A kind of 1. hydrostatic slideway load-bearing capacity analysis method for considering guide rail facial disfigurement, for analyzing hydrostatic slideway in heavy machine tool
Change of the load-carrying properties under the influence of guide rail surface pressure distortion under application platform, it is characterised in that:The analysis method includes
Following steps,
S1. the nondimensionalization of variable is carried out to the parameter in hydrostatic slideway first;
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Wherein:P is fluid pressure;p0For pressure in hydrostatic slideway oil pocket;W is hydrostatic slideway bearing capacity;Q supplies for hydrostatic slideway
Oil stream amount;UxFor hydrostatic slideway translational speed;H is oil film thickness;H0For initial oil film thickness;X is that length is measured to coordinate;Y is
Width is measured to coordinate;Z measures for thickness coordinate;L is hydrostatic slideway lubricating pad length;B is hydrostatic slideway lubricating pad width;dzTo become
Shape degree;η is oil viscosity;For dimensionless pressure;For non-dimensional length;For dimensionless width;Carried for dimensionless
Power;Flow is held for dimensionless;For dimensionless guide moving velocity;For dimensionless oil film thickness;Journey is deformed for dimensionless
Degree;
S2. Reynolds equation and elastomer balance differential equation are simplified;The translational speed of hydrostatic slideway is less demanding, so
Heat problem and unobvious, that is, the viscosity B coefficent of liquid is supported to ignore with variable density;Reynolds equation after simplification is:
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Wherein:L is hydrostatic slideway lubricating pad length;B is hydrostatic slideway lubricating pad width;For dimensionless pressure;For non-dimensional length;For dimensionless width;For dimensionless guide moving velocity;For dimensionless oil film thickness;
The deformation extent of lubricating pad lower guideway and actual conditions are closely related, and physical dimension, material, operating pressure will all influence guide rail
Deformation extent size;But in the elastic range of material, the regularity of distribution of deformation necessarily satisfying for elastomer deformation equation, i.e.,
Meet boundary condition in boundary, remaining meets the regularity of distribution of distortional elastomer;Introduce one-dimensional elastomer balance differential side
Cheng Wei:
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Wherein:X is that length is measured to coordinate;Y is that width is measured to coordinate;Z measures for thickness coordinate;σ is direct stress;τ is to cut
Stress;F is body force;
S3. discrete with elastomer balance differential equation according to finite difference method Reynolds equation after is algebraic equation;Finite difference
Point-score by partial differential equation Approximation Discrete, is converted into the Algebraic Equation set of limited rank, is passing through algebraically side according to the property of differential
The solution of journey group is solved;Reynolds equation is changed into difference equation according to Differential Properties first, and arranges to obtain Reynolds equation
Iterative equation:
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Wherein:L is hydrostatic slideway lubricating pad length;B is hydrostatic slideway lubricating pad width;For dimensionless pressure;It is discrete for x directions
Step-length;For y directions discrete steps;I counts for x directions infinitesimal;J counts for y directions infinitesimal;Moved for dimensionless guide rail
Speed;For dimensionless oil film thickness
According to Hooke's law
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Wherein:σ is direct stress;τ is shearing stress;E is guide material Young's modulus;G is guide material modulus of shearing;ε is linear
Strain;γ is shear strain;
Then one-dimensional elastomer balance differential equation-formula (2) is changed into difference equation according to Differential Properties, and arranges elastic
The iterative equation of body balance differential equation:
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</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>dz</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>dz</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>fz</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msub>
<msub>
<mi>x</mi>
<mrow>
<mi>s</mi>
<mi>t</mi>
<mi>e</mi>
<mi>p</mi>
</mrow>
</msub>
<msub>
<mi>y</mi>
<mrow>
<mi>s</mi>
<mi>t</mi>
<mi>e</mi>
<mi>p</mi>
</mrow>
</msub>
<msub>
<mi>z</mi>
<mrow>
<mi>s</mi>
<mi>t</mi>
<mi>e</mi>
<mi>p</mi>
</mrow>
</msub>
</mrow>
<mrow>
<mn>2</mn>
<msubsup>
<mi>Gy</mi>
<mrow>
<mi>s</mi>
<mi>t</mi>
<mi>e</mi>
<mi>p</mi>
</mrow>
<mn>2</mn>
</msubsup>
<msubsup>
<mi>z</mi>
<mrow>
<mi>s</mi>
<mi>t</mi>
<mi>e</mi>
<mi>p</mi>
</mrow>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<mn>2</mn>
<msubsup>
<mi>Gx</mi>
<mrow>
<mi>s</mi>
<mi>t</mi>
<mi>e</mi>
<mi>p</mi>
</mrow>
<mn>2</mn>
</msubsup>
<msubsup>
<mi>z</mi>
<mrow>
<mi>s</mi>
<mi>t</mi>
<mi>e</mi>
<mi>p</mi>
</mrow>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<mn>2</mn>
<msubsup>
<mi>Ex</mi>
<mrow>
<mi>s</mi>
<mi>t</mi>
<mi>e</mi>
<mi>p</mi>
</mrow>
<mn>2</mn>
</msubsup>
<msubsup>
<mi>y</mi>
<mrow>
<mi>s</mi>
<mi>t</mi>
<mi>e</mi>
<mi>p</mi>
</mrow>
<mn>2</mn>
</msubsup>
</mrow>
</mfrac>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>5</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein:E is guide material Young's modulus;G is guide material modulus of shearing;xstepFor x directions discrete steps;ystepFor y side
To discrete steps;zstepFor z directions discrete steps;K counts for z directions infinitesimal;dzFor deformation extent;F is body force;
S4., algebraic equation is rewritten as to the iterative equation of solution, your alternative manner is solved using Gauss-Saden, and should
Accelerated with successive overrelaxation method, draw the numerical solution of pressure;The solution of pressureAfter obtaining deformation is substituted into as external applied load condition
Iterative formula solve, the solution of deformationThe iterative formula that rear oil film thickness condition brings pressure into is obtained to askSo follow
Ring, until result of calculation meets that essence requires;
S5. the analysis of bearing capacity is carried out according to the above results.