CN104680018A - Analyzing and optimizing method for hydrostatic guideway to inhibit inertia force impact - Google Patents

Abstract

The invention relates to an analyzing and optimizing method for a hydrostatic guideway to inhibit inertia force impact, and belongs to the technical field of hydrostatic support and lubricating design. The hydrostatic guideway is widely applied to a heavy machine tool. When a gantry of the heavy machine tool is started or braked, the heavy machine tool is swung because of the influence of the inertia force, so the influence on the processing accuracy is caused, and the risk exists; when the hydrostatic guideway is designed, the requirement of bearing capacity needs to be met, and the influence of starting and stopping impact needs to be considered. The analyzing and optimizing method has the advantages that according to a hydrostatic guideway model of the heavy machine tool, a Reynolds equation for the change of oil film thickness is introduced; the bending deformation and linear offset are simultaneously introduced into the oil film thickness change process, so as to simulate the actual working condition; a finite difference method is used, and the iteration is performed by a successive overrelaxation method to solve a numerical solution of the pressure; according to the pressure solution and the oil supply parameters, the change of the bearing property under the tilting condition caused by different inertia forces is analyzed; the optimizing scheme is provided for the analysis results under the condition of attempting different oil pad structures, and the capability of the hydrostatic guideway resisting the inertia force impact is improved.

Description

A kind of analysis and optimization method that hydrostatic slideway suppresses inertial force to impact

Technical field

The present invention is a kind of analysis and optimization method that hydrostatic slideway suppresses inertial force impact, belongs to static pressure and supports and Lubrication Design technical field.

Background technology

Current static pressure support system is applied widely in heavy machine tool, and hydrostatic slideway is a kind of typical apply wherein.External oil feed pump provides pressure oil by the lubricating pad installed under pipeline direction guiding rail slide, and the pressure of fluid in oily pocket is the major part of hydrostatic slideway load-bearing capacity, and the hydrostatic effects of oil when flowing through lubricating pad sealing oil edge is the key maintaining pressure in oily pocket.Generally, gantry height of heavy machine tool is some rice, own wt more than hundred tons, so start or braking time, because the impact of inertial force will inevitably be rocked.This rocking not only can affect machining precision, there is the potential danger damaging cutter or workpiece simultaneously.So hydrostatic slideway is when designing, the not only demand of demand fulfillment static bearing capacity, also will consider the impact of start/stop impact simultaneously.If the inertial force impact resistant ability of heavy gantry machine tool can be improved, the acceleration of motion at gantry can be improved on the basis ensureing safety and machining precision, thus increase work efficiency.The inertial force impact resistant ability of gantry machine tool can be passed judgment on from two aspects: the inclined degree of guide rail or the moment size in equal inclined degree lower guideway generation when affecting by the impact of equal inertial force.

When solving the problem of pressure distribution in sealing oil edge in hydrostatic slideway, Reynolds equation is main analytical approach.Solving of Reynolds equation is the basis analyzing hydrostatic slideway load-carrying properties, but due to its equation itself be partial differential equation of second order, asking for of analytic solution is more difficult, so based on numerical method in the analytical approach of static pressure support system more at present.Finite difference method is a kind of very practical numerical method, and the differential equation can change algebraic equation into by finite difference method is approximate, then is solved by the method for value solving of algebraic equation, finally obtains the approximate solution of pressure distribution in sealing oil edge.

Summary of the invention

The present invention, according to the hydrostatic slideway model of heavy machine tool, applies a kind of Reynolds equation introducing oil film thickness change.Introduce flexural deformation and linear deflection to simulate actual condition in the change of oil film thickness simultaneously.Use finite difference method, carry out by successive overrelaxation method the numerical solution that iteration asks for pressure.The change of load-carrying properties in the situation of toppling caused at different inertial force according to the solution of pressure and fuel delivery parameters analysis.Wherein fuel system selects common quantitative oil feed pump.The analysis result attempted under different oil pad structure need look for prioritization scheme, improves the opposing inertial force impact capacity of hydrostatic slideway.

First set up according to the structure of gantry machine tool and inertial force situation and a kind ofly consider the flexural deformation of guide rail slide and the oblique model of linear deflection, to simulate actual condition simultaneously.Substitute into Reynolds equation according to this oblique model as oil clearance condition again, solve, obtain pressure distribution.Bearing capacity and moment of resistance is solved afterwards according to pressure distribution and fuel system.Finally by attempting different oil pad structures, the size of contrast moment of resistance, draws the optimum results of oil pad structure.

