A parameterized design method of variable-thickness involute tooth profile of an incomplete conical gear
Patent Information
- Application Number
- CN202611181754.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-08-05
- Publication Date
- 2026-10-09
AI Technical Summary
通常来说，为了平稳性，需要使用渐开线进行齿廓的参数设置，但在齿廓设计时，需要考虑到作业量和轮齿间的空隙设置，防止啮合传动中轮齿出现运动干扰的情况，这使得设计过程相对复杂，对于一般的齿轮，其轮齿的厚度是一致的，但对于不完全圆锥齿轮，其轮齿的厚度越靠近不完全圆锥齿轮的锥部越小，这会使得设计过程进一步复杂，现有技术对以上因素难以兼顾考虑，导致设计方案的实用性存在一定的提升空间
通过形成基圆的至少一个预备齿廓、从预备齿廓中选择得到特征齿廓以及形成变齿厚部分和基坑部分，从而能在设计时使用渐开线进行设计，保证传动过程中的稳定性，同时，对渐开线的不同设计情况进行筛选，保证传动过程中，啮合的轮齿的运动不会出现干扰，此外，对不完全圆锥齿轮上不同位置的轮齿的厚度进行变更设计，从而保证不完全圆锥齿轮的正常传动，在设计兼顾多种因素，保证设计方案能满足以上因素，且设计过程相对简单，所产生的设计方案的作业量也相对较小，从而能节约加工的时间。
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Figure CN122886220A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of mechanical design technology, specifically to a parametric design method for the variable tooth thickness involute tooth profile of an incomplete bevel gear. Background Technology
[0002] A gear is a mechanical component with teeth on its rim that can continuously mesh to transmit motion and power. Gears have been used in transmission for a long time. In the late 19th century, with the advent of the generating gear cutting method and specialized machine tools and cutting tools using this principle, the smoothness of gear operation became increasingly important as production developed. Generally, for smoothness, involute curves are used to set the parameters of the tooth profile. However, when designing the tooth profile, the workload and the clearance between the teeth must be considered to prevent motion interference during meshing. This makes the design process relatively complex. For general gears, the tooth thickness is uniform, but for incomplete bevel gears, the tooth thickness decreases as it approaches the cone, further complicating the design process. Current technology struggles to simultaneously consider these factors, resulting in room for improvement in the practicality of the design solutions. Summary of the Invention
[0003] To solve the above-mentioned technical problems, a parametric design method for the involute tooth profile of incomplete bevel gears with variable tooth thickness is provided. This technical solution solves the problems mentioned in the background technology.
[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A parametric design method for the variable tooth thickness involute tooth profile of an incomplete bevel gear includes: Obtain a frustum blank for making incomplete bevel gears, take the bottom surface of the frustum blank as the feature surface, and intersect the outer surface of the frustum blank to form a feature circle. To establish an allowable error, at least one base circle concentric with the feature circle is generated within the feature circle, and the radius difference between adjacent base circles is equal to the allowable error. Inscribed in a regular polygon within the base circle, the number of sides of the regular polygon is equal to twice the average number of teeth of the previous gears, rounded down. One of the at least one arcs obtained by dividing the base circle by the vertices of the regular polygon is taken as a local arc. Based on the local arcs and the base circle, an involute segment of the base circle is formed. Based on the involute segment, at least one preliminary tooth profile is formed to form the base circle. Based on the preliminary tooth profile, the tooth profile interval region is analyzed. Based on the tooth profile interval region, the characteristic tooth profile is selected from the preliminary tooth profile. Based on the tooth profile spacing region of the characteristic tooth profile, the characteristic tooth profile is set on the base circle to obtain the characteristic tooth profile layout scheme of the base circle; The frustum blank is completed into a conical blank. Based on the conical blank and the characteristic tooth profile layout scheme, a variable tooth thickness part and a pit part are formed in the frustum blank. Based on the variable tooth thickness part and the pit part, the part of the frustum blank to be removed is formed. The smallest part to be removed is taken as the target parameter, and the gear teeth are generated according to the target parameter.
[0005] Preferably, the formation of the allowable error includes the following steps: The allowable error is obtained by taking the average of the machining errors of at least one gear in the historical machining data.
