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0CALCULATION AND GRAPHIC MODELING OF MILLING FORCE PARAMETERS
Gafurov Akmaljon Mavlonzhonovich Fergana polytechnic insitute, PhD
Kuchkorov Sobirzhon Karimzhonovich
NamECI, PhD
Nomanjonov Sohibjon Nomanjon coals Fergana polytechnic insitute, PhD
Matkarimov Behzod Bakhtiyorzhon coals Fergana polytechnic insitute, PhD
Abstract. Calculation and graphical modeling of strength parameters during machining of parts with a molded surface during milling operations in mechanical engineering remains the most important task today. Before processing the shaped surfaces, it will be necessary to study the working surfaces of the stamping molds. This article presents methods for determining the geometric parameters of the surface when processing stamping molds on shaped surfaces, in particular, data on the structure of the cutting zone of shaped surfaces, the penetration of the cutter into the cutting zone and the control conditions in the cutting zone.
Аннотация. Расчет и графическое моделирование прочностных параметров при механической обработке деталей с формованной поверхностью при фрезерных операциях в машиностроении остается важнейшей задачей на сегодняшний день. Перед обработкой фасонных поверхностей необходимо будет изучить рабочие поверхности штамповочных форм. В данной статье приведены методы определения геометрических параметров поверхности при обработке штамповочными формами на фасонных поверхностях, в частности данные о структуре зоны резания фасонных поверхностей, проникновении резца в зону резания и условиях контроля в зоне резания.
Keywords: calculation of strength parameters, graphical modeling, diagnostics, models, cutting area, strength, durability, stamping, stamping shape, cutting parameters.
Ключевые слова: расчет прочностных параметров, графическое моделирование, диагностика, модели, зона резания, прочность, долговечность, штамповка, форма штамповки, параметры резания.
To solve the problem of automating the calculation and selection of the diagnostic feature of the milling condition, the following mathematical software was developed for the calculation of force parameters during milling and graphical modeling.
Figure 1 shows a diagram of changing the relative position of the working part of the cutting tool for modeling milling types and views, which is provided by a combination of specified values width V and milling depth t. D fr is the diameter of the milling tools, as well as the cutting movement V p and the feed speed V s for the specified cutting directions Xe parameter . F z and components of the cutting force u, z acting on the milling tooth in the plane Cartesian
coordinate system.
Forces F v and F h , F z and the derivatives of the forces are determined by the appropriate sign after calculating v, h s in the flat Cartesian coordinate system: F h in h coordinate , F v in v coordinate .
The chamfer height of the milling tooth when working with pocket (b) and finger mills (c) Figure 1 (b, c) shows parameters b and t.
The presented parameters and the variation of the X e parameters allow modeling the following milling options:
a ) Xr = D fr - Xe - t, if X r < 0 if , then initial information correction; b ) 7 >3- limiting the dependence of the chamfer height and milling width;
c ) a < 0.5 - limit the height of the chamfer; g ) ro< 45-ro angle according to restriction .
Milling tool radius count: R =
Calculation of the turning angle of the milling tool using the B parameter:
Фв
(B - a) - tgto ■ 180 TIR
(1)
а)
b)
Fig. 1 - Milling types and schemes modeling for tool instrument and of the part mutually location change scheme.
The calculated value is limited to the second character and rounded to 0.5 or an
integer.
Calculation of the milling tooth contact angle using the t parameter:
R — X„ R-X„
i(jt = ISO — arccos-
arcxos-
,hereXv =Dév-t-Xa (2)
R R -------
From the expression of some circular functions in terms of others: arccos x=180-arccos(-x)=90-arcsinx..
y is the concept of angle values, limited to the second sign and rounded to 0.5. \|/2face step count:
0.5 or round to an integer.
Calculation of the total contact angle yk: yk = yt + y b
Determine the fixed A discreteness.
A is allowed if an integer (A is set by default, and the allowed samples are specified and set by the operator)^1
A A A A
j. j= t" Determination of the maximum number of milling tool teeth working at the
Z
same time.
If j <1, to Z j = 1. If j >1, from Zj-x +1, where x is the number whole number part .
X e calculation of the turning angle of the milling tool in the presence of dependence.
Calculation of thrust value for tooth S: :
5,.
5„ -
n-Z
,here n —
tt ■ D>
(5)
Determining the values of the function ^i=s(yi), where ^ is the contact angle of the point of application of the cutting force vector on the blade of the cutting tool, which is the initial rotation angle of the milling tooth
a) task y :
b) result
If: then
if : yt>yB then
ф; = г ■ Д,бу here i = 0Д ... Гсф,here Тсф =
ih 2
2
-+Ф0
F zt, z force parameters initial values count Multiplicative power functions used:
in this in this in this
in this in this in this
0 < yi < yB yB < yi
< yt
yt < yi
< yk
0<щ<щ
t
vb<w< щ
F„ =
ISO
ос j. ■ В
. К.I ■ Кп ■ К-, Су, ■ а*.
