CN102371473A - Method for machining standard spherical involute spur bevel gear - Google Patents

Abstract

The invention discloses a method for machining a standard spherical involute spur bevel gear. The method comprises the following steps of: (I) teeth blank machining: manufacturing a teeth blank of a gear by using a forging process; (II) tooth form machining: machining the standard spherical involute spur bevel gear as required by using a gear shaper cutter on a spur bevel gear shaper according to a principle of generating a gear of a gear; (III) thermal treatment of the gear: performing thermal treatment on the gear subjected to initial machining; and (IV) finish machining of the gear: performing finish machining on the gear subjected to thermal treatment to obtain the gear meeting requirements. The gear machined by using the method for machining the standard spherical involute spur bevel gear, provided by the invention has the advantages of high precision in tooth form and tooth profile, transmission stability and high comprehensive performance.

Description

Method for processing standard spherical involute straight-tooth conical gear

Technical Field

The invention relates to a processing method of a transmission part, in particular to a processing method of a standard spherical involute straight bevel gear.

Background

The spherical involute straight bevel gear is one of the most basic parts for transmitting parallel shaft motion and power in the mechanical field, and is widely applied to various mechanical equipment such as mines, metallurgy, buildings, transportation and the like. At present, a spherical involute straight bevel gear is usually arranged on a straight bevel gear shaper, and the tooth profile of the spherical involute straight bevel gear is processed by two standard gear shaping cutters fixedly arranged on a cutter frame according to the principle of 'shape-producing gear'. When in processing, the upper tool rest and the lower tool rest of the straight bevel gear shaper make linear reciprocating cutting motion, the whole tool rest is arranged on the cradle and swings with a certain angle along with the cradle to form unfolding motion together with the positive and negative rotary motion of the corresponding angle of a workpiece, the cradle completes the cutting motion of one tooth after reciprocating up and down once, at the moment, the workpiece exits along with the saddle, rotates by a certain angle to divide teeth, and then the saddle enters the working position again to start cutting a second tooth. The cutting edge of the gear shaper cutter is an oblique straight line, the tooth profile angle of the gear shaper cutter is 20 degrees, an oblique plane is formed in the cutting motion process, namely the tooth surface of the gear shaper, and the tooth surface curved surface of the processed straight bevel gear is enveloped by the oblique plane tooth surface of the gear shaper through generating motion.

Due to errors of processing machinery and installation, obvious errors can be generated near the tooth top and the tooth root of the gear teeth, the thickness of the tooth top is uneven and is smaller than that of the gear teeth of the spherical involute straight-tooth conical gear, namely, the tooth top becomes sharp. The straight bevel gear processed by the method has low precision, and is not a spherical involute straight bevel gear in the standard sense.

Disclosure of Invention

The invention aims to solve the technical problem of designing a method for processing a standard spherical involute straight bevel gear, which can overcome the defects that the precision generated by processing the spherical involute straight bevel gear according to the principle of 'shape-producing gears' is not high and the actually obtained gear is not a standard spherical involute gear, and designs a method for accurately processing the spherical involute straight bevel gear.

Technical scheme

A processing method of a spherical involute straight bevel gear comprises the following steps:

(I) processing a gear blank, namely manufacturing a gear blank of the gear by using a forging process;

(II) processing tooth profiles, namely processing the required standard spherical involute straight bevel gear on a straight bevel gear shaper by using a gear shaper cutter according to the 'shape-producing gear' principle;

(III) gear heat treatment, namely performing heat treatment on the gear subjected to primary processing;

(IV) finish machining of the gear, namely, finish machining is carried out on the gear subjected to heat treatment to obtain the gear meeting the requirements;

the method is characterized in that: the gear shaper cutter used in the step (II) is a novel gear shaper cutter, and the tooth-shaped curved surface of the gear shaper cutter meets a parameter equation:

namely, the tooth form angle of the gear shaper cutter is 19 degrees 53'.

