Finishing technology of incomplete teeth of worm based on spatial Archimedean spiral

Abstract

The present invention relates to the technical field of worm design and processing, and discloses a finishing process for an incomplete tooth of a worm based on a space Archimedean spiral, comprising the following steps: step 1, establishing a three-dimensional model of the worm and determining the position of the incomplete tooth; step 2, obtaining the following information of the incomplete tooth: the angle between the projection of the starting point and the end point of the incomplete tooth and the origin coordinate line on the xy plane and the x-axis, which are respectively recorded as θ min and θ max ; The maximum value of the incomplete tooth in the z-axis direction z max With the minimum value z min ; Maximum radius r of incomplete tooth max and the minimum radius r min ; Step 3, at the maximum radius r max and the minimum radius r min A conical surface is constructed between the sections. The process of the present invention can significantly improve the appearance quality of the incomplete teeth on the end face of the worm, making the product more beautiful, while reducing the subsequent manual grinding workload, improving processing efficiency and product quality. The solution proposed by the present invention is suitable for the tail processing of worms of any size and shape, and has strong applicability.

Description

Technical Field

[0001] The invention relates to the technical field of worm design and processing, and in particular to a finishing process for incomplete teeth of a worm based on a spatial Archimedean spiral. Background Art

[0002] Worm gear transmission is widely used in various industries due to its unique characteristics, including speed reduction in a small space, low noise, high stability and high load capacity. In the worm manufacturing process, the incomplete teeth on the end face of the worm often form sharp edges due to the change in the diameter of the base body, affecting the appearance quality of the product. On the end face of the worm, due to the change in the diameter of the worm base at this position, the incomplete teeth with very sharp tooth tops appear. Figure 1 As shown in the figure, the worm gear is manufactured by combining straight line milling with manual grinding. Figure 2 shown.

[0003] Traditional methods mostly use straight line milling combined with manual grinding, but this method makes the product appearance quality poor and the processing efficiency low. The existing technology lacks a clear solution, and no relevant solution has been found by consulting the materials. Therefore, the above problem has not been effectively solved for a long time for those skilled in the art. Summary of the invention

[0004] In order to improve the appearance quality, processing technology and processing efficiency of the incomplete teeth on the end face of the worm, the edges and corners at the tooth root are eliminated to make the transition smoother and more natural. The present invention proposes a finishing process for incomplete teeth of the worm based on the spatial Archimedean spiral. By constructing a revolving surface and finding a spatial transition curve tangent to the tooth root circle on the surface, the formation of edges and corners at the tooth root is avoided, thereby solving the problem of steep transition surface and poor appearance of the worm in the traditional process. This process not only improves the appearance quality and processing efficiency, but also optimizes the processing technology.

[0005] The present invention is implemented by the following technical solution: The present invention proposes a finishing process for an incomplete tooth of a worm based on a spatial Archimedean spiral, comprising the following steps:

[0006] Step 1: Establish a three-dimensional model of the worm and determine the position of the incomplete teeth;

[0007] Step 2: Obtain the following information of the incomplete tooth:

[0008] The angles between the projections of the lines connecting the starting point and the end point of the incomplete tooth and the origin coordinates on the xy plane and the x-axis are denoted as θ min and θ max ;

[0009] The maximum value of the incomplete tooth in the z-axis direction max With the minimum value zmin ;

[0010] The maximum radius r of an incomplete tooth max and the minimum radius r min ;

[0011] Step 3: At the maximum radius r max and the minimum radius r min A conic surface is constructed between the sections where the conic surface is located, and a transition curve is obtained on the conic surface; the generatrix of the conic surface is a straight line, and the generatrix of the conic surface is parallel to the maximum radius r max and the minimum radius r min The cross-section circles intersect;

[0012] Step 4: The transition curve obtained in step 3 is stretched to both sides to obtain a transition surface, and the incomplete teeth are cut off along the transition surface to obtain a smooth transition surface.

