameters of the gear pair are input as shown in Table 1:

[0128] Table 1 Macroscopic parameters of gear pair

[0129]

[0130] According to the K-shaped diagram representation method for the micro-modification and tolerance of cylindrical gears of the present invention, the modification amounts of the tooth profile and tooth direction of the left and right tooth surfaces of gear 1 are input as shown in Table 2:

[0131] Table 2 Gear 1 Modification Parameters

[0132]

[0133] According to ISO 1328 standard and gear accuracy grades, the gear tooth profile Fα = 11µm and tooth direction error Fβ = 12µm are obtained from the tables. The units are µm. Some errors are shown in Tables 3 and 4.

[0134] Table 3 Tooth profile error Fα

[0135]

[0136] Table 4 Tooth Direction Error Fβ

[0137]

[0138] The tooth width evaluation points are: tooth width start point, tooth width evaluation start point, tooth flank trimming start point 1, tooth width reference point 1, tooth width reference midpoint, tooth width reference point 2, tooth flank trimming start point 2, tooth width evaluation end point, and tooth width end point.

[0139] The tooth profile evaluation points are: the starting point of meshing (SAP), the starting point of tooth root trimming, the expansion reference point 1, the midpoint of expansion reference, the expansion reference point 2, the starting point of tooth tip trimming, and the ending point of meshing (EAP).

[0140] According to the method of this embodiment, the tooth profile modification amount and deviation at each reference point of the micro-modification K-shape diagram of gear 1 are calculated, such as... Figure 4 , Figure 5 As shown in Tables 5 and 6:

[0141] Table 5. K-shaped diagram data for tooth profile modification

[0142]

[0143] Table 6. Tooth profile modification K-line diagram data

[0144]

[0145] In summary, compared with the prior art, the method for expressing the micro-profile tolerance of cylindrical gears based on K-shaped diagrams proposed in this embodiment has the following technical advantages:

[0146] 1. Traditional tolerance representation methods relying on two-dimensional drawings and numerical tables require personnel with extremely high professional skills in spatial imagination and data correlation, which can easily lead to misunderstandings and misjudgments between design, process, and inspection departments. The K-shaped diagram generated by the method of this invention compresses and projects the complex three-dimensional geometry of the tooth surface and its allowable error range into a two-dimensional planar diagram. Its horizontal axis corresponds to the modification amount, and the vertical axis corresponds to the tooth width or extension position. By establishing the mapping relationship between the micro-geometric parameters of the tooth surface and the tolerance domain, different modification amounts and allowable deviation ranges of tooth profile and tooth direction are expressed in a K-shaped diagram. This breaks through the discreteness and static limitations of traditional tolerance annotation and enables the visual analysis of the coupling relationship of micro-parameters. This helps relevant personnel to quickly and accurately determine whether the micro-geometry of the gear tooth surface is up to standard.

[0147] 2. Traditional discrete tolerances struggle to accurately describe continuous shaping features such as parabolic bulges and linear inclinations. This invention's method establishes a mathematical model to calculate the theoretical shaping and tolerance boundaries at any point along the entire evaluation path. This structured K-shaped diagram data representation provides a structured tolerance data interface for CAE simulation and CAM machining, significantly improving the collaborative efficiency of the entire gear design-manufacturing-inspection process, while simultaneously promoting the intelligent and efficient development of gear manufacturing.

[0148] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described with reference to preferred embodiments, those skilled in the art should understand that various changes in form and detail can be made without departing from the spirit and scope of the invention as defined in the appended claims.

Claims

1. A method for expressing the microscopic profile tolerance of cylindrical gears based on K-shaped diagrams, characterized in that, Includes the following steps: S1. Determine multiple evaluation positions for tooth profile modification in the tooth width direction; S2. Based on the gear's tooth profile micro-modification parameters and their tolerances, calculate the tolerance boundaries of tooth profile modification at each evaluation position in the tooth width direction, and generate a tooth profile K-shape diagram. S3. Determine multiple evaluation positions for tooth profile modification in the tooth profile elongation direction; S4. Based on the micro-modification parameters and tolerances of the gear tooth profile, calculate the tolerance boundaries of tooth profile modification at each evaluation position in the tooth profile elongation direction, and generate the tooth profile K-shape diagram. S5. Combining the aforementioned tooth direction K-shape diagram and tooth profile K-shape diagram, determine the K-shape diagram representation data for gear micro-modification.

2. The method for expressing the microscopic profile tolerance of cylindrical gears based on K-shaped diagrams according to claim 1, characterized in that, In step S1, the multiple evaluation positions in the tooth width direction include the tooth width start point, the tooth width evaluation start point, the tooth width reference midpoint, the tooth width evaluation end point, and the tooth width end point.

