CN102681488A - Modeling method for milling surface appearance of workpiece - Google Patents

Modeling method for milling surface appearance of workpiece Download PDF

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CN102681488A
CN102681488A CN2012101623585A CN201210162358A CN102681488A CN 102681488 A CN102681488 A CN 102681488A CN 2012101623585 A CN2012101623585 A CN 2012101623585A CN 201210162358 A CN201210162358 A CN 201210162358A CN 102681488 A CN102681488 A CN 102681488A
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point
tool
angle
workpiece
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CN102681488B (en
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张臣
郭松
周来水
张海艳
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Nanjing University of Aeronautics and Astronautics
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Abstract

本发明公开了一种铣削加工工件表面形貌的建模方法，数控铣削加工领域。步骤为：根据铣削加工刀具切削运动轨迹将球头铣刀切削刃进行离散处理，建立球头铣削刀具切削刃微元切削轨迹方程，切削轨迹方程表面形貌由上述建立的轨迹方程中最外侧的轨迹形成，通过判断这些最外侧轨迹对应切削微元的位置角范围，确定铣削这些最外侧轨迹对应的刀具转角范围，结合由刀具主轴转速获得的旋转角速度计算铣削这些轨迹对应的加工时间，考虑切削微元所在位置处的螺旋滞后角，获得这些最外侧的铣削轨迹，从而得到铣削工件表面形貌。本发明可解决铣削加工过程中工件表面形貌的生成问题。

Figure 201210162358

The invention discloses a modeling method for the surface topography of a milling workpiece and belongs to the field of numerical control milling. The steps are: according to the cutting motion trajectory of the milling tool, the cutting edge of the ball end milling cutter is discretized, and the microelement cutting trajectory equation of the cutting edge of the ball end milling tool is established. The surface shape of the cutting trajectory equation is determined by the outermost Trajectory formation, by judging the position angle range of these outermost trajectories corresponding to the cutting micro-units, determine the tool rotation angle range corresponding to these outermost trajectories for milling, and calculate the processing time corresponding to milling these trajectories by combining the rotation angular velocity obtained by the tool spindle speed. The helical lag angle at the position of the micro-elements is used to obtain these outermost milling trajectories, thereby obtaining the surface topography of the milled workpiece. The invention can solve the problem of generating the surface topography of the workpiece during the milling process.

Figure 201210162358

Description

一种铣削加工工件表面形貌的建模方法A Modeling Method of Milling Workpiece Surface Topography

  the

技术领域 technical field

本发明属于数控铣削加工领域，特别涉及数控铣削加工中刀具磨损引起的工件表面形貌建模领域。 The invention belongs to the field of numerical control milling, in particular to the field of modeling the surface topography of workpieces caused by tool wear in numerical control milling.

背景技术 Background technique

随着现代机械制造业的发展，对零件加工精度的要求越来越高。而在实际的铣削加工过程中，由于受各种因素的影响不可避免地会产生加工误差。加工误差是影响工件加工质量非常重要的因素，会使工件加工精度明显降低，过大的加工误差甚至会造成零件报废，严重影响加工效率和效益。工件表面的微观形貌和工件表面粗糙度有密切的联系，对工件的耐磨性与装配精度有重要影响，同时也是反映工件表面加工质量的重要指标，通过预测工件表面的形貌，可以得到工件上任意位置点的坐标值，将其与该点的理论坐标值进行对比，即可得到该点处的加工误差值。 With the development of modern machinery manufacturing industry, the requirements for machining precision of parts are getting higher and higher. In the actual milling process, due to the influence of various factors, machining errors will inevitably occur. Machining error is a very important factor affecting the machining quality of workpieces, which will significantly reduce the machining accuracy of workpieces. Excessive machining errors will even cause parts to be scrapped, seriously affecting processing efficiency and benefits. The microscopic topography of the workpiece surface is closely related to the surface roughness of the workpiece, which has an important impact on the wear resistance and assembly accuracy of the workpiece. It is also an important index reflecting the processing quality of the workpiece surface. By predicting the surface morphology of the workpiece, we can Comparing the coordinate value of any point on the workpiece with the theoretical coordinate value of the point, the machining error value at the point can be obtained.

为了提高工件表面的加工质量，减小加工误差，降低粗糙度，国内外许多学者从微观角度对工件表面形貌进行了研究，取得了一些成果。先后提出了一些建立工件表面形貌模型的建模方法。 In order to improve the processing quality of the workpiece surface, reduce the processing error, and reduce the roughness, many scholars at home and abroad have studied the surface morphology of the workpiece from the microscopic point of view, and achieved some results. Several modeling methods for establishing workpiece surface topography models have been proposed successively.

现有的工件表面形貌的建模方法多是就切削参数选择、刀具定位误差、切削力引起的刀具变形等因素对工件表面形貌的影响进行的研究，目前还很少有针对球头铣刀铣削过程中的刀具动态磨损对工件表面形貌的影响进行相关的研究。 Most of the existing modeling methods of workpiece surface morphology are researches on the influence of factors such as cutting parameter selection, tool positioning error, and tool deformation caused by cutting force on the workpiece surface morphology. At present, there are few methods for ball-end milling The impact of tool dynamic wear on workpiece surface morphology during tool milling is studied.

为此，本发明克服了上述工件表面形貌的建模方法存在的不足，根据球头铣刀切削刃的特点，建立切削轨迹方程，并进一步将刀具磨损对切削轨迹的影响考虑在内，对刀具磨损后的工件表面形貌进行研究。分析了刀具磨损后球头切削刃外轮廓刃线的形状变化，据此可以进一步分析磨损后的切削刃相对工件的切削轨迹，建立考虑磨损的切削轨迹方程，进而得到加工后的工件表面形貌。 For this reason, the present invention overcomes the deficiencies in the modeling method of the above-mentioned workpiece surface topography. According to the characteristics of the cutting edge of the ball end milling cutter, the cutting trajectory equation is established, and the impact of tool wear on the cutting trajectory is further taken into consideration. The surface morphology of the workpiece after tool wear was studied. The shape change of the outer contour edge line of the ball-end cutting edge after tool wear is analyzed. Based on this, the cutting trajectory of the worn cutting edge relative to the workpiece can be further analyzed, and the cutting trajectory equation considering wear can be established, and then the surface morphology of the processed workpiece can be obtained. .

