CN106225760A - A kind of Model For The Bush-axle Type Parts cuts the radial heat distortion measuring method caused - Google Patents

Abstract

The invention discloses a kind of Model For The Bush-axle Type Parts and cut the radial heat distortion measuring method caused, the impact on geometrical body thermal deformation of the surface residual stress of middle (center) bearing lasso generation is processed for analyzing finish turning, and the radial deformation produced by residual stress in the course of processing is carried out quantitative analysis, set up the thermal deformation mathematical model based on residual stress of sleeve part, and derive more accurate Calculation of Thermal Deformation method, measure simpler, and accurately.

Description

A kind of Model For The Bush-axle Type Parts cuts the radial heat distortion measuring method caused

Technical field

The present invention relates to machinery manufacturing technology field, the radial heat distortion that the cutting of a kind of Model For The Bush-axle Type Parts causes is surveyed Metering method.

Background technology

Thermal deformation theoretical research relates to the rationale of physics and engineering, and being concentrated mainly on should to conduction of heat and heat Research in terms of power scheduling theory, including heat transfer, heat exchange, seethes with excitement, cools down, is incubated, in thermoelasticity and the non-resilient mechanics of heat etc. Holding, thermal expansion theory is the integrated application of each theory.

The most in recent years thermal deformation theory also there is a lot of applied researcies in machining.Darmstadt industry is big Learn and thermal stress during high-rate wireless LAN has been carried out theoretical and applied research, it is thus achieved that fruitful achievement in research.Zhejiang The scientific research personnel of Jiang great Xue is being engaged in the research of thermal deformation of machine tool always, and thermo parameters method and lathe for lathe are in not equality of temperature Degree deformation after the match is analyzed, and then proposes the theoretical and thermo-responsive some identification technology of thermo-responsive point during temperature field determines.With The research worker of Ji university is mainly engaged in the research that in machining, Workpiece Machining Accuracy is affected by heat in metal cutting, its research conclusion pair The thermal deformation analyzed in machining has directive significance；The scientific research team with Fei Yetai professor as academic leader of the HeFei University of Technology 5 are engaged in material thermal expansion coefficient, component of machine thermal deformation theory and the research of application aspect, to part feature dimension in heat General affecting laws in deformation conducts in-depth research.

The size of the thermal deformation of metal cutting process is by the shadow of the factor such as shape, material and surface residual stress of part Ring.The residual stress state of the surface layers serviceability to element part, as reliability and stability etc. have greatly Impact.Theoretical research shows with the result of actual application, by controlling or adjust the stress state of machined surface, it is thus achieved that close Suitable residual compressive stress, can improve fatigue strength and the corrosion resistance of part.It is therefore desirable to Model For The Bush-axle Type Parts cutting is caused Radial heat distortion accurately measure, provide reference man-hour to add, improve part quality.

Summary of the invention

It is an object of the invention to based on engineering service memo and thermodynamic principles, it is provided that a kind of Model For The Bush-axle Type Parts cutting causes Radial heat distortion measuring method, for analyze finish turning processing middle (center) bearing lasso produce surface residual stress to geometric form body heat The impact of deformation, and the radial deformation produced by residual stress in the course of processing is carried out quantitative analysis, for improving shaft sleeve zero Part quality provides data refer.

In order to reach the purpose of the present invention, present invention employs following technical scheme: a kind of Model For The Bush-axle Type Parts cutting causes Radial heat distortion measuring method, set up cylindrical coordinate, click equation computing:

$\left\{\begin{array}{c}{\mathrm{\σ}}_r=\frac{-E}{1-\mathrm{\μ}}g\frac{\mathrm{\λ}}{r^2}\underset{a}{\overset{r}{\∫}}t\left(r\right)rdr+\frac{E}{1+\mathrm{\μ}}\[\frac{C}{1-2\mathrm{\μ}}-\frac{D}{r^2}\]\\ {\mathrm{\σ}}_{\mathrm{\θ}}=\frac{E}{1-\mathrm{\μ}}g\frac{\mathrm{\λ}}{r^2}\underset{a}{\overset{r}{\∫}}t\left(r\right)rdr-\frac{\mathrm{\λ}Et\left(r\right)}{1-\mathrm{\μ}}+\frac{E}{1+\mathrm{\μ}}\[\frac{C}{1-2\mathrm{\μ}}+\frac{D}{r^2}\]\\ {\mathrm{\σ}}_z=\frac{-\mathrm{\λ}Et\left(r\right)}{1-\mathrm{\μ}}+\frac{2\mathrm{\μ}EC}{(1+\mathrm{\μ})(1-2\mathrm{\μ})}\end{array}\right.---\left(1\right)$

