CN110039123B - Method for processing inverted cone teeth by variable-pressure-angle hob - Google Patents

Abstract

The invention relates to a method for processing inverted cone teeth by a variable-pressure-angle hob, which solves the problems that the inverted cone teeth processed by the existing processing method have larger errors when the combined surfaces are matched, and the risk of increasing the gear shift of a transmission is increased. Method for processing inverted cone teeth by variable-pressure-angle hobComprising the steps of 1) passing the back taper tooth pressure angle α_nCalculating standard root angle theta by using formula, 2) determining pressure angle α of pressure angle-variable hob_t(ii) a 3) Calculating a root cone angle theta' after the pressure angle is changed; 4) and (4) debugging the movement path of the machine tool shaft on the gear hobbing machine according to the root cone angle theta' after the pressure angle is changed, and finishing the processing of the inverted bevel gear by the pressure angle-changing hob.

Description

Method for processing inverted cone teeth by variable-pressure-angle hob

Technical Field

The invention relates to a method for processing inverted cone teeth, in particular to a method for processing inverted cone teeth by a variable-pressure angle hob.

Background

The back taper teeth of the automobile synchronizer combined with the gear hub part can be generally processed by hobbing, gear shaping, gear milling and the like, wherein the hobbing processing mode is most widely used due to high efficiency and low use cost. Generally, a gear with one parameter corresponds to a hob with one parameter, but in order to save development cost, an existing hob is used for machining a gear with a new parameter after calculation and analysis, and if no hob with the same module and the same pressure angle as the gear to be machined exists in a database, a variable pressure angle hob (a hob with a different pressure angle from the gear to be machined is collectively called a variable pressure angle hob) can be used for machining inverted bevel teeth.

When designing and processing the inverted cone tooth hob, a pressure angle which is the same as the gear parameter is generally selected as the pressure angle of the hob, under the condition, a standard formula is used for calculating a root angle theta, and a cyclotomic included angle of the inverted cone tooth processed after the value of the root angle theta is input into a gear hobbing machine is the cyclotomic included angle gamma required by a drawing. However, when a variable-pressure-angle hob is used for machining inverted cone teeth in production, a standard formula is used for calculating a root angle theta, the root angle theta is input into an inverted cone tooth cyclotomic included angle gamma value machined by a hobbing machine, and a gamma value required by a drawing has a large error, the larger the gamma value required by the drawing is, the larger the error is, the larger the risk that two inverted cone tooth joint surfaces are matched is increased, and the transmission is out of gear.

Disclosure of Invention

The invention aims to solve the problems that a reverse taper tooth machined by the existing machining method has a large error when a combined surface is matched and the risk of increasing the gear-disengaging of a transmission is increased, and provides a method for machining the reverse taper tooth by using a variable-pressure-angle hob.

The technical scheme of the invention is as follows:

a method for processing inverted cone teeth by a variable pressure angle hob comprises the following steps:

1) pressure angle α through back taper tooth_nCalculating a standard root cone angle theta by using the inverted cone tooth cyclotomic included angle gamma according to a formula (2-2);

2) determining pressure angle α of variable pressure angle hob_t；

3) Calculating a root cone angle theta' after the pressure angle is changed;

4) and (4) debugging the movement path of the machine tool shaft on the gear hobbing machine according to the root cone angle theta' after the pressure angle is changed, and finishing the processing of the inverted bevel gear by the pressure angle-changing hob.

Compared with the prior art, the invention has the following technical effects:

1. the method provides a formula of the change rule of the root angle when the variable-pressure-angle hob machines the inverted cone teeth, and the formula can correctly guide the hobbing machine operator to finish machining the inverted cone teeth, help the gear engineer correctly design parameters of the inverted cone teeth, avoid errors when the combined surfaces of the two inverted cone teeth are matched and further reduce the risk of gear shifting of the transmission.

2. The method can help gear process developers to reduce the investment of new hobs, can find suitable hobs in the existing hob library for processing through analysis and calculation, is a very effective technical means particularly in the new product development trial-manufacturing stage, and perfects the theoretical calculation method of the inverted cone teeth for gear hobbing.