发明内容 Contents of the invention

本发明的目的，在于提供一种铣削加工工件表面形貌的建模方法，其可解决铣削加工过程中刀具磨损引起的工件表面形貌的建模和可视化仿真问题。 The object of the present invention is to provide a method for modeling the surface topography of a milling workpiece, which can solve the problems of modeling and visual simulation of the surface topography of the workpiece caused by tool wear during the milling process.

为了达成上述目的，本发明的解决方案是： In order to achieve the above object, the solution of the present invention is:

一种铣削加工工件表面形貌的建模方法，其特征在于包括如下步骤： A method for modeling the surface topography of a milling workpiece, characterized in that it comprises the following steps:

（1）根据铣削加工刀具切削运动轨迹将球头部分切削刃离散为一系列切削微元，由于不同切削微元在切削时线速度不同，且在加工过程中同时存在直线进给运动与自身绕刀具主轴的旋转运动，因此，除球头刀尖外球头切削刃上其它点的运动轨迹将形成一系列的次摆线，为了分析刀具切削轨迹在工件上形成的形貌，以离散后的切削微元P点作为研究对象，通过分析点P在走刀过程中的运动，得到加工结束后点P在工件上最终留下的切削轨迹，去除在加工中被切除掉的轨迹线即得到最终构成工件形貌的轨迹；考虑直线运动轨迹和旋转轨迹，当刀具未发生磨损时，P点的理论切削轨迹方程如式（1）所示： (1) According to the cutting motion trajectory of the milling tool, the cutting edge of the ball head is discretized into a series of cutting elements. Since different cutting elements have different linear speeds during cutting, and there are linear feed motion and self-circling The rotational movement of the tool spindle, therefore, the trajectory of other points on the cutting edge of the ball except for the tip of the ball will form a series of trochoids. In order to analyze the shape of the tool cutting trajectory on the workpiece, the discretized Cutting microelement point P is taken as the research object. By analyzing the movement of point P during the cutting process, the final cutting track left by point P on the workpiece after machining is obtained. The trajectory that constitutes the shape of the workpiece; considering the linear motion trajectory and the rotation trajectory, when the tool is not worn, the theoretical cutting trajectory equation of point P is shown in formula (1):

Figure 177055DEST_PATH_IMAGE002
              (1)
Figure 177055DEST_PATH_IMAGE002
(1)

其中，

Figure 2012101623585100002DEST_PATH_IMAGE004
、
Figure 2012101623585100002DEST_PATH_IMAGE006
为P点经过切削加工时间后的坐标，
Figure 2012101623585100002DEST_PATH_IMAGE008
、
Figure DEST_PATH_IMAGE010
为P点起始坐标，
Figure DEST_PATH_IMAGE012
为单位时间的刀具进给速度，
Figure 2012101623585100002DEST_PATH_IMAGE014
为切削加工时间，为P点所处位置的螺旋滞后角对该点加工时间的影响，，
Figure 2012101623585100002DEST_PATH_IMAGE020
, 为P点对应的刀具螺旋滞后角，
Figure 2012101623585100002DEST_PATH_IMAGE024
为P点所处的位置角处的刀具径向半径，
Figure DEST_PATH_IMAGE028
，
Figure DEST_PATH_IMAGE030
为未磨损时的球头铣刀半径，
Figure DEST_PATH_IMAGE032
为刀具主轴旋转角速度，为P点与球头中心O的连线与刀具主轴Z的夹角，即为描述切削微元所在位置的角度称为位置角； in,
Figure 2012101623585100002DEST_PATH_IMAGE004
,
Figure 2012101623585100002DEST_PATH_IMAGE006
is the coordinate of point P after the cutting time,
Figure 2012101623585100002DEST_PATH_IMAGE008
,
Figure DEST_PATH_IMAGE010
is the starting coordinate of point P,
Figure DEST_PATH_IMAGE012
is the tool feed rate per unit time,
Figure 2012101623585100002DEST_PATH_IMAGE014
is the cutting time, is the influence of the helical lag angle at the position of point P on the processing time of the point, ,
Figure 2012101623585100002DEST_PATH_IMAGE020
, is the tool helix lag angle corresponding to point P,
Figure 2012101623585100002DEST_PATH_IMAGE024
is the position angle of point P The radial radius of the tool at ,
Figure DEST_PATH_IMAGE028
,
Figure DEST_PATH_IMAGE030
is the radius of the ball end mill without wear,
Figure DEST_PATH_IMAGE032
is the rotational angular velocity of the tool spindle, is the angle between the line connecting point P and the center O of the ball head and the tool spindle Z, which is the angle describing the position of the cutting element, called the position angle;

当把刀具磨损的影响考虑在内时，随着刀具不断磨损，切削刃上同一高度上的点所对应的径向半径

Figure 201960DEST_PATH_IMAGE024
及其所对应的位置角
Figure 155134DEST_PATH_IMAGE026
都将发生变化，因此，当考虑加工过程中的刀具磨损量时，P点的切削轨迹可由式(2)表示： When the effect of tool wear is taken into account, as the tool wears, the radial radius corresponding to a point at the same height on the cutting edge
Figure 201960DEST_PATH_IMAGE024
and its corresponding position angle
Figure 155134DEST_PATH_IMAGE026
will change, therefore, when considering the amount of tool wear during machining, the cutting trajectory of point P can be expressed by formula (2):

   (2) (2)