[0006] Preferably, the involute segment forming the base circle based on the local arc and the base circle includes the following steps: Form a feature rod with a length equal to the circumference of the base circle. Rotate the base circle until the convex part of the local arc on the base circle faces upward. Make the left end point of the feature rod contact the left end point of the local arc, and the feature rod is tangent to the local arc. The feature rod is rolled without slipping on the local arc until the right end of the local arc contacts the feature rod. The trajectory formed by the left end of the feature rod at the left end of the local arc during the movement is taken as the involute segment of the base circle.
[0007] Preferably, the process of forming at least one pre-existing tooth profile based on an involute segment to form the base circle includes the following steps: Take at least one equally divided point on the local arc, connect the equally divided point to the left end point of the local arc to obtain the baseline segment, and take the perpendicular bisector of the baseline segment as the axis of symmetry to obtain the symmetrical segment of the involute segment of the base circle, which is denoted as the adjoint segment. If the involute segment and the accompanying segment do not intersect, connect the endpoints of the involute segment and the accompanying segment away from the local arc to obtain the calibration segment. If the calibration segment is located inside the feature circle, the outline of the area enclosed by the involute segment, the accompanying segment, the calibration segment, and the local arc is used as the preliminary tooth profile.
[0008] Preferably, the step of analyzing the tooth profile interval region based on the prepared tooth profile includes the following steps: The preparatory tooth profile is symmetrical about the horizontal line to obtain the secondary tooth profile. The secondary tooth profile is moved until the lower left vertex of the secondary tooth profile coincides with the lower right vertex of the preparatory tooth profile. Rotate the secondary tooth profile around the lower left vertex until the secondary tooth profile and the prepared tooth profile are tangent at the point of overlap. The secondary tooth profile is rolled without slipping along the accompanying line segment of the prepared tooth profile. The area swept by the secondary tooth profile during the rolling process is taken as the feature region, and the part of the feature region that coincides with the feature circle is taken as the tooth profile interval region.
[0009] Preferably, the step of selecting the characteristic tooth profile from the prepared tooth profile based on the tooth profile interval region includes the following steps: The arc that coincides with the base circle and the prepared tooth profile is taken as the first arc, and the arc on the base circle located inside the tooth profile interval area is taken as the second arc. The arc lengths of the first and second arcs are superimposed to obtain the preliminary arc length. If the circumference of the base circle is an integer multiple of the preliminary arc length, the preliminary tooth profile is taken as the initial tooth profile. The initial tooth profile with the smallest area of the tooth profile interstices is taken as the characteristic tooth profile.
[0010] Preferably, the step of setting the characteristic tooth profile on the base circle to obtain the characteristic tooth profile layout scheme of the base circle includes the following steps: At least one characteristic tooth profile is uniformly arranged on the circumference of the base circle. The characteristic tooth profile is located outside the base circle and is in the same plane as the base circle. The arc length of the base circle between adjacent characteristic tooth profiles is equal to the length of the second arc. This results in a characteristic tooth profile layout scheme for the base circle.
[0011] Preferably, the process of completing the frustum blank into a conical blank includes the following steps: Draw a plane perpendicular to the bottom surface of the frustum blank, passing through the center of the circle; and denote it as the reference plane. The surface of the frustum blank cut by the reference surface is taken as the trapezoidal surface. The two sides of the trapezoidal surface are extended and intersected at the cone point. The cone point is connected to the two vertices at the top of the trapezoidal surface, and together with the entire trapezoidal surface, they form a cone surface. Rotate the conical surface 360 degrees around its axis of symmetry to form a conical blank.
[0012] Preferably, forming the variable tooth thickness portion and the foundation pit portion within the frustum blank includes the following steps: At least one sampling point is uniformly taken on the contour of the characteristic tooth profile, and adjacent sampling points on the contour of the characteristic tooth profile are connected to obtain a sampling line segment. The area enclosed by the sampling line segments on the contour of the characteristic tooth profile is taken as the sampling area. The cone formed with the sampling area as the base and the cone point as the vertex is taken as the reference part. The part of the reference part that coincides with the frustum blank is taken as the variable tooth thickness part. The portion of the base circle that overlaps with the tooth profile interval region is taken as the pit region. The pit regions are arranged in a circumferential array on the base circle. The pit regions are located inside the base circle. The arc length of the base circle sandwiched by adjacent pit regions is equal to the length of the first arc. At least one sampling point is uniformly taken on the outline of the foundation pit area, and adjacent sampling points on the outline of the foundation pit area are connected to obtain a sampling line segment. The area enclosed by the sampling line segments on the outline of the foundation pit area is designated as the sampling area. The cone formed with the sampling area as the base and the cone point as the vertex is designated as the controllable part. The part of the controllable part that overlaps with the frustum blank is designated as the foundation pit part.