Drawings

FIG. 1 is a schematic view of the root angle of an inverted tooth;

FIG. 2 is a schematic view of a cyclotomic angle of an inverted cone tooth;

FIG. 3 is a schematic side relief angle of a partial circular cross-section of an inverted cone tooth;

FIG. 4 is a first schematic view illustrating analysis of a tooth profile of an inverted cone tooth;

fig. 5 is a schematic diagram illustrating analysis of the tooth profile of the inverted cone tooth.

Detailed Description

The invention is described in further detail below with reference to the figures and specific embodiments.

The invention provides a method for processing inverted cone teeth by a variable pressure angle hob, namely a method for processing inverted cone teeth by using an existing variable pressure angle hob, which specifically comprises the following steps: and (4) recalculating to obtain a new root angle during machining, and adjusting the motion path of the shaft of the debugging machine tool according to the calculated root angle, so that the angle between the moving path line of the hob and the central line of the gear is changed, and the machining of the inverted bevel gear is completed. The root cone angle calculation method for machining the inverted cone teeth of the variable-pressure-angle hob does not have related literature documents at present, and is a calculation method summarized according to a series of measures such as problem analysis, calculation, evidence deduction, verification and the like in actual machining of an applicant, so that uniqueness exists.

The application theoretical basis of the variable-pressure angle hob is as follows: the gear meshing must be equal in base circle pitch (formula 2-1), i.e. the same gear can be represented by different sets of modules and pressure angles.

m₁cosα₁＝m₂cosα₂(2-1)

Wherein m is₁To become front modulus, α₁Variable front pressure angle, m₂To become modulus, α₂And changing the pressure angle.

The inverted bevel gear is a common gear structure used in a transmission synchronizer and is theoretically a helical gear (as shown in fig. 2). When the inverted cone teeth are machined, an included angle theta, namely a root cone angle, is formed between the moving path line of the hob and the central line of the gear. The included angle gamma between the root cone angle and the cycloidal angle gamma of the inverted cone tooth (as shown in figure 3), and the key parameter of the inverted cone tooth is the modulus m_nPressure angle α of reverse taper tooth_nWhen the hob with the same parameters as the back taper tooth modulus and the pressure angle is used for machining the back taper teeth, the theoretical relation between the root cone angle and the back taper tooth cyclotomic included angle can be calculated by a standard formula (2-2), so that the theta is generally called as the standard root cone angle for distinguishing, and the following is consistent.

The cyclotomic included angle gamma in the parameters of the inverted cone teeth is an important parameter for detecting the accuracy of the processed tooth parts, but the gamma cannot be input on a hobbing machine, the hobbing machine needs to input a root cone angle theta to process a correct cyclotomic included angle gamma, the relationship between the root cone angle theta and the cyclotomic included angle gamma of the inverted cone teeth can be calculated by a formula (2-2),

in the production process, when the inverted cone teeth machined by the variable-pressure-angle hob are detected, the result that the cyclotomic included angle of the inverted cone teeth machined by the machine tool is adjusted according to the standard root cone angle calculated by the formula (2-2) is inconsistent with a theoretical value, namely the correct root cone angle theta 'needs to be calculated to facilitate distinguishing the root cone angle theta' after the variable pressure angle in order to meet the requirement that the cyclotomic included angle gamma value in the parameters of the inverted cone teeth meets the drawing.

The invention can deduce the relation between the root cone angle theta 'and the cyclotomic angle gamma after the pressure angle is changed in detail, and concretely deduces the relation between theta' and the cyclotomic angle gamma.

As shown in fig. 4 and 5, there is a flank relief angle β ', i.e., the tooth flank helix angle, at any rounded (radius r') interface for the inverted tooth;

where Δ b is the distance between section 1 and section 2, S_n2、S_n1The tooth thickness of the cyclotomic part of the section 1 and the section 2 respectively.

