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CN112395790B - Reservation method for side milling finish machining allowance of thin-wall blade - Google Patents

Reservation method for side milling finish machining allowance of thin-wall blade Download PDF

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CN112395790B
CN112395790B CN202011218817.8A CN202011218817A CN112395790B CN 112395790 B CN112395790 B CN 112395790B CN 202011218817 A CN202011218817 A CN 202011218817A CN 112395790 B CN112395790 B CN 112395790B
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blade
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finishing
allowance
walled
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CN112395790A (en
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郑刚
饶金山
施婕
吴雁
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Shanghai Institute of Technology
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    • G06F30/23Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
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Abstract

The invention discloses a reservation method of a side milling finish machining allowance of a thin-wall blade, which comprises the following steps: step1: dividing the equal parameter finite element of the thin-wall blade; step2: establishing a section rigidity undetermined index epsilon of the thin-wall blade j The method comprises the steps of carrying out a first treatment on the surface of the Step3: establishing the deformation u of the blade tip node at each isoparametric line j And cross-section rigidity undetermined measurement index epsilon j Is a unitary nonlinear regression equation mu j The method comprises the steps of carrying out a first treatment on the surface of the Step4: setting a blade tip finish machining allowance range and a blade root finish machining allowance range; step5: selecting a plurality of blade tip finish machining cutting residual values and blade root finish machining cutting residual values, and substituting the blade tip finish machining cutting residual values and the blade root finish machining cutting residual values into a residual function in Step 3; step6: obtaining a functional expression of the blade tip finish machining allowance, the blade root finish machining allowance and geometric characteristics; step7: and carrying out non-uniform reservation on the blade tip and blade root curves b (u, v) of the thin-wall blade to obtain a blade tip and blade root driving curve b' (u, v) before finish machining. The method realizes non-uniform reservation of the finish machining allowance, so that the thin-wall blade is small in deformation, and machining errors are reduced.

Description

一种薄壁叶片侧铣精加工余量预留方法A Method for Reserving Finishing Allowance in Side Milling of Thin-walled Blades

技术领域technical field

本发明属于薄壁叶片加工技术领域,尤其涉及一种薄壁叶片侧铣精加工余量预留方法。The invention belongs to the technical field of thin-walled blade processing, and in particular relates to a method for reserving a finishing allowance for side milling of a thin-walled blade.

背景技术Background technique

薄壁叶片类零件如涡轮、叶轮,是透平机械中的核心,其制造水平直接影响着整体发动机的能量转换效率。为追求气动性能,叶轮叶片表面常被设计成扭曲度大、几何精度高的复杂曲面,给制造精度提出了更高的要求。Thin-walled blade parts such as turbines and impellers are the core of turbomachinery, and their manufacturing level directly affects the energy conversion efficiency of the overall engine. In order to pursue aerodynamic performance, the surface of impeller blades is often designed as a complex curved surface with large twist and high geometric precision, which puts forward higher requirements for manufacturing precision.

一些直纹面类叶片可利用侧铣方式实现高效率的宽行切削,在实际切削过程中,侧铣由于大轴向切深,产生的大铣削力导致薄壁叶片在加工过程发生弹性变形,造成叶片加工精度较差。为减小加工变形在数控加工过程中产生的不利影响,常采用的策略方法有:优化切削参数以减小切削力来获得较小的叶片变形、恒力切削策略减小颤震发生来获得较好的表面质量、通过二次误差补偿对残余误差进行修正。Some ruled surface blades can use side milling to achieve high-efficiency wide-row cutting. In the actual cutting process, due to the large axial depth of cut, the large milling force generated by side milling causes elastic deformation of thin-walled blades during processing. Resulting in poor machining accuracy of the blade. In order to reduce the adverse effects of machining deformation in the process of CNC machining, the strategies and methods often used are: optimizing cutting parameters to reduce cutting force to obtain smaller blade deformation, and constant force cutting strategy to reduce chatter to obtain better blade deformation. Good surface quality, residual errors are corrected by quadratic error compensation.

上述减小加工变形误差的策略需要额外操作用于获取经验数据,缺乏操作规范且难以保证加工的效率,而通过增强叶片工艺刚度抑制叶片变形来减小加工误差,效率较高且操作相对简单。均匀余量预留方法操作简单,但预留的均匀余量会使不同厚度及高度处的叶片发生的变形相差较大,导致叶面不光滑,叶片误差趋势不统一等缺点,不利用后续的误差修整。The above strategy to reduce machining deformation error requires additional operations to obtain empirical data, lacks operating specifications and is difficult to guarantee machining efficiency. However, reducing machining errors by enhancing blade process stiffness and suppressing blade deformation is more efficient and relatively simple to operate. The uniform margin reservation method is simple to operate, but the reserved uniform margin will cause large differences in the deformation of the blades at different thicknesses and heights, resulting in shortcomings such as rough blade surfaces and uneven blade error trends. Error trimming.

发明内容Contents of the invention

为解决上述问题,本发明的目的是提供一种薄壁叶片侧铣精加工余量预留方法,该方法实现了精加工余量的非均匀预留,使薄壁叶片变形小,减小加工误差。In order to solve the above problems, the object of the present invention is to provide a thin-walled blade side milling finishing allowance reservation method, the method realizes the non-uniform reservation of the finishing allowance, so that the thin-walled blade has small deformation and reduces machining error.