[0013] The step 3 includes the following sub-steps:

[0014] Step 301, construct a space curve equation:

[0015]

[0016] The above formula is a space Archimedean spiral, and the curve is distributed on a conic surface, where θ is the angle between the point after the projection of the space curve on the xy plane is discretized and the line connecting the origin and the x-axis, r is the distance from a point on the space curve to the z-axis, and p is the spiral parameter;

[0017] Step 302, determine the rotation direction of the worm, calculate the values ​​of parameters a, b, and p according to the corresponding calculation formula, substitute them into the spatial curve equation, and finally obtain the transition curve equation;

[0018] The transition curve equation is calculated as follows:

[0019] If the worm is right-handed

[0020] The negative transition curve of z on the right-handed worm gear must satisfy the relationship

[0021]

[0022] The z-direction transition curve on the right-hand worm gear must satisfy the relationship

[0023]

[0024] And the right-handed helix parameter p is obtained by the following formula

[0025]

[0026] If the worm is left-handed

[0027] The negative transition curve of z on the left-handed worm gear must satisfy the relationship:

[0028]

[0029] The z-positive transition curve on the left-handed worm gear must satisfy the relationship

[0030]

[0031] For the left-handed helix parameter p, it is obtained from

[0032]

[0033] The tail of the worm is finished by the above scheme. The worm after the finishing treatment is not only beautiful, but also greatly improves the processing efficiency. Compared with the original method of rough processing on a gantry milling machine through multi-segment broken line processing, the position of the worm needs to be adjusted manually every once in a while, which is time-consuming and labor-intensive. When the worm is processed by the finishing method of the present invention, it can be processed and formed in one time, saving rough processing time and the workload of fitters in the post-processing stage is greatly reduced, which greatly reduces time and labor costs, and plays a role in reducing costs and increasing efficiency for enterprises.

[0034] Compared with the prior art, the present invention has the following beneficial effects:

[0035] Beneficial effects of the invention: The process of the invention can significantly improve the appearance quality of the incomplete teeth on the end face of the worm, making the product more beautiful, while reducing the workload of subsequent manual grinding, improving processing efficiency and product quality. The solution proposed by the invention is suitable for the tail processing of worms of any size and shape, and has strong applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 This is a schematic diagram of the structure of the sharp incomplete teeth at the tail of the worm that need to be processed in the present invention;

[0037] Figure 2 The figure is a schematic diagram of the tail structure of the worm processed by the original technology;

[0038] Figure 3 For z max 、z min 、r max 、r min ,θ max and θ min Schematic diagram of the position on the worm;

[0039] Figure 4 is a schematic diagram of the transition curve;

[0040] Figure 5A three-dimensional schematic diagram of cutting off an incomplete tooth along the transition surface;

[0041] Figure 6 It is a schematic diagram of the tail of the worm after the tail treatment by the method proposed by the present invention;

[0042] Figure 7 Schematic diagram of the overall process flow proposed for this scheme. DETAILED DESCRIPTION

[0043] The present invention is further described below in conjunction with the accompanying drawings and specific implementation methods. It should be noted that, under the premise of no conflict, the various embodiments or technical features described below can be arbitrarily combined to form a new embodiment.

[0044] Example:

[0045] Reference Figure 1-7 , this scheme proposes a finishing process for incomplete teeth of worm based on spatial Archimedean spiral, including the following steps:

[0046] Step 1: Establish a three-dimensional model of the worm and determine the position of the incomplete teeth;

[0047] Step 2: Obtain the following information of the incomplete tooth:

[0048] The angles between the projections of the lines connecting the starting point and the end point of the incomplete tooth and the origin coordinates on the xy plane and the x-axis are denoted as θ min and θ max ;

[0049] The maximum value of the incomplete tooth in the z-axis direction max With the minimum value z min ;

[0050] The maximum radius r of an incomplete tooth max and the minimum radius r min ;

[0051] Step 3: At the maximum radius r max and the minimum radius r min A conic surface is constructed between the sections where the conic surface is located, and a transition curve is obtained on the conic surface; the generatrix of the conic surface is a straight line, and the generatrix of the conic surface is parallel to the maximum radius r max and the minimum radius r min The cross-section circles intersect;

[0052] Step 4: The transition curve obtained in step 3 is stretched to both sides to obtain a transition surface, and the incomplete teeth are cut off along the transition surface to obtain a smooth transition surface.