[0013] Preferably, the process of forming the portion to be removed from the frustum blank based on the variable tooth thickness portion and the pit portion includes the following steps: The cone with the base circle as the base and the cone point as the vertex is taken as the inner cone, and the part of the cone blank that extends beyond the inner cone is taken as the first part; The portion of the first part that overlaps with the frustum blank is taken as the second part. At least one variable tooth thickness portion is removed from the second part to obtain the third part. The third part is merged with at least one foundation pit portion to obtain the portion of the frustum blank to be removed.
[0014] Compared with the prior art, the beneficial effects of the present invention are as follows: By forming at least one preliminary tooth profile of the base circle, selecting a characteristic tooth profile from the preliminary tooth profile, and forming a variable tooth thickness portion and a base pit portion, the involute curve can be used in the design to ensure stability during transmission. At the same time, different involute curve designs are screened to ensure that the movement of the meshing teeth will not be interfered with during transmission. In addition, the thickness of the teeth at different positions on the incomplete bevel gear is modified to ensure normal transmission of the incomplete bevel gear. The design takes into account multiple factors to ensure that the design scheme meets the above factors, and the design process is relatively simple, resulting in a relatively small workload and saving processing time. Attached Figure Description
[0015] Figure 1 This is a flowchart illustrating the parametric design method for the variable tooth thickness involute tooth profile of the incomplete bevel gear of the present invention. Figure 2 This is a schematic diagram of the process of forming an involute segment of the base circle based on a local arc and a base circle according to the present invention; Figure 3 This is a schematic diagram of the process of forming at least one pre-tooth profile of the base circle based on an involute segment according to the present invention. Figure 4 This is a schematic diagram of the process of analyzing and obtaining the tooth profile interval region based on the pre-prepared tooth profile according to the present invention; Figure 5 This is a schematic diagram of the process of selecting a feature tooth profile from a pre-prepared tooth profile based on the tooth profile interval region according to the present invention. Figure 6 This is a schematic diagram of the process of completing a frustum blank into a conical blank according to the present invention; Figure 7This is a schematic diagram of the process of forming the variable tooth thickness portion and the foundation pit portion in the frustum blank according to the present invention. Figure 8 This is a schematic diagram of the process for forming the portion to be removed from a frustum blank based on the variable tooth thickness portion and the pit portion according to the present invention. Detailed Implementation
[0016] The following description is intended to disclose the invention and enable those skilled in the art to implement it. The preferred embodiments described below are merely examples, and other obvious variations will occur to those skilled in the art.
[0017] Reference Figure 1 As shown, a parametric design method for the variable tooth thickness involute tooth profile of an incomplete bevel gear includes: Obtain a frustum blank for making incomplete bevel gears, take the bottom surface of the frustum blank as the feature surface, and intersect the outer surface of the frustum blank to form a feature circle. To establish an allowable error, at least one base circle concentric with the feature circle is generated within the feature circle, and the radius difference between adjacent base circles is equal to the allowable error. Inscribed in a regular polygon within the base circle, the number of sides of the regular polygon is equal to twice the average number of teeth of the previous gears, rounded down. One of the at least one arcs obtained by dividing the base circle by the vertices of the regular polygon is taken as a local arc. Based on the local arcs and the base circle, an involute segment of the base circle is formed. Based on the involute segment, at least one preliminary tooth profile is formed to form the base circle. Based on the preliminary tooth profile, the tooth profile interval region is analyzed. Based on the tooth profile interval region, the characteristic tooth profile is selected from the preliminary tooth profile. Based on the tooth profile spacing region of the characteristic tooth profile, the characteristic tooth profile is set on the base circle to obtain the characteristic tooth profile layout scheme of the base circle; The frustum blank is completed into a conical blank. Based on the conical blank and the characteristic tooth profile layout scheme, a variable tooth thickness part and a pit part are formed in the frustum blank. Based on the variable tooth thickness part and the pit part, the part of the frustum blank to be removed is formed. The smallest part to be removed is taken as the target parameter, and the gear teeth are generated according to the target parameter.
