# residual voltages as a result of surface heat

In process drobemyotnoj handlings in a zone of contact of fraction with a material surface there is a selection of a great many of energy in the form of heat. According to various researches, the instant temperature selected at blow of fraction, makes from 300 ° to 1500 ° With [35, 85, 104].

The indirect sign specifying in presence of such high thermal magnitudes in a zone of contact of fraction with a surface, sparks organised at handling [85,104] are.So strong teploobrazovanie the big impact on mechanical performances of a worked stock makes. Origin of the big instant temperatures at the moment of blow of a working body with a surface leads to thermoplastic strains, and, as consequence, to increase in residual compressing voltages. The further normalisation of temperatures in a contact zone is the reason of change of residual voltages - to lowering of level favorable compressing, and on occasion even to origin stretching IT. Thus, presence so heats in a contact zone negatively affects results of handling of a detail - the above temperature, the the effect of hardening [22] more strongly decreases. It is necessary to recognise, that the thermal component of process of handling of details in fraction makes essential impact on character of distribution epjury residual voltages in a material blanket.

Research of the thermal processes occurring at IID, has enough great value. Study of these processes both in practical, and in theoretical planes is considered in operations of such authors, as Chichinadze A.V., Saverin M. M, Petrosov V.V., Ovseenko A.N., etc.

In particular, Chichinadze A.V. [127] in the operation considers a differential heat conduction equation for a linear thermal stream, solving its method of an integral Laplace transformation and

Receives dependence for calculation of temperature of contact indentora with a job surface at the moment of full transition of mechanical energy in warmth:

Where a_{t} - factor temperaturoprovodnosti a material;

WITH - thermal conduction factor;

t - Any instant;

∆t - Time teplopogloshchenija;

P - The maximum force of blow;

V - speed of flight of fraction.

In Saverina M. M's operation [104] the formula which as a first approximation allows to evaluate the maximum instant amount of warmth brought in a surface is offered:

Where with - a thermal capacity of treated metal, kcal/kg °s;

Y - a specific gravity of treated metal, kg/m^{3};

n - The constant of proportionality considering, in how many times effective in sense of heat a zone naklyopa is more than volume lunki, arising at blow drobinki;

K - Blow factor;

_{Nanometer}, dynes. - shock hardness of metal, kg/mm^{2}.

The basic deficiency of the given design procedure is that fact, that the assumption according to which blow drobinkoj is made instantly initially is accepted and all energy at blow passes in heat. Accordingly, heat exchange between a zone naklyopa and environment is not considered.

According to Petrosova V.V. [85] method, the settlement aspect of the equation for definition of temperature of any point of a body v to a zone of blow in fraction is grounded on the second principal equation of thermophysics (Calvin's differential heat conduction equation) looks as follows:

Where - factor temperaturoprovodnosti a material;

(1 ⅛) - the part of heat passing in a body;

λ_{t} - Thermal conduction factor;

t - Time of a thermal impulse;

R - distance from a source of heat to any point of a blanket;

^{Eu} - energy of blow.

The given method also does not allow to define with sufficient degree of reliability instant temperature in a zone contact, for the same reason - an assumption about equality of thermal and mechanical energy in the course of handling.

On Torbilo V. M's [118] method, the temperature in a contact zone depends on the maximum intensity of a thermal source q_{m}, diameter of the contact

Platforms d (), factor of concentration of a thermal source k, and also an error integral of Gauss F () and Euler's gamma-functions

The above-stated analysis has allowed to define, that at handling of details by methods Ш1Д, in a contact zone the significant amount of warmth which first of all depends on a power component of a condition of handling (in a case with hardening in fraction - from speed of flight of fraction at impact) is organised; the size indentora (at the smaller sizes drobinok there is a density of heat on the small area of contact); properties of a worked stock (its thermal conduction), etc.

Besides it, the output is drawn, that in one of specified above design procedures there is no state estimation of a blanket before handling that does impossible application of these settlement models at an estimation teplofizicheskih parametres of process of handling at restoration of details.