为实现上述目的,本发明的技术方案为:To achieve the above object, the technical solution of the present invention is:

一种薄壁叶片侧铣精加工余量预留方法,包括:A method for reserving a finishing allowance in side milling of a thin-walled blade, comprising:

Step1:采用有限元方法对薄壁叶片进行变形分析,对所述薄壁叶片进行等参数有限元划分,沿所述薄壁叶片的V向形成j个等参截面且沿其叶面V向形成j个等参线,在各个所述等参线处施加侧铣铣削力,获得在所述铣削力作用下各个所述等参线处叶尖节点的变形量uj;且定义U向为沿所述薄壁叶片轴向、V向为沿所述薄壁叶片切向;Step1: Use the finite element method to analyze the deformation of the thin-walled blade, divide the thin-walled blade with equal parameter finite element elements, and form j equal-parameter cross-sections along the V direction of the thin-walled blade and form along the V direction of the blade surface j isoparms, apply a side milling milling force at each of the isoparms, and obtain the deformation u j of the blade tip node at each of the isoparms under the action of the milling force; and define the U direction as along The axial direction and the V direction of the thin-walled blade are along the tangential direction of the thin-walled blade;

Step2:建立所述薄壁叶片的截面刚度待定衡量指标εj,且定义εj越大所述薄壁叶片截面越易变形;Step2: establish the undetermined measure index ε j of the section stiffness of the thin-walled blade, and Definition The larger the ε j is, the easier the section of the thin-walled blade is to deform;

其中,hj为所述薄壁叶片高度,tj为所述薄壁叶片截面平均厚度,m、n为截面刚度待定衡量指标εj的待定衡量系数,m、n为整数且m>0、n<0;Wherein, hj is the height of the thin-walled blade, tj is the average thickness of the section of the thin-walled blade, m and n are the undetermined measurement coefficients of the undetermined measurement index ε j of the section stiffness, m and n are integers and m>0, n<0;

Step3:建立各个所述等参线处叶尖节点的所述变形量uj与所述截面刚度待定衡量指标εj的一元非线性回归方程:μj=b2·εj 2+b1·εj+...+b0;建立各个等参线的叶尖精加工切削余量Δ1j、叶根精加工切削余量Δ2j与叶尖节点的变形量uj的余量函数: Step3: Establish a unary nonlinear regression equation of the deformation u j of the blade tip node at each of the isoparms and the undetermined measure ε j of the section stiffness: μ j = b 2 ·ε j 2 +b 1 · ε j +...+b 0 ; establish the margin function of the blade tip finishing allowance Δ 1j , the blade root finishing allowance Δ 2j and the deformation u j of the blade tip node of each isoparm:

其中,b2、b1、b0为非线性回归方程的系数与常量,k1、k2、c1、c2为余量函数的系数与常量;Among them, b 2 , b 1 , b 0 are the coefficients and constants of the nonlinear regression equation, and k 1 , k 2 , c 1 , c 2 are the coefficients and constants of the residual function;

Step4:设定所述叶尖精加工切削余量范围为:[Δmin,(Δminmax)/2]、所述叶根精加工切削余量范围为:[(Δminmax)/2,Δmax];Step4: Set the range of cutting allowance for blade tip finishing: [Δ min , (Δ minmax )/2], and the range of cutting allowance for blade root finishing: [(Δ minmax )/2, Δ max ];

其中,Δmin为实际精加工切削前余量预留最小值,Δmax为实际精加工切削前余量预留最大值;Among them, Δ min is the minimum value reserved for the actual finishing allowance before cutting, and Δ max is the maximum value reserved for the actual finishing allowance before cutting;

Step5:根据Step4中所述叶尖精加工切削余量范围和所述叶根精加工切削余量范围,选取若干所述叶尖精加工切削余量值和所述叶根精加工切削余量值,代入Step3中的所述余量函数,求得k1、k2、c1、c2值;Step5: According to the blade tip finishing cutting allowance range and the blade root finishing cutting allowance range described in Step4, select a number of the blade tip finishing cutting allowance values and the blade root finishing cutting allowance values , substitute into the margin function in Step3 to obtain k 1 , k 2 , c 1 , c 2 values;

Step6:将Step3中的所述一元非线性回归方程、Step2中的所述截面刚度待定衡量指标εj代入Step3中的所述余量函数,求得所述叶尖精加工切削余量、所述叶根精加工切削余量与几何特征的函数表达式:Step6: Substituting the unary nonlinear regression equation in Step3 and the undetermined measure index εj of section stiffness in Step2 into the margin function in Step3 to obtain the blade tip finish machining allowance, the The functional expression of blade root finishing allowance and geometric features:

其中,Δ1为所述叶尖精加工切削余量函数,Δ2为所述叶根精加工切削余量函数;Wherein, Δ 1 is the cutting allowance function for the finishing of the blade tip, and Δ 2 is the cutting allowance function for the finishing machining of the blade root;

Step7:根据Step6中计算得到的余量函数,对所述薄壁叶片的叶尖和叶根曲线b(u,v)进行非均匀预留,获得精加工前的叶尖和叶根驱动曲线b′(u,v)为:Step7: According to the margin function calculated in Step6, the blade tip and blade root curve b(u, v) of the thin-walled blade is reserved non-uniformly, and the blade tip and blade root driving curve b before finishing is obtained '(u, v) is:

其中,bu为叶尖或叶根的U向向量,bv为叶尖或叶根的V向向量。Among them, b u is the U direction vector of the blade tip or blade root, and b v is the V direction vector of the blade tip or blade root.

根据本发明一实施例,Step1中对所述薄壁叶片的第一叶面和与所述第一叶面相对的第二叶面均进行等参数有限元划分,其中沿V向划分形成21条线:j=1∶1∶21,在V向每条等参线的U向取5个点,i=1∶1∶5。According to an embodiment of the present invention, in Step 1, the first leaf surface of the thin-walled blade and the second leaf surface opposite to the first leaf surface are all divided by equal-parameter finite element elements, wherein 21 lines are formed along the V-direction Line: j=1:1:21, take 5 points in U direction of each isoparametric line in V direction, i=1:1:5.