Arc tooth thickness S of arbitrary circle r' section of gear_n' the calculation formula is as follows (the derivation of the formula refers to the theoretical basis for designing gear cutters, mechanical industry publishers, which is not derived herein):

wherein x 'is the arbitrary section displacement coefficient, α' is the pressure angle at the arbitrary section, inv is the involute function, r₀Is radius of partial circle, modulus m_n，α_nIs the rounding pressure angle; any round section tooth thickness corresponding to circle center half angle

(as shown in figure 5) of the drawings,

will be given in the formula (2-5)

Are respectively composed of

And

alternatively, x' and respectively by x₁And x₂Instead, i.e.

The equation is poor:

the axial distance between the 0 section (displacement coefficient 0) of the gear and the section after displacement is b.

b＝x’m_ntanθ (2-7)

B in the formulas (2-7) is respectively represented by b₁、b₂Alternative, x' and respectively by x₁And x₂Replacement and difference, i.e. b₁、b₂Making a difference:

will be the formula (2-5) S_n' respective S_n1、S_n2Instead, by difference, i.e. tooth thickness S at r' for both sections_n1、S_n2Making a difference:

the formula (2-8), (2-9) and (2-3) are solved simultaneously to obtain

Then the pitch angle β of the gear's base circle at the base circle_b0：

Wherein r is_b0Is the base circle radius;

according to the principle that the base pitch is equal, the base circle helix angle is unchanged, and when the pressure-variable angle hob is adopted:

sinα₀tanθ＝sinα_ttanθ' (2-12)

thereby obtaining a varied pressure angle back root cone angle θ':

in summary, the present invention provides a method for processing inverted cone teeth by a variable pressure angle hob, which comprises the following steps:

1) pressure angle α through back taper tooth_nCalculating a standard root cone angle theta by using the inverted cone tooth cyclotomic included angle gamma according to a formula (2-2);

2) determining pressure angle α of variable pressure angle hob_tThe parameter is a design parameter;

3) calculating a root cone angle theta' after the pressure angle is changed;

4) and (4) debugging the movement path of the machine tool shaft on the gear hobbing machine according to the root cone angle theta' after the pressure is changed, and finishing the processing of the inverted cone teeth by the pressure-change angle hob.

The method of the invention firstly obtains the change formula of the root cone angle when the variable pressure angle hob is used for processing the inverted cone teeth, perfects the theoretical calculation method of the inverted cone teeth for processing the hob, provides theoretical basis for processing the inverted cone teeth by using the existing hob different from the gear pressure angle, and reduces the development cost that a new gear needs to be manufactured into a new hob.

The following provides an analysis of root cone angle error of the inverted cone tooth part processed by a variable pressure angle hob.

Modulus mn	Pressure angle αn	Cyclotomic angle gamma	Hob pressure angle αt	Standard root angle theta	Actual root cone angle theta'
						2.5	30°	6°	25°	5.187°	6.128°

If a cyclotomic included angle measured after hobbing of the inverted bevel gear by using a hobbing cutter with a pressure angle of 25 degrees according to a standard root cone angle theta is 5.07 degrees, the cyclotomic included angle is greatly different from a 6-degree cyclotomic included angle required by a drawing, and a synchronizer has a large gear-disengaging risk. And according to the average value of the cyclotomic included angle after the actual root cone angle theta' is processed to be 6.03 degrees, the theoretical calculation result is met, and the theoretical derivation is verified.

Claims (1)

1. A method for processing inverted cone teeth by a variable pressure angle hob is characterized by comprising the following steps:

1) pressure angle α through back taper tooth_nCalculating a standard root cone angle theta by using the inverted cone tooth cyclotomic included angle gamma according to a formula (2-2);

2) determining pressure angle α of variable pressure angle hob_t；

3) Calculating a root cone angle theta' after the pressure angle is changed;

4) and (4) debugging the movement path of the machine tool shaft on the gear hobbing machine according to the root cone angle theta' after the pressure angle is changed, and finishing the processing of the inverted bevel gear by the pressure angle-changing hob.

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