CN110162930B - Design method of straight toothed spur gear cold extrusion shaping die - Google Patents
Design method of straight toothed spur gear cold extrusion shaping die Download PDFInfo
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Abstract
The invention provides a design method of a straight spur gear cold extrusion shaping die, belonging to the technical field of shaping dies, and the method comprises the following steps: determining the plastic deformation amount of cold extrusion shaping; determining a mathematical model of the elastic deformation of the shaping female die; determining a mathematical model of the elastic recovery of the gear blank; determining a mathematical model of the total deformation of the cold extrusion shaping; determining a calculation formula of geometric parameters of the shaping female die; and calculating the geometric parameters of the shaping female die. The design method of the straight toothed spur gear cold extrusion shaping die provided by the invention can rapidly determine the full-tooth-shaped geometric parameters of the shaping female die used for cold extrusion shaping, comprehensively considers the plastic deformation of the gear blank, the elastic deformation of the shaping female die and the elastic recovery of the gear blank, and is beneficial to improving the cold extrusion shaping precision of the target gear.
Description
Technical Field
The invention belongs to the technical field of shaping dies, and particularly relates to a design method of a straight spur gear cold extrusion shaping die.
Background
Gears are used as one of the most basic components in mechanical transmission systems, and are used in a very wide range of fields in engineering, particularly in the field of equipment manufacture. Among them, the spur gear is the most typical gear component, and its shape is comparatively complicated, and size precision, surface quality and mechanical properties require very high. At present, the gears with higher precision requirements need mechanical finish machining such as gear honing or gear grinding, and the machining equipment is complex and the machining efficiency is low. Particularly, the gear blank manufactured by adopting a warm extrusion forming mode has larger machining allowance and more obvious defects of low efficiency of mechanical finish machining. The cold extrusion shaping method for the gear blank with the tooth shape formed by warm extrusion can effectively solve the problems, and the key is how to scientifically design a cold extrusion shaping die to improve the precision of cold extrusion shaping of the target gear.
Disclosure of Invention
The invention aims to provide a design method of a straight toothed spur gear cold extrusion reshaping die, and aims to improve the precision of cold extrusion reshaping of a target gear.
In order to achieve the purpose, the invention adopts the technical scheme that: the design method of the straight spur gear cold extrusion shaping die comprises the following steps:
acquiring geometric parameters of a gear blank and geometric parameters of a target gear, and determining plastic deformation of cold extrusion shaping according to the geometric parameters of the gear blank and the geometric parameters of the target gear;
establishing a mathematical model of the elastic deformation of the shaping female die according to a material elastic deformation theory;
establishing a mathematical model of the elastic recovery of the gear blank according to a material elastic-plastic deformation theory;
determining a mathematical model of the total deformation of the cold extrusion shaping according to the plastic deformation of the cold extrusion shaping, the mathematical model of the elastic deformation of the shaping female die and the mathematical model of the elastic recovery of the gear blank;
determining a calculation formula of the geometric parameters of the shaping female die according to a calculation formula of the geometric parameters of the target gear and a mathematical model of the total deformation of the cold extrusion shaping;
and substituting the material parameters of the shaping female die and the gear blank, the geometric parameters of the target gear and the plastic deformation of the cold extrusion shaping into the established calculation formula of the geometric parameters of the shaping female die, and calculating the geometric parameters of the shaping female die.
Further, the establishing of the mathematical model of the elastic deformation of the shaping female die according to the material elastic deformation theory comprises:
determining a first calculation formula of the dependent variable of the shaping female die according to a mechanical model of cold extrusion shaping;
determining a second calculation formula of the strain amount of the shaping female die according to a plastic forming theory;
and determining a mathematical model of the elastic deformation of the shaping female die according to the calculation formula of the elastic deformation of the shaping female die, the first calculation formula of the strain of the shaping female die and the second calculation formula of the strain of the shaping female die.
Further, the mathematical model of the elastic deformation of the shaping female die is as follows:
wherein, delta d To reshape the elastic deformation of the die, /) d To shape the dimensions, sigma, of the die x To stabilize the stress value in the extrusion stage, E d The modulus of elasticity of the female mold material.
Further, a female die material stress-strain curve of the shaping female die is obtained through a normal-temperature tensile experiment, the female die material stress-strain curve is fitted into a female die material bilinear material model, and the elastic modulus of the female die material is determined according to the female die material bilinear material model.
