Gear pair, tooth profile design method and gear detection method

Abstract

The application discloses a gear pair, a tooth profile design method and a gear detection method. The gear pair comprises a first gear and a second gear. Tooth profiles of the first gear and the second gear are determined by the following method: a contact path is defined in an engagement plane, the contact path is obtained by normal biasing of a working line of a standard involute gear pair, and the tooth profiles of the first gear and the second gear are inversely obtained from the contact path according to a conjugate engagement differential relationship. A normal biasing function satisfies the following conditions: a function value at a node is zero; a first derivative at the node is zero; and a function value at an end point of the contact path is zero. Since the normal biasing function returns to zero at the end point of the contact path, the addendum and dedendum regions are consistent with the standard involute tooth profile, and existing manufacturing equipment and detection systems of the involute gear can be used for production, without the need to completely replace tools and measuring tools.

Description

Technical Field

[0001] This invention belongs to the field of gear design and manufacturing technology, specifically a gear pair, tooth profile design method, and gear inspection method based on involute reference normal offset. Background Technology

[0002] Involute gears have become the industry standard tooth profile due to their ease of machining, ability to maintain a constant transmission ratio even with center distance errors, mature measurement and inspection systems, and strong interchangeability. However, in scenarios involving small tooth counts, small modules, high speeds, plastic / soft material gear pairs, large negative deviations in the common normal, and fluctuations in assembly center distances, involute tooth profiles may still present challenges such as meshing / exit impacts, excessive local relative curvature, sliding thermal excitation, fluctuations in tooth surface contact stiffness, and difficulty in reducing noise peaks.

[0003] Schemes such as circular arc teeth, cycloidal teeth, hyperbolic teeth, parabolic meshing teeth, and B-spline tooth profiles with relative curvature have been disclosed or applied, but most of these schemes have the following limitations: they are too far removed from the involute mass production system, are sensitive to center distance, have high costs for tooling and inspection standardization, lack strong interchangeability, or only optimize a single index without taking into account the negative bias of the common normal, tooth flank clearance, pressure angle range, overlap, and manufacturing feasibility. Summary of the Invention

[0004] The purpose of this invention is to provide a gear pair and tooth profile design method based on involute reference normal offset, so as to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A gear pair based on involute reference normal offset includes a first gear and a second gear, the tooth profiles of the first gear and the second gear being determined by defining a contact path within the meshing plane. The contact path The line of action of a standard involute gear pair is obtained by offsetting it along the normal direction, and is expressed as:

[0007]

[0008] in: For nodes, These are the signed contact path parameters along the line of action; It is a unit vector along the direction of the line of action; The normal unit vector, It is the normal bias function;

[0009] The tooth profiles of the first gear and the second gear are defined by the contact path. It is obtained by inverse calculation based on the conjugate meshing differential relationship;

[0010] The normal bias function The following constraints must be met:

[0011] (1) The function value at the node is zero;

[0012] (2) The first derivative at the node is zero;

[0013] (3) The function value at the endpoint of the contact path is zero.

[0014] A further technical solution is that the normal bias function Adopt the following form:

[0015]

[0016] in The normalized contact path parameters have a value range of [value range missing]. , It is an adjustable parameter used to control the magnitude and direction of the normal offset.

[0017] A further technical solution is that the normal bias function Further expanded to:

[0018]

[0019] in , This is the expansion factor.

[0020] In a further technical solution, the tooth profiles of the first gear and the second gear are determined by the adjustable parameters. Control, the normal bias function To include only the adjustable parameters The parsing function.

[0021] Further technical solutions, maximum amplitude of normal bias With gear module satisfy:

[0022]

[0023] in .

[0024] Further technical solutions, parameters With modulus The range of the ratio is:

[0025] When the gear module hour, ;

[0026] When the gear is a small-module plastic gear or a dissimilar material mating gear pair and the module hour, .

[0027] A further technical solution is that the normal pressure angle of the gear pair... The value ranges from 18° to 25°.

[0028] In a further technical solution, the gear pair is a helical gear pair, and the value of its helix angle β ranges from 0° to 30°.

[0029] A further technical solution is that the normal module of the gear pair... And the total overlap is greater than or equal to 2.

[0030] In a further technical solution, the first gear and the second gear are made of different materials, wherein at least one gear is made of a polymer material or an elastomer material.