Advantageous effects

The straight bevel gear manufactured by the method for processing the standard spherical involute straight bevel gear has high tooth profile precision, stable transmission, small vibration and low noise, improves the contact ratio of the straight bevel gear, improves the contact and stress conditions of the tooth surface, avoids the tooth jamming phenomenon and improves the precision of a transmission system.

Drawings

Fig. 1 is a schematic cross-sectional view of a conventional gear shaper cutter for machining a spherical involute spur bevel gear.

Fig. 2 is a schematic cross-sectional view of the novel gear shaper cutter according to the present invention.

Fig. 3 is a schematic view of a standard spherical involute spur bevel gear according to a first embodiment of the present invention.

Fig. 4 is a schematic diagram of a standard spherical involute spur bevel gear in a second embodiment of the invention.

Detailed Description

The invention is further illustrated with reference to the following figures and specific examples.

The invention relates to a method for processing a standard spherical involute straight tooth conical gear, which comprises the following steps:

(I) processing a gear blank, namely manufacturing a gear blank of the gear by using a forging process;

(II) processing the tooth profile, namely processing the required spherical involute straight bevel gear on a straight bevel gear shaper by using a gear shaper cutter according to the 'shape-producing gear' principle;

as shown in the attached figure 1, the tooth surface of the conventional forming gear for processing the straight bevel gear is an inclined surface, and the theoretical tooth surface of the forming gear for processing the spherical involute straight bevel gear

The tooth surface equation of the curved surface rather than the plane is as follows:

<math> <mrow> <mover> <msub> <mi>P</mi> <mi>r</mi> </msub> <mo>&RightArrow;</mo> </mover> <mo>=</mo> <mi>R</mi> <mfenced open='(' close=')'> <mtable> <mtr> <mtd> <mi>sin</mi> <msub> <mi>&alpha;</mi> <mn>0</mn> </msub> <mi>sin</mi> <mi>&psi;</mi> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <msub> <mi>&alpha;</mi> <mn>0</mn> </msub> <mi>cos</mi> <mi></mi> <mi>&phi;</mi> <mi>sin</mi> <mi>&psi;</mi> <mo>-</mo> <mi>sin</mi> <mi></mi> <mi>&phi;</mi> <mi>cos</mi> <mi>&psi;</mi> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <msub> <mi>&alpha;</mi> <mn>0</mn> </msub> <mi>sin</mi> <mi></mi> <mi>&phi;</mi> <mi>sin</mi> <mi>&psi;</mi> <mo>+</mo> <mi>cos</mi> <mi></mi> <mi>&phi;</mi> <mi>cos</mi> <mi>&psi;</mi> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow> </math>

-a position vector of a point on a theoretical tooth surface of the generating gear;

wherein R is the cone distance phi psi/cos alpha₀，α₀Is a pressure angle, a standard value alpha₀At 20 °, the cone pitch R and the angle ψ are two basic variables, let z_rC, i.e. z_rThe coordinates being constant, or

<math> <mrow> <mi>R</mi> <mo>=</mo> <mfrac> <mi>C</mi> <mrow> <mi>cos</mi> <msub> <mi>&alpha;</mi> <mn>0</mn> </msub> <mi>sin</mi> <mi></mi> <mi>&phi;</mi> <mi>sin</mi> <mi>&psi;</mi> <mo>+</mo> <mi>cos</mi> <mi></mi> <mi>&phi;</mi> <mi>cos</mi> <mi>&psi;</mi> </mrow> </mfrac> <mo>,</mo> </mrow> </math>

C-is a constant;

substituting the formula to obtain the profile curve of the section of the gear perpendicular to the pitch line as follows:

