Construction method of arc tooth bevel gear pair suitable for multi-shaft intersection angle transmission

Abstract

The application discloses a kind of construction methods of arc tooth bevel gear pair suitable for multi-axis intersection angle transmission in gear design and manufacturing technical field.First, according to gear meshing theory, the tooth surface of driving arc tooth bevel gear and the tooth surface of driven arc tooth bevel gear corresponding to different axis intersection angle are respectively constructed, then the comprehensive tooth surface of driving arc tooth bevel gear and the comprehensive tooth surface of driven arc tooth bevel gear are obtained by surface fitting, finally the fitted comprehensive tooth surface is combined with matrix to obtain arc tooth bevel gear pair.The application fits the tooth surface corresponding to actual axis intersection angle after assembly error and standard axis intersection angle designed by arc tooth bevel gear pair in design stage, so that arc tooth bevel gear pair can meet transmission requirements at standard axis intersection angle and actual axis intersection angle after deviation, thereby avoiding negative influence of assembly error on gear pair contact performance, strength and transmission efficiency, and gear in gear pair can be interchanged, which can improve assembly efficiency.

Description

Technical Field

[0001] This invention relates to the field of gear design and manufacturing technology, and in particular to a method for constructing a spiral bevel gear pair suitable for multi-axis intersecting transmission. Background Technology

[0002] As a key component in mechanical transmission, gear mechanisms are widely used for transmitting force and motion in parallel, intersecting, and staggered shaft conditions. Spiral bevel gears, with their advantages of large transmission ratio, smooth transmission, and high efficiency, are used in intersecting shaft (0 < θ < 180°) transmissions. However, spiral bevel gears are sensitive to installation errors. Installation deviations that cause discrepancies between the designed and actual shaft angles negatively impact the contact performance, strength, and transmission efficiency of the gear pair. Currently, there is no good way to avoid installation deviations; the only solution is to subsequently repair the involute curve of the gear. This repair process is cumbersome, sometimes requiring multiple repairs, significantly impacting production efficiency and making it difficult to guarantee the contact performance, strength, and transmission efficiency of the gear pair. Furthermore, spiral bevel gear pairs with different shaft angles each correspond to a single pair of meshing tooth surfaces, making them non-interchangeable. Summary of the Invention

[0003] To overcome the aforementioned shortcomings of existing spiral bevel gears caused by installation deviations, the technical problem to be solved by this invention is to provide a method for constructing spiral bevel gear pairs suitable for multi-axis intersecting transmission.

[0004] The technical solution adopted by this invention to solve its technical problem is:

[0005] A method for constructing spiral bevel gear pairs suitable for multi-axis intersecting transmissions includes the following steps:

[0006] Step 1: Based on gear meshing theory, construct the gear surfaces for forward turning conditions with shaft intersection angles of θ1, θ2...θn. The concave tooth surface of the meshing driving spiral bevel gear and the convex tooth surface of the driven spiral bevel gear are represented as ra1, ra2...ran and Rt1, Rt2...Rtn, respectively.

[0007] Step 2: By fitting concave tooth surfaces ra1, ra2, ..., ran with axis intersection angles of θ1, θ2, ..., θn, the comprehensive concave tooth surface Ω1f of the active spiral bevel gear is obtained;

[0008] Step 3: By fitting the convex tooth surfaces Rt1, Rt2, ..., Rtn with shaft intersection angles of θ1, θ2, ..., θn, the comprehensive convex tooth surface Ω2r of the driven spiral bevel gear is obtained;

[0009] Step 4: Based on steps 1 to 3, construct the tooth surfaces for reverse machining conditions with shaft intersection angles of θ1, θ2...θn, and fit them to obtain the comprehensive convex tooth surface Ω1r of the driving spiral bevel gear and the comprehensive concave tooth surface Ω2f of the driven spiral bevel gear.

[0010] Step 5: Combining the combined concave tooth surface Ω1f and the combined convex tooth surface Ω1r of the active spiral bevel gear, we obtain the active spiral bevel gear tooth P. The tooth P and the base body constitute the active spiral bevel gear.

[0011] Step 6: Combining the combined concave tooth surface Ω2f and the combined convex tooth surface Ω2r of the driven spiral bevel gear, we obtain the driven spiral bevel gear tooth G. The tooth G and the base body together constitute the driven spiral bevel gear.

[0012] Furthermore, n in the axial angles θ1, θ2...θn is 2 or 3.

[0013] Furthermore, the angle values ​​of all the axial angles θ1, θ2...θn are greater than 0° and less than or equal to 90°.

[0014] Furthermore, n = 3, and θ1 > θ2 > θ3, where θ2 is the standard shaft angle of the gear pair design, and θ1 and θ3 are the two extreme values ​​after errors occur in actual assembly.