The hydrostatic slideway load-bearing capacity analysis method of consideration guide pass distortion provided by the invention comprises the following steps:

S1. the oil film thickness under inertial force percussive action is first introduced:

$d_z=\left\{\begin{array}{cc}\frac{\mathrm{\&delta;}}{2\mathrm{SkL}-S^2}\&CenterDot;x^2,& 0\&le;x\&le;S\\ \frac{\frac{\mathrm{\&delta;}{S}^2}{2\mathrm{SkL}-S^2}-\mathrm{\&delta;}}{S-\mathrm{kL}}\&CenterDot;x+\mathrm{\&delta;}-\frac{\frac{\mathrm{\&delta;}{S}^2}{2\mathrm{SkL}-S^2}-\mathrm{\&delta;}}{S-\mathrm{kL}}\mathrm{kL},& S<x\&le;\mathrm{kL}\end{array}\right.$

Wherein: d _zfor the side-play amount of oil film thickness; S is bending section length; δ is maximum offset.The corresponding a kind of drift condition of each different δ value.

S2. again the parameter in hydrostatic slideway is carried out to the nondimensionalization of variable;

$\stackrel{\&OverBar;}{p}=\frac{p}{p_0},\stackrel{\&OverBar;}{p_0}=1,\stackrel{\&OverBar;}{x}=\frac{x}{L},\stackrel{\&OverBar;}{L}=1,\stackrel{\&OverBar;}{y}=\frac{y}{B},$

$\stackrel{\&OverBar;}{B}=1,\stackrel{\&OverBar;}{d_z}=\frac{d_z}{H_0},\stackrel{\&OverBar;}{\mathrm{\&delta;}}=\frac{\mathrm{\&delta;}}{H_0},\stackrel{\&OverBar;}{h}=\frac{h}{H_0},\stackrel{\&OverBar;}{H_0}=1,$

$\stackrel{\&OverBar;}{U_x}=\frac{U_x}{\frac{H_0^2{p}_0}{\mathrm{L\&eta;}}},\stackrel{\&OverBar;}{W}=\frac{W}{\mathrm{LB}{p}_0},\stackrel{\&OverBar;}{M_y}=\frac{M_y}{L^{2}B{p}_0},\stackrel{\&OverBar;}{q}=\frac{q}{\frac{H_0^3{p}_0}{\mathrm{\&eta;}}}$

Wherein: p is pressure; p ₀for pressure in oily pocket; L is hydrostatic slideway lubricating pad length; B is hydrostatic slideway lubricating pad width; W is load-bearing capacity; M _yfor y direction opposing upsetting moment; Q is flow; U _xfor guide moving velocity; H is oil film thickness; η is oil viscosity. for dimensionless pressure; for non-dimensional length; for dimensionless width; for dimensionless thickness; for dimensionless bearing capacity; for y direction dimensionless opposing upsetting moment; for dimensionless holds flow; for dimensionless guide moving velocity; for dimensionless oil film thickness.

S3. according to model Reynolds equation to be simplified and by discrete by finite difference method for the Reynolds equation after simplifying; Generally, the translational speed of hydrostatic slideway is less demanding, so heat-dissipating problem not obvious, namely the viscosity B coefficent of support liq and variable density can be ignored, and the Reynolds equation after simplification is:

$\frac{\&PartialD;}{\&PartialD;\stackrel{\&OverBar;}{x}}({\stackrel{\&OverBar;}{h}}^3\&CenterDot;\frac{\&PartialD;\stackrel{\&OverBar;}{p}}{\&PartialD;\stackrel{\&OverBar;}{x}})+{\left(\frac{L}{B}\right)}^2\frac{\&PartialD;}{\&PartialD;\stackrel{\&OverBar;}{y}}({\stackrel{\text{-}}{h}}^3\&CenterDot;\frac{\&PartialD;\stackrel{\&OverBar;}{p}}{\&PartialD;\stackrel{\&OverBar;}{y}})=6\frac{\&PartialD;}{\&PartialD;\stackrel{\&OverBar;}{x}}\left(\stackrel{\&OverBar;}{U_x}\stackrel{\&OverBar;}{h}\right)$

