CN102581364B

CN102581364B - Method for calculating milling load of ball-end milling cutter

Info

Publication number: CN102581364B
Application number: CN201210055859.3A
Authority: CN
Inventors: 丁汉; 黄涛; 张小明; 张小俭
Original assignee: Huazhong University of Science and Technology
Current assignee: HUST Wuxi Research Institute
Priority date: 2012-03-05
Filing date: 2012-03-05
Publication date: 2014-08-27
Anticipated expiration: 2032-03-05
Also published as: CN102581364A

Abstract

The invention discloses a method for calculating the milling load of a ball end milling cutter. The entry angle, cut-out angle and instantaneous cutting thickness of each side-tilt milling micro-element involved in cutting, calculate the entry angle, cut-off angle and instantaneous cutting thickness of each forward-leaning milling micro-element involved in cutting, and calculate each side-tilt milling micro-element The instantaneous cutting thickness of the micro-element and the instantaneous cutting thickness of each forward-leaning milling micro-element participating in cutting are superimposed to obtain the instantaneous cutting thickness of the tool micro-element, and the instantaneous cutting thickness of all the cutting tool micro-elements participating in the cutting is summed, To obtain the instantaneous milling load of the ball nose milling cutter. The invention can obtain the instantaneous cutting state and cutting thickness of the cutting edge of the tool and the workpiece when the tool is tilted and tilted forward, so as to realize the prediction of the cutting force in the five-axis milling process.

Description

The method of calculating the milling load of ball end milling cutter

技术领域 technical field

本发明涉及计算机数控加工技术领域，具体涉及一种五轴数控加工中计算球头铣刀铣削负载的方法。The invention relates to the technical field of computer numerical control machining, in particular to a method for calculating the milling load of a ball end milling cutter in five-axis numerical control machining.

背景技术 Background technique

球头铣刀五轴铣削是航空发动机叶轮、叶片类空间曲面和模具类复杂曲面精加工的主要技术手段。由于零件的复杂性，通常需要改变刀具的轴线方向从而避免干涉。为预测五轴铣削过程的切削力，减小加工过程中的变形和振动，首先需要计算铣刀切削工件的瞬时切削厚度。Five-axis milling with ball end milling cutter is the main technical method for the finishing of aero-engine impellers, blade-like space surfaces and mold-like complex surfaces. Due to the complexity of the part, it is often necessary to change the axis direction of the tool to avoid interference. In order to predict the cutting force of the five-axis milling process and reduce the deformation and vibration during the machining process, it is first necessary to calculate the instantaneous cutting thickness of the workpiece cut by the milling cutter.

球头铣刀铣削力建模一般将刀具沿轴线方向分割为若干圆盘状的刀具微元，通过计算微元的切削状态和微元切削力，再将微元的切削力进行叠加而求出整体的铣削力。然而现有的模型一般都是在刀具与工件的相对位置比较特殊(只有侧倾或只有前倾)的情况下进行铣削力预测，并采用矢量计算方法获得切削负载。然而，这种方法无法反映微元在一个周期内切入工件和切出工件的真实过程，也无法计算球头铣刀既侧倾又前倾的铣削负载。The milling force modeling of ball end milling cutter generally divides the tool into several disc-shaped tool elements along the axis direction, and calculates the cutting state and cutting force of the elements, and then superimposes the cutting force of the elements to obtain overall milling force. However, the existing models generally predict the milling force when the relative position of the tool and the workpiece is special (only side tilt or only forward tilt), and the cutting load is obtained by vector calculation method. However, this method cannot reflect the real process of the micro-unit cutting into and out of the workpiece in one cycle, nor can it calculate the milling load of the ball nose milling cutter when it is tilted both sideways and forward.

发明内容Contents of the invention

本发明的目的在于针对现有铣削力建模中存在的缺陷，提供一种计算球头铣刀铣削负载的方法，其能在刀具侧倾和前倾铣削时获得刀具的切削刃与工件的瞬时切削状态以及切削厚度，从而实现五轴铣削加工中切削力的预测。The purpose of the present invention is to provide a method for calculating the milling load of a ball nose milling cutter in view of the defects existing in the existing milling force modeling, which can obtain the instantaneous relationship between the cutting edge of the tool and the workpiece when the tool is tilted and tilted forward. Cutting state and cutting thickness, so as to realize the prediction of cutting force in five-axis milling.