Further, the establishing of the mathematical model of the elastic recovery amount of the tooth blank according to the material elastic-plastic deformation theory comprises the following steps:
determining a first calculation formula of the strain of the tooth blank according to a mechanical model of cold extrusion shaping;
determining a second calculation formula of the strain amount of the gear blank according to a plastic forming theory;
and determining a mathematical model of the elastic recovery quantity of the gear blank according to a calculation formula of the elastic recovery quantity of the gear blank, a first calculation formula of the strain quantity of the gear blank and a second calculation formula of the strain quantity of the gear blank.
Further, the mathematical model of the elastic recovery amount of the tooth blank is as follows:
wherein, delta g The elastic recovery of the tooth blank, /) g For the size of the shaped tooth blank, /) 0 To size of the tooth blank before shaping, σ s Is the yield strength, σ, of the material of the tooth blank x To stabilize the stress value in the extrusion stage, E g Modulus of elasticity of the material of the tooth blank, E pg Is the plastic modulus of the tooth blank material.
Further, a tooth blank material stress-strain curve of the tooth blank is obtained through a normal-temperature tensile experiment, the tooth blank material stress-strain curve is fitted to a tooth blank material bilinear material model, and the elastic modulus, the plastic modulus and the yield strength of the tooth blank material are determined according to the tooth blank material bilinear material model.
Further, the plastic deformation amount of the cold extrusion shaping comprises a single-side tooth side shaping amount of the tooth blank and a tooth top shaping amount of the tooth blank;
the mathematical model of the total deformation of the cold extrusion shaping comprises a mathematical model of the total deformation of the cold extrusion shaping unilateral tooth side and a mathematical model of the total deformation of the cold extrusion shaping tooth top;
the mathematical model of the total deformation of the cold extrusion shaping unilateral tooth side is as follows:
wherein, delta 1 The total deformation of the cold extrusion shaping unilateral tooth side is shown, and delta is the shaping amount of the unilateral tooth side of the tooth blank;
the mathematical model of the total deformation of the cold extrusion shaping tooth top is as follows:
wherein, delta 2 The total deformation of the tooth top of the cold extrusion shaping is shown, and delta' is the tooth top shaping amount of the tooth blank.
Further, the geometric parameters of the shaping female die comprise the tooth side size of the tooth profile of the shaping female die and the tooth crest size of the tooth profile of the shaping female die;
calculating and determining a calculation formula of the geometric parameters of the shaping female die according to an involute equation of the target gear, a calculation formula of the geometric parameters of the target gear and a mathematical model of the total deformation of the cold extrusion shaping;
the calculation formula of the geometric parameters of the shaping female die is as follows:
let l 0 ＝l 0i ，l d ＝l di Determining the geometric parameters of the tooth side of the tooth profile of the shaping female die according to the following calculation formula:
wherein l 0i Is the unilateral flank dimension of the tooth blank, l di The tooth side size of the tooth profile of the shaping female die;
let l 0 ＝r 0 ，l d ＝r d Determining the calculation formula of the geometric parameters of the tooth crest of the tooth profile of the shaping female die as follows:
wherein r is 0 For gear blankAddendum circle size of r d The tooth top size of the tooth profile of the shaping concave die is obtained.
Furthermore, the shaping male die is of a cylindrical structure, and the diameter of the shaping male die is smaller than that of the root circle of the shaping female die.
The design method of the straight spur gear cold extrusion shaping die provided by the invention has the beneficial effects that: compared with the prior art, the design method of the straight toothed spur gear cold extrusion shaping die can quickly determine the full-tooth-shaped geometric parameters of the shaping female die used for cold extrusion shaping, comprehensively considers the plastic deformation of the tooth blank, the elastic deformation of the shaping female die and the elastic recovery of the tooth blank, and is beneficial to improving the cold extrusion shaping precision of the target gear.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the embodiments or the prior art descriptions will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without creative efforts.