3. The method for expressing the micro-profile tolerance of cylindrical gears based on K-shaped diagrams according to claim 2, characterized in that, In step S2, the generation of the tooth-direction K-shape diagram includes the following steps: S201. Obtain the gear tooth profile micro-modification parameters and the corresponding tolerances for each parameter; S202. Based on the micro-modification parameters of the tooth direction and the tolerances corresponding to each parameter, calculate the modification components at each evaluation position in the tooth width direction. S203. For each evaluation position, combine the modification components calculated in step S202 with their corresponding tolerances to determine the upper and lower tolerance boundaries of each modification component, and algebraically superimpose the upper and lower tolerance boundaries of each modification component to obtain the comprehensive tooth modification amount at each evaluation position in the tooth width direction. S204. Based on the comprehensive tooth profile modification amount at each evaluation position, the horizontal coordinate of the tooth profile K-shape diagram at each evaluation position is obtained, thus obtaining the gear tooth profile K-shape diagram.

4. The method for expressing the micro-profile tolerance of cylindrical gears based on K-shaped diagrams according to claim 3, characterized in that, In step S202, the profile modification components at each evaluation position in the tooth width direction include: Tooth-to-drum shape modification amount: ； In the formula, For tooth-to-drum shape modification amount, The amount of the tooth-shaped quadratic parabolic bulge is... This serves as the starting point for the tooth profile modification evaluation. This marks the end point of the tooth profile modification evaluation. The midpoint for tooth profile modification evaluation. For gear tooth width variable, This is the starting point of the tooth width. This is the end point of the tooth width; Tooth-direction trimming amount: ； In the formula, For tooth-shaped edge trimming. This refers to the amount of edge trimming at the starting end of the tooth. This indicates the starting position for edge trimming at the beginning of the tooth direction. This refers to the amount of edge trimming on the tooth flank at the tooth termination end. This is the starting position for edge trimming at the tooth termination end; Tooth inclination modification amount: In the formula, This refers to the amount of tooth profile adjustment by tilting. This is the amount of modification for the gear helix angle.

5. The method for expressing the micro-profile tolerance of cylindrical gears based on K-shaped diagrams according to claim 4, characterized in that, In step S203, the tooth profile modification amount is expressed as: ； In the formula, This refers to the total profile modification amount along the tooth direction.

6. The method for expressing the micro-profile tolerance of cylindrical gears based on K-shaped diagrams according to claim 1, characterized in that, In step S3, the multiple evaluation positions in the tooth profile elongation direction include the meshing start point, the tooth root trimming start point, the elongation reference midpoint, the tooth tip trimming start point, and the meshing end point.

7. The method for expressing the micro-profile tolerance of cylindrical gears based on K-shaped diagrams according to claim 1, characterized in that, In step S4, the generation of the tooth profile K-shape diagram includes the following steps: S401. Obtain the micro-modification parameters of the gear tooth profile and the corresponding tolerances of each parameter; S402. Based on the micro-modification parameters of the tooth profile and the tolerances corresponding to each parameter, calculate the modification components at each evaluation position in the tooth profile elongation direction. S403. For each evaluation position, combine the modification components calculated in step S402 with their corresponding tolerances to determine the upper and lower tolerance boundaries of each modification component, and algebraically superimpose the upper and lower tolerance boundaries of each modification component to obtain the comprehensive tooth profile modification amount at each evaluation position in the tooth profile elongation direction. S404. Based on the comprehensive tooth profile modification amount at each evaluation position, the horizontal coordinate of the tooth profile K-shape diagram at each evaluation position is obtained, thus obtaining the gear tooth profile K-shape diagram.

8. The method for expressing the micro-profile tolerance of cylindrical gears based on K-shaped diagrams according to claim 7, characterized in that, In step S402, the modification components at each evaluation position in the tooth profile elongation direction include: Tooth-shaped and drum-shaped trimming amount: ； In the formula, For tooth-shaped and drum-shaped shaping, The amount of the tooth-shaped quadratic parabolic drum shape. This serves as the starting point for tooth profile modification evaluation. This marks the end point of the tooth profile modification evaluation. The midpoint for tooth profile modification evaluation. For the gear tooth profile position variable; Tooth profile trimming amount: ； In the formula, For tooth profile trimming. For the edge trimming of the tooth tip. This marks the starting point for edge trimming at the tooth tip. To measure the edge of the tooth root. This marks the starting point for tooth root trimming; Tooth profile tilt modification amount: ； In the formula, This refers to the amount of tooth profile tilt modification. This is the amount of gear pressure angle modification.

9. The method for expressing the micro-profile tolerance of cylindrical gears based on K-shaped diagrams according to claim 8, characterized in that, In step S403, the total tooth profile modification amount is expressed as: ； In the formula, This refers to the overall tooth profile modification amount.

10. The method for expressing the micro-profile tolerance of cylindrical gears based on K-shaped diagrams according to claim 1, characterized in that, In step S5, the tooth profile K-shape diagram and the tooth shape K-shape diagram are integrated to generate K-shape diagram representation data for gear micro-modification.

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