其中，

Figure DEST_PATH_IMAGE036
、
Figure DEST_PATH_IMAGE038
为考虑刀具磨损P点经过切削加工时间后的坐标，
Figure 439485DEST_PATH_IMAGE008
、为P点起始坐标，
Figure 739065DEST_PATH_IMAGE012
为单位时间的刀具进给速度，
Figure 920648DEST_PATH_IMAGE014
为切削加工时间，
Figure 375900DEST_PATH_IMAGE016
为P点所处位置的螺旋滞后角对该点加工时间的影响，且
Figure 901822DEST_PATH_IMAGE018
，为P点对应的刀具螺旋滞后角，
Figure 504021DEST_PATH_IMAGE032
为刀具主轴旋转角速度； in,
Figure DEST_PATH_IMAGE036
,
Figure DEST_PATH_IMAGE038
In order to consider the coordinates of the tool wear point P after the cutting time,
Figure 439485DEST_PATH_IMAGE008
, is the starting coordinate of point P,
Figure 739065DEST_PATH_IMAGE012
is the tool feed rate per unit time,
Figure 920648DEST_PATH_IMAGE014
is the cutting time,
Figure 375900DEST_PATH_IMAGE016
is the influence of the helical lag angle at the position of point P on the processing time of the point, and
Figure 901822DEST_PATH_IMAGE018
, is the tool helix lag angle corresponding to point P,
Figure 504021DEST_PATH_IMAGE032
is the rotational angular velocity of the tool spindle;

Figure DEST_PATH_IMAGE040
为刀具磨损后P点高度处的球头径向半径，由式（3）求解；
Figure DEST_PATH_IMAGE040
is the radial radius of the ball head at the height of point P after tool wear, which is solved by formula (3);

Figure DEST_PATH_IMAGE042
                  (4)
Figure DEST_PATH_IMAGE042
(4)

式中，

Figure DEST_PATH_IMAGE044
为球头铣刀未磨损时的半径，
Figure DEST_PATH_IMAGE046
为切削微元所在的截平面高度，
Figure DEST_PATH_IMAGE048
为
Figure 254809DEST_PATH_IMAGE046
高度处刀具切削刃的后刀面磨损量； In the formula,
Figure DEST_PATH_IMAGE044
is the radius of the ball end milling cutter when it is not worn,
Figure DEST_PATH_IMAGE046
is the height of the sectional plane where the cutting element is located,
Figure DEST_PATH_IMAGE048
for
Figure 254809DEST_PATH_IMAGE046
Flank wear of the cutting edge of the tool at the height;

（2）根据铣削轨迹方程获得的铣削轨迹并不是全部构成工件表面形貌，部分轨迹线在加工中会被切除，只有最外侧的轨迹线形成工件表面形貌，为了确定最外侧的轨迹线，需要求解最外侧轨迹线对应的刀具切削刃的位置

Figure 2447DEST_PATH_IMAGE026
角取值范围[
Figure DEST_PATH_IMAGE050
，
Figure DEST_PATH_IMAGE052
]，求出[
Figure 372248DEST_PATH_IMAGE050
,
Figure 528423DEST_PATH_IMAGE052
]区间内各个角对应的刀具切削轨迹线，这些切削轨迹线的集合就构成了加工后的工件表面形貌； (2) The milling trajectory obtained according to the milling trajectory equation does not all constitute the surface topography of the workpiece. Part of the trajectory line will be cut off during processing, and only the outermost trajectory line forms the surface topography of the workpiece. In order to determine the outermost trajectory line, It is necessary to solve the position of the cutting edge of the tool corresponding to the outermost trajectory line
Figure 2447DEST_PATH_IMAGE026
Angle value range[
Figure DEST_PATH_IMAGE050
,
Figure DEST_PATH_IMAGE052
], find [
Figure 372248DEST_PATH_IMAGE050
,
Figure 528423DEST_PATH_IMAGE052
] Each in the interval The tool cutting trajectory lines corresponding to the corners, the collection of these cutting trajectory lines constitutes the surface morphology of the processed workpiece;

刀具沿x轴进给，y轴两侧最终留到工件表面的轨迹线分别为

Figure DEST_PATH_IMAGE054
和
Figure DEST_PATH_IMAGE056
，要想保证最外侧轨迹的存在，切削刃轨迹必须满足轨迹线与进给轴交点的坐标值大于刀具旋转一周的直线进给量
Figure DEST_PATH_IMAGE058
，由此得到式（5）： The tool is fed along the x- axis, and the trajectories left on the workpiece surface on both sides of the y- axis are respectively
Figure DEST_PATH_IMAGE054
and
Figure DEST_PATH_IMAGE056
, in order to ensure the existence of the outermost trajectory, the cutting edge trajectory must meet the coordinate value of the intersection point of the trajectory line and the feed axis greater than the linear feed amount of the tool rotation once
Figure DEST_PATH_IMAGE058
, thus get the formula (5):

Figure DEST_PATH_IMAGE060
      (5)          
Figure DEST_PATH_IMAGE060
(5)

上式得到的为满足条件的最小值； obtained by the above formula is the minimum value that satisfies the condition;

位置角的最大值即为工件表面形貌残高最高处对应的切削点的位置角，也就是刀具前后两次走刀在垂直进给方向轴向截面内的截交角； The maximum value of the position angle is the position angle of the cutting point corresponding to the highest residual height on the surface of the workpiece, that is, the intersection angle of the two tool passes before and after the tool in the axial section in the vertical feed direction;

对于进给方向右侧

Figure 569522DEST_PATH_IMAGE054
这段轨迹来说，
Figure 580203DEST_PATH_IMAGE052
的大小要分两种情况进行讨论； For the right side of the feed direction
Figure 569522DEST_PATH_IMAGE054
For this trajectory,
Figure 580203DEST_PATH_IMAGE052
The size of is discussed in two cases;

1)第一次走刀，

Figure 548159DEST_PATH_IMAGE052
可以直接根据切削深度
Figure DEST_PATH_IMAGE062
与在此切削深度下的刀具与工件接触点中Z值最大点的几何关系计算得到式（6）： 1) The first knife pass,
Figure 548159DEST_PATH_IMAGE052
directly according to the depth of cut
Figure DEST_PATH_IMAGE062
The geometric relationship between the point with the maximum Z value in the contact point between the tool and the workpiece at this depth of cut is calculated to obtain the formula (6):