根据本发明一实施例,Step2中所述薄壁叶片平均厚度tj计算为两等参线处对应点的距离的平均值:According to an embodiment of the present invention, the average thickness t j of the thin-walled blade described in Step2 is calculated as the average value of the distances between the corresponding points at the two isoparms:

其中,为所述薄壁叶片的第一叶面在U向第i处、V向第j处的点,/>为所述薄壁叶片的第二叶面在U向第i处、V向第j处的点。in, is the point of the first leaf surface of the thin-walled blade at the i-th position in the U direction and the j-th position in the V direction, /> is the point of the second blade surface of the thin-walled blade at the i-th position in the U direction and the j-th position in the V direction.

根据本发明一实施例,Step2中,取若干m和n的值进行组合,建立各个所述等参线处叶尖节点的所述变形量uj与任意组合的非线性回归分析,当且仅当非线性回归分析的标准偏差最小时选定该m、n的值。According to an embodiment of the present invention, in Step2, a number of values of m and n are combined to establish the deformation amount u j of the blade tip node at each of the isoparms and any combination The nonlinear regression analysis of , if and only when the standard deviation of the nonlinear regression analysis is the smallest, the values of m and n are selected.

根据本发明一实施例,Step5中,所述叶尖精加工切削余量值取值与所述截面刚度待定衡量指标εj值呈反比,所述叶根精加工切削余量值取值与所述截面刚度待定衡量指标εj值呈正比。According to an embodiment of the present invention, in Step5, the value of the cutting allowance for the finishing of the blade tip is inversely proportional to the value of the undetermined measure index εj of the section stiffness, and the value of the cutting allowance for the finishing of the blade root is inversely proportional to the value of the cutting allowance for the finishing of the blade root. The undetermined measure index ε j value of the section stiffness is proportional to it.

本发明由于采用以上技术方案,使其与现有技术相比具有以下的优点和积极效果:Compared with the prior art, the present invention has the following advantages and positive effects due to the adoption of the above technical scheme:

(1)通过本发明实施例中Step1-Step7对精加工切削前余量预留,能大幅增强薄壁叶片侧铣时的工艺刚度,有效抑制侧铣过程中薄壁叶片的变形,且能在保证效率的同时实现薄壁叶片变形的最佳抑制,提高薄壁叶片表面的加工质量。(1) Through Step1-Step7 in the embodiment of the present invention, the margin before finishing machining is reserved, which can greatly enhance the process stiffness of the thin-walled blade during side milling, effectively suppress the deformation of the thin-walled blade during the side milling process, and can While ensuring efficiency, the best suppression of thin-walled blade deformation is achieved, and the processing quality of the thin-walled blade surface is improved.

(2)本发明实施例中进一步限定Step5中,叶尖精加工切削余量值取值与截面刚度待定衡量指标εj值呈反比,叶根精加工切削余量值取值与截面刚度待定衡量指标εj值呈正比,使得计算结果更加准确,使薄壁叶片的变形更小。(2) In the embodiment of the present invention, it is further defined in Step5 that the value of cutting allowance for blade tip finishing is inversely proportional to the undetermined measurement index εj value of section stiffness, and the value of cutting allowance for blade root finishing is inversely proportional to the undetermined measurement index for section stiffness. The value of εj is proportional, which makes the calculation result more accurate and makes the deformation of the thin-walled blade smaller.

附图说明Description of drawings

下面结合附图对本发明的具体实施方式作进一步详细说明,其中:The specific embodiment of the present invention is described in further detail below in conjunction with accompanying drawing, wherein:

图1为本发明的一种薄壁叶片侧铣精加工余量预留方法薄壁叶片等参数有限元划分图;Fig. 1 is a thin-walled blade side milling finishing allowance reservation method for thin-walled blades and other parameters finite element division diagram of the present invention;

图2为本发明的一种薄壁叶片侧铣精加工余量预留方法薄壁叶片高度与变形结果图;Fig. 2 is a thin-walled blade height and deformation result diagram of a thin-walled blade side milling finishing allowance reservation method according to the present invention;

图3为本发明的一种薄壁叶片侧铣精加工余量预留方法薄壁叶片平均厚度与变形结果图;Fig. 3 is a graph showing the average thickness and deformation results of a thin-walled blade according to the method for reserving the finishing allowance in side milling of the thin-walled blade according to the present invention;

图4为本发明的一种薄壁叶片侧铣精加工余量预留方法薄壁叶片截面刚度待定衡量指标与变形结果图;Fig. 4 is a thin-walled blade side milling finishing allowance reservation method according to the present invention;

图5为本发明的一种薄壁叶片侧铣精加工余量预留方法薄壁叶片叶尖节点变形量与变形结果图;Fig. 5 is a thin-walled blade tip node deformation amount and deformation result diagram of a thin-walled blade side milling finishing allowance reservation method according to the present invention;

图6为本发明的一种薄壁叶片侧铣精加工余量预留方法薄壁叶片等参线处叶尖节点的变形量与与截面刚度待定衡量指标εj的一元非线性回归方程函数图;Fig. 6 is a kind of thin-walled blade side milling finishing allowance reservation method according to the present invention. The deformation of the tip node at the isoparameter of the thin-walled blade and the unitary nonlinear regression equation function diagram of the undetermined measurement index ε j of the section stiffness ;

图7为本发明的一种薄壁叶片侧铣精加工余量预留方法叶根精加工切削余量与叶尖节点的变形量的余量函数图;Fig. 7 is a margin function diagram of a thin-walled blade side milling finishing allowance reservation method of the present invention, the blade root finishing cutting allowance and the deformation of the blade tip node;

图8为本发明的一种薄壁叶片侧铣精加工余量预留方法精加工前的叶尖和叶根驱动曲线。Fig. 8 is a driving curve of the blade tip and blade root before finishing according to a thin-walled blade side milling finishing allowance reservation method according to the present invention.