[0031] A tooth profile design method includes the following steps:

[0032] Step S1: Input the basic parameters of the gear, including the number of teeth, module, pressure angle, helix angle, displacement coefficient, addendum coefficient, tooth width, material properties, and tolerance parameters;

[0033] Step S2: Apply the normal bias function Adjustable parameters Perform scanning or continuous optimization to make the objective function meet preset constraints. The objective function includes at least a relative curvature index and a sliding heat surcharge index.

[0034] Step S3: Based on the optimized parameters The contact path according to claim 1 The tooth profile curves of the first gear and the second gear are obtained by inversely calculating the conjugate meshing differential relationship;

[0035] Step S4: Output the tooth profile point list or spline curve.

[0036] A further technical solution is that the objective function in step S2 is expressed as:

[0037]

[0038] in The 95th percentile of relative curvature For sliding heat transfer parameters, This is an indicator of pressure angle offset. It includes at least one of the following: insufficient overlap constraint, undercut constraint, loss of meshing constraint due to center distance deviation, excessively pointed tooth tip constraint, excessively thin tooth root constraint, and minimum curvature radius constraint for manufacturing.

[0039] A gear inspection method includes fitting a series of measurement points on the tooth profile. Equivalent values, contact path deviations, and pressure angle drift ranges are used to determine whether a gear belongs to the target gear pair.

[0040] The beneficial effects of this invention are:

[0041] Retain compatibility with involute systems: Since the normal bias function returns to zero at the contact path endpoints, the tooth tip and root regions are consistent with the standard involute tooth profile, allowing production to be carried out using existing involute gear manufacturing equipment and inspection systems without the need to completely replace cutting tools and measuring fixtures.

[0042] Low-degree-of-freedom controllable optimization: The tooth profile shape is controlled by only one adjustable parameter D. Compared with multi-degree-of-freedom methods such as B-splines and NURBS, the parameter adjustment and optimization process is simple and intuitive, and has strong engineering applicability.

[0043] Significantly reduced relative curvature peak: Theoretical calculations show that, in typical embodiments, the 95th percentile of the relative curvature of the main load-bearing area can be reduced by about 33% to 37%, the 95th percentile of the Hertzian contact pressure can be reduced by about 18% to 21%, and the sliding thermal surcharge index can be reduced by about 9% to 10%.

[0044] Minimal overlap loss: The end face overlap decreases by less than 1%, and the total overlap remains basically unchanged, which helps to maintain the smoothness of the transmission.

[0045] Robust design: The optimization of D incorporates center distance tolerance and common normal deviation constraints, so that the gear pair can still maintain good meshing performance under actual manufacturing and assembly deviation conditions.

[0046] Other features and advantages of the present invention will be described in detail in the following detailed description section. Attached Figure Description

[0047] Figure 1 : Schematic diagram of the involute straight contact path and the offset contact path of the present invention.

[0048] Figure 2 The node fitting and endpoint regression characteristics of the curvature fusion function of this invention are shown in the figure. Detailed Implementation

[0049] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0050] Please refer to Figure 1-2 ;

[0051] The present invention aims to propose a gear pair based on involute reference normal offset, in order to reduce the generation of friction and heat during operation;

[0052] Define two gears, with the first gear and the second gear having pitch circle radii of respectively... and center distance The pressure angle is , with nodes As a reference point near the origin, take a unit vector along the direction of the involute's line of action. Its normal bias direction is ;

[0053] The standard involute contact path is:

[0054]

[0055] The contact path of this invention is as follows:

[0056]

[0057] in: For nodes; For the signed contact path parameters along the line of action, Corresponding to the engagement side, Corresponding to the biting-out side;

[0058] It is the normal bias function;

[0059] (1) The involute curve reverts at the node to ensure the stability of the transmission characteristics near the node;

[0060] (2) First-order smooth connections are made at nodes to avoid sharp points or inflections in the contact path.

[0061] (3) The involute curve is reverted at both ends of the contact path to ensure that the tooth tip and root regions are compatible with the standard involute curve, which facilitates manufacturing and testing.

[0062] Constraints (1) and (2) together ensure that the contact path is in first-order contact with the involute action line at the node, that is, the tangent of the contact path at the node coincides with the involute action line; constraint (3) ensures that the contact path returns to the involute at both ends. Since the normal bias function returns to zero at the endpoints of the contact path, the tooth tip and tooth root regions are consistent with the standard involute tooth profile. The existing involute gear manufacturing equipment and inspection system can be used for production without completely replacing the cutting tools and measuring instruments.