Figure DEST_PATH_IMAGE064
                     （6）
Figure DEST_PATH_IMAGE064
(6)

2)从第二次走刀开始，

Figure 768925DEST_PATH_IMAGE052
与走刀行距
Figure 480529DEST_PATH_IMAGE058
的大小有直接关系，可以得出它们之间的关系式（7）所示： 2) From the second pass,
Figure 768925DEST_PATH_IMAGE052
and walk distance
Figure 480529DEST_PATH_IMAGE058
There is a direct relationship between the size of them, and the relationship between them can be drawn as shown in (7):

Figure DEST_PATH_IMAGE066
                       （7）
Figure DEST_PATH_IMAGE066
(7)

对于进给方向左侧的

Figure 237395DEST_PATH_IMAGE056
轨迹来说， 的大小与
Figure 694101DEST_PATH_IMAGE054
存在相对的关系，对于最后一次走刀而言，
Figure 209396DEST_PATH_IMAGE052
大小为式（8）所示： For the left side of the feed direction
Figure 237395DEST_PATH_IMAGE056
In terms of trajectory, the size of
Figure 694101DEST_PATH_IMAGE054
There is a relative relationship, for the last pass,
Figure 209396DEST_PATH_IMAGE052
The size is shown in formula (8):

Figure 319303DEST_PATH_IMAGE064
                     （8）
Figure 319303DEST_PATH_IMAGE064
(8)

第一次走刀到倒数第二次走刀的过程中，左侧最外面的轨迹线对应的

Figure 629062DEST_PATH_IMAGE052
的值都为式（9）所示： During the process from the first tool pass to the penultimate tool pass, the outermost trajectory line on the left corresponds to
Figure 629062DEST_PATH_IMAGE052
The values of are all shown in formula (9):

Figure 434207DEST_PATH_IMAGE066
                       （9）
Figure 434207DEST_PATH_IMAGE066
(9)

（3）为了获得各个位置

Figure 487613DEST_PATH_IMAGE026
角对应的切削轨迹线，需要分别得到最外侧轨迹线
Figure 953492DEST_PATH_IMAGE054
段和
Figure 434152DEST_PATH_IMAGE056
段区间内刀具运动时间，通过求出在此区间内P点的转角，再结合刀具的主轴转速求得对应的加工时间，考虑切削微元所在位置处的螺旋滞后角，即可获得最外侧的形貌轨迹，从而得到工件的表面形貌模型；  (3) In order to obtain each position
Figure 487613DEST_PATH_IMAGE026
The cutting trajectory line corresponding to the angle needs to be obtained separately from the outermost trajectory line
Figure 953492DEST_PATH_IMAGE054
paragraph and
Figure 434152DEST_PATH_IMAGE056
The movement time of the tool in the interval, by calculating the rotation angle of point P in this interval, and then combining the spindle speed of the tool to obtain the corresponding processing time, considering the helical lag angle at the position of the cutting element, the outermost Topography trajectory, so as to obtain the surface topography model of the workpiece;

为了建立

Figure DEST_PATH_IMAGE068
和对应的转角和
Figure DEST_PATH_IMAGE074
的公式，分析
Figure 116806DEST_PATH_IMAGE068
及
Figure 708324DEST_PATH_IMAGE070
点在铣削过程中的转角； in order to establish
Figure DEST_PATH_IMAGE068
and corresponding corner and
Figure DEST_PATH_IMAGE074
formula, analysis
Figure 116806DEST_PATH_IMAGE068
and
Figure 708324DEST_PATH_IMAGE070
The corner of the point during milling;

对于

Figure 668190DEST_PATH_IMAGE068
点，从起点负y轴，x=0处转到
Figure 945850DEST_PATH_IMAGE068
时，满足下面的式（10）： for
Figure 668190DEST_PATH_IMAGE068
point, from the negative y-axis of the starting point, to x=0
Figure 945850DEST_PATH_IMAGE068
, satisfy the following formula (10):

Figure DEST_PATH_IMAGE076
                         （10）
Figure DEST_PATH_IMAGE076
(10)

即：

Figure DEST_PATH_IMAGE078
                  Right now:
Figure DEST_PATH_IMAGE078

其中，

Figure 725587DEST_PATH_IMAGE012
为球头刀具单位时间的进给量，为刀具轴旋转速度，R为刀具半径，
Figure DEST_PATH_IMAGE080
为
Figure 59802DEST_PATH_IMAGE068
点的位置角，为位置角
Figure 149298DEST_PATH_IMAGE080
处对应的刀具转角，且满足
Figure DEST_PATH_IMAGE082
； in,
Figure 725587DEST_PATH_IMAGE012
is the feed rate per unit time of the ball nose tool, is the rotational speed of the tool shaft, R is the tool radius,
Figure DEST_PATH_IMAGE080
for
Figure 59802DEST_PATH_IMAGE068
point position angle, is the position angle
Figure 149298DEST_PATH_IMAGE080
The corresponding tool angle at , and satisfy
Figure DEST_PATH_IMAGE082
;

对于

Figure 974297DEST_PATH_IMAGE070
点，从起点负y轴，x=0处转到
Figure 643176DEST_PATH_IMAGE070
时，满足下面的式（11）： for
Figure 974297DEST_PATH_IMAGE070
point, from the negative y-axis of the starting point, to x=0
Figure 643176DEST_PATH_IMAGE070
, satisfy the following formula (11):

Figure DEST_PATH_IMAGE084
                      （11）
Figure DEST_PATH_IMAGE084
(11)

即：

Figure DEST_PATH_IMAGE086
               Right now:
Figure DEST_PATH_IMAGE086

其中，

Figure 761173DEST_PATH_IMAGE012
为球头刀具单位时间的进给量，
Figure 515503DEST_PATH_IMAGE032
为刀具轴旋转速度，R为刀具半径，
Figure DEST_PATH_IMAGE088
为点的位置角，为位置角
Figure 667578DEST_PATH_IMAGE088
处对应的刀具转角，且满足
Figure DEST_PATH_IMAGE092
； in,
Figure 761173DEST_PATH_IMAGE012
is the feed rate per unit time of the ball nose tool,
Figure 515503DEST_PATH_IMAGE032
is the rotational speed of the tool shaft, R is the tool radius,
Figure DEST_PATH_IMAGE088
for point position angle, is the position angle
Figure 667578DEST_PATH_IMAGE088
The corresponding tool angle at , and satisfy
Figure DEST_PATH_IMAGE092
;