At definition of the stretching residual voltages arising owing to thermal processes during handling, with the account mnogofaktornosti process and complexities at analytical calculation, some assumptions (a process schematization) have been accepted:

1) the fraction is represented absolutely rigid spherical body;

2) a worked stock - the steel - is isotropic and homogeneous;

3) heat source - pointwise;

4) the temperature of a working body and a material at the moment of blow are identical;

5) under fraction blow introduction process drobinki in a surface with the further exit from it is considered;

6) movement of fraction at the moment of blow about a surface is considered ravnouskorennym.

The graphic illustration of process of blow of fraction with a material surface is presented on fig. 3.4.:

Fig. 3.4. The circuit of process of blow drobinki with a detail blanket

According to the introduced circuit and the accepted assumptions, definition of time of effect of a thermal source on a worked stock directly depends on speed and depth of introduction, and also speed of flying away of a working body.

For definition of a thermoplastic component IT we will take advantage of the law of the Hooke for a relative stretching (compression) (3.17) and

The dependences defining a relative strain (3.18) and factor of a linear thermal expansion (3.19 [59]:

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Where - a relative strain of a material;

- Magnitude of residual voltages, Pas;

E - A coefficient of elasticity;

∆l - Magnitude of absolute compression of a material, m;

l - The linear size of not compressed material, m;

And - factor of a linear thermal expansion;

∆T - Change of temperature in a contact zone, °s.

By substitution of magnitude of absolute compression of a material ∆lиз formulas (3.19) in (3.18), we will receive dependence for definition of a relative strain of a material (3.20):

Having expressed magnitude residual naprjazhenijiz the law of the Hooke (3.17), and having substituted the formula (3.20) in turned out expressions, we will receive the required initial dependence most full mapping a thermoplastic component for calculation of residual voltages in a blanket of details [35]:

As the coefficient of elasticity for isotropic materials is magnitude of a constant (E = const.), and factor of a linear thermal expansion and - help magnitude the dependence final form will be defined by specification of magnitude of change of temperature ∆Tв to a zone of contact of a working body with a material.

∆T, considering the accepted assumption about equality of temperatures of a source and a material, it is possible to evaluate temperature change by means of Calvin's decision of a differential heat conduction equation (the second principal equation of thermophysics) [85]:

Where T - temperature of any point of a body to which thermal effect has been affixed;

Q - The amount of heat brought in a body by a source, J;

R - Distance from a source of warmth to a considered point, sm;

Y - Thermal conduction factor;

^{o} - Factor temperaturoprovodnosti;

t - A time window of effect of a source of heat on a body, with.

Amount of heat which brings a source (drobinka) in a worked stock, it is possible to evaluate by means of energy of impact:

Where χ - factor of distribution of thermal streams;

E - Energy of impact.

The factor %распределения thermal streams depends on the basic thermal performances of a material and is defined under the following formula [127]:

Where λ_{1}и λ_{2} - factors of thermal conduction of a material and fraction accordingly;

c_{1}и с_{2} - factors of a thermal capacity of a material and fraction

Accordingly;

p_{1}и р_{2} - material and fraction density accordingly. [35]

The thermal conduction factor, factor of a thermal capacity and material density are linked among themselves by expression for factor definition temperaturoprovodnosti a material:

Energy of impact is defined by a difference of kinetic energies of introduction and flying away drobinki from a blanket of a material and evaluated by means of well-known dependences:

Where m - mass drobinki, kg;

V_{1} - Speed drobinki before blow (at introduction), km/s;

V_{2} - Speed drobinki after blow (at flying away), km/s. [35]

Thus, with the aforesaid account, the formula (3.23) takes the following form:

For simplification of support of the further calculations, we will enter the high-speed factor K_{1} depending on speeds of blow V_{1}и of flying away V_{2}дроби from a job surface:

Having expressed from the formula (3.28) speed V_{2}отлёта fractions, and having substituted turned out expression in dependence (3.27), we will receive a definitive aspect of dependence for definition of amount of heat Q:

Time of effect of a source of heat for a worked stock can be calculated as follows:

Where t_{1} - introduction time drobinki in a material, with;

t_{2} - Flying away time drobinki from a material, with.