[0063] In embodiments of the present invention, the two ends of the contact area are respectively normalized to ,in The parameter values ​​corresponding to the endpoints of the contact path. ;

[0064] Preferably, the normal bias function is:

[0065]

[0066] This function satisfies:

[0067] The function value at the node is zero;

[0068] The first derivative at the node is zero;

[0069] The function value is zero at the endpoints.

[0070] The normalized maximum value of this function is ( (at which point), therefore the maximum magnitude of the normal bias is:

[0071]

[0072] parameter For a given real number, its sign determines the bias direction, and its absolute value determines the bias strength.

[0073] Furthermore, to cover a wider range of tooth profile design needs, the normal bias function Expandable to:

[0074]

[0075] in , For expansion coefficients, when When that happens, the basic function is used. By adjusting , While maintaining the first-order fit of nodes and the regression characteristics of endpoints, the shape of the bias curve can be fine-tuned to adapt to different optimization objectives;

[0076] The tooth profiles of the first gear and the second gear are controlled by the adjustable parameter D, and the normal bias function d(s) is an analytical function that contains only the adjustable parameter D.

[0077] It should be noted that the present invention is not limited to the two specific function forms mentioned above. Other analytic functions that satisfy the constraints (1), (2), and (3) in Embodiment 1 also fall within the protection scope of the present invention. The common technical feature of this type of function family is that it is first-orderly aligned with the involute action line at the node and returns to the involute at the endpoint, so that the entire contact path achieves controllable curvature fusion while retaining the compatibility of the involute system.

[0078] This invention also proposes a method for designing the tooth profile of a conjugate gear, comprising the following steps:

[0079] Step S1: Input the basic parameters of the gear, including the number of teeth, module, pressure angle, helix angle, displacement coefficient, addendum coefficient, tooth width, material properties, and tolerance parameters;

[0080] Step S2: Adjust the normal bias function Adjustable parameters Perform scanning or continuous optimization to ensure that the objective function meets the preset constraints. The objective function must include at least the relative curvature index and the sliding heat surcharge index.

[0081] Step S3: Based on the optimized parameters According to the contact path The tooth profile curves of the first and second gears are obtained by inversely calculating the conjugate meshing differential relationship;

[0082] Step S4: Output the tooth profile point list or spline curve.

[0083] Furthermore, the tooth profiles of the first and second gears are determined by the contact path. Based on the conjugate meshing differential relationship, it is obtained that for a given contact path... Take the contact normal unit vector:

[0084]

[0085] Let the centers of the first gear and the second gear be respectively , Let be a unit vector perpendicular to the gear end face. The rotation angle function satisfying conjugate meshing is determined by the following differential relation:

[0086]

[0087]

[0088] in , Let be the rotation angle functions of the first gear and the second gear, respectively. The tooth profile curves expressed in the body coordinate system are as follows:

[0089]

[0090]

[0091] in Indicates the rotation angle around the center of the gear. For helical gears, the rotation matrix can be combined with the helix angle based on the end face tooth profile. Form a spiral swept surface and according to the normal module The gear pair is a helical gear pair, and its helix angle β ranges from 0° to 30°.

[0092] Normal pressure angle The conversion relationship with the end face parameters determines the end face tooth profile, and the normal pressure angle of the gear pair is determined. The value ranges from 18° to 25°.

[0093] Furthermore, the maximum amplitude of the normal bias With gear module satisfy:

[0094]

[0095] in .

[0096] parameter With modulus The range of the ratio is:

[0097] When the gear module hour, ;

[0098] When the gear is a small-module plastic gear or a dissimilar material mating gear pair and the module hour, .

[0099] Based on the parameter range and recommended parameters for the above implementation methods:

[0100]

[0101] Recommended method for determining the optimal parameters: First, specify the number of teeth, module, pressure angle, displacement coefficient, addendum coefficient, tooth width, material, and center distance / common normal tolerance. Then, evaluate the candidate parameters. Perform scanning or continuous optimization. The objective function can be set as:

[0102]

[0103] in The 95th percentile of relative curvature For sliding heat transfer parameters, This is an indicator of pressure angle offset. It includes at least one of the following: insufficient overlap constraint, undercut constraint, loss of meshing constraint due to center distance deviation, excessively pointed tooth tip constraint, excessively thin tooth root constraint, and minimum curvature radius constraint for manufacturing.

[0104] The following will illustrate this with specific data;

[0105] Example 1: A standard spur gear with 17 teeth / 31 teeth, m=4, and 20°;

[0106]

[0107] Example 2: 0.5 module 11 / 33 helical small module low-noise gear;

[0108]

[0109] The performance metrics in the above embodiments are theoretical calculations or simulation proxy metrics based on the contact path and conjugate tooth profile model, used to illustrate the relative improvement direction.