运用牛顿迭代法求解非线性方程式(10)与(11)，得到对应位置

Figure 831843DEST_PATH_IMAGE026
角的刀具转角值，结合刀具的旋转角速度，可以求得该切削段内的切削时间
Figure DEST_PATH_IMAGE094
； Using the Newton iteration method to solve the nonlinear equations (10) and (11), get the corresponding position
Figure 831843DEST_PATH_IMAGE026
The cutting time in the cutting segment can be obtained by combining the tool rotation angle value of the cutting angle with the rotation angular velocity of the tool
Figure DEST_PATH_IMAGE094
;

由于球头铣刀的螺旋切削刃将引起螺旋滞后现象，将对不同位置角处切削点参与切削的时间产生影响，进而影响切削轨迹，各个位置角

Figure 198102DEST_PATH_IMAGE026
对应的刀具螺旋滞后角
Figure 738805DEST_PATH_IMAGE022
可表示为式（12）： Because the helical cutting edge of the ball end milling cutter will cause the helical hysteresis phenomenon, it will affect the cutting time of the cutting point at different position angles, and then affect the cutting trajectory.
Figure 198102DEST_PATH_IMAGE026
Corresponding tool helix lag angle
Figure 738805DEST_PATH_IMAGE022
Can be expressed as formula (12):

Figure DEST_PATH_IMAGE096
                       (12)
Figure DEST_PATH_IMAGE096
(12)

其中，

Figure DEST_PATH_IMAGE098
为刀具的最大螺旋滞后角，
Figure 116697DEST_PATH_IMAGE026
为切削点在刀具切削刃上的位置角，螺旋滞后产生的时间影响； in,
Figure DEST_PATH_IMAGE098
is the maximum helix lag angle of the tool,
Figure 116697DEST_PATH_IMAGE026
is the position angle of the cutting point on the cutting edge of the tool, and the time influence caused by the helical lag ;

将求得的位置角

Figure 343541DEST_PATH_IMAGE026
的范围、刀具在所求得的
Figure 806883DEST_PATH_IMAGE026
的区间内的转角、刀具转过该转角的时间代入到考虑刀具磨损的切削轨迹方程式（2）中，即可得到球头铣刀铣削的工件表面形貌，表示为式（13）； The obtained position angle
Figure 343541DEST_PATH_IMAGE026
The scope of the tool, the obtained
Figure 806883DEST_PATH_IMAGE026
Substituting the rotation angle in the interval and the time when the tool rotates through the rotation angle into the cutting trajectory equation (2) considering tool wear, the surface morphology of the workpiece milled by the ball end milling cutter can be obtained, which is expressed as formula (13);

Figure DEST_PATH_IMAGE102
      （13）
Figure DEST_PATH_IMAGE102
(13)

采用上述方案后，本发明根据铣削加工刀具切削运动轨迹将球头铣刀切削刃进行离散处理，建立球头铣刀刀具切削刃微元铣削轨迹方程，切削轨迹方程表面形貌由上述建立的轨迹方程中最外侧的轨迹形成，通过判断这些最外侧轨迹对应切削微元的位置角范围，确定铣削这些最外侧轨迹对应的刀具转角范围，结合由刀具主轴转速获得的旋转角速度计算铣削这些轨迹对应的加工时间，考虑切削微元所在位置处的螺旋滞后角，获得这些最外侧的铣削轨迹，从而得到铣削工件表面形貌，解决铣削加工过程中由刀具磨损引起的工件表面形貌问题。 After adopting the above scheme, the present invention performs discrete processing on the cutting edge of the ball end milling cutter according to the cutting motion track of the milling tool, and establishes the microelement milling trajectory equation of the cutting edge of the ball end milling cutter. The outermost trajectories in the equation are formed. By judging the position angle ranges of these outermost trajectories corresponding to the cutting elements, the range of tool rotation angles corresponding to these outermost trajectories for milling is determined, and the angle of rotation corresponding to these trajectories is calculated by combining the rotation angular velocity obtained by the tool spindle speed. The processing time, considering the helical lag angle at the position of the cutting micro-element, obtains these outermost milling trajectories, thereby obtaining the surface topography of the milled workpiece, and solving the problem of the surface topography of the workpiece caused by tool wear during the milling process.

附图说明 Description of drawings

图1是本发明中球头切削刃离散示意图； Fig. 1 is a discrete schematic diagram of a ball-end cutting edge in the present invention;

图2是本发明中球头铣刀切削刃切削轨迹； Fig. 2 is the cutting track of the cutting edge of the ball end milling cutter in the present invention;

图3是本发明中构成表面形貌的轨迹点； Fig. 3 is the track point that constitutes surface topography among the present invention;

图4是本发明中刀具磨损前后切削微元位置示意图； Fig. 4 is a schematic diagram of the position of cutting elements before and after tool wear in the present invention;

图5是本发明中球头铣刀单齿切削轨迹示意图； Fig. 5 is a schematic diagram of the single-tooth cutting track of the ball end milling cutter in the present invention;

图6是本发明中相邻两次走刀截交角示意图； Fig. 6 is a schematic diagram of the intersection angle of two adjacent tool passes in the present invention;

图7是本发明刀具切削过程中的刀具转角示意图； Fig. 7 is a schematic diagram of the tool turning angle during the tool cutting process of the present invention;

图中标号名称：1-第一切削刃；2-第二切削刃，3-切削轨迹，4-保留下来的点，5-切除掉的点，6-工件最终表面，7-保留下来的点。 Label names in the figure: 1-first cutting edge; 2-second cutting edge, 3-cutting track, 4-retained point, 5-removed point, 6-final surface of workpiece, 7-retained point .

