CN102539315B - Method for quickly and accurately confirming friction coefficient in metal forming processes - Google Patents

Abstract

The invention relates to the field of metal forming manufacturing, in particular to a method for quickly and accurately confirming friction coefficient in metal forming processes. The method comprises n groups of ring upsetting tests: a first group of ring upsetting tests contain three samples, the dimensional proportion of the outer diameter, the inner diameter and the height of a ring sample is 3:2:1, the press-down rate is smaller than 50%, the inner diameter, the outer diameter and the height of the deformed ring sample is measured, each size is measured from three different directions and obtained from the average, the average inner diameter, the outer diameter and the height of the three samples are calculated, the radius of a neutral layer is calculated, friction factor m is calculated, and the best friction factor mi is obtained by calculation. The method is simple and practical, and simultaneously takes bulging and material hardening in the ring sample upsetting test into consideration. Thus, the defect that an existing analytic method cannot simultaneously take bulging and material hardening into consideration is overcome, and complex data processing caused by using a rating curve method is avoided.

Description

A kind of method of quick and precisely determining metal plastic forming processes friction factor

Technical field

The present invention relates to Metal Forming field, specifically relate to and a kind ofly can quick and precisely determine the method for metal friction factor in plastic forming process.

Background technology

In Metal Forming, be to carry out under the condition contacting with workpiece at instrument, at this moment certainly lead to the friction force that stops metal flow.This occurring between workpiece and instrument surface of contact, hinders the friction of metal flow, claims external friction.Due to the effect of friction, instrument produces wearing and tearing, and workpiece is scratched; Flow of metal power, can increase and cause flow of metal uneven; When serious, make workpiece occur crackle, also will regularly replace instrument.Therefore, in plastic working, must study friction factor, research friction force, must be lubricated.

The friction that is accompanied by plastic yield and produces is out of shape due under high pressure in plastic history, can constantly increase new surface in contact, and the contact conditions between instrument and metal is constantly changed.On surface of contact, Plastic Flow situation is everywhere different, some slips, and some adhesions, what have is fast, and what have is slow, thereby the friction of each point is also different on surface of contact.

Be different from the friction in mechanical transmission course, the friction in Metal Forming process is often attended by plastic yield, and the relative velocity of each particle is different, thereby the friction of each point is also different.Pressure during metal plastic deformation on surface of contact is very high, andfrictional conditions is complicated during more than common mechanical transmission, friction under high pressure is also often the friction under high temperature simultaneously, and all these have determined complicacy and the difficulty of definite metal plastic forming processes friction factor.The sixties in last century have proposed to utilize ring compression experiment to determine the analytic method of friction factor, and the cydariform occurring while not considering jumping-up at first, is desirable mathematical analysis solution.This method need to utilize analytic formula to make calibration curve to the differentiated friction factor, then utilizes experimental result interpolation calculation to go out friction factor, wastes time and energy.Have scholar to propose above-mentioned analytic formula to improve, the cydariform occurring after Deformed ring as considered, adopts the improvement numerical solution of Hill theory etc. later.These methods have been improved precision to a certain extent, but can not consider the material plasticity sclerosis behavior in when distortion, and still need to do calibration curve.The domestic expert of having adopts the numerical simulation technology of elastic-plastic material model to determine friction factor, the sclerosis behavior of the cydariform in the time of can considering ring compression and metal plastic deformation, but still need to make calibration curve.

Therefore, be necessary the definite of friction factor to further improve, reach quick, accurate.

Summary of the invention

The object of this invention is to provide the method that metal plastic forming processes is a kind of fast, accurately determine friction factor.

Object of the present invention is achieved by following technical scheme:

Quick and precisely determine a method for metal plastic forming processes friction factor, it is characterized in that:

Neutral layer radius when if ρ is ring compression, R ₁, R ₀, H is respectively internal diameter after distortion, external diameter and height, the friction factor m while trying to achieve ring compression according to traditional analytical method.