[0110] This invention only requires adjusting one parameter D to obtain different tooth surface contact characteristics over a wide range, and the computational resources required for one-dimensional optimization are significantly reduced compared to multi-dimensional optimization.

[0111] A single parameter facilitates quality control and inspection during the manufacturing process, and the impact of D on performance indicators can be obtained through simple sensitivity analysis.

[0112] Preferably, the tolerance parameters in step S1 include center distance tolerance and common normal deviation, and the preset constraint conditions include that the gear pair still maintains normal meshing under the conditions of center distance tolerance ±0.03 mm and common normal negative deviation −0.03 to −0.06 mm;

[0113] If the common normal of both gears is between -0.03 mm and -0.06 mm, and the center distance fluctuates by ±0.03 mm, the actual total normal backlash may reach approximately 0.04 mm to 0.14 mm. Under these conditions, the benefits of low noise are easily masked by backlash knocking and load fluctuations. Therefore, D recommends a value of -0.08 mm to -0.10 mm, rather than pursuing the more aggressive value of -0.15 to -0.20 mm.

[0114] In embodiments of the present invention, the first gear and the second gear are made of different materials, wherein at least one gear is made of a polymer material or an elastomer material, which is particularly suitable for small-module dissimilar material gear pairs, such as the pairing of metal gears and polymer gears. In such application scenarios:

[0115] 1. The elastic modulus of polymer gears is much lower than that of metal gears, resulting in greater contact deformation of the tooth surface and a more significant effect of relative curvature;

[0116] 2. Polymer gears have poor thermal conductivity, and sliding thermal excitation can easily lead to excessive temperature rise on the tooth surface;

[0117] 3. Small module gears have relatively low tooth root strength reserves, so it is necessary to avoid excessive increase in tooth root stress;

[0118] 4. Polymer gears are usually injection molded, and the machining accuracy of the mold cavity for the tooth profile is limited by the tool radius and the shrinkage compensation accuracy.

[0119] By using a controllable normal bias function, the peak relative curvature can be reduced while keeping the increase in tooth root stress below 10%, and the tooth profile curve can be directly input into the mold cavity machining system from NURBS splines, making it particularly suitable for the above-mentioned application scenarios.

[0120] This invention also discloses a gear inspection method for determining whether the gear under test belongs to a tooth profile family based on an involute reference normal offset, and for assessing whether its manufacturing deviation is within the allowable range, including the following steps:

[0121] Step T1: Obtain the tooth profile measurement point sequence of the gear under test;

[0122] Preferably, a gear measuring center or a coordinate measuring machine is used to collect several measuring points along the tooth profile direction of the end face of the gear being measured. It is recommended that the number of measuring points be no less than 20, and that they cover the complete tooth profile working area from the tooth root to the tooth tip. For gears with a module m ≥ 1, it is recommended that the spacing between measuring points be no greater than 0.1 mm; for small module gears (m < 1), it is recommended that the spacing between measuring points be no greater than 0.05 mm.

[0123] Step T2: Fit the measured point sequence to the theoretical tooth profile generated based on the contact path, and extract the normal bias function. Adjustable parameters equivalent value ;

[0124] For the gear under test, based on its basic parameters (number of teeth, module, pressure angle, helix angle, displacement coefficient, etc.), the contact path described in this invention is followed. And the conjugate meshing differential relationship, generating the theoretical tooth profile curve, with adjustable parameters For the variable to be fitted, the least squares method or orthogonal distance regression method is used to minimize the sum of squares of the deviations between the measured point sequence and the theoretical tooth profile, that is:

[0125]

[0126] The optimal result The value is denoted as That is, the gear being tested. Equivalent value. The root mean square (RMSE) value of the fitted residuals can be used as an auxiliary evaluation index for the manufacturing accuracy of the tooth profile.

[0127] Step T3: Based on the equivalent value With design value The deviation is used to determine whether the gear under test belongs to the tooth profile family based on the involute reference normal offset.

[0128] Setting a threshold for judgment, generally:

[0129] when When the gear being tested is determined to belong to the target tooth profile family;

[0130] when When the edge is deemed acceptable, a comprehensive judgment must be made based on the contact path deviation and the pressure angle drift range.

[0131] when At that time, it is determined that it does not belong to the target tooth family.