Fig. 1 is a schematic flow chart of a design method of a spur gear cold extrusion shaping die according to an embodiment of the present invention;
fig. 2 is a schematic implementation flow diagram of S102 in fig. 1 according to an embodiment of the present invention;
fig. 3 is a schematic diagram illustrating an implementation flow of S103 in fig. 1 according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of a cold extrusion forming process according to an embodiment of the present invention;
fig. 5 is a schematic structural diagram of a shaping male die in a front view according to an embodiment of the present invention;
fig. 6 is a schematic top view of a shaping male die provided in an embodiment of the present invention;
FIG. 7 is a schematic structural diagram of a target gear provided in an embodiment of the present invention;
FIG. 8 is a material model of a shaping cavity die provided in an embodiment of the present invention;
FIG. 9 is a material model of a tooth blank provided in accordance with an embodiment of the present invention;
FIG. 10 is a schematic view of the amount of plastic deformation of a tooth blank according to an embodiment of the present invention;
FIG. 11 is an enlarged view of a portion of FIG. 10 at A;
FIG. 12 is a schematic diagram of a reshaping process according to an embodiment of the present invention;
fig. 13 is a schematic view of a tooth blank profile, a target gear profile and a shaping die profile provided by an embodiment of the present invention.
In the figure: 1. shaping a male die; 2. shaping a female die; 3. a gear blank; 4. a target gear.
Detailed Description
In order to make the technical problems, technical solutions and advantageous effects to be solved by the present invention more clearly apparent, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The design method of the straight spur gear cold extrusion shaping die provided by the invention is explained. In fig. 8, E is a female die material bilinear material model, and F is a female die material stress-strain curve; in fig. 9, G is a tooth blank material bilinear material model, and K is a tooth blank material stress-strain curve; in fig. 10 and 11, X is a tooth blank profile and Y is a target gear profile; m in fig. 12 is the amount of plastic deformation of the tooth blank; in fig. 13, X is a tooth blank profile, Y is a target gear profile, and Z is a shaping die profile.
Fig. 1 shows an implementation process of a design method of a spur gear cold extrusion shaping die provided by an embodiment of the present invention, and the process thereof is detailed as follows:
in S101, the geometric parameters of the tooth blank 3 and the geometric parameters of the target gear 4 are obtained, and the plastic deformation amount of the cold extrusion shaping is determined according to the geometric parameters of the tooth blank 3 and the geometric parameters of the target gear 4.
In the present embodiment, the tooth blank 3 is a blank having a tooth profile obtained by shaping a blank by warm extrusion. The tooth blank 3 has a contour dimension larger than that of the target gear 4. The geometric parameters of the tooth blank 3 include a tooth flank dimension of the tooth blank 3 and a tooth crest dimension of the tooth blank 3, and the geometric parameters of the target gear 4 include a tooth flank dimension of the target gear 4 and a tooth crest dimension of the target gear 4.
In S102, a mathematical model of the elastic deformation amount of the shaping die 2 is established based on the material elastic deformation theory.
In S103, a mathematical model of the elastic recovery amount of the tooth blank 3 is established based on the material elastic-plastic deformation theory.
In S104, a mathematical model of the total deformation amount of the cold extrusion shaping is determined from the mathematical model of the plastic deformation amount of the cold extrusion shaping, the elastic deformation amount of the shaping die 2, and the mathematical model of the elastic recovery amount of the tooth blank 3.
In the present embodiment, the total deformation amount of the cold extrusion molding is the sum of the plastic deformation amount of the cold extrusion molding, the elastic deformation amount of the shaping die 2, and the elastic recovery amount of the tooth blank 3.
In S105, a calculation formula of the geometric parameter of the shaping die 2 is determined based on the calculation formula of the geometric parameter of the target gear 4 and the mathematical model of the total deformation amount of the cold extrusion shaping.
In S106, the material parameters of the shaping die 2 and the tooth blank 3, the geometric parameters of the target gear 4, and the plastic deformation amount of the cold extrusion shaping are substituted into the established calculation formula of the geometric parameters of the shaping die 2, and the geometric parameters of the shaping die 2 are calculated.
In the present embodiment, the material parameters of the shaping die 2 are the elastic modulus of the die material, and the material parameters of the tooth blank 3 are the elastic modulus, the plastic modulus and the yield strength of the tooth blank material.
It can be known from the above embodiments that the embodiments of the present invention can rapidly determine the geometric parameters of the full tooth shape of the shaping concave die 2 used for cold extrusion shaping, and comprehensively consider the plastic deformation of the tooth blank 3, the elastic deformation of the shaping concave die 2, and the elastic recovery of the tooth blank 3, which is beneficial to the improvement of the cold extrusion shaping precision of the target gear 4.
As shown in fig. 2, in an embodiment of the present invention, fig. 2 shows an implementation flow of S102 in fig. 1, and the process thereof is detailed as follows:
in S201, a first calculation formula of the strain amount of the shaping die 2 is determined according to the mechanical model of the cold extrusion shaping.