By the Reynolds equation after finite difference method Approximation Discrete be:

${\stackrel{\&OverBar;}{p}}_{i,j}=\frac{\left[\begin{array}{c}{\stackrel{\&OverBar;}{y}}_{\mathrm{step}}^2{\stackrel{\&OverBar;}{h}}_{i,j}^3{\stackrel{\&OverBar;}{p}}_{i+1,j}+{\stackrel{\&OverBar;}{y}}_{\mathrm{step}}^2{\stackrel{\&OverBar;}{h}}_{i-1,j}^3{\stackrel{\&OverBar;}{p}}_{i-1,j}\\ +{\left(\frac{L}{B}\right)}^2{\stackrel{\&OverBar;}{x}}_{\mathrm{step}}^2{\stackrel{\&OverBar;}{h}}_{i,j}^3{\stackrel{\&OverBar;}{p}}_{i,j+1}\\ +{\left(\frac{L}{B}\right)}^2{\stackrel{\&OverBar;}{x}}_{\mathrm{step}}^2{\stackrel{\&OverBar;}{h}}_{i,j-1}^3{\stackrel{\&OverBar;}{p}}_{i,j-1}\\ +6({\stackrel{\&OverBar;}{\mathrm{Ux}}}_{i,j}{\stackrel{\&OverBar;}{h}}_{i,j}-{\stackrel{\&OverBar;}{\mathrm{Ux}}}_{i-1,j}{\stackrel{\&OverBar;}{h}}_{i-1,j}){\stackrel{\&OverBar;}{x}}_{\mathrm{step}}{\stackrel{\&OverBar;}{y}}_{\mathrm{step}}^2\end{array}\right]}{\left[\begin{array}{c}{\stackrel{\&OverBar;}{y}}_{\mathrm{step}}^2{\stackrel{\&OverBar;}{h}}_{i,j}^3+{\stackrel{\&OverBar;}{y}}_{\mathrm{step}}^2{\stackrel{\&OverBar;}{h}}_{i-1,j}^3\\ +{\left(\frac{L}{B}\right)}^2{\stackrel{\&OverBar;}{x}}_{\mathrm{step}}^2{\stackrel{\&OverBar;}{h}}_{i,j}^3+{\left(\frac{L}{B}\right)}^2{\stackrel{\&OverBar;}{x}}_{\mathrm{step}}^2{\stackrel{\&OverBar;}{h}}_{i,j-1}^3\end{array}\right]}$

Wherein: for x direction discrete steps; for y direction discrete steps; I is x direction infinitesimal counting; J is y direction infinitesimal counting.

S4. bearing capacity and moment of resistance is solved after obtaining the numerical solution of pressure:

$\left\{\begin{array}{c}\stackrel{\&OverBar;}{W}=\mathrm{\&Sigma;}\frac{1}{4}({\stackrel{\&OverBar;}{p}}_{i,j}+{\stackrel{\&OverBar;}{p}}_{i+1,j}+{\stackrel{\&OverBar;}{p}}_{i,j+1}+{\stackrel{\&OverBar;}{p}}_{i+1,j+1})\&CenterDot;{\stackrel{\&OverBar;}{x}}_{\mathrm{step}}\&CenterDot;{\stackrel{\&OverBar;}{y}}_{\mathrm{step}}\\ W=\frac{\stackrel{\&OverBar;}{W}\mathrm{LB\&eta;}}{\stackrel{\&OverBar;}{q}{H}_0^3}\&CenterDot;Q_e\\ {\stackrel{\&OverBar;}{M}}_y=\mathrm{\&Sigma;}\frac{1}{4}({\stackrel{\&OverBar;}{p}}_{i,j}+{\stackrel{\&OverBar;}{p}}_{i+1,j}+{\stackrel{\&OverBar;}{p}}_{i,j+1}+{\stackrel{\&OverBar;}{p}}_{i+1,j+1})\&CenterDot;\frac{1}{2}({\stackrel{\&OverBar;}{r}}_{i,j}+{\stackrel{\&OverBar;}{r}}_{i+1,j})\&CenterDot;{\stackrel{\&OverBar;}{x}}_{\mathrm{step}}\&CenterDot;{\stackrel{\&OverBar;}{y}}_{\mathrm{step}}\\ M_y=\frac{{\stackrel{\&OverBar;}{M}}_y{L}^2\mathrm{B\&eta;}}{\stackrel{\&OverBar;}{q}{H}_0^3}\&CenterDot;Q_e\end{array}\right.$

Wherein: Q _efor the fuel supply flow rate of each lubricating pad; for the distance that coordinate is i, j nodal point separation slide center.