[0132] Furthermore, the contact path deviation and pressure angle drift range can be detected simultaneously. The contact path deviation is obtained by comparing the normal deviation between the measured tooth profile and the theoretical tooth profile at different meshing positions, and the pressure angle drift range is obtained by measuring the pressure angle change at different positions of the tooth profile. By combining the above indicators, the tooth profile classification and manufacturing quality grade of the gear can be determined more accurately.

[0133] Tooth profile parameters of the present invention Simultaneously, it serves as a detection indicator, achieved through tooth profile measurement point fitting. Equivalent values ​​enable closed-loop control of "design parameters - manufacturing parameters - testing parameters," facilitating rapid identification and quality traceability of tooth profile families.

[0134] This detection method is particularly suitable for the following scenarios:

[0135] (1) Sampling or full inspection of mass-produced gears to quickly determine whether the tooth profile meets the design requirements;

[0136] (2) Trial production verification of molds or cutting tools, and reverse the source of manufacturing deviation through the D equivalent value;

[0137] (3) Gear pair pairing screening: the matching effect is evaluated by detecting the D_eff value of the paired gears.

[0138] Noise spectrum comparison tests were conducted on the novel compatible linear tooth profile gear and the ordinary involute tooth profile gear under the same gearbox housing, driving conditions, and test environment. The test results show that the overall spectral trends of the two tooth profiles are basically similar, and the novel compatible linear tooth profile does not introduce significant additional abnormal noise.

[0139] Further comparison reveals that, near the meshing characteristic frequency of approximately 1000 Hz, the spectral peak value of the novel compatible linear tooth profile is significantly lower than that of the conventional involute tooth profile. This result indicates that the novel compatible linear tooth profile can weaken the periodic excitation in the key meshing frequency band, reduce the peak value of meshing noise, and thus improve the dynamic meshing smoothness and noise performance of the gear pair.

[0140] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0141] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style of the specification is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A gear pair, characterized in that, It includes a first gear and a second gear, the tooth profiles of which are determined by defining a contact path within the meshing plane. The contact path The line of action of a standard involute gear pair is obtained by offsetting it along the normal direction, and is expressed as: in: For nodes, These are the signed contact path parameters along the line of action; It is a unit vector along the direction of the line of action; The normal unit vector; It is the normal bias function; The tooth profiles of the first gear and the second gear are defined by the contact path. It is obtained by inverse calculation based on the conjugate meshing differential relationship; The normal bias function The following constraints must be met: (1) The function value at the node is zero; (2) The first derivative at the node is zero; (3) The function value at the endpoint of the contact path is zero.

2. A gear pair according to claim 1, characterized in that: The normal bias function Adopt the following form: in The normalized contact path parameters have a value range of [value range missing]. , It is an adjustable parameter used to control the magnitude and direction of the normal offset.

3. A gear pair according to claim 2, characterized in that, The normal bias function Further expanded to: in , This is the expansion factor.

4. A gear pair according to claim 2, characterized in that, The tooth profiles of the first gear and the second gear are determined by the adjustable parameters. Control, the normal bias function To include only the adjustable parameters The parsing function.

5. A gear pair according to claim 4, characterized in that, Maximum amplitude of normal bias With gear module satisfy: in .

6. A gear pair according to claim 5, characterized in that, parameter With modulus The range of the ratio is: When the gear module hour, ; When the gear is a small-module plastic gear or a dissimilar material mating gear pair and the module hour, .

7. A gear pair according to claim 6, characterized in that, The normal module of the gear pair And the total overlap is greater than or equal to 2.

8. A gear pair according to claim 6, characterized in that, The first gear and the second gear are made of different materials, wherein at least one gear is made of a polymer material or an elastomer material.

9. A tooth profile design method, characterized in that, Includes the following steps: Step S1: Input the basic parameters of the gear, including the number of teeth, module, pressure angle, helix angle, displacement coefficient, addendum coefficient, tooth width, material properties, and tolerance parameters; Step S2: Apply the normal bias function Adjustable parameters Perform scanning or continuous optimization to make the objective function meet preset constraints. The objective function includes at least a relative curvature index and a sliding heat surcharge index. Step S3: Based on the optimized parameters The contact path according to claim 1 The tooth profile curves of the first gear and the second gear are obtained by inversely calculating the conjugate meshing differential relationship; Step S4: Output the tooth profile point list or spline curve.

10. A gear inspection method, characterized in that, Fitting the tooth profile measurement point series The equivalent value, contact path deviation, and pressure angle drift range are used to determine whether the gear belongs to the tooth profile family of the gear pair according to any one of claims 1 to 8.

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