In this embodiment, the mechanical model of the cold extrusion shaping is simplified into a unidirectional stress-strain state, and a first calculation formula of the strain amount of the shaping female die 2 is obtained according to the unidirectional stress-strain state.
In S202, a second calculation formula of the amount of strain of the shaping die 2 is determined according to the plastic forming theory.
In S203, a mathematical model of the elastic deformation amount of the shaping die 2 is determined based on the calculation formula of the elastic deformation amount of the shaping die 2, the first calculation formula of the strain amount of the shaping die 2, and the second calculation formula of the strain amount of the shaping die 2.
In this embodiment, the mathematical model of the elastic deformation of the shaping concave die 2 is:
wherein, delta d To reshape the elastic deformation of the die, /) d To shape the dimensions of the die, σ x To stabilize the stress value in the extrusion phase, E d The modulus of elasticity of the female die material.
As shown in fig. 8, in this embodiment, a female die material stress-strain curve of the shaping female die 2 is obtained through a normal temperature tensile experiment, the female die material stress-strain curve is fitted to a female die material bilinear material model, and the elastic modulus of the female die material is determined according to the female die material bilinear material model.
As shown in fig. 3, in an embodiment of the present invention, fig. 3 shows an implementation flow of S103 in fig. 1, and the process thereof is detailed as follows:
in S301, a first calculation formula of the amount of strain of the tooth blank 3 is determined from the mechanical model of cold extrusion shaping.
In this embodiment, the mechanical model of the cold extrusion shaping is simplified into a unidirectional stress-strain state, and a first calculation formula of the strain amount of the tooth blank 3 is obtained according to the unidirectional stress-strain state.
In S302, a second calculation formula of the strain amount of the tooth blank 3 is determined according to the plastic forming theory.
In S303, a mathematical model of the elastic recovery amount of the tooth blank 3 is determined from the calculation formula of the elastic recovery amount of the tooth blank 3, the first calculation formula of the strain amount of the tooth blank 3, and the second calculation formula of the strain amount of the tooth blank 3.
In this embodiment, the mathematical model of the elastic recovery amount of the tooth blank 3 is:
wherein, delta g The elastic recovery of the tooth blank, /) g For the size of the shaped tooth blank, /) 0 To size of the tooth blank before shaping, σ s Is the yield strength, σ, of the material of the tooth blank x To stabilize the stress value in the extrusion phase, E g Elastic modulus of tooth blank material, E pg Is the plastic modulus of the tooth blank material.
As shown in fig. 9, in this embodiment, a tooth blank material stress-strain curve of the tooth blank 3 is obtained through a normal temperature tensile experiment, the tooth blank material stress-strain curve is fitted to a tooth blank material bilinear material model, and the elastic modulus, the plastic modulus and the yield strength of the tooth blank material are determined according to the tooth blank material bilinear material model.
In this embodiment, the plastic deformation amount of the cold extrusion molding includes the single-side tooth flank molding amount of the tooth blank 3 and the tooth crest molding amount of the tooth blank 3.
The mathematical model of the total deformation of the cold extrusion shaping comprises a mathematical model of the total deformation of the cold extrusion shaping unilateral tooth side and a mathematical model of the total deformation of the cold extrusion shaping tooth top.
The mathematical model of the total deformation of the cold extrusion shaping unilateral tooth side is as follows:
wherein, delta 1 The total deformation of the cold extrusion shaping unilateral tooth side is shown, and delta is the shaping amount of the unilateral tooth side of the tooth blank;
the mathematical model of the total deformation of the cold extrusion shaping tooth top is as follows:
wherein, delta 2 The total deformation of the tooth top of the cold extrusion shaping is shown, and delta' is the tooth top shaping amount of the tooth blank.
In this embodiment, the geometric parameters of the shaping die 2 include the tooth flank size of the tooth profile of the shaping die 2 and the tooth crest size of the tooth profile of the shaping die 2.