[0018] In this solution, the design of the teeth on the incomplete bevel gear is required. In fact, it is only necessary to complete the design of the teeth on the bevel gear, because the teeth used by the incomplete bevel gear are the same as the teeth on the bevel gear, and the gap area between adjacent teeth is also the same. The only difference between the two is the number of teeth. The incomplete bevel gear uses the continuous part of the teeth on the bevel gear. Therefore, it is only necessary to complete the design of the teeth on the bevel gear. When designing the teeth on a bevel gear, it is necessary to consider the stability of the transmission, the interference of motion, and the amount of machining work. The stability of a transmission depends primarily on the stability of the force applied during transmission. To illustrate this, consider the gear providing power as the first gear, and its teeth as the first gear teeth. The driven gear is considered the second gear, and its teeth as the second gear teeth. When the first gear teeth move, they contact the second gear teeth, and the force is transmitted along the normal direction of the tangent plane of the contact surface. The contact positions of the first and second gear teeth are the first point and the second point, respectively. The first point is located on the first gear teeth, and the second point is located on the second gear teeth. Therefore, the direction of the force on the first gear teeth is along the normal direction of the tangent plane at the first point, denoted as the first normal direction. The effective direction of the force on the second gear teeth is along the normal direction of the tangent plane at the second point, denoted as the second normal direction. If the profiles of the first and second gear teeth are not specially designed, the first and second normal directions are not parallel. Therefore, the force acting in the first normal direction is the component projected onto the second normal direction. The force acting in the first normal direction is... When the power generated by the first gear tooth is constant, the force in the first normal direction will not change much. However, since the first gear tooth will move, it will drive the second gear tooth in contact with it to move. As a result, the angle between the first and second normal directions will change significantly. Consequently, the component projected onto the second normal direction will change significantly, leading to unstable force on the second gear tooth and unstable rotation. To avoid this situation, an involute curve is used as the basis to design the same profile for the first and second gear teeth. Based on the geometric properties of the involute curve, it can be found that it can ensure that the first and second normal directions are parallel. Therefore, the profile can be determined. However, the design of the tooth profile is not limited to the gear teeth but also includes the part between adjacent gear teeth. This part needs to ensure that the gear teeth will not interfere with the subsequent gear teeth during meshing to achieve a seamless connection. During rotation, the subsequent gear teeth will hinder the movement of the previous gear teeth. Therefore, the design of the tooth profile also includes the part between adjacent gear teeth. The amount of processing work will affect processing efficiency, so it must also be considered. Since bevel gears are machined on a circular platform, they are usually not machined using a cone. The closer to the cone, the smaller the area. However, if the thickness of the gear teeth remains constant, the gap between the gear teeth closer to the cone will be smaller. But since the thickness of the gear teeth remains constant, the gap between the gear teeth near the cone cannot accommodate the thickness of the gear teeth, resulting in the inability to mesh properly for transmission. To avoid this situation, the thickness of the gear teeth needs to be changed according to the surface condition of the circular platform. The corresponding steps will be set up to address the issues mentioned above in the future in order to overcome these problems.
[0019] The steps to establish the allowable error are as follows: The allowable error is obtained by taking the average of the machining errors of at least one gear in the historical machining data.
[0020] Reference Figure 2 As shown, the involute segment forming the base circle, based on the local arc and the base circle, includes the following steps: Form a feature rod with a length equal to the circumference of the base circle. Rotate the base circle until the convex part of the local arc on the base circle faces upward. Make the left end point of the feature rod contact the left end point of the local arc, and the feature rod is tangent to the local arc. The feature rod is rolled without slipping on the local arc until the right end of the local arc contacts the feature rod. The trajectory formed by the left end of the feature rod at the left end of the local arc during the movement is taken as the involute segment of the base circle.
[0021] Rotating the base circle so that the convex portion of the local arc faces upwards ensures consistency in its left-right description. If the convex portion of the local arc faces downwards, the described phenomenon is prone to being reversed. The feature rod remains tangent to the local arc when it does not slide or roll on it. This generates the involute segment of the base circle. Here, at least one base circle concentric with the feature circle is generated within the feature circle. Not all involute segments of the base circles are usable; therefore, they need to be screened in subsequent steps.