本发明是通过以下技术方案实现的：The present invention is achieved through the following technical solutions:

一种计算球头铣刀铣削负载的方法，包括如下步骤：A method for calculating the milling load of a ball end milling cutter, comprising the steps of:

(1)获得刀具与工件的相对位置参数模型；(1) Obtain the relative position parameter model of the tool and the workpiece;

(2)根据刀具与工件的相对位置参数模型确定参与切削的全部刀具微元，刀具微元包括侧倾铣削微元与前倾铣削微元；(2) According to the relative position parameter model of the tool and the workpiece, all the tool elements involved in the cutting are determined, and the tool elements include the side-tilt milling elements and the forward-inclining milling elements;

(3)根据刀具与工件的相对位置参数模型计算每个参与切削的侧倾铣削微元的切入角、切出角以及瞬时切削厚度；(3) According to the relative position parameter model of the tool and the workpiece, calculate the cut-in angle, cut-out angle and instantaneous cutting thickness of each side tilting milling element involved in cutting;

(4)根据刀具与工件的相对位置参数模型计算每个参与切削的前倾铣削微元的切入角、切出角以及瞬时切削厚度；(4) Calculate the entry angle, exit angle and instantaneous cutting thickness of each forward-inclined milling element participating in cutting according to the relative position parameter model of the tool and the workpiece;

(5)将每个侧倾铣削微元的瞬时切削厚度和每个参与切削的前倾铣削微元的瞬时切削厚度进行叠加，以获得刀具微元的瞬时切削厚度；(5) Superimpose the instantaneous cutting thickness of each side-tilt milling element and the instantaneous cutting thickness of each forward-leaning milling element participating in cutting, so as to obtain the instantaneous cutting thickness of the tool element;

(6)将参与切削的所有刀具微元的瞬时切削厚度进行求和，以获取球头铣刀的瞬时铣削负载。(6) Sum the instantaneous cutting thickness of all the cutter elements involved in cutting to obtain the instantaneous milling load of the ball end milling cutter.

本发明具有以下的优点和技术效果：通过将球头铣刀切削过程进行分解，揭示刀具不同轴向位置的刀具微元切入与切出工件的过程，以及微元瞬时切削的厚度，获得瞬时参与切削的切削点，从而计算刀具倾斜情况下的切削厚度，以预测五轴加工瞬时切削力。The present invention has the following advantages and technical effects: by decomposing the cutting process of the ball end milling cutter, revealing the process of cutting in and out of the workpiece by the micro-element of the tool at different axial positions of the tool, as well as the thickness of the instantaneous cutting of the micro-element, and obtaining instantaneous participation The cutting point of cutting, so as to calculate the cutting thickness under the condition of tool tilt, so as to predict the instantaneous cutting force of five-axis machining.

附图说明 Description of drawings

图1为本发明计算球头铣刀铣削负载的方法的流程图Fig. 1 is the flow chart of the method for calculating ball end milling cutter milling load of the present invention

图2为刀具与工件的相对空间位置示意图。Figure 2 is a schematic diagram of the relative spatial positions of the tool and the workpiece.

图3(a)至图3(c)为刀具球面参与切削的部分与进给方向的关系。Figure 3(a) to Figure 3(c) show the relationship between the cutting part of the tool spherical surface and the feeding direction.

图4为刀具微元进给方向的分解示意图。Fig. 4 is an exploded schematic view of the feed direction of the micro-elements of the cutter.

图5为侧倾铣削示意图。Figure 5 is a schematic diagram of side tilt milling.

图6(a)为前倾铣削示意图。Figure 6(a) is a schematic diagram of forward milling.

图6(b)至图6(e)为前倾铣削微元的不同铣削状态示意图。Fig. 6(b) to Fig. 6(e) are schematic diagrams of different milling states of the forward-tilted milling cells.

图7(a)和(b)示出采用本发明方法计算得到的铣削负载结果。Figure 7(a) and (b) show the milling load results calculated by the method of the present invention.