Calculating and determining a calculation formula of the geometric parameters of the shaping female die 2 according to an involute equation of the target gear 4, a calculation formula of the geometric parameters of the target gear 4 and a mathematical model of the total deformation of the cold extrusion shaping;
the calculation formula of the geometric parameters of the shaping concave die 2 is as follows:
let l 0 ＝l 0i ，l d ＝l di The calculation formula for determining the geometric parameters of the tooth flank of the tooth profile of the shaping die 2 is as follows:
wherein l 0i Is the unilateral flank dimension of the tooth blank, l di The tooth side size of the tooth profile of the shaping female die;
let l 0 ＝r 0 ，l d ＝r d The calculation formula for determining the geometrical parameters of the tooth crest of the tooth profile of the shaping female die 2 is as follows:
wherein r is 0 Is the addendum circle size of the tooth blank, r d The tooth top size of the tooth profile of the shaping concave die is obtained.
In this embodiment, the shaping male die 1 is of a cylindrical structure, and the diameter D of the shaping male die 1 p Is smaller than the diameter of the tooth root circle of the shaping concave die 2. The shaping male die 1 is of a cylindrical structure, is easy to process and effectively reduces the production cost.
Now, the modulus m =2, the tooth number Z =31 and the tooth crest height coefficient h a The design of a cold extrusion shaping die of a standard involute straight toothed spur gear with a pressure angle of alpha =20 degrees is taken as an example. The dimensional parameters of the target gear 4 are: reference circle diameter D =62mm, addendum circle diameter D a =66mm, root circle diameter D f =57mm, tooth width B =25mm. Referring to fig. 1 to 13, the steps are as follows:
1) Determining plastic deformation of cold extrusion
The tooth blank 3 is a blank having a tooth profile obtained by shaping the blank by warm extrusion. The tooth blank 3 has a contour dimension larger than that of the target gear 4. The geometric parameters of the tooth blank 3 include a tooth flank dimension of the tooth blank 3 and a tooth crest dimension of the tooth blank 3, and the geometric parameters of the target gear 4 include a tooth flank dimension of the target gear 4 and a tooth crest dimension of the target gear 4. And measuring the geometric parameters of the tooth blank 3 to be shaped by using a geometric dimension detection device such as a three-coordinate measuring machine, wherein the geometric parameters of the target gear 4 are known, analyzing and comparing the geometric parameters of the tooth blank 3 with the geometric parameters of the target gear 4, and calculating to obtain the unilateral tooth side shaping quantity delta =0.3mm of the tooth blank 3 and the tooth top shaping quantity delta' =0.25mm of the tooth blank 3. The single-side tooth flank truing amount of the tooth blank 3 and the tooth crest truing amount of the tooth blank 3 are plastic deformation amounts for cold extrusion truing because they are deformation amounts for unrecoverable deformation that occurs after the cold extrusion truing of the tooth blank 3.
2) Mathematical model for determining elastic deformation of shaping female die
The tooth blank 3 passes through the shaping female die 2 (the shaping female die 2 is a tooth-shaped female die) under the pushing of the shaping male die 1, so that the shaping effect is achieved. In the cold extrusion shaping process, the shaping female die 2 can generate elastic deformation. In order to improve the precision of cold extrusion shaping, the elastic deformation of the shaping female die 2 needs to be taken into consideration when designing the cold extrusion shaping die.
The calculation formula of the elastic deformation of the shaping female die 2 is as follows:
Δ d ＝l' d -l d (1)
wherein, delta d To reshape the elastic deformation of the die, /) d Is the size of the shaping die, < l >' d The size of the shaping concave die after elastic deformation.
Simplifying a mechanical model of cold extrusion shaping into a one-way stress-strain state, and determining a first calculation formula of the strain quantity of the shaping female die 2;
the first calculation formula of the strain amount of the shaping die 2 is as follows:
wherein epsilon d Amount of strain, σ, for shaping the die x To stabilize the stress value in the extrusion phase, E d The modulus of elasticity of the female mold material.
Determining a second calculation formula of the strain amount of the shaping female die 2 according to a plastic forming theory;
the second calculation formula of the strain amount of the shaping die 2 is as follows:
deducing a mathematical model of the elastic deformation of the shaping female die 2 according to the formula (1), the formula (2) and the formula (3);
the mathematical model of the elastic deformation of the shaping female die 2 is as follows:
the shaping female die 2 is made of Cr12MoV coldThe method comprises the steps of using the die steel as die steel, obtaining a female die material stress-strain curve of a shaping female die 2 through a normal-temperature stretching experiment, fitting the female die material stress-strain curve into a bilinear material model of a female die material to realize calculation of elastic deformation of the female die material, determining the elastic modulus E of the female die material by using the elastic modulus of the female die material as a slope value of an elastic deformation stage in the bilinear material model of the female die material d ＝210×10 3 N/mm 2 。
3) Mathematical model for determining elastic recovery of tooth blank
In the cold extrusion shaping process, the gear blank 3 is in an elastic deformation stage before plastic deformation. After the cold extrusion shaping is finished, the deformation generated in the elastic deformation stage can be recovered, namely, elastic recovery. In order to improve the precision of cold extrusion shaping, the elastic recovery of the tooth blank 3 is taken into consideration when designing the cold extrusion shaping die.