具体实施方式 Detailed ways

以下将结合附图，对本发明的技术方案进行详细说明。 The technical solutions of the present invention will be described in detail below in conjunction with the accompanying drawings.

一种铣削加工工件表面形貌的建模方法，包括如下步骤： A method for modeling the surface topography of a milling workpiece, comprising the steps of:

（1）球头铣刀切削刃离散，建立球头铣刀刀具切削刃微元铣削轨迹方程。 (1) The cutting edge of the ball-end milling cutter is discrete, and the micro-element milling trajectory equation of the cutting edge of the ball-end milling cutter is established.

根据铣削加工刀具切削运动轨迹将球头部分切削刃离散为一系列切削微元，如图1所示为本发明中球头切削刃离散示意图，图中虚线所示为球头部分上的一条螺旋切削刃，P为其上的一个切削微元，O为球头部分中心，

Figure 275911DEST_PATH_IMAGE026
为P点与球头中心O的连线与刀具主轴Z的夹角，即为描述切削微元所在位置的角度称为位置角。由于不同切削微元在切削时线速度不同，且在加工过程中同时存在直线进给运动与自身绕刀具主轴的旋转运动，因此，除球头刀尖外球头切削刃上其它点的运动轨迹实际为一系列的次摆线，次摆线形成的切削轨迹如图2所示，实线表示球头铣刀第一切削刃上某点切削轨迹，虚线表示球头铣刀第二切削刃上同一高度某点的切削轨迹，轨迹上方和下方最外侧的轨迹点构成了工件形貌，将这一区域的轨迹点放大显示后如图3所示。图3中，空心点代表在切削加工过程中被切削掉的点，实心点为保留下来的点，也就是构成工件表面形貌的点。 Discretize the cutting edge of the ball head part into a series of cutting microelements according to the cutting motion trajectory of the milling tool, as shown in Figure 1, it is a schematic diagram of the separation of the ball head cutting edge in the present invention, and the dotted line shows a helix on the ball head part in the figure Cutting edge, P is a cutting element on it, O is the center of the ball head,
Figure 275911DEST_PATH_IMAGE026
is the angle between the line connecting point P and the center O of the ball head and the tool spindle Z, which is the angle describing the position of the cutting element, called the position angle. Since different cutting microelements have different linear speeds during cutting, and there are both linear feed motion and self-rotating motion around the tool spindle during machining, the motion trajectory of other points on the cutting edge of the ball except for the tip of the ball It is actually a series of trochoids, and the cutting trajectory formed by the trochoids is shown in Figure 2. The solid line indicates the cutting trajectory at a certain point on the first cutting edge of the ball end mill, and the dotted line indicates the cutting trajectory at a certain point on the second cutting edge of the ball end mill. The cutting trajectory at a certain point at the same height, the outermost trajectory points above and below the trajectory constitute the workpiece morphology, and the trajectory points in this area are enlarged and displayed, as shown in Figure 3. In Figure 3, the hollow points represent the points that are cut off during the cutting process, and the solid points are the remaining points, that is, the points that constitute the surface morphology of the workpiece.

为了分析刀具切削轨迹在工件上形成的形貌，以离散后的切削微元P点作为研究对象，通过分析点P在走刀过程中的运动，得到加工结束后点P在工件上最终留下的切削轨迹，去除在加工中被切除掉的轨迹线即得到最终构成工件形貌的轨迹。刀具上Ｐ点空间运动轨迹由直线运动和旋转运动构成，因此 当刀具未发生磨损时，P点的理论切削轨迹方程如式（1）所示： In order to analyze the shape of the tool cutting track formed on the workpiece, the discrete cutting micro-element point P is taken as the research object, and by analyzing the movement of the point P during the cutting process, it is obtained that the point P finally leaves on the workpiece after machining. The cutting trajectory of the workpiece is removed, and the trajectory that is cut off in the process is removed to obtain the trajectory that finally constitutes the shape of the workpiece. The spatial trajectory of point P on the tool is composed of linear motion and rotary motion, so when the tool is not worn, the theoretical cutting trajectory equation of point P is shown in formula (1):

Figure 508309DEST_PATH_IMAGE002
              (1)
Figure 508309DEST_PATH_IMAGE002
(1)

其中，

Figure 279956DEST_PATH_IMAGE004
、
Figure 230594DEST_PATH_IMAGE006
为P点经过切削加工时间后的坐标，、
Figure 91682DEST_PATH_IMAGE010
为P点起始坐标，
Figure 34230DEST_PATH_IMAGE012
为单位时间的刀具进给速度，
Figure 472165DEST_PATH_IMAGE014
为切削加工时间，
Figure 158361DEST_PATH_IMAGE016
为P点所处位置的螺旋滞后角对该点加工时间的影响，
Figure 489985DEST_PATH_IMAGE018
，
Figure 603435DEST_PATH_IMAGE020
，
Figure 528666DEST_PATH_IMAGE022
为P点对应的刀具螺旋滞后角，为P点所处的位置角
Figure 706148DEST_PATH_IMAGE026
处的刀具径向半径，
Figure 724920DEST_PATH_IMAGE028
，
Figure 137447DEST_PATH_IMAGE044
为未磨损时的球头铣刀半径，
Figure 165446DEST_PATH_IMAGE032
为刀具主轴旋转角速度。 in,
Figure 279956DEST_PATH_IMAGE004
,
Figure 230594DEST_PATH_IMAGE006
is the coordinate of point P after the cutting time, ,
Figure 91682DEST_PATH_IMAGE010
is the starting coordinate of point P,
Figure 34230DEST_PATH_IMAGE012
is the tool feed rate per unit time,
Figure 472165DEST_PATH_IMAGE014
is the cutting time,
Figure 158361DEST_PATH_IMAGE016
is the influence of the helical lag angle at the position of point P on the processing time of the point,
Figure 489985DEST_PATH_IMAGE018
,
Figure 603435DEST_PATH_IMAGE020
,
Figure 528666DEST_PATH_IMAGE022
is the tool helix lag angle corresponding to point P, is the position angle of point P
Figure 706148DEST_PATH_IMAGE026
The radial radius of the tool at ,
Figure 724920DEST_PATH_IMAGE028
,
Figure 137447DEST_PATH_IMAGE044
is the radius of the ball end mill without wear,
Figure 165446DEST_PATH_IMAGE032
is the rotational angular velocity of the tool spindle.

