CN117610176A - Method for calculating cutting angle of continuous generating face gear machining tool - Google Patents
Method for calculating cutting angle of continuous generating face gear machining tool Download PDFInfo
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- CN117610176A CN117610176A CN202311500265.3A CN202311500265A CN117610176A CN 117610176 A CN117610176 A CN 117610176A CN 202311500265 A CN202311500265 A CN 202311500265A CN 117610176 A CN117610176 A CN 117610176A
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- 238000005520 cutting process Methods 0.000 title claims abstract description 60
- 238000003754 machining Methods 0.000 title claims abstract description 28
- 238000000034 method Methods 0.000 title claims abstract description 21
- 238000004364 calculation method Methods 0.000 abstract description 2
- 239000013598 vector Substances 0.000 description 12
- 230000009286 beneficial effect Effects 0.000 description 2
- 238000010862 gear shaping Methods 0.000 description 2
- 238000009434 installation Methods 0.000 description 2
- 239000000463 material Substances 0.000 description 2
- 238000005299 abrasion Methods 0.000 description 1
- 230000021615 conjugation Effects 0.000 description 1
- 238000005553 drilling Methods 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 238000003801 milling Methods 0.000 description 1
- 230000000750 progressive effect Effects 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
- 230000009466 transformation Effects 0.000 description 1
- 238000007514 turning Methods 0.000 description 1
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/17—Mechanical parametric or variational design
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
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Abstract
The invention provides a calculation method, which is a method for calculating the cutting angle of a continuously generated face gear machining tool, and mainly comprises the following steps: based on the meshing principle of the staggered shaft gears and the continuous generation of the face gears, a machining motion model is established, a cutter structure model is established, a cutter cutting angle reference plane is determined in consideration of the cutter cutting angle required in the machining process, and the size of the cutter cutting angle is calculated according to projection on the cutting plane. The configuration method can calculate the real-time cutter cutting angle in the continuous generating process of the face gear, and is convenient for designers to optimally design the cutter structure.
Description
Technical Field
The invention relates to the technical field of gear cutter design, in particular to a method for calculating a cutting angle of a continuously generated face gear machining cutter, which mainly solves the cutting angle of the cutter in the machining process.
Background
The cutting angle is an important parameter affecting the tooth surface machining quality. Because the continuous generation of the face gear is complex in machining movement form, the cutting angle of the face gear is changed continuously along with time unlike simple turning, milling and drilling, and the change rule of the cutting angle of the cutter in the machining process is required to be analyzed, so that the influence rule of the design parameters of the cutter on the cutting angle is researched.
Disclosure of Invention
The technical problems to be solved by the invention are as follows: the continuous generation processing cutter for the face gear is complex in structure, the cutting angle of the cutter is continuously changed along with the processing process, and the processing quality is difficult to control. Therefore, a method for calculating the cutting angle of the continuous generating face gear machining tool is required to be established, and the tool structure is convenient to optimally design by a designer.
The face gear machining tool cutting angle calculation is based on a staggered shaft gear meshing principle and a face gear continuous generation machining motion model, a tool structure model is established, a tool cutting angle reference plane is determined in consideration of the tool cutting angle required in the machining process, and the tool cutting angle is calculated according to projection on the cutting plane.
The invention aims to provide a method for calculating the cutting angle of a continuously generated face gear machining tool, which is used for analyzing the change rule of the continuously generated machining cutting angle of the face gear and guiding a designer to optimize the tool structure.
1. The technical method of the invention is as follows: a method for calculating the cutting angle of a continuous generating face gear machining tool is characterized by comprising the following steps of:
the cutter needs a positive rake angle and a relief angle, and the cutter tooth structure consists of a rake face, a main relief face, left and right relief faces, a top edge and left and right side edges. The rake and relief angles of the tool are defined in the main profile. The method can be applied to calculating the front angle and the rear angle of the top edge, the left side edge and the right side edge of the cutter.
The rake angle and relief angle are not a fixed value for the tool, which varies continuously as the face gear continues to develop the machining.
In the machining process, the cutter and the face gear rotate at high speed around the axes of the cutter and the face gear respectively, meanwhile, as the axis of the cutter and the radial direction of the face gear form a sigma angle, the cutter performs feeding motion along the radial direction of the workpiece, the workpiece is machined layer by layer from outside to inside, and the whole face gear can be machined when the cutter radially translates from the outer circle of the workpiece to the inner circle of the workpiece.
