RU2041788C1 - Method of grinding - Google Patents

Abstract

FIELD: grinding of bodies of revolution. SUBSTANCE: free displacement of workpiece is provided in the stages of coarse and finish grinding, prior to grinding, the workpiece is placed relative to the center line of the grinding wheels at such a distance that condition B = 2π/N₁ is ensured, where N₁ in the number of the predominant harmonic component of the shape error; B is the angle between the longitudinal axis of the workpiece and longitudinal axes of the grinding wheels. In the process of coarse grinding, after the predominant error is corrected the workpiece is displaced in the vertical direction in such a way that condition B = 2π/N₂ is ensured for the remaining harmonic component, where N₂ is the number of the remaining harmonic error component. EFFECT: enhanced grinding capacity. 2 dwg

Description

 The invention relates to mechanical engineering and can be used in metalworking when grinding bodies of revolution, mainly shafts.

 The closest in technical essence and the achieved results is the grinding method, in which the part is installed in the center, having the ability to freely move in the direction of the transverse feed at the final grinding stage, rotated from an autonomous drive and grinded simultaneously with two circles on both sides.

 The disadvantage of this method is not high enough productivity, due to the fact that at the insertion stage, when the center is fixed from movement, simultaneous grinding with two circles is difficult due to the different wear of each of the circles, and predominant grinding with one circle leads to a deterioration in surface quality, which forces to reduce the feed or increase the allowance for fine grinding.

 The objective of the invention is to provide a method of grinding free from the above disadvantages.

The invention consists in a grinding method, in which the part is installed in the center, which can freely move in the direction of the transverse feed at the stages of rough and finish grinding, rotate from a standalone drive and grind simultaneously with two circles on both sides, and before processing, the part is set relative to lines of centers of grinding wheels at such a distance that the condition
B 2 π / N ₁ , where N _{1 is the} number of the dominant harmonic component of the error;
The angle between the longitudinal axis of the workpiece and the longitudinal axes of the grinding wheels. During rough grinding, after correcting the dominant error, the part is moved in the vertical direction so that for the remaining harmonic component of the error the condition
In 2 π / N ₂ , where N _{2 is the} number of the remaining harmonic component.

 The technical result of the invention is to increase the productivity of the processing process by reducing grinding time.

 The drawing shows a diagram of a device for implementing the method.

 The essence of the method is as follows.

+

A_пsin(N_φ+φ_o), устанавливают в центра 2, расположенные в кронштейнах 3 относительно линии центров шлифовальных кругов таким образом, чтобы выступы профиля, соответствующие доминирующей погрешности (имеющей наибольшую амплитуду Ап), находились в контакте одновременно с обоими шлифовальными кругами 4 и 5. Такое расположение детали определяется по зависимости:
B

где N число вершин определенной гармоники, т.е. при известной доминирующей гармонике определяется угол наладки В.Workpiece 1 with a known transverse profile, presented in the form of a harmonic Fourier series
r (φ) =

+

A _p sin (N _φ + φ _o ), is installed in the center 2 located in the brackets 3 relative to the line of centers of the grinding wheels so that the protrusions of the profile corresponding to the dominant error (having the largest amplitude Ap) are in contact simultaneously with both grinding wheels 4 and 5. This location of the part is determined by the dependence:
B

where N is the number of vertices of a certain harmonic, i.e. with a known dominant harmonic, the adjustment angle B is determined.

 According to the work (Gurin F.V. et al. Technology of tractor engineering. M. Mashinostroenie, 1981) to evaluate geometric accuracy, it is sufficient to determine and take into account the first six harmonics.

It is obvious that even harmonics are effectively corrected with the location of the workpiece on the center line of the grinding wheel, and odd harmonics at the following values of B: N 5 for B 72 ^°; N 3 when B ^120; N 1 at 360 ^o .

 Then the workpiece 1 is brought into rotation by an autonomous drive (not shown in the drawing), two grinding wheels 4 and 5 are brought in and the part is ground by cutting. By setting the part in the position corresponding to the most intensive correction of a certain harmonic, this harmonic is corrected most quickly. After correcting the dominant error to the required value, turn on the engine 6 and, using the lead screw 7, change the position of the table 8 with the bracket 3 mounted on it to such a position of the workpiece relative to the grinding wheels, at which the adjustment angle B takes on a value that ensures the greatest intensity of correction of the remaining error.

 The moment of time at which it is necessary to change the position of the workpiece relative to the line of the centers of the circles, occurs after grinding the allowance equal to the amplitude of the dominant harmonic, and is determined by the active control device 9, according to the limb of the machine or in some other way.