当把刀具磨损的影响考虑在内时，随着刀具不断磨损，切削刃上同一高度上的点所对应的径向半径

Figure 347028DEST_PATH_IMAGE024
及其所对应的位置角都将发生变化，因此，当考虑加工过程中的刀具磨损量时，P点的切削轨迹可由式(2)表示： When the effect of tool wear is taken into account, as the tool wears, the radial radius corresponding to a point at the same height on the cutting edge
Figure 347028DEST_PATH_IMAGE024
and its corresponding position angle will change, therefore, when considering the amount of tool wear during machining, the cutting trajectory of point P can be expressed by formula (2):

   (2) (2)

其中，

Figure 127268DEST_PATH_IMAGE036
、
Figure 428937DEST_PATH_IMAGE038
为考虑刀具磨损P点经过切削加工时间后的坐标，
Figure 681189DEST_PATH_IMAGE008
、
Figure 802728DEST_PATH_IMAGE010
为P点起始坐标，
Figure 172530DEST_PATH_IMAGE012
为单位时间的刀具进给速度，
Figure 328705DEST_PATH_IMAGE014
为切削加工时间，
Figure 250393DEST_PATH_IMAGE016
为P点所处位置的螺旋滞后角对该点加工时间的影响，且
Figure 859229DEST_PATH_IMAGE018
，
Figure 767142DEST_PATH_IMAGE022
为P点对应的刀具螺旋滞后角，为刀具磨损后P点高度处的球头径向半径，
Figure 745780DEST_PATH_IMAGE032
为刀具主轴旋转角速度。 in,
Figure 127268DEST_PATH_IMAGE036
,
Figure 428937DEST_PATH_IMAGE038
In order to consider the coordinates of the tool wear point P after the cutting time,
Figure 681189DEST_PATH_IMAGE008
,
Figure 802728DEST_PATH_IMAGE010
is the starting coordinate of point P,
Figure 172530DEST_PATH_IMAGE012
is the tool feed rate per unit time,
Figure 328705DEST_PATH_IMAGE014
is the cutting time,
Figure 250393DEST_PATH_IMAGE016
is the influence of the helical lag angle at the position of point P on the processing time of the point, and
Figure 859229DEST_PATH_IMAGE018
,
Figure 767142DEST_PATH_IMAGE022
is the tool helix lag angle corresponding to point P, is the radial radius of the ball head at the height of point P after tool wear,
Figure 745780DEST_PATH_IMAGE032
is the rotational angular velocity of the tool spindle.

图4显示了位置角

Figure 468010DEST_PATH_IMAGE026
处选取的切削微元P在切削刃磨损前后所处位置的变化，未发生刀具磨损时，P点位于球头最外的轮廓上，在刀具经过一段时间加工后，球头部分发生磨损，在与P点所在高度相同的
Figure 179614DEST_PATH_IMAGE046
截面处，P点磨损后的实际位置变为
Figure DEST_PATH_IMAGE104
，为在加工过程中被磨损掉的部分。因此，当位置角
Figure 169436DEST_PATH_IMAGE026
取不同的数值时，就可以求解出一系列切削刃磨损后的切削微元的位置坐标，从而建立磨损后刀具外轮廓刃线的几何关系模型。 Figure 4 shows the position angle
Figure 468010DEST_PATH_IMAGE026
The position change of the cutting element P selected at the position before and after cutting edge wear. When no tool wear occurs, point P is located on the outermost contour of the ball head. After the tool has been processed for a period of time, the ball head part is worn. at the same height as point P
Figure 179614DEST_PATH_IMAGE046
At the section, the actual position of point P after wear becomes
Figure DEST_PATH_IMAGE104
, It is the part that is worn away during processing. Therefore, when the position angle
Figure 169436DEST_PATH_IMAGE026
When different values are taken, the position coordinates of a series of cutting microelements after the cutting edge wear can be solved, so as to establish the geometric relationship model of the edge line of the outer contour of the worn tool.

图4中，未发生磨损时，P点所在平面高度

Figure 308293DEST_PATH_IMAGE046
处对应的球头铣刀径向半径可以表示为： In Figure 4, when no wear occurs, the height of the plane where point P is located
Figure 308293DEST_PATH_IMAGE046
The radial radius of the ball end mill corresponding to It can be expressed as:

           

Figure 407016DEST_PATH_IMAGE028
                              (3)
Figure 407016DEST_PATH_IMAGE028
(3)

式中，

Figure 126711DEST_PATH_IMAGE030
为球头铣刀未磨损时的半径，
Figure 62568DEST_PATH_IMAGE026
为刀具未磨损时P点对应的位置角。 In the formula,
Figure 126711DEST_PATH_IMAGE030
is the radius of the ball end milling cutter when it is not worn,
Figure 62568DEST_PATH_IMAGE026
is the position angle corresponding to point P when the tool is not worn.

加工一段时间之后，刀具球头部分将发生磨损，球头铣刀同一高度处切削刃上的切削点的实际加工位置发生了变化，由P点变化为P ’ 点，如图4所示。此时，该高度所处平面对应的球头铣刀截面圆径向半径由理论值变化为

Figure 26479DEST_PATH_IMAGE040
，因此，磨损后
Figure 631772DEST_PATH_IMAGE046
高度处对应的刀具的径向半径可以表示为： After processing for a period of time, the ball head part of the tool will wear out, and the ball end milling cutter will be at the same height The actual machining position of the cutting point on the cutting edge has changed from point P to point P ' , as shown in Figure 4. At this time, the radial radius of the ball end mill section circle corresponding to the plane where the height is located is changed from the theoretical value change to
Figure 26479DEST_PATH_IMAGE040
, therefore, after wear
Figure 631772DEST_PATH_IMAGE046
The radial radius of the tool corresponding to the height can be expressed as:

     

Figure 189793DEST_PATH_IMAGE042
                  (4)
Figure 189793DEST_PATH_IMAGE042
(4)

式中，

Figure 781311DEST_PATH_IMAGE044
为球头铣刀未磨损时的半径，
Figure 475598DEST_PATH_IMAGE046
为切削微元所在的截平面高度，为
Figure 798574DEST_PATH_IMAGE046
高度处刀具切削刃的后刀面磨损量。 In the formula,
Figure 781311DEST_PATH_IMAGE044
is the radius of the ball end milling cutter when it is not worn,
Figure 475598DEST_PATH_IMAGE046
is the height of the sectional plane where the cutting element is located, for
Figure 798574DEST_PATH_IMAGE046
The amount of flank wear on the cutting edge of the tool at height.