$u_0=\frac{1+\mathrm{\μ}}{1-\mathrm{\μ}}g\frac{\mathrm{\λ}}{r}\underset{a}{\overset{r}{\∫}}t\left(r\right)rdr+Cr+\frac{D}{r}---\left(2\right)$

The elastic modelling quantity of E-bearing material in formula

The linear expansion coefficient of λ-bearing material

The Poisson's ratio of μ-bearing material

The Changing Pattern of t-temperature, t=t (r)

σ_rSome radial stresses on-bearing inner race

σ_θSome tangential stresses on-bearing inner race

σ_zSome axial stresses on-bearing inner race

u₀Some radial displacements on-bearing inner race

C and D is integral constant, boundary condition determine.

$\mathrm{\μ}={\mathrm{\μ}}_0-\frac{{\mathrm{\μ\σ}}_{a}r}{E}---\left(3\right)$

The rule that the elastic modelling quantity of material varies with temperature can be represented by the formula:

$E=E_0\[1+{\mathrm{\λ}}_{E}t\left(r\right)\]=\frac{E_0}{1-{\mathrm{\λ}}_{E}t\left(r\right)}---\left(4\right)$

E in formula₀-temperature is t₀Time material elastic modelling quantity, take t₀=0；

λ_EThe temperature coefficient of-elastic modelling quantity, much smaller than 1 and be negative value；

When bearing inner circle temperature is t (a), and cylindrical temperature is t (b), and internal diameter is a, and when external diameter is b, then in bearing, temperature is divided Cloth situation is:

$t\left(r\right)=t\left(a\right)+\frac{t\left(b\right)-t\left(a\right)}{ln(b/a)}ln(r/a)---\left(5\right)$

By formula (3) (4) (5) for people's formula (2), show that the radial displacement at internal diameter r=a, r=b of race ring is as follows:

$\begin{array}{c}{\mathrm{\μ}}_a=\frac{1-{\mathrm{\λ}}_{E}t\left(a\right)}{E_0}g\{1+\frac{\mathrm{\μ}(b^2+a^2)}{b^2-a^2}\}{\mathrm{ga\σ}}_{\mathrm{\θ}a}+\mathrm{\λ}at\left(a\right)\\ +\frac{(1+\mathrm{\μ})b^2\mathrm{\λ}}{(1-\mathrm{\μ})(b^2-a^2)}\[a(1-2\mathrm{\μ})-1\]g\[t\left(b\right)-t\left(a\right)\]\end{array}---\left(6\right)$

$\begin{array}{c}{\mathrm{\μ}}_b=\frac{1-{\mathrm{\λ}}_{E}t\left(b\right)}{E_0}g\[1-\frac{\mathrm{\μ}(b^2+a^2)}{b^2-a^2}\]{\mathrm{gb\σ}}_{\mathrm{\θ}b}+\mathrm{\λ}bt\left(a\right)\\ +\frac{(1+\mathrm{\μ})b\mathrm{\λ}}{(1-\mathrm{\μ})(b^2-a^2)}\[b^2(1-2\mathrm{\μ})-a\]g\[t\left(b\right)-t\left(a\right)\]\end{array}---\left(7\right)$

Compared with prior art, the invention has the beneficial effects as follows: analyze essence based on engineering service memo and thermodynamic principles The surface residual stress impact on geometrical body thermal deformation that Vehicle Processing middle (center) bearing lasso produces, and in the course of processing by remnants The radial deformation that stress produces carries out quantitative analysis, sets up the thermal deformation mathematical model based on residual stress of sleeve part, And derive more accurate Calculation of Thermal Deformation method, measure simpler, and accurately.

Accompanying drawing explanation

Fig. 1 is bearing coordinate system figure；

Fig. 2 is radical continuous run-out error measurement figure；

Fig. 3 is the graph of relation of deflection and temperature.

Detailed description of the invention

Below in conjunction with the drawings and specific embodiments, the present invention will be described in detail.