[0022] Reference Figure 3 As shown, forming at least one preliminary tooth profile of the base circle based on an involute segment includes the following steps: Take at least one equally divided point on the local arc, connect the equally divided point to the left end point of the local arc to obtain the baseline segment, and take the perpendicular bisector of the baseline segment as the axis of symmetry to obtain the symmetrical segment of the involute segment of the base circle, which is denoted as the adjoint segment. If the involute segment and the accompanying segment do not intersect, connect the endpoints of the involute segment and the accompanying segment away from the local arc to obtain the calibration segment. If the calibration segment is located inside the feature circle, the outline of the area enclosed by the involute segment, the accompanying segment, the calibration segment, and the local arc is used as the preliminary tooth profile.
[0023] The tooth profile is set on the base circle. The tooth profile is symmetrical on both sides and is set with involute segments on both sides. However, the thickness is unknown. Therefore, multiple pre-prepared tooth profiles need to be formed for selection. Since the involute segments and the accompanying segments are the tooth profiles of gear teeth, they must not intersect. In addition, since it is cut and machined, it must be inside the frustum blank. Therefore, the marking segment needs to be located inside the feature circle. If it is outside, the tooth profile cannot be cut and formed. Based on these constraints, at least one pre-prepared tooth profile is formed. Here, we need to further explain the regular polygon inscribed in the base circle. The number of sides of the regular polygon is equal to twice the average number of teeth of the previous gears, rounded down. This is because the gap between teeth can be approximated as two teeth, and the position of the arc divided by each side of the regular polygon is used to set the gap between teeth. Therefore, its number of sides can be set to twice the average number of teeth of the previous gears, rounded down.
[0024] Reference Figure 4 As shown, the analysis of the tooth profile interval region based on the prepared tooth profile includes the following steps: The preparatory tooth profile is symmetrical about the horizontal line to obtain the secondary tooth profile. The secondary tooth profile is moved until the lower left vertex of the secondary tooth profile coincides with the lower right vertex of the preparatory tooth profile. Rotate the secondary tooth profile around the lower left vertex until the secondary tooth profile and the prepared tooth profile are tangent at the point of overlap. The secondary tooth profile is rolled without slipping along the accompanying line segment of the prepared tooth profile. The area swept by the secondary tooth profile during the rolling process is taken as the feature region, and the part of the feature region that coincides with the feature circle is taken as the tooth profile interval region.
[0025] The preparatory tooth profile will pass through a certain area during meshing transmission. This area must be empty; otherwise, it will interfere with the movement of the preparatory tooth profile. Therefore, a secondary tooth profile that meshes with the preparatory tooth profile is generated. Based on its movement, a tooth profile gap region is generated. The secondary tooth profile remains tangent to the preparatory tooth profile during movement.
[0026] Reference Figure 5 As shown, selecting a feature tooth profile from a pre-selected tooth profile based on the tooth profile interval region includes the following steps: The arc that coincides with the base circle and the prepared tooth profile is taken as the first arc, and the arc on the base circle located inside the tooth profile interval area is taken as the second arc. The arc lengths of the first and second arcs are superimposed to obtain the preliminary arc length. If the circumference of the base circle is an integer multiple of the preliminary arc length, the preliminary tooth profile is taken as the initial tooth profile. The initial tooth profile with the smallest area of the tooth profile interstices is taken as the characteristic tooth profile.
[0027] Assuming that the pre-set tooth profiles can be uniformly set on the base circle according to the pre-set tooth profiles and their corresponding tooth profile spacing regions, if the number of pre-set tooth profiles is N, then the number of tooth profile spacing regions is also N. The pre-set tooth profiles contact the base circle with the first arc, and the tooth profile spacing regions occupy the second arc of the base circle. Since the sum of all the first arcs and all the second arcs is the circumference of the base circle, the circumference of the base circle is N times the length of the pre-set arc. If it is not an integer multiple, it means that it is impossible to uniformly set the parameters of the pre-set tooth profiles on the base circle. The gear meshing with the incomplete bevel gear is a bevel gear, which will cause the bevel gear to need to be redesigned. It is impossible to directly sample the parameters of the teeth of the incomplete bevel gear, which will cause design waste. Therefore, feature tooth profiles are selected from at least one pre-set tooth profile generated by a single base circle. That is, for the base circle that has generated pre-set tooth profiles, the feature tooth profile corresponding to the base circle is selected, and its cutting amount is relatively small.
