Treatment process for the incomplete tooth ending of a worm based on a spatial Galilean helix

Abstract

The present invention relates to the technical field of worm design and processing, and discloses a process for finishing the incomplete teeth of a worm based on a spatial Galilean helix, including the following steps: 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 teeth. The present invention constructs a revolving surface using the root circle and the addendum circle of the incomplete teeth, searches for a transition curve on this surface, selects the tangent point of the transition curve and the root circle, and establishes and solves a space curve equation according to the tangency condition. Finally, a space curve tangent to the root circle can be obtained. The tooth root at the incomplete part of the end of the worm processed by the method proposed in this solution will not have edges and corners, making the product more beautiful. At the same time, it reduces the subsequent manual grinding workload, improves the processing efficiency and product quality. The solution proposed by the present invention is applicable to the tail treatment of worms of any size and shape, and has strong applicability.

Description

Technical Field

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

[0002] Worm gear drives operate smoothly and quietly, so they are widely used in the fields of hydraulics, hoisting and transportation machinery, automobiles, machine tools, etc. During the manufacturing process of a worm, due to the change in the base diameter, the incomplete teeth on the end face of the worm often form sharp edges, affecting the appearance quality of the product. The incomplete teeth with sharp tooth tips, as shown in Figure 1 and the worm manufactured by the method of combining straight-line milling and manual grinding, as shown in Figure 2

[0003] In view of the above problems, there is a lack of a clear solution in the prior art, and no relevant solutions are found by consulting materials. Therefore, the above problems have not been effectively solved by those skilled in the art for a long time. Although most current worm manufacturing enterprises adopt the method of combining multi-segment straight-line combination transition and fitter trimming to process the tail of the worm, this method is not satisfactory in terms of appearance quality and processing efficiency. Therefore, there is an urgent need to propose a beautiful and efficient finishing method to improve the processing efficiency and appearance quality of the worm. Summary of the Invention

[0004] To solve the technical problems raised in the background art, the present invention provides a finishing process for incomplete teeth of a worm based on a spatial Galilean spiral.

[0005] The present invention is implemented by adopting the following technical solutions: A finishing process for incomplete teeth of a worm based on a spatial Galilean spiral includes 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 teeth:

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

[0009] The maximum value z max and the minimum value z min of the incomplete teeth in the z-axis direction;

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

[0011] Step 3: At the maximum radius r max ​and the minimum radius r min Construct a conical surface between the cross-sections where it is located, and obtain a transition curve on this conical surface; the generatrix of the conical surface is not a straight line, and the generatrix of the conical surface is tangent to the cross-sectional circles where the maximum radius r max and the minimum radius r min are located;

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

[0013] Optionally, the generatrix of the conical surface is a parabola.

[0014] Specifically, Step 3 includes the following sub-steps:

[0015] Step 301: Construct a space curve equation:

[0016]

[0017] The above formula is a space Galileo spiral, and this curve is distributed on a revolving surface with a parabola as the generatrix, where θ is the angle between the line connecting the discrete points of the projection of the space curve on the XY plane and the origin and the X axis

[0018] r is the distance from a point on the space curve to the z-axis, and p is the spiral parameter;

[0019] Step 302: Determine the helix direction of the worm, and according to the corresponding calculation formula, calculate the values of parameters a, b, c, and p, and substitute them into the space curve equation to finally obtain the transition curve equation;

[0020] The calculation formula is as follows

[0021] If the helix direction of the worm is right-handed

[0022] The z-negative transition curve on the right-handed worm needs to satisfy the relationship:

[0023]

[0024] The z-positive transition curve on the right-handed worm needs to satisfy the relationship:

[0025]

[0026] For the right-handed spiral parameter p, it can be obtained from the following formula:

[0027]

[0028] If the helix direction of the worm is left-handed

[0029] The z-negative transition curve on the left-handed worm needs to satisfy the relationship:

[0030]

[0031] The positive z transition curve on the left-handed worm needs to satisfy the relationship:

[0032]

[0033] For the left-handed helix parameter p, it can be obtained by the following formula:

[0034]

[0035] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0036] The present invention constructs a revolving surface by using the root circle and the tip circle of the incomplete teeth, and searches for the transition curve on this surface. By selecting the tangent point of the transition curve and the root circle, and establishing and solving the space curve equation according to the tangency condition, the space curve tangent to the root circle can be finally obtained. Therefore, there will be no sharp corners at the root of the incomplete part at the end of the worm processed by the method proposed in this solution.

[0037] The solution proposed by the present invention performs finishing treatment on the tail of the worm, making the worm not only more beautiful, but also greatly improving the processing efficiency, saving the rough machining time, and greatly reducing the fitter workload in the post-processing stage, significantly reducing the time and labor costs, and playing a role in cost reduction and efficiency increase for the enterprise.

[0038] The solution proposed by the present invention is applicable to the tail treatment of worms with any size and shape, and has strong applicability. Description of the Drawings

[0039] Figure 1 The sharp incomplete teeth at the tail of the worm that need to be processed in the present invention;

[0040] Figure 2 The tail of the worm processed by the original technology;

[0041] Figure 3 For z max 、z min 、r max 、r min 、θ max and θ min Schematic diagram of the positions on the worm

[0042] Figure 4 Schematic diagram of the transition curve;

[0043] Figure 5 Three-dimensional schematic diagram of cutting off the incomplete teeth along the transition surface;

[0044] Figure 6Schematic diagram of the worm tail after the finishing process of the present invention;

[0045] Figure 7 Physical diagram after the finishing process of the present invention. Detailed implementation manners

[0046] Next, in combination with the accompanying drawings and specific implementation manners, the present invention will be further described. It should be noted that, on the premise of no conflict, the following-described embodiments or technical features can be arbitrarily combined to form new embodiments.