A kind of Model For The Bush-axle Type Parts cuts the radial heat distortion measuring method caused, as it is shown in figure 1, set the two of Model For The Bush-axle Type Parts End is freely, and temperature is radially distributed and is symmetrical in z axis, and its size is only the most relevant with radial dimension and unrelated with Z axis.Set up The cylindrical coordinate of bearing shown in Fig. 1.For ease of calculating, first suppose that the axial displacement of A point is zero, when the temperature varies, point In analysis axle, the radial displacement of any point A and the relation of temperature, determine the radial displacement of A point, the thermal deformation letter of the available diameter of axle Breath.

$\left\{\begin{array}{c}{\mathrm{\σ}}_r=\frac{-E}{1-\mathrm{\μ}}g\frac{\mathrm{\λ}}{r^2}\underset{a}{\overset{r}{\∫}}t\left(r\right)rdr+\frac{E}{1+\mathrm{\μ}}\[\frac{C}{1-2\mathrm{\μ}}-\frac{D}{r^2}\]\\ {\mathrm{\σ}}_{\mathrm{\θ}}=\frac{E}{1-\mathrm{\μ}}g\frac{\mathrm{\λ}}{r^2}\underset{a}{\overset{r}{\∫}}t\left(r\right)rdr-\frac{\mathrm{\λ}Et\left(r\right)}{1-\mathrm{\μ}}+\frac{E}{1+\mathrm{\μ}}\[\frac{C}{1-2\mathrm{\μ}}+\frac{D}{r^2}\]\\ {\mathrm{\σ}}_z=\frac{-\mathrm{\λ}Et\left(r\right)}{1-\mathrm{\μ}}+\frac{2\mathrm{\μ}EC}{(1+\mathrm{\μ})(1-2\mathrm{\μ})}\end{array}\right.---\left(1\right)$

$u_0=\frac{1+\mathrm{\μ}}{1-\mathrm{\μ}}g\frac{\mathrm{\λ}}{r}\underset{a}{\overset{r}{\∫}}t\left(r\right)rdr+Cr+\frac{D}{r}---\left(2\right)$

The elastic modelling quantity of E-bearing material in formula

The linear expansion coefficient of λ-bearing material

The Poisson's ratio of μ-bearing material

The Changing Pattern of t-temperature, t=t (r)

σ_rSome radial stresses on-bearing inner race

σ_θSome tangential stresses on-bearing inner race

σ_zSome axial stresses on-bearing inner race

u₀Some radial displacements on-bearing inner race

C and D is integral constant, boundary condition determine.

To cylindrical component, surface residual stress should be three-dimensional stress in theory, is represented by tangential stress σ_θ, axially should Power σ_zWith radial stress σ_r, cutting force is also classified into 3 directions, i.e. tangential component F_t, axial thrust load F_aWith radial component F_r, different The proportionate relationship that cutting process respectively cuts between component also differs.Thus the proportionate relationship between the residual stress caused is the most not Identical, therefore, when utilizing boundary condition to determine integral constant C above with D, calculate for simplifying, can only consider tangential remaining Stress σ_θImpact.

Assume that the tangential stress in race ring inner and outer diameter is respectively σ_θaAnd σ_θbSubstitute into above-mentioned (1) equation, C and D can be obtained Value also substitutes into (2) and obtains μ₀。

For meeting free end condition, at above-mentioned μ₀On the basis of solution, then in cylinder both ends of the surface, apply a uniform axle To power σ_z, make end axially to make a concerted effort be zero, now radial displacement is because of by axial stress σ_zImpact, must increase by one

I.e.

The rule that the elastic modelling quantity of material varies with temperature can be represented by the formula.

$E=E_0\[1+{\mathrm{\λ}}_{E}t\left(r\right)\]=\frac{E_0}{1-{\mathrm{\λ}}_{E}t\left(r\right)}---\left(4\right)$

E in formula₀-temperature is t₀Time material elastic modelling quantity, take t₀=0.λ_EThe temperature coefficient of-elastic modelling quantity, is much smaller than 1 and be negative value.