具体实施方式 Detailed ways

以下结合附图和实施例对本发明的接受方案作进一步的详细描述，但本实施例并不用于限制本发明。The acceptance scheme of the present invention will be described in further detail below in conjunction with the drawings and examples, but the examples are not intended to limit the present invention.

本发明采用的球头铣刀的参数如下：直径10毫米，刃数为4，螺旋角30度，被加工表面为平面，切削方式采用铣槽方式，切削深度为1毫米，每齿进给为0.1毫米。The parameters of the ball end milling cutter adopted in the present invention are as follows: 10 millimeters in diameter, 4 blades, 30 degrees of helix angle, the machined surface is a plane, the cutting method adopts the groove milling method, the cutting depth is 1 millimeter, and the feed of each tooth is 0.1mm.

如图1所示，本发明计算球头铣刀铣削负载的方法包括以下步骤：As shown in Figure 1, the method for calculating the milling load of the ball end milling cutter of the present invention comprises the following steps:

1、获得刀具与工件的相对位置参数模型；1. Obtain the relative position parameter model of the tool and the workpiece;

如图2所示，T为刀具轴线方向，切削进给方向与X轴方向相同，刀具的倾斜方向和角度见右图，O为刀具的球心点，OA表示刀具轴线，α表示刀具轴线与加工表面法向所成的角度，φ表示刀具微元的转角，即刀具轴线在加工表面投影与进给方向X的夹角，A′表示A点在加工表面的投影(如图3(a)至(c)所示)，当φ＝0时，为前倾铣削；当φ＝π/2时，为侧倾铣削。As shown in Figure 2, T is the direction of the tool axis, the cutting feed direction is the same as the X axis direction, the inclination direction and angle of the tool are shown in the figure on the right, O is the spherical center point of the tool, OA indicates the tool axis, and α indicates the relationship between the tool axis and The angle formed by the normal direction of the processing surface, φ represents the rotation angle of the tool element, that is, the angle between the projection of the tool axis on the processing surface and the feed direction X, and A′ represents the projection of point A on the processing surface (as shown in Figure 3(a) As shown in (c), when φ=0, it is forward milling; when φ=π/2, it is side milling.

2、根据刀具与工件的相对位置参数模型确定参与切削的全部刀具微元，刀具微元包括侧倾铣削微元和前倾铣削微元，并且刀具微元的进给运动可分解为侧倾铣削微元进给运动与前倾铣削微元进给运动；2. According to the relative position parameter model of the tool and the workpiece, all the tool elements involved in cutting are determined. The tool elements include the side tilt milling elements and the forward tilt milling elements, and the feed motion of the tool elements can be decomposed into side tilt milling Micro-element feed motion and forward-tilt milling micro-element feed motion;

刀具微元的进给运动如图4所示，刀具微元的进给可以分为侧倾铣削进给f_c和前倾铣削进给f_q，并由下式(1)计算：The feed motion of the cutter microelement is shown in Fig. 4. The feed of the cutter microelement can be divided into side tilt milling feed f _c and forward tilt milling feed f _q , which are calculated by the following formula (1):

$\{\begin{matrix} {f f}_{c c} = = f f sin sin φ φ \\ {f f}_{q q} = = f f cos cos φ φ \end{matrix} - - - - - - ((11))$

式中f为球头铣刀的进给。In the formula, f is the feed of the ball end milling cutter.

如图5所示，θ表示刀具微元的位置角，设参与切削的区域最小位置角为θ_s，最大的为θ_e，则As shown in Fig. 5, θ represents the position angle of the micro-element of the tool. Suppose the minimum position angle of the area involved in cutting is θ _s , and the maximum is θ _e , then

$\{\begin{matrix} {θ θ}_{s the s} = = α α - - arccos arccos \frac{| | OH Oh | |}{R R} \\ {θ θ}_{e e} = = α α + + arccos arccos \frac{| | OH Oh | |}{R R} \end{matrix} - - - - - - ((22))$

当θ_s＜θ＜θ_e时，则微元参与切削。其中R为球头铣刀的半径，|OH|表示球心O到垂足H的线段长度。When θ _s <θ<θ _e , the micro-element participates in cutting. Where R is the radius of the ball end milling cutter, |OH| represents the length of the line segment from the center of the sphere O to the vertical foot H.