附图标记说明:Explanation of reference signs:

1:叶尖;2:叶根;3:等参线;4:叶尖驱动曲线;5:叶根驱动曲线;6:薄壁叶片的第一叶面;7:薄壁叶片的第二叶面。1: tip; 2: root; 3: isoparm; 4: driving curve of tip; 5: driving curve of root; 6: first leaf surface of thin-walled blade; 7: second leaf of thin-walled blade noodle.

具体实施方式Detailed ways

以下结合附图和具体实施例对本发明作进一步详细说明。根据下面说明和权利要求书,本发明的优点和特征将更清楚。需说明的是,附图均采用非常简化的形式且均使用非精准的比率,仅用以方便、明晰地辅助说明本发明实施例的目的。The present invention will be described in further detail below in conjunction with the accompanying drawings and specific embodiments. Advantages and features of the present invention will be apparent from the following description and claims. It should be noted that the drawings are all in a very simplified form and use imprecise ratios, which are only used to facilitate and clearly assist the purpose of illustrating the embodiments of the present invention.

需要说明,本发明实施例中所有方向性指示(诸如上、下、左、右、前、后……)仅用于解释在某一特定姿态(如附图所示)下各部件之间的相对位置关系、运动情况等,如果该特定姿态发生改变时,则该方向性指示也相应地随之改变。It should be noted that all directional indications (such as up, down, left, right, front, back...) in the embodiments of the present invention are only used to explain the relationship between the components in a certain posture (as shown in the accompanying drawings). Relative positional relationship, movement conditions, etc., if the specific posture changes, the directional indication will also change accordingly.

参看图1至8,本发明的核心是提供一种薄壁叶片侧铣精加工余量预留方法,包括如下步骤:Referring to Figures 1 to 8, the core of the present invention is to provide a thin-walled blade side milling finishing allowance reservation method, including the following steps:

Step1:采用有限元方法对薄壁叶片进行变形分析,对薄壁叶片进行等参数有限元划分,沿薄壁叶片的V向形成j个等参截面且沿其叶面V向形成j个等参线3,在各个等参线3处施加侧铣铣削力,获得在铣削力作用下各个等参线3处叶尖1节点的变形量uj;且定义U向为沿薄壁叶片轴向、V向为沿薄壁叶片切向;Step1: Use the finite element method to analyze the deformation of thin-walled blades, divide the thin-walled blades into equal-parameter finite element, form j equal-parameter cross-sections along the V direction of the thin-walled blades and form j equal-parameter sections along the V direction of the blade surface Line 3, the side milling force is applied at each isoparametric line 3, and the deformation u j of the blade tip 1 node at each isoparametric line 3 under the action of milling force is obtained; and the U direction is defined as along the thin-walled blade axial direction, The V direction is the tangential direction along the thin-walled blade;

具体的,通过有限元分析软件对薄壁叶片进行有限元受力变形分析。Specifically, the thin-walled blade is subjected to finite element force deformation analysis by finite element analysis software.

Step2:建立所述薄壁叶片的截面刚度待定衡量指标εj,且定义εj越大所述薄壁叶片截面越易变形;Step2: establish the undetermined measure index ε j of the section stiffness of the thin-walled blade, and Definition The larger the ε j is, the easier the section of the thin-walled blade is to deform;

其中,hj为所述薄壁叶片高度,tj为所述薄壁叶片截面平均厚度,m、n为截面刚度待定衡量指标εj的待定衡量系数,m、n为整数且m>0、n<0;Wherein, hj is the height of the thin-walled blade, tj is the average thickness of the section of the thin-walled blade, m and n are the undetermined measurement coefficients of the undetermined measurement index ε j of the section stiffness, m and n are integers and m>0, n<0;

叶片高度为等参截面的截面长度,也就是等参线3长度。薄壁叶片平均厚度tj计算为两等参线3处对应点的距离的平均值:其中,/>为薄壁叶片的第一叶面6在U向第i处、V向第j处的点,/>为薄壁叶片的第二叶面7在U向第i处、V向第j处的点。The blade height is the section length of the isoparametric section, that is, the length of the isoparametric line 3 . The average thickness t j of the thin-walled blade is calculated as the average value of the distances between the corresponding points at the two isoparms 3: where, /> is the point of the first blade surface 6 of the thin-walled blade at the i-th position from U and the j-th position from V, /> It is the point of the second blade surface 7 of the thin-walled blade at the i-th position in the U direction and the j-th position in the V direction.

优选的,为了使m、n的取值更加合理,先试取若干m和n的值进行组合,建立各个等参线3处叶尖1节点的变形量uj与任意组合的非线性回归分析,当且仅当非线性回归分析的标准偏差最小时选定该m、n的值。Preferably, in order to make the values of m and n more reasonable, first try to combine several values of m and n, and establish the deformation amount u j of node 1 of the blade tip at 3 positions of each isoparametric line and any combination The nonlinear regression analysis of , if and only when the standard deviation of the nonlinear regression analysis is the smallest, the values of m and n are selected.

Step3:建立各个等参线3处叶尖1节点的变形量uj与截面刚度待定衡量指标εj的一元非线性回归方程:μj=b2·εj 2+b1·εj+...+b0;建立各个等参线3的叶尖1精加工切削余量Δ1j、叶根2精加工切削余量Δ2j与叶尖1节点的变形量uj的余量函数: Step3: Establish the unary nonlinear regression equation of the deformation u j of the blade tip 1 node at the 3 positions of each isoparameter and the undetermined measure index ε j of the section stiffness: μ j = b 2 ·ε j 2 +b 1 ·ε j +. ..+b 0 ; establish the margin function of the blade tip 1 finish machining allowance Δ 1j , the blade root 2 finish machining allowance Δ 2j and the deformation u j of the blade tip 1 node of each isoparm 3:

其中,b2、b1、b0为非线性回归方程的系数与常量,k1、k2、c1、c2为余量函数的系数与常量;Among them, b 2 , b 1 , b 0 are the coefficients and constants of the nonlinear regression equation, and k 1 , k 2 , c 1 , c 2 are the coefficients and constants of the residual function;