The elastic recovery quantity of the gear blank 3 is calculated by the following formula:
Δ g ＝l g -l' g (4)
wherein, delta g The elastic recovery of the tooth blank, /) g Is the size of the tooth blank after shaping l' g Is the size of the elastic recovery front tooth blank.
Simplifying a mechanical model of cold extrusion shaping into a one-way stress strain state, and determining a first calculation formula of the strain capacity of the gear blank 3;
the first calculation formula of the amount of strain of the tooth blank 3 is:
wherein epsilon g Amount of strain, σ, of tooth blank s Is the yield strength, σ, of the material of the tooth blank x To stabilize the stress value in the extrusion stage, E g Elastic modulus of tooth blank material, E pg Is the plastic modulus of the tooth blank material.
Determining a second calculation formula of the strain amount of the gear blank 3 according to the plastic forming theory;
the second calculation formula of the amount of strain of the tooth blank 3 is:
wherein l 0 The size of the tooth blank before shaping;
deducing a mathematical model of the elastic recovery quantity of the gear blank 3 according to the formula (4), the formula (5) and the formula (6);
the mathematical model of the elastic recovery of the tooth blank 3 is:
the material of the gear blank 3 is 45 steel, a gear blank material stress-strain curve of the gear blank 3 is obtained through a normal-temperature tensile experiment, the gear blank material stress-strain curve is fitted to a gear blank material bilinear material model to realize calculation of the elastic recovery of the gear blank 3, the elastic modulus of the gear blank material is a slope value of an elastic deformation stage in the gear blank material bilinear material model, the plastic modulus of the gear blank material is a slope value of a plastic deformation stage in the gear blank material bilinear material model, and the elastic modulus E of the gear blank material is determined g ＝210×10 3 N/mm 2 Plastic modulus E pg ＝100×10 3 N/mm 2 Yield strength σ s ＝355N/mm 2 。
4) Mathematical model for determining total deformation of cold extrusion shaping
The mathematical model of the total deformation of the cold extrusion shaping comprises a mathematical model of the total deformation of the cold extrusion shaping unilateral tooth side and a mathematical model of the total deformation of the cold extrusion shaping tooth top. The total deformation of the cold extrusion shaping is the sum of the plastic deformation of the cold extrusion shaping, the elastic deformation of the shaping female die 2 and the elastic recovery of the gear blank 3.
The mathematical model of the total deformation of the cold extrusion shaping unilateral tooth side is as follows:
wherein, delta 1 The total deformation of the cold extrusion shaping unilateral tooth side is shown, and delta is the shaping amount of the unilateral tooth side of the tooth blank;
the mathematical model of the total deformation of the cold extrusion shaping tooth top is as follows:
wherein, delta 2 The total deformation of the tooth top of the cold extrusion shaping is shown, and delta' is the tooth top shaping amount of the tooth blank.
5) Calculation formula for determining geometric parameters of shaping female die
The 1/2 tooth thickness corresponding to any circle on the tooth form of the standard involute straight tooth cylindrical gear is s i ；
According to the involute equation, the following can be obtained:
wherein s is the reference circle tooth thickness,
r i is any circle radius, r is reference circle radius,
α i is any circle pressure angle, and alpha is a reference circle pressure angle; z is the number of teeth and m is the modulus.
The addendum circle radius of the standard involute straight tooth cylindrical gear is as follows:
wherein Z is the number of teeth, m is the modulus, h a Is the crest factor.