3、根据刀具与工件的相对位置参数模型计算每个参与切削的侧倾铣削微元的切入角、切出角以及瞬时切削厚度；3. Calculate the entry angle, exit angle and instantaneous cutting thickness of each side tilt milling element involved in cutting according to the relative position parameter model of the tool and the workpiece;

侧倾铣削截面如图5所示，进给方向垂直于纸面向外。对于参与切削的不同微元，其切入切出角是不相同的。位置角为θ处的刀具微元，其切削半径为|AD|，切出角Φ_ex，切入角Φ_st表达式为：The side-tilt milling section is shown in Fig. 5, and the feed direction is perpendicular to the paper surface outward. For different micro-elements involved in cutting, the cutting-in and cutting-out angles are different. The cutter microelement at the position angle θ, its cutting radius is |AD|, the cut-out angle Φ _ex , and the cut-in angle Φ _st are expressed as:

$\{\begin{matrix} {Φ Φ}_{st st} = = arccos arccos ((- - \frac{| | AC AC | |}{| | AD AD | |})) \\ {Φ Φ}_{ex ex} = = 22 π π - - {Φ Φ}_{st st} \end{matrix} - - - - - - ((33))$

式中，|AC|和|AD|的值可通过相似ΔBAC和ΔBHO：where the values of |AC| and |AD| can be obtained by similarity ΔBAC and ΔBHO:

$\{\begin{matrix} | | AC AC | | = = | | OH Oh | | \cdot \cdot \frac{| | AB AB | |}{| | HB HB | |} = = | | OH Oh | | \cdot \cdot \frac{| | OB OB | | - - | | OA OA | |}{| | OH Oh \cdot &Center Dot; tan the tan α α | |} = = \frac{| | OH Oh \cdot &Center Dot; sec sec α α | | - - | | R R \cdot \cdot cos cos θ θ | |}{tan the tan α α} \\ | | AD AD | | = = R R \cdot &Center Dot; sin sin θ θ \end{matrix} - - - - - - ((44))$

在侧倾铣削中，由于刀具轴线垂直于进给方向，当刀具微元的转角满足时，其切削厚度表达式为：In side tilt milling, since the tool axis is perpendicular to the feed direction, when the rotation angle of the tool element satisfy When , the cutting thickness expression is:

由于在变化中可取正值和负值，所以h_c可能为负值，此时表示该刀刃远离工件切削表面。because exist Positive and negative values can be taken in the change, so h _c may be a negative value, which means that the cutting edge is far away from the cutting surface of the workpiece.

4、根据刀具与工件的相对位置参数模型计算每个参与切削的前倾铣削微元的切入角、切出角以及瞬时切削厚度；4. Calculate the entry angle, exit angle and instantaneous cutting thickness of each forward-leaning milling element involved in cutting according to the relative position parameter model of the tool and the workpiece;

如图6(a)，在前倾铣削中，设当前参与切削的刀具微元的位置角为θ，而前一次切削该处的刀具微元位置角为θ′，垂直于刀轴方向的每齿进给量f_θ可表示为：As shown in Fig. 6(a), in forward-tilt milling, suppose the position angle of the tool micro-element participating in the current cutting is θ, and the position angle of the tool micro-element in the previous cutting is θ′. The tooth feed f _θ can be expressed as:

±f_θ＝Rsinθ+f_qcosα-Rsinθ′(6)±f _θ = Rsinθ+f _q cosα-Rsinθ′(6)

Rcosθ＝Rcosθ′+f_qsinα (7)Rcosθ＝Rcosθ′+f _q sinα (7)

即f_θ与θ满足等式：That is, f _θ and θ satisfy the equation:

${((R R sin sin θ θ + + {f f}_{q q} cos cos α α \overset{&OverBar; &OverBar;}{+ +} {f f}_{θ θ}))}^{22} + + {((R R cos cos θ θ - - {f f}_{q q} sin sin α α))}^{22} = = {R R}^{22} - - - - - - ((88))$

式中f_q为前倾铣削的每齿进给量，式(6)中，在深色区域取正号，在浅色区域取负号，在式(8)中，与此相反。In the formula, f _q is the feed per tooth of the forward milling. In the formula (6), the positive sign is taken in the dark area, and the negative sign is taken in the light area. In the formula (8), it is the opposite.