Step4:设定叶尖1精加工切削余量范围为:[Δmin,(Δminmax)/2]、叶根2精加工切削余量范围为:[(Δminmax)/2,Δmax];Step4: Set the cutting allowance range for finishing blade tip 1 to [Δ min , (Δ minmax )/2], and the range of cutting allowance for finishing machining at blade root 2: [(Δ minmax )/ 2, Δmax ];

其中,Δmin为实际精加工切削前余量预留最小值,Δmax为实际精加工切削前余量预留最大值;Among them, Δ min is the minimum value reserved for the actual finishing allowance before cutting, and Δ max is the maximum value reserved for the actual finishing allowance before cutting;

Step5:根据Step4中叶尖1精加工切削余量范围和叶根2精加工切削余量范围,选取若干叶尖1精加工切削余量值和叶根2精加工切削余量值,代入Step3中的余量函数,求得k1、k2、c1、c2值;Step5: According to the range of cutting allowance for finishing machining of blade tip 1 and the range of cutting allowance for finishing machining of blade root 2 in Step4, select a number of cutting allowance values for finishing machining of blade tip 1 and finishing machining of blade root 2, and substitute them in Step3 Residual function, obtain k 1 , k 2 , c 1 , c 2 values;

在对叶尖1精加工切削余量值和叶根2精加工切削余量值取值时,叶尖1精加工切削余量值取值与截面刚度待定衡量指标εj值呈反比,叶根2精加工切削余量值取值与截面刚度待定衡量指标εj值呈正比。When selecting the value of cutting allowance for finishing machining of blade tip 1 and cutting allowance for finishing machining of blade root 2, the value of cutting allowance for finishing machining of blade tip 1 is inversely proportional to the value of the undetermined measurement index ε j of section stiffness, and 2. The value of cutting allowance in finishing machining is proportional to the undetermined measure index ε j value of section stiffness.

也就是说,截面刚度待定衡量指标εj值较大时,取较小的叶尖1精加工切削余量值和较大的叶根2精加工切削余量值;截面刚度待定衡量指标εj值较小时,取较大的叶尖1精加工切削余量值和较小的叶根2精加工切削余量值。That is to say, when the value of the undetermined measurement index ε j of the section stiffness is relatively large, the smaller value of the finishing cutting allowance of the blade tip 1 and the larger value of the finishing cutting allowance of the blade root 2 are taken; the undetermined measurement index of the section stiffness ε j When the value is small, take the larger cutting allowance value for the finishing of blade tip 1 and the smaller value of cutting allowance for finishing machining of blade root 2.

因为截面刚度待定衡量指标εj值越大,薄壁叶片在此位置越容易变形,所以就要取较小的叶尖1精加工切削余量值和较大的叶根2精加工切削余量值以抑制变形;相对的,截面刚度待定衡量指标εj值越小,说明薄壁叶片在此位置的变形受几何参数的影响小,可以取较大的叶尖1精加工切削余量值和较小的叶根2精加工切削余量值。当截面刚度待定衡量指标εj值最大时,取叶尖1精加工切削余量为最小值,叶根2精加工切削余量为最大值;当截面刚度待定衡量指标εj值最小时,取叶尖1精加工切削余量为最大值,叶根2精加工切削余量为最小值。Because the greater the value of the undetermined measurement index ε j of section stiffness, the thinner blade is more likely to deform at this position, so it is necessary to take a smaller value of the blade tip 1 finish machining allowance and a larger blade root 2 finish machining allowance Relatively, the smaller the value of the undetermined section stiffness εj value, it means that the deformation of the thin-walled blade at this position is less affected by the geometric parameters, and a larger cutting allowance value for finishing machining of the blade tip 1 and Smaller blade root 2 finish machining allowance value. When the value of the undetermined section stiffness εj is the largest, take the blade tip 1 finishing allowance as the minimum value, and the blade root 2 finishing cutting allowance as the maximum value; when the section stiffness undetermined measurement index εj value is the smallest, take The cutting allowance for finishing machining of blade tip 1 is the maximum value, and the cutting allowance for finishing machining of blade root 2 is the minimum value.

Step6:将Step3中的一元非线性回归方程、Step2中的截面刚度待定衡量指标εj代入Step3中的余量函数,求得叶尖1精加工切削余量、叶根2精加工切削余量与几何特征的函数表达式:Step6: Substitute the unary nonlinear regression equation in Step3 and the undetermined measure index εj of section stiffness in Step2 into the allowance function in Step3 to obtain the finishing cutting allowance of blade tip 1, the finishing cutting allowance of blade root 2 and Functional expressions for geometric features:

其中,Δ1为叶尖1精加工切削余量函数,Δ2为叶根2精加工切削余量函数;Wherein, Δ 1 is the blade tip 1 finishing cutting allowance function, and Δ 2 is the blade root 2 finishing cutting allowance function;

Step7:根据Step6中计算得到的余量函数,对薄壁叶片的叶尖1和叶根2曲线b(u,v)进行非均匀预留,获得精加工前的叶尖驱动曲线4和叶根驱动曲线5b′(u,v)为:Step7: According to the margin function calculated in Step6, the blade tip 1 and blade root 2 curves b(u, v) of the thin-walled blade are non-uniformly reserved, and the blade tip driving curve 4 and blade root before finishing are obtained The driving curve 5b'(u, v) is:

其中,bu为叶尖1或叶根2的U向向量,bv为叶尖1或叶根2的V向向量。Among them, b u is the U direction vector of blade tip 1 or blade root 2, and b v is the V direction vector of blade tip 1 or blade root 2.

