MATHEMATICAL MODEL OF THE PART SHAPE AND AUTOMATION ON ITS BASIS OF THE PROCESS OF DEVELOPING THE DRAWING PARAMETERS OF THE AXISYMMETRIC FORGING

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The Turkish Online Journal of Design, Art and Communication - TOJDAC ISSN: 2146-5193, March 2018 Special Edition, p. 458-464

MATHEMATICAL MODEL OF THE PART SHAPE AND AUTOMATION ON ITS BASIS OF THE PROCESS OF DEVELOPING THE DRAWING

PARAMETERS OF THE AXISYMMETRIC FORGING

I.V. Telegin, V.V. Telegin

Lipetsk state technical University, Russia ABSTRACT

A method for constructing a mathematical model of a part is proposed, the semi-finished product of which is produced by the method of hot forging (HF) on crank hot-tamping presses (CHTP) and the construction on its basis of a circular drawing in terms of forgings. The description of the program for ECM allowing to automate both process of performance of the calculations executed according to the given technique, and appointment of allowances, tolerances and blacksmith surplus is given.

Keywords: mathematical model, drawing parameters, axisymmetric forging

INTRODUCTION

The goal of the task to be solved in this work is the development of high-performance HF technological schemes at the CHTP, round in the plan of forgings, characterized by minimal loss of metal during their subsequent machining. As initial data, in accordance with the proposed methodology, the shape of the part (not forgings), simplified to the set of bodies of revolution (model of the part shape) is considered. The mathematical model of a part is a structure of numerical parameters that determine the dimensions and relative positions of these bodies, as well as a number of dependencies on the basis of which the volume (mass) of allowances, tolerances and blacksmith surplus, assigned in accordance with known methods [1], can be calculated each of the surfaces of the part shape model.

The original software solution designed to automate the design of the forging parameters, in conjunction with HF simulation software products based on 3D modeling methods [2], makes it possible to scientifically justify the most effective scheme of hot hot forging from among the possible ones [3, 4], estimate the condition work of stamping equipment [5, 6].

METHODS AND SOFTWARE

Pictures 1 and 2 shows the stages of construction of some structural diagrams of parts obtained from axisymmetric forgings. The building blocks for creating external shapes are rings, with an internal diameter of Di-1 and an outer diameter of Di. The height of the ring is Hi, the size determining its position is Li. The initial or initial form is a cylinder of diameter D0 and height H0. Theoretically, the number of rings is unlimited, in practice 0 ≤ i ≤ 3. The number of variants of the outer forms of the parts is large enough: for i = 0 – 1, i = 2 – 4, i = 3 – 16, i = 3 – 64.

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Picture 1: Stages of construction of the structural scheme of the external shape of the part.

Picture 2: Stages of construction of the structural scheme of the internal shape of a part As in the case with external forms, theoretically the number of internal forms is unlimited, in practice the number of holes is two on top and two from below.

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The configuration of a part depends on the ratio of its dimensions. For the holes, in accordance with Picture 2, these interrelation are obvious:

. ,

,

, ,

0 1 0 1 0

0 1 0 1

0 0 0 0

H bH bH tH tH

bD bD tD tD

D bD D tD

≤ + + +

<

(1)

In expression (1), D₀ and H₀ are the diameter and height of the initial cylinder of the outer shape of the part (see Picture 1).

Picture 3: Possible locations (a, b, c, d) of the subsequent (i-th) element of the outer shape of the part relative to the element of the previous (i-1-th)

The ratio of the sizes determining the position of the i-th element (ring) of the outer form relative to the previous i-1-th element, as follows from Pic. 3, can be written as follows:

a –

⎪⎩

⎪ ⎨

⎧

≤

<

>

−

1 1 1

i i i

i i

H L H

H H

D D

, b –

⎪⎩

⎪ ⎨

⎧

Δ

≥

− +

≤

>

−

i i i

i i

L H H

L H

D D

1 1

, c –

⎪

⎩

⎪ ⎨

⎧

≤

≤ Δ

>

−

1 1

i i

H L

L H

D D

, d –

⎪

⎩

⎪ ⎨

⎧

>

−

1 1 1

i i i

i i

H L H

H H

D D

(2) where ∆ > 0 is the minimum permissible value of the intersection of the heights of the previous and subsequent elements.