<math> <mrow> <mfenced open='(' close=')'> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mi>P</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>y</mi> <mi>P</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>z</mi> <mi>P</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfrac> <mi>C</mi> <mrow> <mi>cos</mi> <msub> <mi>&alpha;</mi> <mn>0</mn> </msub> <mi>sin</mi> <mi></mi> <mi>&phi;</mi> <mi>sin</mi> <mi>&psi;</mi> <mo>+</mo> <mi>cos</mi> <mi></mi> <mi>&phi;</mi> <mi>cos</mi> <mi>&psi;</mi> </mrow> </mfrac> <mfenced open='(' close=')'> <mtable> <mtr> <mtd> <mi>sin</mi> <msub> <mi>&alpha;</mi> <mn>0</mn> </msub> <mi>sin</mi> <mi>&psi;</mi> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <msub> <mi>&alpha;</mi> <mn>0</mn> </msub> <mi>cos</mi> <mi></mi> <mi>&phi;</mi> <mi>sin</mi> <mi>&psi;</mi> <mo>-</mo> <mi>sin</mi> <mi></mi> <mi>&phi;</mi> <mi>cos</mi> <mi>&psi;</mi> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <msub> <mi>&alpha;</mi> <mn>0</mn> </msub> <mi>sin</mi> <mi></mi> <mi>&phi;</mi> <mi>sin</mi> <mi>&psi;</mi> <mo>+</mo> <mi>cos</mi> <mi></mi> <mi>&phi;</mi> <mi>cos</mi> <mi>&psi;</mi> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow> </math>

x_P，y_P，z_P-coordinates of a point on the section profile curve.

Obviously, the section tooth profile is a curve instead of a straight line, the shape-producing gear of the spherical involute straight bevel gear is processed as a gear cutting tool, namely, the shape-producing gear tool is equivalent to a gear planing tool, obviously, the tooth profiles of the two tools are different, and the tooth profile angle alpha of the traditional standard gear planing tool₀20 deg. is equal to. The tooth profiles of the cutter for processing the shape-producing gear of the spherical involute straight bevel gear are basically overlapped near a pitch line, but the farther the tooth profiles are away from the pitch line, the larger the deviation of the tooth profiles of the two cutters is, the maximum is the tooth top and the tooth bottom, the larger the modulus is, the larger the deviation of the tooth top and the tooth bottom is, the larger the deviation of the tooth profiles of the two cutters is, the larger the deviation of the tooth surfaces of the two processed corresponding bevel gears is, and in order to enable the tooth surfaces of the processed bevel gears to be closer to the curved surface of the tooth surface of the spherical involute₀Linear tooth profile not equal to 20 degrees.

From the spherical triangular sine formula, the addendum angle theta_aOr root angle theta_f，θ_a＝θ_fCan be expressed as sin theta_a＝sinα₀sinψ_aIn addition, the first and second substrates are, in addition,

<math> <mrow> <mi>tan</mi> <msub> <mi>&theta;</mi> <mi>a</mi> </msub> <mo>=</mo> <mfrac> <msub> <mi>h</mi> <mi>a</mi> </msub> <mi>R</mi> </mfrac> <mo>=</mo> <mfrac> <mn>2</mn> <mrow> <msub> <mi>z</mi> <mn>1</mn> </msub> <msqrt> <mn>1</mn> <mo>+</mo> <msup> <mi>i</mi> <mn>2</mn> </msup> </msqrt> </mrow> </mfrac> </mrow> </math>

wherein,

z₁number of teeth, typically z₁＝13～30，

The transmission ratio of the i-single-stage gear is generally 1-6,

therefore theta_a＝0.1-3.2°，ψ_a＝0.29°～9.4°；

The tooth profile of a spherical involute gear cutter is required to satisfy the condition that a linear equation of unary regression is y ═ a + bx

a-constant term, b-regression coefficient, and

$b=\frac{l_{\mathrm{xy}}}{l_{\mathrm{xx}}}$

<math> <mrow> <mi>a</mi> <mo>=</mo> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mo>-</mo> <mi>b</mi> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> </mrow> </math>

whereinAs an arithmetic mean, i.e.

<math> <mrow> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> <mo>=</mo> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>x</mi> <mi>i</mi> </msub> </mrow> </math>

<math> <mrow> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mo>=</mo> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>y</mi> <mi>i</mi> </msub> </mrow> </math>

Order to

<math> <mrow> <msub> <mi>l</mi> <mi>xx</mi> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </math>

<math> <mrow> <msub> <mi>l</mi> <mi>xy</mi> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>-</mo> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <msub> <mi>l</mi> <mi>yy</mi> </msub> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>-</mo> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </math>

Then the correlation coefficient

$r=\frac{l_{\mathrm{xy}}}{\sqrt{l_{\mathrm{xx}}{l}_{\mathrm{yy}}}}$

x_iAbscissa of the sample point

y_i-ordinate of the sampling point.