下面举一具体计算实施例:A specific calculation example is given below:

Step1中对薄壁叶片的第一叶面6和与第一叶面相对的第二叶面均进行等参数有限元划分,其中沿V向划分形成21条线:j=1∶1∶21,在V向每条等参线3的U向取5个点,i=1∶1∶5。In Step1, the first blade surface 6 of the thin-walled blade and the second blade surface opposite to the first blade surface are all subjected to equal-parameter finite element division, wherein 21 lines are formed along the V-direction division: j=1:1:21, Take 5 points in the U direction of each isoparm 3 in the V direction, i=1:1:5.

根据划分结果计算出薄壁叶片高度,结合公式:Calculate the height of thin-walled blades according to the division results, combined with the formula:

计算出薄壁叶片平均厚度,根据叶尖1变形分布状态及Step2的优选实施例确定m=1,n=-1,截面刚度待定衡量指标结合图4、图5,当截面刚度待定衡量指标εj越大时,薄壁叶片等参截面越容易发生变形。Calculate the average thickness of the thin-walled blade, and determine m=1, n=-1 according to the deformation distribution state of the blade tip 1 and the preferred embodiment of Step2, and the section stiffness is to be determined. Combining Fig. 4 and Fig. 5, when the section stiffness undetermined index ε j is larger, the isoparametric section of the thin-walled blade is more likely to be deformed.

根据21个等参线3处的叶尖1节点变形量μj与截面刚性待定衡量指标εj的分布状态建立的一元非线性回归方程,当回归方程的次数为2次时,获得的回归函数效果最好,此时最小标准偏差为0.71%,建立的一元非线性回归方程为:μj=(0.1009·εj 2+0.2492·εj+2.6176)·10-3,如图6所示。A one-variable nonlinear regression equation established according to the distribution state of the blade tip 1 node deformation μ j at the position 3 of the 21 isoparameters and the undetermined measure ε j of the section rigidity. When the order of the regression equation is 2 times, the obtained regression function The effect is the best, when the minimum standard deviation is 0.71%, the established one-variable nonlinear regression equation is: μ j = (0.1009·ε j 2 +0.2492·ε j +2.6176)·10 -3 , as shown in Figure 6 .

根据实际精加工前的余量允许范围0.05-0.2mm设定精加工余量的允许预留范围:叶尖1精加工切削余量范围:0.05-0.12mm,叶根2精加工切削余量允许范围:0.13-0.2;根据截面刚度待定衡量指标的定义,在εj=5.1523的最小处,该处薄壁叶片截面处刚度指标较好,薄壁叶片变形受叶片结构特征影响较小,因此,赋予叶尖1精加工切削余量最大允许余量0.12mm,赋予叶根2精加工切削余量最小允许余量0.13mm;在εj=24.1790的最大的薄壁叶片截面处,薄壁叶片变形受叶片结构特征影响较大,该处刚性指标较差,因此,赋予叶根2精加工切削余量最大允许余量0.2mm,叶尖1精加工切削余量最小允许余量0.05mm。Set the allowable reserved range of finishing allowance according to the allowable range of allowance before finishing: 0.05-0.2mm: blade tip 1 finishing cutting allowance range: 0.05-0.12mm, blade root 2 finishing cutting allowance allowable Range: 0.13-0.2; according to the definition of the undetermined measure index of section stiffness, at the minimum point of ε j = 5.1523, the stiffness index of the section of the thin-walled blade is better, and the deformation of the thin-walled blade is less affected by the structural characteristics of the blade. Therefore, The maximum allowable cutting allowance for finishing machining of blade tip 1 is 0.12 mm, and the minimum allowable cutting allowance for finishing machining of blade root 2 is 0.13 mm; at the largest thin-walled blade section where ε j = 24.1790, the thin-walled blade deforms The structural characteristics of the blade are greatly affected, and the rigidity index here is poor. Therefore, the maximum allowable cutting allowance for finishing machining of blade root 2 is 0.2 mm, and the minimum allowable cutting allowance for finishing machining of blade tip 1 is 0.05 mm.

建立各个等参线3的叶尖1精加工切削余量Δ1j、叶根2精加工切削余量Δ2j与叶尖1节点的变形量uj的余量函数为: The margin function of the blade tip 1 finishing allowance Δ 1j , the blade root 2 finishing allowance Δ 2j and the deformation u j of the blade tip 1 node of each isoparm 3 is established as follows:

将截面刚度待定衡量指标以薄壁叶片几何参数表达:ε=h1t-1,并将一元非线性回归方程带入余量函数,求得如图7所示的函数为:The undetermined measure of the section stiffness is expressed as the geometric parameters of the thin-walled blade: ε=h 1 t -1 , and the unary nonlinear regression equation is brought into the margin function, and the function shown in Figure 7 is obtained as:

叶尖1精加工切削余量函数为:Δ1=-0.0001h2a-2+0.0003ha-1+0.119。The cutting allowance function for finishing the blade tip 1 is: Δ 1 =-0.0001h 2 a -2 +0.0003ha -1 +0.119.

叶根2精加工切削余量函数为:Δ2=0.0001h2a-2+0.00029ha-1+0.131。The cutting allowance function for finishing machining of the blade root 2 is: Δ 2 =0.0001h 2 a -2 +0.00029ha -1 +0.131.

根据计算得到的叶尖1精加工切削余量函数和叶根2精加工切削余量函数,求得薄壁叶片任意V向处的余量并对叶尖1精加工切削余量和叶根2精加工切削余量进行预留,对薄壁叶片曲面的其中一面的叶尖1或叶根2曲线b(u,v)在叶面法向进行非均匀偏置,获得如图8所示的精加工前的叶尖驱动曲线4及叶根驱动曲线5。According to the calculated cutting allowance function of tip 1 finish machining and blade root 2 finish machining allowance function, the allowance at any V direction of the thin-walled blade is obtained, and the finishing cutting allowance of blade tip 1 and blade root 2 are calculated. The cutting allowance for finishing machining is reserved, and the blade tip 1 or blade root 2 curve b(u, v) on one side of the curved surface of the thin-walled blade is non-uniformly offset in the normal direction of the blade surface, as shown in Figure 8 Tip driving curve 4 and blade root driving curve 5 before finishing.