As ρ≤R ₁time:

$m=\frac{H}{2(R_1-R_0)}\ln \left[{\left(\frac{R_1}{R_0}\right)}^2\frac{1+\sqrt{1+3{\left(\frac{R_0}{\mathrm{\ρ}}\right)}^4}}{1+\sqrt{1+3{\left(\frac{R_1}{R_0}\right)}^4{\left(\frac{R_0}{\mathrm{\ρ}}\right)}^4}}\right]---\left(1\right)$

Work as R ₁< ρ < R ₀time:

$m=\frac{H}{2(2\mathrm{\&rho;}-R_1-R_0)}\ln \left[{\left(\frac{R_1}{R_0}\right)}^2\frac{1+\sqrt{1+3{\left(\frac{R_0}{\mathrm{\&rho;}}\right)}^4}}{1+\sqrt{1+3{\left(\frac{R_1}{R_0}\right)}^4{\left(\frac{R_0}{\mathrm{\&rho;}}\right)}^4}}\right]---\left(2\right)$

$\mathrm{\&rho;}=\sqrt{(H_{i-1}{R}_{1i-1}^2-H_i{R}_{1i}^2)/(H_{i-1}-H_i)}---\left(3\right)$

Here H _i-1, R _1i-1for height and the internal diameter of a upper time step, H _i, R _1iheight and internal diameter for current time step;

Do the experiment of n group ring compression:

1. do the 1st group, every group of 3 samples, the dimension scale of ring specimen is got external diameter: internal diameter: highly=3:2:1, reduction ratio is below 50%, measure internal diameter, external diameter and height after sample deformation, each size is got its average from three different directions measurements, calculates mean inside diameter, external diameter and the height of 3 samples;

2. press formula (3) and calculate neutral layer radius;

If 3. ρ≤R ₁, by formula (1), calculate friction factor m; If R ₁< ρ < R ₀, by formula (2), calculate friction factor m;

4. by axisymmetric model, carry out finite element modeling, according to experimental result, simulation be set and depress height and calculate step-length, adopt quadrilateral axisymmetric element grid to divide, adopt firm hardening Plastic material model:

the yield limit σ of K, α and material wherein _sone way tensile test or material supplier by material obtain, σ _swith ε ₀correspondence, ε _pequivalent plastic strain for material;

5. according to 3. definite friction factor of step, do the finite element numerical simulation of ring compression, calculate

in formula

for mean inside diameter and the external diameter that step (1) obtains, R ₁', R' ₀the internal diameter and the external diameter that obtain for numerical simulation;

6. adjust up or down friction factor, and obtain obtain optimum friction factor m _i.

7. adjust the height of depressing of ring compression experiment, repeating step 1.～6., do 2nd～3 groups of ring compressions and test and calculate optimum friction factor m _i, ask

Quick and precisely determine according to claim 1 the method for metal plastic forming processes friction factor, it is characterized in that described n=1～3.According to actual needs, within the scope of this, select, be enough to obtain result accurately.

Beneficial effect of the present invention: the initial value of friction factor when first the present invention adopts existing analytic formula to determine ring compression fast, then adjust up and down friction factor make the inside/outside diameter size of numerical simulation annulus and experimental result the most approaching, thereby obtain optimum friction factor.

Above method is simple, and the bulge while simultaneously having considered ring specimen jumping-up and material sclerosis behavior.Overcome analytic method in the past and can not consider the defect of bulge and material sclerosis behavior simultaneously, and avoided adopting the loaded down with trivial details data processing of calibration-curve method.

Accompanying drawing explanation

Fig. 1 is a kind of method of quick and precisely determining metal plastic forming processes friction factor of the present invention, the structure cut-open view of ring specimen;

Fig. 2 is a kind of method of quick and precisely determining metal plastic forming processes friction factor of the present invention, and a kind of situation of neutral layer radius while having shown ring compression represents friction factor hour, and neutral layer radius is less than stressed, the deformation state figure of internal radius;

Fig. 3 is a kind of method of quick and precisely determining metal plastic forming processes friction factor of the present invention, a kind of situation of neutral layer radius while having shown ring compression, while representing that friction factor is larger, stressed, the deformation state figure of neutral layer radius between annulus internal-and external diameter.