[0028] Setting the feature tooth profile on the base circle to obtain the feature tooth profile layout scheme of the base circle includes the following steps: At least one characteristic tooth profile is uniformly arranged on the circumference of the base circle. The characteristic tooth profile is located outside the base circle and is in the same plane as the base circle. The arc length of the base circle between adjacent characteristic tooth profiles is equal to the length of the second arc. This results in a characteristic tooth profile layout scheme for the base circle.
[0029] Here, the feature tooth profile array is set on the circumference of the base circle.
[0030] Reference Figure 6 As shown, completing the frustum blank into a conical blank includes the following steps: Draw a plane perpendicular to the bottom surface of the frustum blank, passing through the center of the circle; and denote it as the reference plane. The surface of the frustum blank cut by the reference surface is taken as the trapezoidal surface. The two sides of the trapezoidal surface are extended and intersected at the cone point. The cone point is connected to the two vertices at the top of the trapezoidal surface, and together with the entire trapezoidal surface, they form a cone surface. Rotate the conical surface 360 degrees around its axis of symmetry to form a conical blank.
[0031] The trapezoidal surface is a trapezoid, and the two sides can be extended to form an isosceles triangle. Therefore, by rotating, the conical blank can be obtained.
[0032] Reference Figure 7 As shown, forming the variable tooth thickness portion and the foundation pit portion within the frustum blank includes the following steps: At least one sampling point is uniformly taken on the contour of the characteristic tooth profile, and adjacent sampling points on the contour of the characteristic tooth profile are connected to obtain a sampling line segment. The area enclosed by the sampling line segments on the contour of the characteristic tooth profile is taken as the sampling area. The cone formed with the sampling area as the base and the cone point as the vertex is taken as the reference part. The part of the reference part that coincides with the frustum blank is taken as the variable tooth thickness part. The portion of the base circle that overlaps with the tooth profile interval region is taken as the pit region. The pit regions are arranged in a circumferential array on the base circle. The pit regions are located inside the base circle. The arc length of the base circle sandwiched by adjacent pit regions is equal to the length of the first arc. At least one sampling point is uniformly taken on the outline of the foundation pit area, and adjacent sampling points on the outline of the foundation pit area are connected to obtain a sampling line segment. The area enclosed by the sampling line segments on the outline of the foundation pit area is designated as the sampling area. The cone formed with the sampling area as the base and the cone point as the vertex is designated as the controllable part. The part of the controllable part that overlaps with the frustum blank is designated as the foundation pit part.
[0033] The tooth profile of the incomplete bevel gear on the bottom surface of the frustum blank is determined, that is, the characteristic tooth profile, but there are multiple characteristic tooth profiles, and further screening is required. The formation of the variable tooth thickness portion and the pit portion is similar. Taking the pit portion as an example, the portion outside the base circle except for the characteristic tooth profile needs to be removed. However, there is an overlap between the base circle and the tooth profile interval area. The portion of the tooth profile interval area inside the base circle needs to be considered separately. The portion of the tooth profile interval area outside the base circle is necessarily removed and does not need to be considered. Thus, the pit area is obtained. The sampling area is a polygon. When the number of sampling points is sufficient, the pit area is approximately equal to the sampling area. Therefore, the pit portion is a configuration obtained by changing the characteristic tooth profile at different positions according to the trend of the frustum blank. Its thickness is smaller as it gets closer to the cone, thus meeting the requirements.
[0034] Reference Figure 8 As shown, based on the variable tooth thickness portion and the foundation pit portion, the process of forming the portion to be removed from the frustum blank includes the following steps: The cone with the base circle as the base and the cone point as the vertex is taken as the inner cone, and the part of the cone blank that extends beyond the inner cone is taken as the first part; The portion of the first part that overlaps with the frustum blank is taken as the second part. At least one variable tooth thickness portion is removed from the second part to obtain the third part. The third part is merged with at least one foundation pit portion to obtain the portion of the frustum blank to be removed.
[0035] Based on the geometric relationships of solids, the rationale for obtaining the part to be removed is easy to understand, therefore, it will not be elaborated upon.
[0036] Furthermore, this solution also proposes a storage medium on which a computer-readable program is stored. When the computer-readable program is invoked, it executes the above-mentioned parametric design method for the variable tooth thickness involute tooth profile of incomplete bevel gears.
[0037] It is understandable that the storage medium can be a magnetic medium, such as a floppy disk, hard disk, or magnetic tape; an optical medium, such as a DVD; or a semiconductor medium, such as a solid-state drive (SSD).