Obviously, the linear correlation is larger as the | r | is closer to 1, the point on the tooth profile of the spherical involute gear shaper cutter can be obtained by the curve equation of the section tooth profile of the generating gear perpendicular to the pitch line, and the point on the tooth profile of the spherical involute gear shaper cutter can be obtained by a method for taking a special value according to the prior art_aTaking n as 11 points in the range of 0 to 9.4 degrees, this can obtain b as 2.765, obviously, b is independent of the size of the bevel gear, a as-0.0001R, a is dependent on the taper distance R of the bevel gear and is proportional, and substituting into the unary regression linear equation, and obtaining the regression linear equation in the rectangular coordinate system oxy, see fig. 2

<math> <mrow> <mi>y</mi> <mo>=</mo> <mo>&PlusMinus;</mo> <mn>0.0001</mn> <mi>R</mi> <mover> <mo>+</mo> <mo>&OverBar;</mo> </mover> <mn>2.765</mn> <mi>x</mi> </mrow> </math>

For right flank profiles the first term is positive, the second term is negative, and the left flank profile the first term is negative, the second term is positive, the correlation coefficient r is 0.99999, then highly correlated, and this equation is available. From tan^-1(2.765) ═ 70 ° 7', resulting in the tooth angle α of the shaper cutter₀When the gear is made at 19 degrees and 53' degrees, the precision is the highest, and the tooth profile of the new gear shaper cutter satisfies the equation

I.e. the tooth form angle alpha₀19 deg. 53'.

For straight bevel gears with the cone distance R less than or equal to 100mm, the term of +/-0.0001R is ignored, and then an oblique straight line is takenAs a tool profile, i.e. the pitch point coincides with the pitch point of a conventional standard tool, but the tool profile angle is α₀The gear shaper with the angle of 19 degrees 53' is processed to obtain the standard spherical involute straight tooth conical gear as shown in the attached figure 3.

(III) heat-treating the gear subjected to primary processing;

(IV) finish machining of the gear, wherein the gear subjected to heat treatment is subjected to finish machining;

using the tooth form angle alpha₀The gear shaper cutter is used for processing the required standard spherical involute straight-tooth conical gear according to the ' shape-producing gear ' principle on a novel gear shaper cutter straight-tooth conical gear shaper with an angle of 19 degrees and 53 ', so that the defect of uneven tooth top thickness caused by machining and installation errors of the gear shaper cutter can be avoided;

another embodiment of the invention is to reserve the terms of +/-0.0001R for the straight bevel gear with the cone distance R being more than 100mm, and then take an oblique straight line

As tool tooth form, i.e. the pitch point does not coincide with that of a conventional standard tool, i.e. the tool tooth form angle is still alpha₀19 deg. 53' as shown in figure 4 for a standard spherical involute spur bevel gear.

Claims (1)

1. A processing method of a spherical involute straight bevel gear comprises the following steps:

(I) processing a gear blank, namely manufacturing a gear blank of the gear by using a forging process;

(II) processing the tooth profile, namely processing the required spherical involute straight bevel gear on a straight bevel gear shaper by using a gear shaper cutter according to the 'shape-producing gear' principle;

(III) gear heat treatment, namely performing heat treatment on the gear subjected to primary processing;

(IV) finish machining of the gear, namely, finish machining is carried out on the gear subjected to heat treatment to obtain the gear meeting the requirements;

the method is characterized in that: the gear shaper cutter used in the step (II) is a novel gear shaper cutter, and the tooth-shaped curved surface of the gear shaper cutter meets a parameter equation:

namely, the tooth form angle of the gear shaper cutter is 19 degrees and 53';

x-the abscissa of a point on the tooth surface; y-ordinate of a point on the tooth surface;

r-cone distance.

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