In the cold extrusion shaping process, the gear blank 3 is completely attached to the shaping concave die 2, so that the gear blank is elastically deformedThe dimension of the rear shaping die 2 is the same as that of the elastically restored front tooth blank 3, i.e. 'l' d ＝l' g 。
From the formula (1) and the formula (4), the calculation formula for deriving the size of the shaping die 2 is:
l d ＝l g -Δ g -Δ d (9)
the elastic recovery amount delta of the gear blank 3 g And the elastic deformation amount Delta of the shaping die 2 d Substituting into equation (9), the calculation equation for determining the size of the shaping die 2 is:
the unilateral flank dimension of the tooth blank 3 is:
l 0i ＝s i +Δ (11)
the addendum circle radius of the gear blank 3 is as follows:
r 0 ＝r a +Δ′ (12)
substituting the formula (7) and the formula (11) into the formula (10),
let l 0 ＝l 0i ，l d ＝l di The calculation formula for determining the geometric parameters of the tooth flank of the tooth profile of the shaping die 2 is as follows:
wherein l 0i The one-sided flank dimension of the tooth blank, /) di The size of the tooth side of the tooth profile of the shaping die is determined.
Substituting the formula (8) and the formula (12) into the formula (10),
let l 0 ＝r 0 ，l d ＝r d The calculation formula for determining the geometrical parameters of the tooth crest of the tooth profile of the shaping female die 2 is as follows:
wherein r is 0 Is the tip circle size of the tooth blank, r d The tooth top size of the tooth profile of the shaping concave die is obtained.
6) Calculating the geometric parameters of the shaping die
The stress value of the stable extrusion stage can be obtained by calculation according to the extrusion theory or by finite element simulation analysis, in this embodiment, the stress value of the stable extrusion stage is sigma x ＝470N/mm 2 . The material parameter (E) of the shaping concave die 2 d ＝210×10 3 N/mm 2 ) Material parameters (E) of the tooth blank 3 g ＝210×10 3 N/mm 2 ，E pg ＝100×10 3 N/mm 2 ，σ s ＝355N/mm 2 ) Geometric parameters of the target gear 4 (m =2,z =31,h) a =1, α =20 °), amount of plastic deformation (Δ =0.3mm, Δ' =0.25 mm), and stress value (σ) at stable extrusion stage x ＝470N/mm 2 ) And substituting the geometrical parameters into the established calculation formula of the geometrical parameters of the tooth side and the tooth top of the tooth profile of the shaping female die 2 to calculate the geometrical parameters of the shaping female die 2. And processing the shaping female die 2 of the cold extrusion shaping die according to the calculated geometric parameters of the shaping female die 2.
In one embodiment, the shaping male die 1 is of a cylindrical structure, and the diameter D of the shaping male die 1 p Is smaller than the diameter of the tooth root circle of the shaping concave die 2. Diameter D of the shaping punch 1 p =55mm, height H =20mm. The shaping male die 1 is of a cylindrical structure, is easy to process and effectively reduces the production cost.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (9)
1. A design method of a straight spur gear cold extrusion shaping die is characterized by comprising the following steps:
acquiring geometric parameters of a gear blank and geometric parameters of a target gear, and determining plastic deformation of cold extrusion shaping according to the geometric parameters of the gear blank and the geometric parameters of the target gear;
establishing a mathematical model of the elastic deformation of the shaping female die according to a material elastic deformation theory;
establishing a mathematical model of the elastic recovery of the gear blank according to a material elastic-plastic deformation theory;
determining a mathematical model of the total deformation of the cold extrusion shaping according to the plastic deformation of the cold extrusion shaping, the mathematical model of the elastic deformation of the shaping female die and the mathematical model of the elastic recovery of the tooth blank;
determining a calculation formula of the geometric parameters of the shaping female die according to a calculation formula of the geometric parameters of the target gear and a mathematical model of the total deformation of the cold extrusion shaping;
the material parameters of the shaping female die and the gear blank, the geometric parameters of the target gear and the plastic deformation of the cold extrusion shaping are brought into the established calculation formula of the geometric parameters of the shaping female die, and the geometric parameters of the shaping female die are calculated;
the geometric parameters of the shaping female die comprise the tooth side size of the tooth profile of the shaping female die and the tooth crest size of the tooth profile of the shaping female die;
calculating and determining a calculation formula of the geometric parameters of the shaping female die according to an involute equation of the target gear, a calculation formula of the geometric parameters of the target gear and a mathematical model of the total deformation of the cold extrusion shaping;
the calculation formula of the geometric parameters of the shaping female die is as follows:
let l 0 ＝l 0i ，l d ＝l di Determining a calculation formula of geometric parameters of the tooth side of the tooth profile of the shaping female die, wherein the calculation formula comprises the following steps:
wherein l 0i The one-sided flank dimension of the tooth blank, /) di The tooth side size of the tooth profile of the shaping female die;
let l 0 ＝r 0 ，l d ＝r d Determining the calculation formula of the geometric parameters of the tooth crest of the tooth profile of the shaping female die as follows:
wherein r is 0 Is the tip circle size of the tooth blank, r d The tooth crest size of the tooth profile of the shaping die is s is the reference circle tooth thickness r i Is an arbitrary circle radius, r is a reference circle radius, alpha i Is any circular pressure angle, and alpha is a reference circular pressure angle; z is the number of teeth, m is the modulus, h a The crest coefficient.