At the same time as the dominant component, other harmonics are corrected, but with less intensity. In this regard, it is desirable to know the remaining error of each harmonic by the time it is necessary to change the position of the part relative to the circles. This will reduce the processing time by reducing the margin of error correction. To determine the residual error, it is necessary to consider the laws of the process of correcting various harmonics. Error correction is interconnected with the features of double-sided grinding in moving centers, namely with the condition of simultaneous contact of two circles with the workpiece. This condition consists in the correspondence of the sum of the radii r ₁ and r ₂ (Fig. 1) in the direction of the axes of the circles to a certain distance between the circles. When considering each harmonic individually, the radii r ₁ and r ₂ change according to one harmonic law with an offset by an angle B.

+A_пcosN_φ
r₂=

+A_пcosN(φ+β) Сумма радиусов
r_s=r₁+r₂=2

+A_scos(N_φ+B_s) A_s и B_s параметры суммарной функции.r ₁ =

+ A _p cosN _φ
r ₂ =

+ A _p cosN (φ + β) Sum of radii
r _s = r ₁ + r ₂ = 2

+ A _s cos (N _φ + B _s ) A _s and B _{s are} parameters of the total function.

Thus, the pattern of change in the profile of the part relative to two grinding wheels is obtained. It allows you to determine the patterns of change in the shape of the part during grinding. The larger the total amplitude A _s with respect to the original A _p , the more intensively the error is corrected.

получим:
Ca=

(1)
Для определения угла наладки В, при котором величина уточнения максимальна и исправление погрешности также максимально, необходимо продифференцировать функцию Са f(B) и, приравняв результат к нулю, выразить В.We denote the ratio A _s / A _{n by} Ca and substituting instead of A _s its expression
A _s = A

we get:
Ca =

(1)
To determine the adjustment angle B, at which the refinement value is maximum and the error correction is also maximum, it is necessary to differentiate the function Ca f (B) and, equating the result to zero, express B.

0 откуда
B

Таким образом получена зависимость угла наладки В от составляющей погрешности N, при которой интенсивность исправления погрешности N-гармоники максимальна.

0 from
B

Thus, the dependence of the adjustment angle B on the error component N is obtained, at which the intensity of correction of the N-harmonic error is maximum.

After grinding the workpiece with a dominant error of N ₁ on set-up B ₁ , to the required value, we change the set-up by moving the workpiece vertically to obtain an angle B ₂ optimal for correcting the remaining error N ₂ .

(2) где Δ N величина погрешности N (амплитуда гармоники N), мм;
t_м радиальная подача при шлифовании, мм/мин;
Са коэффциент (характеристика) исправления погрешности.Processing time τ of error N is determined by the dependence
τ

(2) where Δ N is the error N (harmonic amplitude N), mm;
t _m radial feed during grinding, mm / min;
Sa is the coefficient (characteristic) of error correction.

 Since other harmonics are corrected simultaneously with the dominant error, but with a lower intensity, it is necessary to determine the correction time or residual error for these harmonics.

For this also use the formula (2) or the formula
_Ost ΔN = ΔN _{m 2} -t ˙τ˙ Ca ₂ where Δ N _ost error remaining after grinding during the time τ, mm;
Δ N ₂ initial error N ₂ harmonics, mm;
τ grinding time, mm;
Ca _{2 is} the correction intensity factor.

Coefficient Ca _{2 is} determined by the formula (1), its value will not be maximum, since for harmonics N ₂ adjustment with an angle of B _{1 is} not optimal.

For simplicity of determining the coefficient Ca is convenient to use the graph (FIG. 2) constructed for different harmonics and the angles N 1.6 In ^about 90,180. It can be seen from the graph that, for angles close to optimal B B _opt ± 5 ^{°, the} value of Ca changes insignificantly, which simplifies commissioning and makes it more technological.

 We will illustrate the characteristic of the intensive correction of Ca errors by an example.

For B ¹⁸⁰ (i.e., at the location of the items on the grinding wheel center line) the error items, shaped cut tricrotic (N 3), and therefore, Ca 0 corrected characteristic is extremely difficult, and roundness (N 2) is corrected most intensively, while the characteristic of CA 2 is maximum.

To determine the residual error, use the formula:
Δ _ost = ΔN-t _m ˙τ˙ Ca, where Δ N is the value of the initial error of the N-vertex cut, mm;
t _m radial feed of each grinding wheel, mm / min;
τ grinding time min.