[0015] The beneficial effects of this invention are: by fitting the tooth surface corresponding to the actual shaft intersection angle after assembly error with the designed standard shaft intersection angle during the design stage of the spiral bevel gear pair, the spiral bevel gear pair can meet the transmission requirements at both the standard shaft intersection angle and the actual shaft intersection angle after deviation, thereby avoiding the negative impact of assembly error on the contact performance, strength and transmission efficiency of the gear pair. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the spiral bevel gear pair structure of the present invention;

[0017] Figure 2 This is a schematic diagram of the spiral bevel gear structure of the present invention;

[0018] Figure 3 This is a schematic diagram of the driving gear tooth in the spiral bevel gear pair of the present invention;

[0019] Figure 4 This is a schematic diagram of the driven gear teeth in the spiral bevel gear pair of the present invention;

[0020] The diagram is labeled as follows: 1-driving spiral bevel gear, 2-driven spiral bevel gear, 3-base. Detailed Implementation

[0021] The invention will be further described below with reference to the accompanying drawings.

[0022] like Figure 1-4 As shown, the present invention relates to a method for constructing a spiral bevel gear pair for multi-axis intersecting transmission, comprising the following steps:

[0023] Step 1: Based on gear meshing theory, construct the gear surfaces for forward turning conditions with shaft intersection angles of θ1, θ2...θn respectively. The concave tooth surface of the meshing driving spiral bevel gear 1 and the convex tooth surface of the driven spiral bevel gear 2 are represented as ra1, ra2...ran and Rt1, Rt2...Rtn respectively.

[0024] Step 2: By fitting concave tooth surfaces ra1, ra2, ..., ran with axis intersection angles of θ1, θ2, ..., θn, the comprehensive concave tooth surface Ω1f of the active spiral bevel gear is obtained;

[0025] Step 3: By fitting the convex tooth surfaces Rt1, Rt2, ..., Rtn with shaft intersection angles of θ1, θ2, ..., θn, the comprehensive convex tooth surface Ω2r of the driven spiral bevel gear is obtained;

[0026] Step 4: Based on steps 1 to 3, construct the tooth surfaces for reverse machining conditions with shaft intersection angles of θ1, θ2...θn, and fit them to obtain the comprehensive convex tooth surface Ω1r of the driving spiral bevel gear 1 and the comprehensive concave tooth surface Ω2f of the driven spiral bevel gear 2;

[0027] Step 5: Combine the combined concave tooth surface Ω1f and the combined convex tooth surface Ω1r of the active spiral bevel gear 1 to obtain the gear tooth P of the active spiral bevel gear 1. The gear tooth P and the base 3 together constitute the active spiral bevel gear 1.

[0028] Step 6: Combining the combined concave tooth surface Ω2f and the combined convex tooth surface Ω2r of the driven spiral bevel gear 2, the gear teeth G of the driven spiral bevel gear 2 are obtained. The gear teeth G and the base body 3 constitute the driven spiral bevel gear 2.

[0029] In this context, n in the shaft angles θ1, θ2...θn is 2 or 3. Fitting too many surfaces may affect the smoothness of the transmission. Theoretically, any angle value of the shaft angles θ1, θ2...θn that is greater than 0° and less than or equal to 90° can meet the surface fitting requirements. However, in reality, the differences between the included angles are not significant because installation errors or gear interchanges usually only result in differences within 10°. Since installation errors may cause the actual shaft angles to be greater or less than the standard shaft angles, the preferred solution is that n = 3, and θ1 > θ2 > θ3, where θ2 is the standard shaft angle of the gear pair design, and θ1 and θ3 are the two extreme values ​​after errors occur during actual assembly.

[0030] The specific construction process is as follows: Figure 1 , Figure 2 As shown, the spiral bevel gear pair consists of a driving spiral bevel gear 1 and a driven spiral bevel gear 2 meshing together, where the axes of the driving spiral bevel gear 1 and the driven spiral bevel gear 2 form an axial angle of θ. During transmission, a contact area is formed on the tooth surface of the spiral bevel gear pair; this contact area is the actual meshing area during the transmission process. For example... Figure 3 , Figure 4As shown, the tooth P of the driving spiral bevel gear 1 consists of a convex tooth surface and a concave tooth surface. The contact area of ​​the convex tooth surface is St, which includes St1 and St2, and the contact area of ​​the concave tooth surface is Sa, which includes Sa1 and Sa2. The contact area of ​​the convex tooth surface of the tooth G of the driven spiral bevel gear 2 is Ct, which includes Ct1 and Ct2, and the contact area of ​​the concave tooth surface is Ca, which includes Ca1 and Ca2.