Compared with the prior art, the invention has the beneficial effects that: the cutting angle of the gear cutter at each moment can be calculated, and a design basis is provided for cutter designers.
Drawings
FIG. 1 is a face gear continuous generation machining motion model
FIG. 2 shows a cutter structure
FIG. 3 shows a side edge cutting angle reference plane
FIG. 4 is a main section internal cutting angle definition
Detailed Description
The invention is further described below with reference to the drawings.
Referring to the motion mechanism of the staggered shaft helical gear pair, the efficient forming method of the tooth surface of the face gear is provided on the basis of the meshing principle of the staggered shaft helical gear, as shown in fig. 1, the cutter is similar to a helical gear, and the processing object is the face gear. This machining method can be seen as a combination of hobbing and gear shaping, in which the tool and workpiece are rotated simultaneously about their axes at high speeds, similar to the indexing motion in hobbing, while the tool rotates with a progressive cutting into the workpiece from the outside to the inside, similar to gear shaping, due to the fact that the tool axis makes a sigma angle with the face gear in the radial direction. The cutter performs feeding motion along the radial direction (Y direction in the figure) of the workpiece, the workpiece is scraped layer by layer from outside to inside, and the whole face gear can be machined when the cutter radially translates from the outer circle of the workpiece to the inner circle of the workpiece.
The tool axis forms a mounting angle Σ with the radial direction of the workpiece, which provides a cutting angle for machining, enabling removal of workpiece material. The size of the installation included angle sigma is determined by the spiral angle of the cutter pitch circle, and the specific relation is sigma=beta, wherein beta is the spiral angle of the cutter pitch circle, namely the size of the installation included angle is equal to the spiral angle of the cutter pitch circle.
The working process can also be regarded as the meshing motion of the cutter and the face gear, assuming that the number of teeth of the cutter is Z s The number of teeth of the face gear is Z 2 According to the gear meshing principle, the ratio of the angular speeds of the rotary motion of the cutter and the face gear is as follows:
in order to ensure that the cutter can normally cut workpiece materials, the following structural design requirements of the cutter are summarized from the design angles of the cutter and the contact characteristics of the cutter and the workpiece:
the cutter cutting edge should be located on the tooth surface of the generating wheel. According to the conjugation principle of the cutter and the workpiece, the forming wheel and the workpiece belong to conjugate curved surfaces, so that the conjugated tooth surface can be processed only when the cutting edge is positioned on the tooth surface of the forming wheel;
the tool requires a positive rake angle as well as a relief angle. Considering that cutting is accumulated on a rake face during machining, a certain positive rake angle is required to form chip flutes while improving cutting performance of a tool. In order to prevent interference abrasion between the cutter and the machined surface of the workpiece, a certain relief angle is needed;
the cutter should have the function of sharpening. Because the prior cutter has high manufacturing cost, the cutter can be resharpened after being worn, and the deviation of the processing effect of the cutter after sharpening is ensured to be as small as possible.
As shown in fig. 2, the cutting-related structure of the cutter tooth after the rake angle and the relief angle are added mainly comprises: a front cutter surface, a main rear cutter surface, left and right rear cutter surfaces, a top edge and left and right side edges.
The cutting angle is an important parameter affecting the tooth surface machining quality. According to the definition mode of the traditional cutter angle, firstly, a cutter angle reference plane needs to be determined, and then the cutting rake angle is judged according to the projection on the chip plane.
A tool angle reference plane is established at any point M on the tool side edge as shown in fig. 3. Assuming a cutting speed V at a cutting edge point M, a base plane P r Perpendicular to cutting speed V, cutting plane P s Is composed of cutting speed V and tangential vector q at side edge point M, and main section P o Then at the same time perpendicular to the base plane P r And a cutting plane P s . In the main section P o The rake and relief angles of the tool are defined as shown in fig. 4, gamma 0 And alpha 0 The front angle and the rear angle on the cutting plane of the point M are respectively, and the size of the front angle and the rear angle is a 1 、a 2 、a 3 、a 4 The included angle of the four vectors is determined.