[0038] In summary, the advantages of this invention are as follows: by forming at least one preliminary tooth profile of the base circle, selecting a characteristic tooth profile from the preliminary tooth profile, and forming a variable tooth thickness portion and a base pit portion, an involute curve can be used in the design, ensuring stability during transmission. Simultaneously, different involute curve designs are screened to ensure that the movement of the meshing teeth does not interfere during transmission. Furthermore, the thickness of the teeth at different positions on the incomplete bevel gear is modified to ensure normal transmission of the incomplete bevel gear. The design considers multiple factors, ensuring that the design scheme meets the above requirements. The design process is relatively simple, and the workload of the resulting design scheme is relatively small, thus saving processing time.
[0039] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention. The scope of protection claimed by the appended claims and their equivalents is defined.
Claims
1. A parametric design method for the involute tooth profile of an incomplete bevel gear with variable tooth thickness, characterized in that, include: Obtain a frustum blank for making incomplete bevel gears, take the bottom surface of the frustum blank as the feature surface, and intersect the outer surface of the frustum blank to form a feature circle. To establish an allowable error, at least one base circle concentric with the feature circle is generated within the feature circle, and the radius difference between adjacent base circles is equal to the allowable error. Inscribed in a regular polygon within the base circle, the number of sides of the regular polygon is equal to twice the average number of teeth of the previous gears, rounded down. One of the at least one arcs obtained by dividing the base circle by the vertices of the regular polygon is taken as a local arc. Based on the local arcs and the base circle, an involute segment of the base circle is formed. Based on the involute segment, at least one preliminary tooth profile is formed to form the base circle. Based on the preliminary tooth profile, the tooth profile interval region is analyzed. Based on the tooth profile interval region, the characteristic tooth profile is selected from the preliminary tooth profile. Based on the tooth profile spacing region of the characteristic tooth profile, the characteristic tooth profile is set on the base circle to obtain the characteristic tooth profile layout scheme of the base circle; The frustum blank is completed into a conical blank. Based on the conical blank and the characteristic tooth profile layout scheme, a variable tooth thickness part and a pit part are formed in the frustum blank. Based on the variable tooth thickness part and the pit part, the part of the frustum blank to be removed is formed. The smallest part to be removed is taken as the target parameter, and the gear teeth are generated according to the target parameter.
2. The parametric design method for the variable tooth thickness involute tooth profile of an incomplete bevel gear according to claim 1, characterized in that, The formation of the allowable error includes the following steps: The allowable error is obtained by taking the average of the machining errors of at least one gear in the historical machining data.
3. The parametric design method for the variable tooth thickness involute tooth profile of an incomplete bevel gear according to claim 2, characterized in that, The process of forming the involute segment of the base circle based on the local arc and the base circle includes the following steps: Form a feature rod with a length equal to the circumference of the base circle. Rotate the base circle until the convex part of the local arc on the base circle faces upward. Make the left end point of the feature rod contact the left end point of the local arc, and the feature rod is tangent to the local arc. The feature rod is rolled without slipping on the local arc until the right end of the local arc contacts the feature rod. The trajectory formed by the left end of the feature rod at the left end of the local arc during the movement is taken as the involute segment of the base circle.
4. The parametric design method for the variable tooth thickness involute tooth profile of an incomplete bevel gear according to claim 3, characterized in that, The process of forming at least one pre-existing tooth profile based on an involute segment to form a base circle includes the following steps: Take at least one equally divided point on the local arc, connect the equally divided point to the left end point of the local arc to obtain the baseline segment, and take the perpendicular bisector of the baseline segment as the axis of symmetry to obtain the symmetrical segment of the involute segment of the base circle, which is denoted as the adjoint segment. If the involute segment and the accompanying segment do not intersect, connect the endpoints of the involute segment and the accompanying segment away from the local arc to obtain the calibration segment. If the calibration segment is located inside the feature circle, the outline of the area enclosed by the involute segment, the accompanying segment, the calibration segment, and the local arc is used as the preliminary tooth profile.