[0053] Specifically, the staff designs the milling tool path along the transition surface, determines the cutting depth according to the material thickness between the surface and the incomplete tooth, and completes the processing through the milling machine. The above solution does not require manual movement of the workpiece for multiple processing, which greatly reduces the workload of the fitter.

[0054] The step 3 includes the following sub-steps:

[0055] Step 301, construct a space curve equation:

[0056]

[0057] The above formula is a space Archimedean spiral, and the curve is distributed on a conic surface, where θ is the angle between the point after the projection of the space curve on the xy plane is discretized and the line connecting the origin and the x-axis, r is the distance from a point on the space curve to the z-axis, and p is the spiral parameter;

[0058] Step 302, determine the rotation direction of the worm, calculate the values ​​of parameters a, b, and p according to the corresponding calculation formula, substitute them into the spatial curve equation, and finally obtain the transition curve equation;

[0059] The calculation formula is as follows:

[0060] If the worm is right-handed

[0061] The negative transition curve of z on the right-handed worm gear must satisfy the relationship

[0062]

[0063] The z-direction transition curve on the right-hand worm gear must satisfy the relationship

[0064]

[0065] And the right-handed helix parameter p is obtained by the following formula

[0066]

[0067] If the worm is left-handed

[0068] The negative transition curve of z on the left-handed worm gear must satisfy the relationship:

[0069]

[0070] The z-positive transition curve on the left-handed worm gear must satisfy the relationship

[0071]

[0072] For the left-handed helix parameter p, it is obtained from

[0073]

[0074] The curve obtained by the above scheme is not tangent to the tooth root circle, and sharp corners will appear at the tooth root. However, the process of the present invention can significantly improve the appearance quality of the incomplete teeth on the end face of the worm, making the product more beautiful, while reducing the subsequent manual grinding workload, improving processing efficiency and product quality.

[0075] The above-mentioned embodiments are only preferred embodiments of the present invention and cannot be used to limit the scope of protection of the present invention. Any non-substantial changes and substitutions made by technicians in this field on the basis of the present invention shall fall within the scope of protection required by the present invention.

Claims

1. A finishing process for incomplete teeth of a worm based on a spatial Archimedean spiral, characterized in that: The steps include: Step 1: Establish a three-dimensional model of the worm and determine the position of the incomplete teeth; Step 2: Obtain the following information of the incomplete tooth: The angles between the projections of the lines connecting the starting point and the end point of the incomplete tooth and the origin coordinates on the xy plane and the x-axis are denoted as θ min and θ max ; The maximum value of the incomplete tooth in the z-axis direction max With the minimum value z min ; The maximum radius r of an incomplete tooth max and the minimum radius r min ; Step 3: At the maximum radius r max and the minimum radius r min A conic surface is constructed between the sections where the conic surface is located, and a transition curve is obtained on the conic surface; the generatrix of the conic surface is a straight line, and the generatrix of the conic surface is parallel to the maximum radius r max and the minimum radius r min The cross-section circles intersect; Step 4, stretching the transition curve obtained in step 3 to both sides to obtain a transition surface, and cutting off the incomplete teeth along the transition surface to obtain a smooth transition surface; The step 3 includes the following sub-steps: Step 301, construct a space curve equation: The above formula is the equation of the space Archimedean spiral. The curve is distributed on the conic surface, where θ is the angle between the point after the projection of the space curve on the xy plane is discretized and the line connecting the origin and the x-axis, r is the distance from a point on the space curve to the z-axis, and p is the spiral parameter; Step 302, determine the rotation direction of the worm, calculate the values ​​of parameters a, b, and p according to the corresponding calculation formula, substitute them into the spatial curve equation, and finally obtain the transition curve equation.

2. The finishing process for incomplete teeth of a worm based on a spatial Archimedean spiral as claimed in claim 1, characterized in that: The calculation formula of the transition curve equation is as follows: If the worm is right-handed The negative transition curve of z on the right-handed worm gear must satisfy the relationship The z-direction transition curve on the right-handed worm gear must satisfy the relationship And the right-handed helix parameter p is obtained by the following formula If the worm is left-handed The negative transition curve of z on the left-handed worm gear must satisfy the relationship: The z-positive transition curve on the left-handed worm gear must satisfy the relationship For the left-handed helix parameter p, it is obtained from

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