Definition composed t_{1}и t_{2}из dependences (3.30) is possible from a condition ravnouskorennosti movements of a source of heat (fraction) in the course of blow on a worked stock surface (fig. 3.4), thus it is necessary to consider, that heat transmission occurs at fraction introduction in

Surface and flying away from a surface at average speed accordingly. Thus, expressions for definition of time of introduction and time of flying away of a working body look as follows:

Where H - depth of full introduction of a working body in a material surface, m;

h_{y} - Depth of elastic introduction of a working body in a material surface, m.

By analogy to high-speed factor K_{1} (3.28), we will enter

The surface factor K_{2} depending on depth of full introduction Hдроби, and elastic introduction h_{y}:

Let's express from high-speed factor K_{1}скорость V_{2}отлёта of fraction:

Let's express from surface factor K_{2}глубину of elastic introduction h_{y}дроби in a worked stock:

Having substituted formulas (3.34) and (3.35) in (3.32), we will receive the specified variant of record of the formula for definition of a time window of flying away of fraction:

Having substituted turned out expression (3.36) and expression (3.31) in an assumption formula (3.30), we will receive a preliminary aspect of dependence for definition of time of effect of a source of heat on a worked stock [35]:

For simplification of support of the further calculations, we will enter the generalised factor of an elastic refacing To „,„., which will allow to reflect to the full physicomechanical changes in a material at its handling, considering factors of handling and property of a material. For definition of the given factor K_{κo β}. We will take advantage of data of operations of some scientists [53, 89, 106].

First of all it is necessary to determine depth of penetration uprugoplasticheskoj strains to, with the account of fidelity of the following expression linking among themselves high-speed and surface koeffitsianty [35]:

Process of dynamic blow of a working body (drobinki) with a worked stock surface can be compared to static impression of a sphere of the same size in a surface. In that case,

Elastic introduction at blow and static impression is defined by the identical energy expended on elastic restoration. Thus, energy it is possible to present equality as follows:

Where f_{y} - the area of an elastic print from introduction of a working body on depth h_{y};

M _{v} - a volume coefficient of elasticity;

ε - a relative strain.

The area of an elastic print from introduction of a working body depends on the sizes of a sphere (radius R) and direct depth of elastic introduction, is defined by the formula:

The volume coefficient of elasticity in case of an isotropic material depends on a young's modulus and factor of the Poisson, and is calculated as follows:

After substitution, expression (3.38) takes the following form:

Considering mass drobinki, we receive initial expression for magnitude definition uprugoplasticheskogo sphere introductions in a surface:

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The relative strain is defined as a magnitude ratio uprugoplasticheskogo introductions hк to distance h_{M}. From a surface of a worked stock to depth of penetration uprugoplasticheskoj strains (fig. 3.4). Also, considering, that process of the thermal

Deformations is short-term, the relative strain can be defined a following parity:

Considering, that h_{M}. It is possible to define from criterion of similarity of nonstationary thermal processes:

Where F_{0} - number Fure, according to experimental data F_{0} ≈ 1,73;

About - factor temperaturoprovodnosti a material;

t - Time of effect of a source of heat, with.

As heat transmission occurs only at uprugoplasticheskom sphere introduction in a worked stock surface probably to use the formula (3.31), substituting instead of H expression (3.45), as a result we will receive:

Accordingly the relative strain of a material can be defined now as follows:

By substitution of expressions for depth definition uprugoplasticheskoj strains h_{m}. (3.43) and a relative strain of a material ε (3.47) in the formula (3.38) for calculation of the generalised factor of elastic refacing K_{no β}., we will receive:

It is necessary to mark, that the received factor depends as on handling factors - radius of fraction and speed of impact, and from properties of a material, and in detail enough illustrates change mechanical and physical properties of a worked stock.

Considering a parity (3.38), it is possible to tell, that truly following equality:

Thus, taking into consideration a parity (3.49), dependence (3.37) for definition of time of effect of a source of heat on a worked stock tпринимает the following aspect:

Also it is necessary to specify expression (3.29) for definition of amount of heat Q which brings a source (drobinka) in a worked stock:

As a result, substituting turned out expressions in an assumption formula (3.21), also we will receive a definitive aspect of expression for definition of a thermoplastic component of residual voltages in a blanket of details [35]:

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