5. The parametric design method for the involute tooth profile of an incomplete bevel gear with variable tooth thickness according to claim 4, characterized in that, The process of analyzing the tooth profile interval region based on the pre-existing tooth profile includes the following steps: The preparatory tooth profile is symmetrical about the horizontal line to obtain the secondary tooth profile. The secondary tooth profile is moved until the lower left vertex of the secondary tooth profile coincides with the lower right vertex of the preparatory tooth profile. Rotate the secondary tooth profile around the lower left vertex until the secondary tooth profile and the prepared tooth profile are tangent at the point of overlap. The secondary tooth profile is rolled without slipping along the accompanying line segment of the prepared tooth profile. The area swept by the secondary tooth profile during the rolling process is taken as the feature region, and the part of the feature region that coincides with the feature circle is taken as the tooth profile interval region.
6. The parametric design method for the variable tooth thickness involute tooth profile of an incomplete bevel gear according to claim 5, characterized in that, The process of selecting a feature tooth profile from a pre-prepared tooth profile based on the tooth profile interval region includes the following steps: The arc that coincides with the base circle and the prepared tooth profile is taken as the first arc, and the arc on the base circle located inside the tooth profile interval area is taken as the second arc. The arc lengths of the first and second arcs are superimposed to obtain the preliminary arc length. If the circumference of the base circle is an integer multiple of the preliminary arc length, the preliminary tooth profile is taken as the initial tooth profile. The initial tooth profile with the smallest area of the tooth profile interstices is taken as the characteristic tooth profile.
7. The parametric design method for the involute tooth profile of an incomplete bevel gear with variable tooth thickness according to claim 6, characterized in that, The step of setting the characteristic tooth profile on the base circle to obtain the characteristic tooth profile layout scheme of the base circle includes the following steps: At least one characteristic tooth profile is uniformly arranged on the circumference of the base circle. The characteristic tooth profile is located outside the base circle and is in the same plane as the base circle. The arc length of the base circle between adjacent characteristic tooth profiles is equal to the length of the second arc. This results in a characteristic tooth profile layout scheme for the base circle.
8. The parametric design method for the variable tooth thickness involute tooth profile of an incomplete bevel gear according to claim 7, characterized in that, The process of completing the frustum blank into a conical blank includes the following steps: Draw a plane perpendicular to the bottom surface of the frustum blank, passing through the center of the circle; and denote it as the reference plane. The surface of the frustum blank cut by the reference surface is taken as the trapezoidal surface. The two sides of the trapezoidal surface are extended and intersected at the cone point. The cone point is connected to the two vertices at the top of the trapezoidal surface, and together with the entire trapezoidal surface, they form a cone surface. Rotate the conical surface 360 degrees around its axis of symmetry to form a conical blank.
9. A parametric design method for the involute tooth profile of an incomplete bevel gear with variable tooth thickness according to claim 8, characterized in that, The process of forming the variable tooth thickness portion and the foundation pit portion within the frustum blank includes the following steps: At least one sampling point is uniformly taken on the contour of the characteristic tooth profile, and adjacent sampling points on the contour of the characteristic tooth profile are connected to obtain a sampling line segment. The area enclosed by the sampling line segments on the contour of the characteristic tooth profile is taken as the sampling area. The cone formed with the sampling area as the base and the cone point as the vertex is taken as the reference part. The part of the reference part that coincides with the frustum blank is taken as the variable tooth thickness part. The portion of the base circle that overlaps with the tooth profile interval region is taken as the pit region. The pit regions are arranged in a circumferential array on the base circle. The pit regions are located inside the base circle. The arc length of the base circle sandwiched by adjacent pit regions is equal to the length of the first arc. At least one sampling point is uniformly taken on the outline of the foundation pit area, and adjacent sampling points on the outline of the foundation pit area are connected to obtain a sampling line segment. The area enclosed by the sampling line segments on the outline of the foundation pit area is designated as the sampling area. The cone formed with the sampling area as the base and the cone point as the vertex is designated as the controllable part. The part of the controllable part that overlaps with the frustum blank is designated as the foundation pit part.
10. The parametric design method for the variable tooth thickness involute tooth profile of an incomplete bevel gear according to claim 9, characterized in that, The process of forming the portion to be removed from the frustum blank based on the variable tooth thickness portion and the pit portion includes the following steps: The cone with the base circle as the base and the cone point as the vertex is taken as the inner cone, and the part of the cone blank that extends beyond the inner cone is taken as the first part; The portion of the first part that overlaps with the frustum blank is taken as the second part. At least one variable tooth thickness portion is removed from the second part to obtain the third part. The third part is merged with at least one foundation pit portion to obtain the portion of the frustum blank to be removed.