Ф[ « "z ïi
fi
(6)
tt, + 90)
2,5'
180
а** -Б7? -К, ■К2 Л' + С. ■ ■ ■ С* ■ ■ К{ ■ К\
ïi Ф[ Ъ nv Ïi Ф; 3 d'
H-
(7)
if+9Q\F1
In these formulas, \ 'iec. ) a variable is used that takes into account the increase in power parameters during the transition from opposite and transverse milling schemes.
a) Calculation of the initial thickness of the cut layer tif,: = Ss ■ sin
b) Primary milling width count Bvi. If: yt > ^b
5,. after: :
of
B,
rzR ф^ тгЯСф—фг )
If^Tj < фя after
айегфс < ф; < фк
В,,. =
тгЯ-ф
айегф, < ф; <
^ï tgu 100
11. Fh andf,,. calculation of initial values of power parameters.
x i can be greater than 90, so the calculation is required taking into account the functions the sum and difference of the angles. For example:— 90) = cos^ ■ cos90-|- sinîj ■ sin90 = sin^
It allows to calculate the initial values of the considered power parameters with the participation of the teeth of the above-mentioned milling tool. If several milling teeth are
involved in the work at the same time, then finding the common initial values of Fziz, iz, Fviz, Fuz is done.
The calculation of the total force parameters is limited to 360°-limited to the last step of the level i|rz = because they are periodically repeated with a period of \|/z.
1. General initial strength count Fs.z: FZ:Z =
2. General initial strength count
here:
Power l negative is obtained if 0 <x i < 90 ( Fig. 2, a).
If 90< x i < 180 (Fig. 4.2.2, a), then the force l will be positive .
a) calculating initial forces . Fj^iF^y
b) calculating angle coordinates
Fig. -2 - Diagrams of the force vectors acting on the teeth of the milling tool in the presence of several teeth of the milling tool.
Formulas (1) and (2) are found after bringing the force vectors to the center of the flat rectangular coordinate system as shown in Fig. 2.
F vis, F his calculation of total initial forces. (Fig.2, b)
FVjIand calculate the initial total forces, it is necessary to determine the angular
coordinate of the point of application on the circle with the total force R fr . The angular coordinate corresponds to the general angle as shown in Fig. 2-b.
if Fj, E < 0, (Fig. 2, b, picture I -quarter ), then^£ = arc sin— ^ ^ —у
if Fj,e > 0, ( Fig. 2, b, picture II -quarter ), then
Figure 2 presents the algorithm for calculating and selecting the informatics diagnostic feature of the milling condition from the parameters of the milling force. The algorithm works in the following order.
After the task data is set, they are checked position 1.
If the initial data is set incorrectly, then a message about the need to correct them will be displayed on the computer screen. The calculated main parameters are rounded to numerical values limited to the first decimal place of 2, which is sufficient in the actual range of the assigned milling parameters, since the calculation error does not exceed 1%. Then the maximum number of simultaneously working milling teeth necessary for classification after programming to find forces when one (Z i =1) or several (Z i =1) milling teeth are involved in the milling process is determined from their total number Z.
The fixed limit Д4 is introduced in milling in order to exclude uncertain values of the forces at the end of the working contact of the milling tooth, since dividing the total contact angle yk by Д can be a non-indexable residue. This leads to the fact that the function does not reach zero at the end of the working contact of the milling tooth in milling, which leads to uncertainty and large errors in calculations during subsequent mathematical operations on force vectors F=f(y). The fixed data is displayed on the computer screen. This allows the operator to zoom in on the resultant force graphs versus the rotation angle of the tool tooth.
In order to calculate the values of the parameters of the force acting on the tooth of the milling tool when it is rotated by a discrete Д5, it is necessary to determine the values of the angle of rotation of the point of application of the cutting force obtained on the blade of the cutting tool ^ and the values of the width of the milling tool at each moment of cutting 6,7.
After performing calculations of the forces Fz and resulting from the operation of one tooth of the milling tool, a decision is made to display the results on the computer screen according to the criterion of simultaneous participation in the operation of the teeth of the cutting
tool. If z>1, then the transition to the subroutine for calculating the components of the cutting force is performed when several teeth of the cutting tool 8 are involved.
One of the most important criteria for evaluating the results of algorithms in computer programs in which physical parameters are modeled is the adequacy of the modeling results to the analogues obtained in practice.
For this purpose, appropriate experiments were conducted using the described force parameters measurement tools.
F h obtained by milling with a standard six-tooth milling tool with a diameter of Dfr =40 mm from a transverse steel SKD is presented. The processed material CKD was processed at the following milling speed: V = 3 mm, t = 20 mm, V = 30 m/min, S min = 100 mm/min.
The calculated oscillogram obtained by computer software with the help of the developed algorithm corresponds to the experimental oscillogram.
The experimental oscillogram is characterized by the presence of a radial deviation of the milling cutter, which is determined by different maximum values of forces that are cyclically repeated with one cycle of the milling cutter. The value of modeling in terms of the nature and magnitude of the shear force change is almost indistinguishable from the average experimental values. In general, the degree of convergence of the calculated data with the results of experimental studies is at least 90%. Thus, we can state the high adequacy of the developed models and the algorithm for calculating the initial values of the force parameters for the real milling process.
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