When bearing inner circle temperature is t (a), and cylindrical temperature is t (b), and internal diameter is a, and when external diameter is b, then in bearing, temperature is divided Cloth situation is

$t\left(r\right)=t\left(a\right)+\frac{t\left(b\right)-t\left(a\right)}{ln(b/a)}ln(r/a)---\left(5\right)$

Residual stress in view of surface layer is local stress, only works the local deformation of surface layer.Therefore, at meter When calculating the deformation of inner surface, do not consider extexine residual stress σ_θbImpact.Equally, when calculating the deformation of outer surface, do not examine Consider endosexine residual stress σ_θaImpact, by formula (3) (4) (5) for people's formula (2), then draw at internal diameter r=a, r=b of race ring Radial displacement respectively as follows:

$\begin{array}{c}{\mathrm{\μ}}_a=\frac{1-{\mathrm{\λ}}_{E}t\left(a\right)}{E_0}g\{1+\frac{\mathrm{\μ}(b^2+a^2)}{b^2-a^2}\}{\mathrm{ga\σ}}_{\mathrm{\θ}a}+\mathrm{\λ}at\left(a\right)\\ +\frac{(1+\mathrm{\μ})b^2\mathrm{\λ}}{(1-\mathrm{\μ})(b^2-a^2)}\[a(1-2\mathrm{\μ})-1\]g\[t\left(b\right)-t\left(a\right)\]\end{array}---\left(6\right)$

$\begin{array}{c}{\mathrm{\μ}}_b=\frac{1-{\mathrm{\λ}}_{E}t\left(b\right)}{E_0}g\[1-\frac{\mathrm{\μ}(b^2+a^2)}{b^2-a^2}\]{\mathrm{gb\σ}}_{\mathrm{\θ}b}+\mathrm{\λ}bt\left(a\right)\\ +\frac{(1+\mathrm{\μ})b\mathrm{\λ}}{(1-\mathrm{\μ})(b^2-a^2)}\[b^2(1-2\mathrm{\μ})-a\]g\[t\left(b\right)-t\left(a\right)\]\end{array}---\left(7\right)$

From formula (6) and (7), bearing radial deformation is made up of two parts, and Part I is produced by surface residual stress, It is relevant with the internal-and external diameter of the size of residual stress, direction and bearing, i.e. the 1st in above formula, and Part II is then by material The thermal expansion of material produces, and it includes the 2nd in above formula and the 3rd, due to the impact of surface residual stress, makes bearing inner race Actual thermal deformation is not equal to the deformation produced by simple thermal expansion.

In order to verify the accuracy of above-mentioned measurement, and by experiment test, the part deformation mathematics that residual stress is caused Model is verified.

The size of the heat distortion amount that bearing inner race is caused by the residual stress processing generation can use radical continuous run-out error Weighing, runout error is a comprehensive error project, and it can reflect form error and the site error of element to be measured.It Contain cylindricity tolerance band and roundness tolerance band, it is possible to use total run-out allowance control deviation from cylindrical form, moreover it is possible to control end face, The face of cylinder is for the perpendicularity of reference axis, parallelism error.Radially the tolerance range of total run-out be semidiameter be tolerance value t, and with Region between the two cylindrical surface that datum axis is coaxial, its tolerance range is limited in the range of three dimensional space coordinate as shown in Figure 2.This Measured bearing inner ring is slowly turned round when measuring by invention, and moves linearly in the axial direction, makes dial indicator measuring head whole Outer ring and inner ring finished surface streak, and write down full-scale reading and the least count of dial gauge pointer, take the difference of two readings as this The radical continuous run-out error of element to be measured.

The temperature that will measure, thermal deformation data list is as follows:

Temperature and thermal deformation value

Trend avatars thermal deformation varied with temperature is illustrated in fig. 3 shown below.

It can be seen that the actual measured value of (1) heat distortion amount is the most identical with value of calculation from table above and figure, explanation The mathematical model set up can reflect the change of the thermal deformation of hard turning.(2) between temperature and heat distortion amount it is non-linear dependence.Cause This is non-uniform temperature field, and it is clearly distinguished from the line relationship of the variations in temperature in homogeneous temperature field with deflection, essence Really calculate heat distortion amount, it has to be taken into account the impact of non-linear relation

The preferred embodiment of the present invention described in detail above, be inventor take a large amount of talent's financial resources and time Between, test of many times out it will be appreciated that, as a result, the ordinary skill of this area just can be according to this without creative work Many modifications and variations are made in bright design.Therefore, all technical staff in the art according to present inventive concept in prior art On the basis of by logical analysis, reasoning or according to the limited available technical scheme of experiment, all should be by this right Among protection domain determined by claim.