In figure: d ₀annulus overall diameter before distortion, d ₁be annulus interior diameter before distortion, h is the height before distortion, and H is the height after distortion, neutral layer radius when ρ is distortion, r ₁for being out of shape front annulus inside radius, r ₀for being out of shape front annulus external radius.

Embodiment

Below in conjunction with accompanying drawing, further describe structure of the present invention.

Experiment blank is 10 steel, by analyzing, determine and process by D:d:H=3:2:1, annulus external diameter is 18mm, internal diameter is 12mm, be highly 6mm, adopts turning to process according to design proposal and processes annulus blank.This experiment adopts 2 groups of test specimens to test, every group of 3 samples, and wherein the 1st group of test specimen on average hits height 2.4mm, and the 2nd group of test specimen on average hits height 2.8mm, and experimental result is as shown in table 1.

Because ring compression is axisymmetric problem in geometry and load, utilize the symmetry of annulus part, the rotational symmetry geometric model of part is carried out to discretize, adopt rotational symmetry 4 Node Quadrilateral Element unit to carry out finite element modeling, and apply rotational symmetry constraint condition.

1. according to experimental result 1, by formula (3), determine neutral layer radius:

${\mathrm{\&rho;}}_1=\sqrt{({\mathrm{<figure-callout\; id="1"\; label="hr"\; filenames="HDA0000124604400000013.png"\; state="\{\{state\}\}">hr</figure-callout>}}_1^2-{\mathrm{<figure-callout\; id="1"\; label="HR"\; filenames="HDA0000124604400000013.png"\; state="\{\{state\}\}">HR</figure-callout>}}_1^2)/(h-H)}=\sqrt{(6\&times;6^2-3.6\&times;{5.9}^2)/(6-3.6)}=6.1469$

2. by the known neutral layer radius of experimental result 1 after jumping-up between internal-and external diameter, by formula (2) analytical Calculation friction factor:

${\mathrm{<figure-callout\; id="1"\; label="m"\; filenames="HDA0000124604400000013.png"\; state="\{\{state\}\}">m</figure-callout>}}_1^{\&prime;}=\frac{H}{2(2{\mathrm{\&rho;}}_1-R_1-R_0)}\ln \left[{\left(\frac{R_1}{R_0}\right)}^2\frac{1+\sqrt{1+3{\left(\frac{R_0}{\mathrm{\&rho;}}\right)}^4}}{1+\sqrt{1+3{\left(\frac{R_1}{R_0}\right)}^4{\left(\frac{R_0}{\mathrm{\&rho;}}\right)}^4}}\right]=0.1744$

Table 1 ring compression experimental measurements

3. according to the friction factor of analytical Calculation, carry out ring compression numerical experiments, and carry out test findings processing, obtain optimum friction factor m ₁.Numerical experiments result treatment is in Table 2.

Table 2 experiment 1 numerical simulation result is processed

Can obtain optimum friction factor m thus ₁=0.22.

4. according to experimental result 2, by formula (3), determine neutral layer radius:

${\mathrm{\&rho;}}_2=\sqrt{({\mathrm{<figure-callout\; id="1"\; label="hr"\; filenames="HDA0000124604400000013.png"\; state="\{\{state\}\}">hr</figure-callout>}}_1^2-{\mathrm{<figure-callout\; id="1"\; label="HR"\; filenames="HDA0000124604400000013.png"\; state="\{\{state\}\}">HR</figure-callout>}}_1^2)/(h-H)}=\sqrt{(6\&times;6^2-3.2\&times;{5.75}^2)/(6-3.2)}=6.2735$

5. by the known neutral layer radius of experimental result 2 after jumping-up between internal-and external diameter, by formula (2) analytical Calculation friction factor:

$m_2^{\&prime;}=\frac{H}{2(2{\mathrm{\&rho;}}_2-R_1-R_0)}\ln \left[{\left(\frac{R_1}{R_0}\right)}^2\frac{1+\sqrt{1+3{\left(\frac{R_0}{\mathrm{\&rho;}}\right)}^4}}{1+\sqrt{1+3{\left(\frac{R_1}{R_0}\right)}^4{\left(\frac{R_0}{\mathrm{\&rho;}}\right)}^4}}\right]=0.1812$

6. according to the friction factor of analytical Calculation, carry out ring compression numerical experiments, and carry out test findings processing, obtain optimum friction factor m ₂.

Numerical experiments result treatment refers to table 3.

Table 3 experiment 2 numerical simulation results are processed

Can obtain optimum friction factor m thus ₂=0.24.

7. according to formula

the friction factor that can obtain ring compression experiment is:

Claims (1)

1. quick and precisely determine a method for metal plastic forming processes friction factor, it is characterized in that:

Neutral layer radius when if ρ is ring compression, R ₁, R ₀, H is respectively internal diameter after distortion, external diameter and height, the friction factor m while trying to achieve ring compression according to traditional analytical method is as ρ≤R ₁time:

$m=\frac{H}{2(R_1-R_0)}\ln \left[{\left(\frac{R_1}{R_0}\right)}^2\frac{1+\sqrt{1+3{\left(\frac{R_0}{\mathrm{\&rho;}}\right)}^4}}{1+\sqrt{1+3{\left(\frac{R_1}{R_0}\right)}^4{\left(\frac{R_0}{\mathrm{\&rho;}}\right)}^4}}\right]---\left(1\right)$

Work as R ₁< ρ < R ₀time:

$m=\frac{H}{2(2\mathrm{\&rho;}-R_1-R_0)}\ln \left[{\left(\frac{R_1}{R_0}\right)}^2\frac{1+\sqrt{1+3{\left(\frac{R_0}{\mathrm{\&rho;}}\right)}^4}}{1+\sqrt{1+3{\left(\frac{R_1}{R_0}\right)}^4{\left(\frac{R_0}{\mathrm{\&rho;}}\right)}^4}}\right]---\left(2\right)$

$\mathrm{\&rho;}=\sqrt{(H_{i-1}{R}_{1i-1}^2-H_i{R}_{1i}^2)/(H_{i-1}-H_i)}---\left(3\right)$

Here H _i-1, R _1i-1for height and the internal diameter of a upper time step, H _i, R _1iheight and internal diameter for current time step;

Do the experiment of n group ring compression:

1. do the 1st group, every group of 3 samples, the dimension scale of sample is got external diameter: internal diameter: highly=3:2:1, reduction ratio is below 50%, measure internal diameter, external diameter and height after sample deformation, each size is got its average from three different directions measurements, calculates mean inside diameter, external diameter and the height of 3 samples;

2. press formula (3) and calculate neutral layer radius;

If 3. ρ≤R ₁, by formula (1), calculate friction factor m; If R ₁< ρ < R ₀, by formula (2), calculate friction factor m;

4. by axisymmetric model, carry out finite element modeling, according to experimental result, simulation be set and depress height and calculate step-length, adopt quadrilateral axisymmetric element grid to divide, adopt firm hardening Plastic material model: the yield limit σ of K, α and material wherein _sone way tensile test or material supplier by material obtain, σ _swith ε ₀correspondence, ε _pequivalent plastic strain for material;

5. according to 3. definite friction factor of step, do the finite element numerical simulation of ring compression, calculate in formula

for mean inside diameter and the external diameter that 1. step obtains, R ₁', R' ₀the internal diameter and the external diameter that obtain for numerical simulation;

6. adjust up or down friction factor, and obtain

obtain optimum friction factor m _i;

7. adjust the height of depressing of ring compression experiment, repeating step 1.～6., do 2nd～3 groups of ring compressions and test and calculate optimum friction factor m _i, ask

Described n=1～3.

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