在前倾的铣削方式中，微元的瞬时未变形切削厚度如图6。图6(a)中虚线轮廓为一齿进给之前刀具的位置，实线为当前切削刀具的轮廓位置。前倾铣削时，刀具微元存在四个典型位置，如图6(a)中1、2、3、4所示的四个位置，图6(b)、(c)、(d)、(e)是A向的平面图。位置1，当前刀具的相应微元切削前，该处工件未被前一位置刀具切过，因此相应微元的切削状态如图6(b)所示，剖面线表示为为正切削；位置2，如图6(c)，虚线表示被前一位置刀具所切，当前刀具的相应微元切削之前，该处工件已被前一位置刀具切过，但当前微元仍能切到工件表面，剖面线表示为正切削；位置3，相应微元的切削状态如图6(d)所示，当前相应微元切削之前，该处工件已被前一位置刀具切过，但当前微元不能切到工件表面，剖面线为正切削区域，刀齿切入和切出时刻为负切削区域；位置4时，如图6(e)，当前刀具微元不能切到工件，刀齿处在负切削区域。In the forward milling mode, the instantaneous undeformed cutting thickness of micro-elements is shown in Figure 6. The dotted outline in Fig. 6(a) is the position of the tool before one tooth feed, and the solid line is the outline position of the current cutting tool. In forward milling, there are four typical positions of the micro-units of the tool, such as the four positions shown in 1, 2, 3, and 4 in Fig. 6(a), and Fig. 6(b), (c), (d), ( e) is the plan view of direction A. Position 1, before the corresponding element of the current tool is cut, the workpiece at this position has not been cut by the tool at the previous position, so the cutting state of the corresponding element is shown in Figure 6(b), and the section line indicates positive cutting; position 2 , as shown in Figure 6(c), the dotted line indicates that it was cut by the tool at the previous position. The section line represents positive cutting; at position 3, the cutting state of the corresponding micro-element is shown in Figure 6(d). to the workpiece surface, the section line is the positive cutting area, and the cutting-in and cutting-out time of the cutter teeth is the negative cutting area; at position 4, as shown in Figure 6(e), the current tool element cannot cut the workpiece, and the cutter teeth are in the negative cutting area .

如图6(b)所示，在位置1处，刀具微元的位置角θ满足下式：As shown in Figure 6(b), at position 1, the position angle θ of the tool element satisfies the following formula:

$arccos arccos \frac{R R cos cos {θ θ}_{e e} + + {f f}_{q q} sin sin α α}{R R} \leq \leq θ θ < < {θ θ}_{e e}$

式中，θ_e由式(2)给出。where _θe is given by equation (2).

设点O2到水平线的距离为d_θ，等同于式(4)中的|AC|：Set the distance from point O2 to the horizontal line as d _θ , which is equivalent to |AC| in formula (4):

${d d}_{θ θ} = = \frac{| | OH Oh | | \cdot &Center Dot; sec sec α α - - R R cos cos θ θ}{tan the tan α α}$

切入切出角可表示为：The lead-in and lead-out angles can be expressed as:

$\{\begin{matrix} {Φ Φ}_{st st} = = π π - - arccos arccos \frac{{d d}_{θ θ}}{R R sin sin θ θ} \\ {Φ Φ}_{ex ex} = = π π + + arccos arccos \frac{{d d}_{θ θ}}{R R sin sin θ θ} \end{matrix}$

当刀具微元转角满足时，其切削厚度表达式为：When the tool micro-element angle satisfy When , the cutting thickness expression is:

因为小于零，所以上式用正号。because is less than zero, so the above formula uses a positive sign.

同理可求出位置2、位置3和位置4刀具的切入切出角和瞬时切削厚度。In the same way, the entry and exit angles and instantaneous cutting thickness of the tools at position 2, position 3 and position 4 can be obtained.