[0047] Embodiment:

[0048] Referring to Figures 1-7 , this solution proposes a finishing process for the incomplete teeth of a worm based on a spatial Galilean helix, including the following steps:

[0049] Step 1: Establish a three-dimensional model of the worm and determine the position of the incomplete teeth;

[0050] Step 2: Obtain the following information of the incomplete teeth:

[0051] The angles between the lines connecting the starting point and the ending point of the incomplete teeth to the origin coordinate and the x-axis in the xy plane are respectively denoted as θ min and θ max ;

[0052] The maximum value z max and the minimum value z min of the incomplete teeth in the z-axis direction;

[0053] The maximum radius r max and the minimum radius r min of the incomplete teeth;

[0054] Step 3: Construct a conical surface between the cross-sections where the maximum radius r max and the minimum radius r min are located, and obtain a transition curve on this conical surface; the generatrix of the conical surface is non-linear, and the generatrix of the conical surface is tangent to the cross-sectional circles where the maximum radius r max , the minimum radius r min are located;

[0055] Step 4: Stretch the transition curve obtained in Step 3 to both sides to obtain a transition surface, and cut off the incomplete teeth along the transition surface to obtain a smooth transition surface.

[0056] Optionally, the generatrix of the conical surface is a parabola.

[0057] In this solution, Step 3 includes the following sub-steps:

[0058] Step 301: Construct a space curve equation:

[0059]

[0060] The above equation represents a space Galileo helix, which is distributed on a surface of revolution with a parabolic generatrix. Here, θ is the angle between the line connecting a discrete point on the projection of the space curve on the XY plane and 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 helix parameter;

[0061] Step 302: Determine the helix direction of the worm. According to the corresponding calculation formulas, calculate the values of parameters a, b, c, and p, and substitute them into the space curve equation to finally obtain the transition curve equation;

[0062] Specifically, use circles r1 and r2 to construct a surface of revolution (with a non-linear generatrix). Search for the transition curve on this surface. By selecting special positions (establishing and solving the tangent point equations for a, b, c according to the tangency conditions), a space curve tangent to the root circle can be obtained, and there will be no sharp corners at the root. The transition curve of this solution is as Figure 4 shown. Calculate r min , r max , θ min , θ max , z min and z max theoretically or measure them in the 3D model and the manufactured worm, then determine the helix direction of the worm and substitute it into the following equations to solve, and a space curve tangent to the root circle can be obtained. Therefore, there will be no sharp corners at the root. The 3D model of the worm obtained by processing with this solution is as Figure 5 , 6 shown.

[0063] The calculation formulas are as follows

[0064] If the helix direction of the worm is right-handed

[0065] The negative z-direction transition curve on a right-handed worm needs to satisfy the relationship:

[0066]

[0067] The positive z-direction transition curve on a right-handed worm needs to satisfy the relationship:

[0068]

[0069] For the right-handed helix parameter p, it can be obtained from the following formula:

[0070]

[0071] If the helix direction of the worm is left-handed

[0072] The z-negative transition curve on the left-handed worm must satisfy the relationship:

[0073]

[0074] The z-positive transition curve on the left-handed worm must satisfy the relationship:

[0075]

[0076] For the left-handed helix parameter p, it can be obtained by the following formula:

[0077]

[0078] The worm tail after finishing treatment obtained by using this solution is as Figure 7 shown.

[0079] The worm after finishing treatment is not only beautiful, but also greatly improves the processing efficiency. When rough machining on a gantry milling machine according to the original method of processing with multiple broken lines, it is necessary to manually adjust the position of the worm at regular intervals, which is time-consuming and laborious. While for the worm before being processed by the finishing method of the present invention, it can be processed into a finished product at one time, saving the rough machining time and greatly reducing the workload of fitters in the post-processing stage, greatly reducing the time and labor costs, and playing a role in cost reduction and efficiency improvement for the enterprise.

[0080] The above-mentioned embodiments are only the 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 those skilled in the art 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 space Galilean 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, and a transition curve is obtained on the conic surface; the generatrix of the conic surface is not a straight line, and the generatrix of the conic surface and the maximum radius r max、 Minimum radius r min The cross-section circle is tangent to it; 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 space Galilean spiral, which is distributed on the surface of revolution whose generatrix is ​​a parabola, where θ is the angle between the line connecting the discrete point of the projection of the space curve on the XY plane and 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, c, and p according to the corresponding calculation formula, substitute them into the spatial curve equation, and finally obtain the transition curve equation; The calculation formula 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-positive transition curve on the right-hand worm gear must satisfy the relationship: The right-handed helix parameter p can be 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: The left-handed helix parameter p can be obtained by the following formula:

2. The process for finishing incomplete teeth of a worm based on a spatial Galilean spiral as claimed in claim 1, characterized in that: The generatrix of the conic surface is a parabola.

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