Claims (1)

1. a Model For The Bush-axle Type Parts cuts the radial heat distortion measuring method caused, it is characterised in that: set up cylindrical coordinate, by one Lower equation computing:

$\left\{\begin{array}{c}{\mathrm{\σ}}_r=\frac{-E}{1-\mathrm{\μ}}g\frac{\mathrm{\λ}}{r^2}\underset{a}{\overset{r}{\∫}}t\left(r\right)rdr+\frac{E}{1+\mathrm{\μ}}\[\frac{C}{1-2\mathrm{\μ}}-\frac{D}{r^2}\]\\ {\mathrm{\σ}}_{\mathrm{\θ}}=\frac{E}{1-\mathrm{\μ}}g\frac{\mathrm{\λ}}{r^2}\underset{a}{\overset{r}{\∫}}t\left(r\right)rdr-\frac{\mathrm{\λ}Et\left(r\right)}{1+\mathrm{\μ}}+\frac{E}{1+\mathrm{\μ}}\[\frac{C}{1-2\mathrm{\μ}}+\frac{D}{r^2}\]\\ {\mathrm{\σ}}_z=\frac{-\mathrm{\λ}Et\left(r\right)}{1-\mathrm{\μ}}+\frac{2\mathrm{\μ}EC}{(1+\mathrm{\μ})(1-2\mathrm{\μ})}\end{array}\right.---\left(1\right)$

$u_0=\frac{1+\mathrm{\μ}}{1-\mathrm{\μ}}g\frac{\mathrm{\λ}}{r}\underset{a}{\overset{r}{\∫}}t\left(r\right)rdr+Cr+\frac{D}{r}---\left(2\right)$

The elastic modelling quantity of E-bearing material in formula

The linear expansion coefficient of λ-bearing material

The Poisson's ratio of μ-bearing material

The Changing Pattern of t-temperature, t=t (r)

σ_rSome radial stresses on-bearing inner race

σ_θSome tangential stresses on-bearing inner race

σ_zSome axial stresses on-bearing inner race

u₀Some radial displacements on-bearing inner race

C and D is integral constant, boundary condition determine.

$\mathrm{\μ}={\mathrm{\μ}}_0-\frac{{\mathrm{\μ\σ}}_{a}r}{E}---\left(3\right)$

The rule that the elastic modelling quantity of material varies with temperature can be represented by the formula:

$E=E_0\[1+{\mathrm{\λ}}_{E}t\left(r\right)\]=\frac{E_0}{1-{\mathrm{\λ}}_{E}t\left(r\right)}---\left(4\right)$

E in formula₀-temperature is t₀Time material elastic modelling quantity, take t₀=0；

λ_EThe temperature coefficient of-elastic modelling quantity, much smaller than 1 and be negative value；

When bearing inner circle temperature is t (a), and cylindrical temperature is t (b), and internal diameter is a, when external diameter is b, then Temperature Distribution shape in bearing Condition is:

$t\left(r\right)=t\left(a\right)+\frac{t\left(b\right)-t\left(a\right)}{1n(b/a)}ln(r/a)---\left(5\right)$

By formula (3) (4) (5) for people's formula (2), show that the radial displacement at internal diameter r=a, r=b of race ring is as follows:

$\begin{array}{c}{\mathrm{\μ}}_a=\frac{1-{\mathrm{\λ}}_{E}t\left(a\right)}{E_0}g\{1+\frac{\mathrm{\μ}(b^2+a^2)}{b^2-a^2}\}{\mathrm{ga\σ}}_{\mathrm{\θ}a}+\mathrm{\λ}at\left(a\right)\\ +\frac{(1+\mathrm{\μ})b^2\mathrm{\λ}}{(1-\mathrm{\μ})(b^2-a^2)}\[a(1-2\mathrm{\μ})-1\]g\[t\left(b\right)-t\left(a\right)\]\end{array}---\left(6\right)$

$\begin{array}{c}{\mathrm{\μ}}_b=\frac{1-{\mathrm{\λ}}_{E}t\left(b\right)}{E_0}g\[1-\frac{\mathrm{\μ}(b^2+a^2)}{b^2-a^2}\]{\mathrm{gb\σ}}_{\mathrm{\θ}b}+\mathrm{\λ}bt\left(a\right)\\ +\frac{(1+\mathrm{\μ})b\mathrm{\λ}}{(1-\mathrm{\μ})(b^2-a^2)}\[b^2(1-2\mathrm{\μ})-a\]g\[t\left(b\right)-t\left(a\right)\]\end{array}---\left(7\right).$