PRI me R. Harmonic analysis found that the workpiece has a dominant ovality (N 2) error of Δ ₂ 0.4 mm; the following errors are three-vertex cut (N 3) Δ ₃ 0.3 mm and five-vertex cut (N 5) Δ _s 0.2 mm. Radial feed t _m 1 mm / min.

 The first processing option.

Grinding begins at installation parts laps on the center line in ^180, the Ca ₂ 2.0; Ca ₃ 0; Ca _s 0.

To correct ovality, the part must be sanded within 0.2 minutes, then:
Δ _ost2 0.4 1 ˙ 0.2 ˙ 2.0 0 mm
Δ _ost3 0.3 1. 0.2 ˙ 2.0 ˙ 0 0.3 mm
Δ _ost5 0.2 1 ˙ 0.2 ˙ 2.0 ˙ 0 0.2 mm
After 0.2 minutes of grinding change the position of the workpiece relative to the center line circles value in ^120, in which the Ca _s 2,0; Ca ₅ 1.0.

To correct the trihedral, a time τ of 0.15 minutes is required. Then
Δ _ost3 0.3 1 x 0.15 x 2.0 0 mm
Δ _osts 0.2 1 x 0.15 x 1.0 0.05 mm
The residual error of the five-vertex cut is corrected at B 145 ° ^for 0.025 minutes, or at B 120 ° ^for 0.05 minutes. Thus, the total grinding time is
τ 0.2 + 0.15 + 0.025 0.375 min
It should be noted that in order to ensure a constant radial feed to the part when changing the position of the part relative to the wheels, the speed of the linear movement of the grinding wheels must be adjusted by increasing the speed of the headstock with decreasing angle B and decreasing speed with increasing B.

 It is necessary to strive for the minimum processing time for the radial feed to the part when changing the position of the part relative to the wheels, the speed of the linear movement of the grinding wheels must be adjusted by increasing the speed of the headstock with decreasing angle B and decreasing speed with increasing B.

 It is necessary to strive for the minimum processing time and, if possible, the minimum number of movements of the part relative to the circles.

 With the same initial data, we consider the second processing option.

Grinding begins at B 145 ^about , with Ca ₂ 1.7; Ca ₃ 1.7; Ca ₅ 2.0.

0,24 мин
для исправления трехгранки:
τ₃

0,18 мин
для исправления пятигранки:
τ₃

0,1 мин
Таким образом за время τ 0,24 мин будут исправлены все доминирующие составляющие, причем для этого потребуется меньше времени, чем в предыдущем примере, кроме того, здесь отсутствует необходимость перемещения детали в процессе обработки, так как время исправления овальности перекрывает время исправления других гармоник, что является частным случаем.To correct ovality, time is required:
τ ₂

0.24 min
to fix the trihedral:
τ ₃

0.18 min
to fix pentahedral:
τ ₃

0.1 min
Thus, for the time τ 0.24 min, all dominant components will be corrected, and this will require less time than in the previous example, in addition, there is no need to move the part during processing, since the ovality correction time overlaps the correction time of other harmonics, what is a special case.

 In the practice of traditional centerless grinding, the distance between the axis of the part and the line of centers of the grinding wheels is set as the setting parameter.

 The installation height of the part depends on the diameters of the wheels and the part in such a way that at the same angles B and different diameters of the circles and the part, the installation height will be different, therefore, when double-sided grinding, it is convenient to use parameter B for calculations.

где D диаметры кругов;
d диаметр обрабатываемой детали.To recalculate the distance from the line of the centers of circles H and the adjustment angle B, you can use the dependence:
B = arccos

where D are the diameters of the circles;
d diameter of the workpiece.

 Thus, the use of the proposed method provides an increase in the productivity of the grinding process.

Claims (1)

GRINDING METHOD, including the stages of rough and finish grinding, in which the part is installed in the center, which can move freely in the direction of the transverse feed at the stage of finishing grinding, are rotated from an autonomous drive and are ground simultaneously on two sides, characterized in that free movement details in steps and create rough and finish grinding, wherein before processing item is set with respect to the grinding wheel center line by a distance B = 2π / N ₁ where N ₁ but ep dominant harmonic component of the error forms, B angle between the longitudinal axis of the workpiece and the longitudinal axes of the grinding wheel, and during rough grinding after correction dominant error item is moved in the vertical direction so that for the remainder of the harmonic component satisfy the condition B = 2π / N _2, where N ₂ number of the remaining harmonic error.

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