5、将每个侧倾铣削微元的瞬时切削厚度和每个参与切削的前倾铣削微元的瞬时切削厚度进行叠加，以获得刀具微元的瞬时切削厚度；5. Superimpose the instantaneous cutting thickness of each side-tilt milling element and the instantaneous cutting thickness of each forward-leaning milling element involved in cutting, so as to obtain the instantaneous cutting thickness of the tool element;

令α＝45°，φ＝45°，计算结果如图7(a)，图中的曲线为刀具旋转一周一个刀刃的不同位置切削工件的状态，小于等于零表示没有切削工件，大于零表示切削工件的瞬时切削厚度。图中可见，微元的切削最大厚度发生在切入工件的瞬时，之后切削厚度随时间逐渐减小，直到切出工件。令α＝45°，φ＝10°，计算结果如图7(b)，微元的切削最大厚度发生在切入工件后的某一时刻，同时可计算任意时刻刀刃上任意点的切削厚度。Let α=45°, φ=45°, the calculation result is shown in Figure 7(a), the curve in the figure is the state of cutting the workpiece at different positions of one blade in one rotation of the tool, less than or equal to zero means no cutting workpiece, and greater than zero means cutting workpiece The instantaneous cutting thickness. It can be seen from the figure that the maximum cutting thickness of the micro-element occurs at the moment of cutting into the workpiece, and then the cutting thickness gradually decreases with time until the workpiece is cut out. Let α = 45°, φ = 10°, the calculation result is shown in Figure 7(b), the maximum cutting thickness of the micro-element occurs at a certain moment after cutting into the workpiece, and the cutting thickness at any point on the cutting edge at any time can be calculated at the same time.

6、将参与切削的所有刀具微元的瞬时切削厚度进行求和，以获取球头铣刀的瞬时铣削负载。6. Sum the instantaneous cutting thickness of all the cutter elements involved in cutting to obtain the instantaneous milling load of the ball end milling cutter.

Claims

1. a method of calculating rose cutter five axle milling loads, is characterized in that, comprises the steps:

(1) obtain the relative position parameter model of cutter and workpiece, in this step, the cutter centre of sphere point of rose cutter is defined as to O, tool axis is defined as OA, the projection of tool axis OA on finished surface is defined as OA ', between tool axis and finished surface normal direction, angulation is expressed as α, and the described projection OA ' of tool axis on finished surface and the angle between direction of feed are expressed as φ, build in this way the relative position parameter model between cutter and workpiece;

(2) according to the above-mentioned relative position parameter model of cutter and workpiece, determine the whole cutter infinitesimals that participate in cutting, described cutter infinitesimal comprises inclination milling infinitesimal simultaneously and leans forward milling infinitesimal, thus the feed motion of all cutter infinitesimals is decomposed into separately to the inclination milling infinitesimal feed motion and the milling infinitesimal feed motion of leaning forward that by following formula (), are represented:

(1)

Wherein, f _crepresent to roll the feed motion amount of milling infinitesimal, f _qrepresent the to lean forward feed motion amount of milling infinitesimal, the corner that represents each cutter infinitesimal, is also formed angle respectively between the projection of its corresponding tool axis on finished surface and direction of feed, and f represents the total feed of rose cutter;

(3) according to the above-mentioned relative position parameter model of cutter and workpiece calculate described each participate in cutting inclination milling infinitesimal entrance angle and cut out angle, based on following formula (two), calculate the momentary cutting thick h that each rolls milling infinitesimal simultaneously _c:

(2)

Wherein, f _crepresent that each rolls the feed motion amount of milling infinitesimal, its numerical value calculates in step (2);

(4) according to the relative position parameter model of described cutter and workpiece calculate described each participate in cutting the milling infinitesimal that leans forward entrance angle and cut out angle, based on following formula (three) and (four), calculate the momentary cutting thick h of each milling infinitesimal that leans forward simultaneously _q:

(3)

d_{θ} = \frac{| OH | \cdot \sec α - R \cos θ}{\tan α}

(4)

Wherein, R represents the radius of rose cutter, and θ represents the position angle of each cutter infinitesimal, | OH| represents that the cutter centre of sphere of milling cutter is to the line segment length between its intersection point;

(5) momentary cutting thick of the milling infinitesimal that leans forward of the momentary cutting thick of described each inclination milling infinitesimal and described each participation cutting is superposeed, to obtain the momentary cutting thick of described cutter infinitesimal;

(6) momentary cutting thick that participates in all cutter infinitesimals of cutting is sued for peace, to obtain the Instantaneous Milling load of rose cutter.