S5. according to the above results, the analysis that multiple different lubricating pad size carries out load-bearing capacity is attempted, the optimum solution that under searching same tilt degree, moment of resistance is maximum.

Consider that the hydrostatic slideway load-bearing capacity analysis method tool of guide pass distortion has the following advantages.

1, introduce flexural deformation and linear deflection when analyzing the guide rail slide that causes of inertial force and tilting to simulate actual operating conditions simultaneously, obtain the oil film oblique form tallied with the actual situation.

2, apply finite difference method and solve the Reynolds equation being difficult to obtain analytic solution, and carry out load-carrying properties analysis according to the pressure distribution drawn.

3, the mode by changing lubricating pad size improves the moment of resistance that hydrostatic slideway produces under equal inclined degree, thus improves its inertial force impact resistant ability, improves the reliability of guide rail work.

Accompanying drawing explanation

Fig. 1 is inertial force impact resistant capability analysis and the optimization method process flow diagram of hydrostatic slideway.

Fig. 2 is the structural representation of hydrostatic slideway.

Fig. 3 is the structural representation of hydrostatic slideway lubricating pad.

Fig. 4 a is the situation of change of hydrostatic slideway moment of resistance with side-play amount.

Fig. 4 b is the situation of change of oil film thickness of hydrostatic guide way with side-play amount.

Embodiment

With guide rail slide offset delta=2 × 10 ^-5m, Q _e=3.3 × 10 ^-6m ³/ s is example when single slide is equipped with 5 lubricating pads.As shown in Figure 2, if the long L of lubricating pad, wide B; The wide b of the oil long l of pocket; Design oil film thickness is H ₀.

When solving pressure, introduce Reynolds equation boundary condition:

Process flow diagram according to Fig. 1, calculates pressure distribution and guide rail surface distortion distribution in each lubricating pad, and calculates bearing capacity and the moment of resistance of guide rail according to this result.Wherein the bearing capacity of hydrostatic slideway act as the weight supporting gantry frame, and the deadweight of gantry frame changes hardly in the course of the work, so the actual carrying capacity of hydrostatic slideway is constant, but due to the change of dimensionless bearing capacity, oil film will be caused thinning, and this is the embodiment that a kind of load-bearing capacity reduces.Result of calculation is as shown in Fig. 4 a-4b.

The guide rail of each lubricating pad supports the contribution difference of resistance to capsizing, if only change the length L of each lubricating pad and do not change the overall length of oily pocket proportion l/L and slide, hydrostatic slideway is being constant without the static load-carrying properties under inclination conditions, so just can improve the ability that opposing inertial force impacts under the prerequisite not affecting static supporting effect.Consider the symmetry of inertial force when acceleration or deceleration, so when changing L, 1 ensured _stwith 5 _thequal, 2 _ndwith 4 _ththe size of the length of equal, 5 lubricating pads and each lubricating pad simultaneously of remaining unchanged is greater than zero.Optimizing constraint condition is:

$\left\{\begin{array}{c}{L}_{1\mathrm{st}}=L_{5\mathrm{th}}\\ L_{2\mathrm{nd}}=L_{4\mathrm{th}}\\ \mathrm{\&Sigma;}{L}_k=3m\\ L_k>0\end{array}\right.$

By attempting the length dimension of multiple lubricating pad, calculating oil film thickness and moment of resistance, finding optimum solution wherein.Under this constraint condition, work as L _1st=0.9, L _2nd=0.15, L _3rdobtain optimum solution when=0.9, opposing upsetting moment is just improved about 100% by the oil film thickness that only have lost less than 10%.