本发明针对现有侧铣加工工艺方法的不足,对精加工前的余量预留进行改进,根据薄壁叶片实际几何特征,在精加工余量允许范围内实现叶尖1及叶根2的连续的非均匀余量预留,对叶片变形实现最佳的抑制效果,尽可能减小变形带来的加工误差。The present invention aims at the deficiencies of the existing side milling processing method, improves the margin reservation before finishing, and realizes the blade tip 1 and blade root 2 within the allowable range of the finishing margin according to the actual geometric characteristics of the thin-walled blade. The continuous non-uniform margin is reserved to achieve the best suppression effect on blade deformation and minimize the processing error caused by deformation.

由于薄壁叶片的自身几何特征,侧铣时产生的铣削力易使薄壁叶片在铣削接触区法向发生弹性变形,对薄壁叶片进行参数划分并通过赋值径向铣削力获得叶片各参数划分位置的变形,计算该位置的截面刚度衡量待定指标并建立叶尖1节点变形与截面刚度衡量待定指标的联系,在上述基础上利用截面刚度衡量待定指标的定义对精加工的叶尖1及叶根2余量进行非均匀余量预留,获得预留余量与薄壁叶片几何特征参数的函数方程。按照本方法对半精加工后的余量进行计算并预留,能大幅增强侧铣薄壁叶片侧铣时的工艺刚度,有效抑制侧铣过程中薄壁叶片的变形,减小变形误差。该方法能在精加工过程中保证效率的同时实现叶片变形的最佳抑制,提高叶片表面的加工质量。Due to the geometric characteristics of thin-walled blades, the milling force generated during side milling is likely to cause elastic deformation of the thin-walled blades in the normal direction of the milling contact area. The parameters of the thin-walled blades are divided and the parameters of the blades are obtained by assigning radial milling forces. The deformation of the position, calculate the undetermined index of section stiffness at this position and establish the connection between the deformation of the tip 1 node and the undetermined index of section stiffness, on the basis of the above, use the definition of section stiffness to measure the undetermined index for the finished blade tip 1 and blade The non-uniform allowance is reserved according to the 2 allowance, and the functional equation of the reserved allowance and the geometric characteristic parameters of the thin-walled blade is obtained. According to this method, the margin after semi-finishing is calculated and reserved, which can greatly enhance the process rigidity during side milling of thin-walled blades, effectively suppress the deformation of thin-walled blades during side milling, and reduce deformation errors. The method can ensure the efficiency in the finishing process and at the same time realize the best suppression of blade deformation and improve the processing quality of the blade surface.

上面结合附图对本发明的实施方式作了详细说明,但是本发明并不限于上述实施方式。即使对本发明作出各种变化,倘若这些变化属于本发明权利要求及其等同技术的范围之内,则仍落入在本发明的保护范围之中。The embodiments of the present invention have been described in detail above with reference to the accompanying drawings, but the present invention is not limited to the above embodiments. Even if various changes are made to the present invention, if these changes fall within the scope of the claims of the present invention and equivalent technologies, they still fall within the protection scope of the present invention.

Claims (5)