The data structure of the shape of the investigated part (the part formula) in the general case is written as follows:

∑

=

−

= ^N

n n n

M

m m m

K

i Di Hi Li tD tL bD bL

N M K P

0 0 0

, ,

, , )

, ,

( _∪

, (3)

where K is the number of elements of the outer form, M, N is the number of holes at the top and bottom defining the internal shape of the part, and the symbol "P" is any combination of words, for example, the name of the part.

The data structure of the shape of the part accurately determines its size and configuration, without taking into account, of course, the radii of curvatures, chamfers, various types of grooves, for example, keyways, slots, gear teeth and other similar elements. The presence of a data structure represented by the part formula is a prerequisite for creating a forging drawing. The main difference between the forging drawing and the detail drawing is the availability of allowances for machining, tolerances and blacksmith surplus. Picture 4 shows the input and processing windows for the part formula data and the results window of the software solution [3], which allows you to automate the process of developing the forging drawing based on the part formula and its 3D model.

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a

b

Figure 4: Automating the process of developing the drawing forging: a - data entry and processing window, b - results window

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The Turkish Online Journal of Design, Art and Communication - TOJDAC ISSN: 2146-5193, March 2018 Special Edition, p. 458-464 RESULTS AND DISCUSSION

To test the developed methodology and software for constructing the data structure of the part shape (part formula) with subsequent automation of the drawing design for the forgings of the part, consisting in assigning allowances, tolerances and allowances, the "Gear wheel" part was used.

Pictures 5 and 6 shows the drawing, data structure of the form and the structural diagram of the "Gear wheel" part.

Figure 5: Drawing of the part "Gear wheel"

Picture 6: Structure of the form data and a block diagram of the part "Gear wheel"

The drawing of the forgings, developed in accordance with the data structure of the part shape (see Picture 6) is shown in Pic. 7. The mass of the part is 1.83 kg.

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Picture 7: Drawing of the forging of the part "Gear"

CONCLUSIONS

The researchpresents a technique for constructing the data structure of a part shape and for automating the process of creating a prototype of a circular drawing in terms of forging, which makes it possible to automate the process:

• Research of metal consumption of various variants of its technological schemes of hot forging on CHTP;

• estimation of the influence of the allowances for machining, tolerances and blacksmith surplus consumption of the HF process at the CHTP.

At present, new, higher-quality die-cast steels have appeared and, accordingly, the durability of the engraving of stamps has increased, more modern ejection systems have been created. In this regard, it became possible to minimize the values of such parameters of forgings as allowances for machining and tolerances for them, stamping inclinations and radiuses of curvatures of external and internal angles. Accordingly, the requirements for the accuracy of the calculation of metal losses due to the implementation of HF technology, the creation of appropriate mathematical models and software solutions for their implementation are relevant and in demand.

The results were obtained within of the state assignment of the Ministry of Education and Science of Russia (project No. 11.9505.2017/8.9).

REFERENCES

Forging and bulk punching: reference. Under the Society. red. E.I. Semenova. V 4 т. Т. 2. Hot forging, М.: Mechanical engineering. (2010). 720 с.

Telegin, V.V., Kozlov, A.M., Sakalo, V.I. Solid Modeling and Dynamic Analysis of Mechanisms of Press- forging Machines, Procedia Engineering. (2017), P. 1258-1263.

Telegin, I.V., Volodin, I.M., Zolotukhin, P.I. The mathematical modeling for assessing the effectiveness of hot forging extruded round in plan forgings on crank presses, International Journal of Engineering and Technology(UAE). (2018), P. 30-34.

Zolotukhin, P.I., Volodin, I.M., Karpaitis, E.P., Volodin, A.I., Schmidt, A.A. Study of the spring back of

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