Claims (1)

1. hydrostatic slideway suppresses the analysis and optimization method that inertial force impacts, and it is characterized in that: the implementation procedure of the method is as follows,

S1. the oil film thickness under inertial force percussive action is first introduced:

$d_z=\left\{\begin{array}{cc}\frac{\mathrm{\&delta;}}{2\mathrm{SkL}{-S}^2}\&CenterDot;x^2,& 0\&le;x\&le;S\\ \frac{\frac{{\mathrm{\&delta;S}}^2}{2\mathrm{SkL}-S^2}-\mathrm{\&delta;}}{S-\mathrm{kL}}\&CenterDot;x+\mathrm{\&delta;}-\frac{\frac{{\mathrm{\&delta;S}}^2}{2\mathrm{SkL}-S^2}-\mathrm{\&delta;}}{S-\mathrm{kL}}\mathrm{kL},& S<x\&le;\mathrm{kL}\end{array}\right.$

Wherein: d _zfor the side-play amount of oil film thickness; S is bending section length; δ is maximum offset; The corresponding a kind of drift condition of each different δ value;

S2. again the parameter in hydrostatic slideway is carried out to the nondimensionalization of variable;

$\stackrel{\&OverBar;}{p}=\frac{p}{p_0},\stackrel{\&OverBar;}{p_0}=1,\stackrel{\&OverBar;}{x}=\frac{x}{L},\stackrel{\&OverBar;}{L}=1,\stackrel{\&OverBar;}{y}=\frac{y}{B},$

$\stackrel{\&OverBar;}{B}=1,\stackrel{\&OverBar;}{d_z}=\frac{d_z}{H_0},\stackrel{\&OverBar;}{\mathrm{\&delta;}}=\frac{\mathrm{\&delta;}}{H_0},\stackrel{\&OverBar;}{h}=\frac{h}{H_0},\stackrel{\&OverBar;}{H_0}=1,$

$\stackrel{\&OverBar;}{U_x}=\frac{U_x}{\frac{H_0^2{p}_0}{\mathrm{L\&eta;}}},\stackrel{\&OverBar;}{W}=\frac{W}{{\mathrm{LBp}}_0},\stackrel{\&OverBar;}{M_y}=\frac{M_y}{L^2{\mathrm{Bp}}_0},\stackrel{\&OverBar;}{q}=\frac{q}{\frac{H_0^3{p}_0}{\mathrm{\&eta;}}}$

Wherein: p is pressure; p ₀for pressure in oily pocket; L is hydrostatic slideway lubricating pad length; B is hydrostatic slideway lubricating pad width; W is load-bearing capacity; M _yfor y direction opposing upsetting moment; Q is flow; U _xfor guide moving velocity; H is oil film thickness; η is oil viscosity; for dimensionless pressure; for non-dimensional length; for dimensionless width; for dimensionless thickness; for dimensionless bearing capacity; for y direction dimensionless opposing upsetting moment; for dimensionless holds flow; for dimensionless guide moving velocity; for dimensionless oil film thickness;

S3. according to model Reynolds equation to be simplified and by discrete by finite difference method for the Reynolds equation after simplifying; Generally, the translational speed of hydrostatic slideway is less demanding, so heat-dissipating problem not obvious, namely the viscosity B coefficent of support liq and variable density can be ignored, and the Reynolds equation after simplification is:

$\frac{\&PartialD;}{\&PartialD;\stackrel{\&OverBar;}{x}}({\stackrel{\&OverBar;}{h}}^3\&CenterDot;\frac{\&PartialD;\stackrel{\&OverBar;}{p}}{\&PartialD;\stackrel{\&OverBar;}{x}})+{\left(\frac{L}{B}\right)}^2\frac{\&PartialD;}{\&PartialD;\stackrel{\&OverBar;}{y}}({\stackrel{\&OverBar;}{h}}^3\&CenterDot;\frac{\&PartialD;\stackrel{\&OverBar;}{p}}{\&PartialD;\stackrel{\&OverBar;}{y}})=6\frac{\&PartialD;}{\&PartialD;\stackrel{\&OverBar;}{x}}\left(\stackrel{\&OverBar;}{U_x}\stackrel{\&OverBar;}{h}\right)$

By the Reynolds equation after finite difference method Approximation Discrete be:

${\stackrel{\&OverBar;}{p}}_{i,j}=\frac{\left[\begin{array}{c}{\stackrel{\&OverBar;}{y}}_{\mathrm{step}}^2{\stackrel{\&OverBar;}{h}}_{i,j}^3{\stackrel{\&OverBar;}{p}}_{i+1,j}+{\stackrel{\&OverBar;}{y}}_{\mathrm{step}}^2{\stackrel{\&OverBar;}{h}}_{i-1,j}^3{\stackrel{\&OverBar;}{p}}_{i-1,j}\\ +{\left(\frac{L}{B}\right)}^2{\stackrel{\&OverBar;}{x}}_{\mathrm{step}}^2{\stackrel{\&OverBar;}{h}}_{i,j}^3{\stackrel{\&OverBar;}{p}}_{i,j}+1\\ +{\left(\frac{L}{B}\right)}^2{\stackrel{\&OverBar;}{x}}_{\mathrm{xtep}}^2{\stackrel{\&OverBar;}{h}}_{i,j-1}^3{\stackrel{\&OverBar;}{p}}_{i,j-1}\\ +6({\stackrel{\&OverBar;}{\mathrm{Ux}}}_{i,j}{\stackrel{\&OverBar;}{h}}_{i,j}-{\stackrel{\&OverBar;}{\mathrm{Ux}}}_{i-1,j}{\stackrel{\&OverBar;}{h}}_{i-1,j}){\stackrel{\&OverBar;}{x}}_{\mathrm{step}}{\stackrel{\&OverBar;}{y}}_{\mathrm{step}}^2\end{array}\right]}{\left[\begin{array}{c}{\stackrel{\&OverBar;}{y}}_{\mathrm{step}}^2{\stackrel{\&OverBar;}{h}}_{i,j}^3+{\stackrel{\&OverBar;}{y}}_{\mathrm{step}}^2{\stackrel{\&OverBar;}{h}}_{i-1,j}^3\\ +{\left(\frac{L}{B}\right)}^2{\stackrel{\&OverBar;}{x}}_{\mathrm{step}}^2{\stackrel{\&OverBar;}{h}}_{i,j}^3+{\left(\frac{L}{B}\right)}^2{\stackrel{\&OverBar;}{x}}_{\mathrm{step}}^2{\stackrel{\&OverBar;}{h}}_{i,j-1}^3\end{array}\right]}$

Wherein: for x direction discrete steps; for y direction discrete steps; I is x direction infinitesimal counting; J is y direction infinitesimal counting;

S4. bearing capacity and moment of resistance is solved after obtaining the numerical solution of pressure:

$\left\{\begin{array}{c}\stackrel{\&OverBar;}{W}=\mathrm{\&Sigma;}\frac{1}{4}({\stackrel{\&OverBar;}{p}}_{i,j}+{\stackrel{\&OverBar;}{p}}_{i,j+1}+{\stackrel{\&OverBar;}{p}}_{i,j+1}+{\stackrel{\&OverBar;}{p}}_{i+1,j+1})\&CenterDot;{\stackrel{\&OverBar;}{x}}_{\mathrm{step}}\&CenterDot;{\stackrel{\&OverBar;}{y}}_{\mathrm{step}}\\ W=\frac{\stackrel{\&OverBar;}{W}\mathrm{LB\&eta;}}{\stackrel{\&OverBar;}{q}{H}_0^3}\&CenterDot;Q_e\\ {\stackrel{\&OverBar;}{M}}_y=\mathrm{\&Sigma;}\frac{1}{4}({\stackrel{\&OverBar;}{p}}_{i,j}+{\stackrel{\&OverBar;}{p}}_{i+1,j}+{\stackrel{\&OverBar;}{p}}_{i,j+1}+{\stackrel{\&OverBar;}{p}}_{i+1,j+1})\&CenterDot;\frac{1}{2}({\stackrel{\&OverBar;}{r}}_{i,j}+{\stackrel{\&OverBar;}{r}}_{i+1,j})\&CenterDot;{\stackrel{\&OverBar;}{x}}_{\mathrm{step}}\&CenterDot;{\stackrel{\&OverBar;}{y}}_{\mathrm{step}}\\ M_y=\frac{{\stackrel{\&OverBar;}{M}}_y{L}^2\mathrm{B\&eta;}}{\stackrel{\&OverBar;}{q}{H}_0^3}\&CenterDot;Q_e\end{array}\right.$

Wherein: Q _efor the fuel supply flow rate of each lubricating pad; for the distance that coordinate is i, j nodal point separation slide center;

S5. according to the above results, the analysis that multiple different lubricating pad size carries out load-bearing capacity is attempted, the optimum solution that under searching same tilt degree, moment of resistance is maximum.