2. The design method of a cold extrusion shaping die for a spur gear according to claim 1, wherein the establishing of the mathematical model of the elastic deformation of the shaping female die according to the material elastic deformation theory comprises:
determining a first calculation formula of the dependent variable of the shaping female die according to a mechanical model of cold extrusion shaping;
determining a second calculation formula of the strain capacity of the shaping female die according to a plastic forming theory;
and determining a mathematical model of the elastic deformation of the shaping female die according to the calculation formula of the elastic deformation of the shaping female die, the first calculation formula of the strain of the shaping female die and the second calculation formula of the strain of the shaping female die.
3. The design method of the cold extrusion shaping die for the straight toothed spur gear according to claim 2, wherein the mathematical model of the elastic deformation of the shaping female die is as follows:
wherein, delta d To reshape the elastic deformation of the die, /) d To shape the dimensions, sigma, of the die x To stabilize the stress value in the extrusion stage, E d The modulus of elasticity of the female mold material.
4. The method for designing a cold extruding and shaping die for a spur gear according to claim 2, wherein a female die material stress-strain curve of the shaping female die is obtained through a normal temperature stretching experiment, the female die material stress-strain curve is fitted to a female die material bilinear material model, and the elastic modulus of a female die material is determined according to the female die material bilinear material model.
5. The design method of a cold extrusion shaping die for a spur gear according to claim 1, wherein the establishing of the mathematical model of the elastic recovery amount of the tooth blank according to the material elastic-plastic deformation theory comprises:
determining a first calculation formula of the strain of the tooth blank according to a mechanical model of cold extrusion shaping;
determining a second calculation formula of the strain amount of the gear blank according to a plastic forming theory;
and determining a mathematical model of the elastic recovery quantity of the tooth blank according to the calculation formula of the elastic recovery quantity of the tooth blank, the first calculation formula of the strain quantity of the tooth blank and the second calculation formula of the strain quantity of the tooth blank.
6. The design method of the cold extrusion shaping die for the straight toothed spur gear according to claim 5, wherein the mathematical model of the elastic recovery amount of the toothed blank is as follows:
wherein, delta g The elastic recovery of the tooth blank, /) g For the size of the shaped tooth blank, /) 0 To size of the tooth blank before shaping, σ s Is the yield strength, σ, of the material of the tooth blank x To stabilize the stress value in the extrusion phase, E g Modulus of elasticity of the material of the tooth blank, E pg Is the plastic modulus of the tooth blank material.
7. The method for designing a cold extrusion die for a spur gear according to claim 5, wherein a tooth blank material stress-strain curve of the tooth blank is obtained through a normal temperature tensile test, the tooth blank material stress-strain curve is fitted to a tooth blank material bilinear material model, and the elastic modulus, the plastic modulus and the yield strength of the tooth blank material are determined according to the tooth blank material bilinear material model.
8. The method of claim 5, wherein the amount of plastic deformation of the cold extrusion truing includes an amount of single flank truing of the tooth blank and an amount of crest truing of the tooth blank;
the mathematical model of the total deformation of the cold extrusion shaping comprises a mathematical model of the total deformation of the cold extrusion shaping unilateral tooth side and a mathematical model of the total deformation of the cold extrusion shaping tooth top;
the mathematical model of the total deformation of the cold extrusion shaping unilateral tooth side is as follows:
wherein, delta 1 The total deformation of the cold extrusion shaping unilateral tooth side is shown, and delta is the shaping amount of the unilateral tooth side of the tooth blank;
the mathematical model of the total deformation of the cold extrusion shaping tooth top is as follows:
wherein, delta 2 The total deformation of the tooth top of the cold extrusion shaping is shown, and delta' is the tooth top shaping amount of the tooth blank.
9. The design method of a cold extrusion shaping die for a spur gear according to claim 1, wherein the shaping punch has a cylindrical structure, and the diameter of the shaping punch is smaller than that of the root circle of the shaping die.
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