Cutting rake angle gamma is defined according to the cutting angle 0 Can be expressed as:
wherein a is 1 Is the base plane P r In the main section P o Projection onto a, a 2 Rake face and main profile P o Is tangential to the intersection line at point M.
The cutting speed V, rake surface normal N being known from the preceding section q The rear tool face is a theoretical spiral face, and any point normal vector N on the theoretical spiral face h It can also be determined. Since the tangential vector q at point M is simultaneously perpendicular to N q And N h Thus, there are:
q＝N q ×N h #(3)
due to the cutting plane P s Is composed of cutting speed V and cutting vector q, and cutting plane normal vector N s Can be expressed as:
N s ＝V×q#(4)
due to the main section P o With the base plane P r Intersecting line direction vector a 1 Perpendicular to the cutting plane P s Normal to the cutting plane N s Collinear, take N s Is the reverse of a 1 Is in the forward direction of (2):
a 1 ＝-N s #(5)
principal profile normal N o By cutting the planar normal N s And a base normal direction, since the direction of the cutting speed V is the base normal direction, there are:
N o ＝N s ×V#(6)
due to the rake normal N q Tangential vector in any direction on the rake face perpendicular to point M, so the rake face normal vector N q Must be perpendicular to a 2 And due to a 2 In main section P o Inside, thus a 2 Normal to principal cross-section normal N o The method can be used for obtaining:
a 2 ＝N o ×N q #(7)
similarly, the cutting relief angle may be expressed as:
wherein a is 3 Is a clearance surface and a main section P o Tangent vector of intersection line at point M, a 4 For cutting plane P s In the main section P o Projection onto a projection plane.
Due to the relief surface normal N h Tangential vector in any direction on the flank surface perpendicular to point M, so flank normal vector N h Must be perpendicular to a 3 And due to a 3 In main section P o Inside, thus a 3 Normal to principal cross-section normal N o The method can be used for obtaining:
a 3 ＝N o ×N h #(9)
obviously a 4 Is collinear with the cutting speed V, and the opposite direction of the cutting speed V is a 4 Is the positive direction of (2), to obtain:
a 4 ＝-V#(10)
the invention can be applied to the design of face gear cutters and is beneficial to the designers to improve the cutting performance of the cutters.
The invention is not described in detail in part as being well known in the art. All technical methods formed by equivalent transformation or equivalent substitution fall within the protection scope of the invention.
Claims (3)
1. A method for calculating the cutting angle of a continuous generating face gear machining tool is characterized by comprising the following steps of:
(1) The cutter needs a positive rake angle and a relief angle, and the cutter tooth structure consists of a rake face, a main relief face, left and right relief faces, a top edge and left and right side edges;
(2) Defining a rake angle and a relief angle of the tool in the main profile;
(3) The method can be applied to calculating the front angle and the rear angle of the top edge, the left side edge and the right side edge of the cutter.
2. The rake and relief angles of claim 1, wherein:
the rake angle and relief angle are not a fixed value for the tool, which varies continuously as the face gear continues to develop the machining.
3. The face gear continuous generating process of claim 2, wherein:
in the machining process, the cutter and the face gear rotate at high speed around the axes of the cutter and the face gear respectively, meanwhile, as the axis of the cutter and the radial direction of the face gear form a sigma angle, the cutter performs feeding motion along the radial direction of the workpiece, the workpiece is machined layer by layer from outside to inside, and when the cutter radially translates from the outer circle of the workpiece to the inner circle of the workpiece, the machining of the whole face gear can be completed.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202311500265.3A CN117610176A (en) | 2023-11-13 | 2023-11-13 | Method for calculating cutting angle of continuous generating face gear machining tool |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202311500265.3A CN117610176A (en) | 2023-11-13 | 2023-11-13 | Method for calculating cutting angle of continuous generating face gear machining tool |
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| Publication Number | Publication Date |
|---|---|
| CN117610176A true CN117610176A (en) | 2024-02-27 |
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| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202311500265.3A Pending CN117610176A (en) | 2023-11-13 | 2023-11-13 | Method for calculating cutting angle of continuous generating face gear machining tool |
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| CN (1) | CN117610176A (en) |
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2023
- 2023-11-13 CN CN202311500265.3A patent/CN117610176A/en active Pending
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