1.一种薄壁叶片侧铣精加工余量预留方法,其特征在于,包括:1. A thin-walled blade side milling finishing allowance reservation method, characterized in that, comprising: Step1:采用有限元方法对薄壁叶片进行变形分析,对所述薄壁叶片进行等参数有限元划分,沿所述薄壁叶片的V向形成j个等参截面且沿其叶面V向形成j个等参线,在各个所述等参线处施加侧铣铣削力,获得在所述铣削力作用下各个所述等参线处叶尖节点的变形量uj;且定义U向为沿所述薄壁叶片轴向、V向为沿所述薄壁叶片切向;Step1: Use the finite element method to analyze the deformation of the thin-walled blade, divide the thin-walled blade with equal parameter finite element elements, and form j equal-parameter cross-sections along the V direction of the thin-walled blade and form along the V direction of the blade surface j isoparms, apply a side milling milling force at each of the isoparms, and obtain the deformation u j of the blade tip node at each of the isoparms under the action of the milling force; and define the U direction as along The axial direction and the V direction of the thin-walled blade are along the tangential direction of the thin-walled blade; Step2:建立所述薄壁叶片的截面刚度待定衡量指标εj,且定义εj越大所述薄壁叶片截面越易变形;Step2: establish the undetermined measure index ε j of the section stiffness of the thin-walled blade, and Definition The larger the ε j is, the easier the section of the thin-walled blade is to deform; 其中,hj为所述薄壁叶片高度,tj为所述薄壁叶片截面平均厚度,m、n为截面刚度待定衡量指标εj的待定衡量系数,m、n为整数且m>0、n<0;Wherein, hj is the height of the thin-walled blade, tj is the average thickness of the section of the thin-walled blade, m and n are the undetermined measurement coefficients of the undetermined measurement index ε j of the section stiffness, m and n are integers and m>0, n<0; Step3:建立各个所述等参线处叶尖节点的所述变形量uj与所述截面刚度待定衡量指标εj的一元非线性回归方程:μj=b2·εj 2+b1·εj+...+b0;建立各个等参线的叶尖精加工切削余量Δ1j、叶根精加工切削余量Δ2j与叶尖节点的变形量uj的余量函数: Step3: Establish a unary nonlinear regression equation of the deformation u j of the blade tip node at each of the isoparms and the undetermined measure ε j of the section stiffness: μ j = b 2 ·ε j 2 +b 1 · ε j +...+b 0 ; establish the margin function of the blade tip finishing allowance Δ 1j , the blade root finishing allowance Δ 2j and the deformation u j of the blade tip node of each isoparm: 其中,b2、b1、b0为非线性回归方程的系数与常量,k1、k2、c1、c2为余量函数的系数与常量;Among them, b 2 , b 1 , b 0 are the coefficients and constants of the nonlinear regression equation, and k 1 , k 2 , c 1 , c 2 are the coefficients and constants of the residual function; Step4:设定所述叶尖精加工切削余量范围为:[Δmin,(Δminmax)/2]、所述叶根精加工切削余量范围为:[(Δminmax)/2,Δmax];Step4: Set the range of cutting allowance for blade tip finishing: [Δ min , (Δ minmax )/2], and the range of cutting allowance for blade root finishing: [(Δ minmax )/2, Δ max ]; 其中,Δmin为实际精加工切削前余量预留最小值,Δmax为实际精加工切削前余量预留最大值;Among them, Δ min is the minimum value reserved for the actual finishing allowance before cutting, and Δ max is the maximum value reserved for the actual finishing allowance before cutting; Step5:根据Step4中所述叶尖精加工切削余量范围和所述叶根精加工切削余量范围,选取若干所述叶尖精加工切削余量值和所述叶根精加工切削余量值,代入Step3中的所述余量函数,求得k1、k2、c1、c2值;Step5: According to the blade tip finishing cutting allowance range and the blade root finishing cutting allowance range described in Step4, select a number of the blade tip finishing cutting allowance values and the blade root finishing cutting allowance values , substitute into the margin function in Step3 to obtain k 1 , k 2 , c 1 , c 2 values; Step6:将Step3中的所述一元非线性回归方程、Step2中的所述截面刚度待定衡量指标εj代入Step3中的所述余量函数,求得所述叶尖精加工切削余量、所述叶根精加工切削余量与几何特征的函数表达式:Step6: Substituting the unary nonlinear regression equation in Step3 and the undetermined measure index εj of section stiffness in Step2 into the margin function in Step3 to obtain the blade tip finish machining allowance, the The functional expression of blade root finishing allowance and geometric features: 其中,Δ1为所述叶尖精加工切削余量函数,Δ2为所述叶根精加工切削余量函数;Wherein, Δ 1 is the cutting allowance function for the finishing of the blade tip, and Δ 2 is the cutting allowance function for the finishing machining of the blade root; Step7:根据Step6中计算得到的余量函数,对所述薄壁叶片的叶尖和叶根曲线b(u,v)进行非均匀预留,获得精加工前的叶尖和叶根驱动曲线b′(u,v)为:Step7: According to the margin function calculated in Step6, the blade tip and blade root curve b(u, v) of the thin-walled blade is reserved non-uniformly, and the blade tip and blade root driving curve b before finishing is obtained '(u, v) is: 其中,bu为叶尖或叶根的U向向量,bv为叶尖或叶根的V向向量。Among them, b u is the U direction vector of the blade tip or blade root, and b v is the V direction vector of the blade tip or blade root. 2.根据权利要求1所述的薄壁叶片侧铣精加工余量预留方法,其特征在于,Step1中对所述薄壁叶片的第一叶面和与所述第一叶面相对的第二叶面均进行等参数有限元划分,其中沿V向划分形成21条线:j=1∶1∶21,在V向每条等参线的U向取5个点,i=1∶1∶5。2. The thin-walled blade side milling finishing allowance reservation method according to claim 1, characterized in that, in Step1, the first blade surface of the thin-walled blade and the second blade surface opposite to the first blade surface are The two leaf surfaces are divided by isoparametric finite element elements, in which 21 lines are formed along the V direction: j=1:1:21, and 5 points are taken in the U direction of each isoparametric line in the V direction, i=1:1 : 5. 3.根据权利要求1所述的薄壁叶片侧铣精加工余量预留方法,其特征在于,Step2中所述薄壁叶片平均厚度tj计算为两等参线处对应点的距离的平均值:3. The thin-walled blade side milling finishing allowance reservation method according to claim 1 is characterized in that, the average thickness t of the thin-walled blade described in Step2 is calculated as the average of the distances at the corresponding points at the two isoparms value: 其中,为所述薄壁叶片的第一叶面在U向第i处、V向第j处的点,/>为所述薄壁叶片的第二叶面在U向第i处、V向第j处的点。in, is the point of the first leaf surface of the thin-walled blade at the i-th position in the U direction and the j-th position in the V direction, /> is the point of the second blade surface of the thin-walled blade at the i-th position in the U direction and the j-th position in the V direction. 4.根据权利要求1所述的薄壁叶片侧铣精加工余量预留方法,其特征在于,Step2中,取若干m和n的值进行组合,建立各个所述等参线处叶尖节点的所述变形量uj与任意组合的非线性回归分析,当且仅当非线性回归分析的标准偏差最小时选定该m、n的值。4. The thin-walled blade side milling finishing allowance reservation method according to claim 1, characterized in that, in Step2, a number of m and n values are combined to establish blade tip nodes at each of the isoparms The deformation amount u j in any combination with The nonlinear regression analysis of , if and only when the standard deviation of the nonlinear regression analysis is the smallest, the values of m and n are selected. 5.根据权利要求1所述的薄壁叶片侧铣精加工余量预留方法,其特征在于,Step5中,所述叶尖精加工切削余量值取值与所述截面刚度待定衡量指标εj值呈反比,所述叶根精加工切削余量值取值与所述截面刚度待定衡量指标εj值呈正比。5. The thin-walled blade side milling finishing allowance reservation method according to claim 1, characterized in that, in Step5, the value of the blade tip finishing cutting allowance value and the undetermined measurement index ε of the section stiffness The value of j is inversely proportional, and the value of the blade root finishing cutting allowance is directly proportional to the value of the undetermined measure index εj of the section stiffness.
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