[0031] Taking n=2 as an example, under the forward rotation condition, i.e., when the shaft angle is θ1, the contact area Sa1 on the concave tooth surface of the tooth P of the driving bevel gear 1 meshes with the contact area Ct1 on the convex tooth surface of the tooth G of the driven bevel gear 2; when the shaft angle is θ2, the contact area Sa2 on the concave tooth surface of the tooth P meshes with the contact area Ct2 on the convex tooth surface of the tooth G. Using surface fitting technology, the concave tooth surface ra1 corresponding to the contact area Sa1 and the concave tooth surface ra2 corresponding to the contact area Sa2 are fitted to obtain the comprehensive concave tooth surface Ω1f of the driving bevel gear 1; the convex tooth surface Rt1 corresponding to the contact area Ct1 and the convex tooth surface Rt2 corresponding to the contact area Ct2 are fitted to obtain the comprehensive convex tooth surface Ω2r of the driven bevel gear 2. Similarly, in the reverse operation, i.e., when the driving bevel gear 1 reverses, the convex tooth surface of the tooth P of the driving bevel gear 1 contacts the concave tooth surface of the tooth G of the driven bevel gear 2. Following the same method, at shaft angles θ1 and θ2, the combined convex tooth surface Ω1r of the driving bevel gear 1 and the combined concave tooth surface Ω2f of the driven bevel gear 2 can be obtained. Combining the combined concave tooth surface Ω1f and the combined convex tooth surface Ω1r of the driving bevel gear 1, the tooth P of the driving bevel gear 1 can be obtained. Tooth P, together with the base 3, constitutes the driving bevel gear 1. Combining the combined concave tooth surface Ω2f and the combined convex tooth surface Ω2r of the driven bevel gear 2, the tooth G of the driven bevel gear 2 can be obtained. Tooth G, together with the base, constitutes the driven bevel gear 2.

[0032] This invention fits the tooth surface corresponding to the actual shaft intersection angle after assuming assembly errors with the designed standard shaft intersection angle during the design stage of the spiral bevel gear pair. This ensures that the spiral bevel gear pair meets the transmission requirements at both the standard shaft intersection angle and the actual shaft intersection angle after deviation, thereby avoiding the negative impact of assembly errors on the contact performance, strength, and transmission efficiency of the gear pair. At the same time, the gears in the gear pair constructed by this method can be interchanged, which can improve assembly efficiency.

Claims

1. A method for constructing spiral bevel gear pairs suitable for multi-axis intersecting angle transmissions, characterized in that, Includes the following steps: Step 1: Based on the gear meshing theory, construct the gear surfaces for the forward turning condition with shaft intersection angles of θ1, θ2...θn respectively. The concave tooth surface of the meshing driving spiral bevel gear (1) and the convex tooth surface of the driven spiral bevel gear (2) are represented as ra1, ra2...ran and Rt1, Rt2...Rtn respectively. Step 2: By fitting concave tooth surfaces ra1, ra2, ..., ran with shaft intersection angles of θ1, θ2, ..., θn, the comprehensive concave tooth surface Ω1f of the active spiral bevel gear (1) is obtained; Step 3: By fitting the tooth surfaces Rt1, Rt2, ..., Rtn with shaft intersection angles of θ1, θ2, ..., θn, the comprehensive tooth surface Ω2r of the driven arc bevel gear (2) is obtained; Step 4: Based on steps 1 to 3, construct the reverse working condition tooth surface with shaft intersection angles of θ1, θ2...θn, and fit to obtain the comprehensive convex tooth surface Ω1r of the active arc bevel gear (1) and the comprehensive concave tooth surface Ω2f of the driven arc bevel gear (2); Step 5: Combine the concave tooth surface Ω1f and the convex tooth surface Ω1r of the active spiral bevel gear (1) to obtain the gear teeth (P) of the active spiral bevel gear (1). The gear teeth (P) and the base (3) together constitute the active spiral bevel gear (1). Step 6: Combine the concave tooth surface Ω2f and the convex tooth surface Ω2r of the driven spiral bevel gear (2) to obtain the gear teeth (G) of the driven spiral bevel gear (2). The gear teeth (G) together with the base (3) constitute the driven spiral bevel gear (2).

2. The method for constructing a spiral bevel gear pair suitable for multi-axis intersecting transmission as described in claim 1, characterized in that: In the axial angles θ1, θ2...θn, n is 2 or 3.

3. The method for constructing a spiral bevel gear pair suitable for multi-axis intersecting transmission as described in claim 1, characterized in that: All the angle values ​​of the axial angles θ1, θ2...θn are greater than 0° and less than or equal to 90°.

4. The method for constructing a spiral bevel gear pair suitable for multi-axis intersecting transmission as described in claim 2, characterized in that: The n = 3, and θ1 > θ2 > θ3, where θ2 is the standard shaft angle of the gear pair design, and θ1 and θ3 are the two extreme values ​​after errors occur in the actual assembly.

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