（2）求解最外侧轨迹线对应的刀具切削刃的位置角取值范围[

Figure 8155DEST_PATH_IMAGE050
，
Figure 830618DEST_PATH_IMAGE052
] (2) Solve the position of the tool cutting edge corresponding to the outermost trajectory line Angle value range[
Figure 8155DEST_PATH_IMAGE050
,
Figure 830618DEST_PATH_IMAGE052
]

根据铣削轨迹方程获得的铣削轨迹并不是全部构成工件表面形貌，部分轨迹线在加工中会被切除，只有最外侧的轨迹线形成工件表面形貌，为了确定最外侧的轨迹线，需要求解最外侧轨迹线对应的刀具切削刃的位置角取值范围[

Figure 421185DEST_PATH_IMAGE050
，
Figure 90064DEST_PATH_IMAGE052
]，求出[
Figure 83428DEST_PATH_IMAGE050
,
Figure 463856DEST_PATH_IMAGE052
]区间内各个
Figure 200867DEST_PATH_IMAGE026
角对应的刀具切削轨迹线，这些切削轨迹线的集合就构成了加工后的工件表面形貌； The milling trajectory obtained according to the milling trajectory equation does not completely constitute the surface topography of the workpiece. Part of the trajectory line will be cut off during processing, and only the outermost trajectory line forms the surface topography of the workpiece. In order to determine the outermost trajectory line, it is necessary to solve the most The position of the cutting edge of the tool corresponding to the outer trajectory line Angle value range[
Figure 421185DEST_PATH_IMAGE050
,
Figure 90064DEST_PATH_IMAGE052
], find [
Figure 83428DEST_PATH_IMAGE050
,
Figure 463856DEST_PATH_IMAGE052
] Each in the interval
Figure 200867DEST_PATH_IMAGE026
The tool cutting trajectory lines corresponding to the corners, the collection of these cutting trajectory lines constitutes the surface morphology of the processed workpiece;

分析图5，刀具沿x轴进给，y轴两侧最终留到工件表面的轨迹线分别为

Figure 724253DEST_PATH_IMAGE054
和
Figure 154097DEST_PATH_IMAGE056
这些最外侧的轨迹。为了求得这部分最终构成工件表面形貌的轨迹，去掉其余在加工中被切除的轨迹，需要分别求出刀具铣削
Figure 395722DEST_PATH_IMAGE054
和
Figure 795480DEST_PATH_IMAGE056
时对应的切削刃位置角
Figure 438951DEST_PATH_IMAGE026
的范围，下面具体说明如何求得
Figure 774117DEST_PATH_IMAGE054
和所对应的
Figure 207952DEST_PATH_IMAGE026
角值。 Analyzing Figure 5, the tool feeds along the x- axis, and the trajectories left on the workpiece surface on both sides of the y- axis are respectively
Figure 724253DEST_PATH_IMAGE054
and
Figure 154097DEST_PATH_IMAGE056
These outermost trajectories. In order to obtain this part of the trajectory that finally constitutes the surface topography of the workpiece, and remove the remaining trajectory that was cut off during processing, it is necessary to calculate the tool milling
Figure 395722DEST_PATH_IMAGE054
and
Figure 795480DEST_PATH_IMAGE056
corresponding cutting edge position angle
Figure 438951DEST_PATH_IMAGE026
range, the following describes how to obtain
Figure 774117DEST_PATH_IMAGE054
and Corresponding
Figure 207952DEST_PATH_IMAGE026
Angle value.

要想保证

Figure 705929DEST_PATH_IMAGE056
存在，即切削刃的轨迹为长幅摆线这种情况，必须满足图5中点的x坐标值大于刀具旋转一周的直线进给量。结合图5所示，实线代表位置角为
Figure 428215DEST_PATH_IMAGE026
2 的某点的切削轨迹，该点的切削轨迹最终会形成工件表面形貌；虚线代表位置较为
Figure 435354DEST_PATH_IMAGE026
1的某点的切削轨迹，该点的切削轨迹最终不会形成工件表面形貌。即满足以下关系时切削轨迹最终会形成工件表面形貌，也就是转角为90°对应的x坐标大于转角为（360+270）°的x坐标，即： want to guarantee
Figure 705929DEST_PATH_IMAGE056
Existence, that is, the trajectory of the cutting edge is a long-amplitude cycloid, it must satisfy the point in Figure 5 The x- coordinate value is greater than the straight-line feed for one rotation of the tool . As shown in Figure 5, the solid line represents the position angle of
Figure 428215DEST_PATH_IMAGE026
The cutting trajectory of a certain point in 2 , the cutting trajectory of this point will eventually form the surface morphology of the workpiece; the dotted line represents a relatively
Figure 435354DEST_PATH_IMAGE026
1 , the cutting trajectory at this point will not eventually form the surface morphology of the workpiece. That is, when the following relationship is satisfied, the cutting trajectory will eventually form the surface morphology of the workpiece, that is, the x-coordinate corresponding to the rotation angle of 90° is greater than the x-coordinate of the rotation angle of (360+270)°, namely:

Figure 787838DEST_PATH_IMAGE060
             （5）
Figure 787838DEST_PATH_IMAGE060
(5)

式（5）得到的

Figure 730386DEST_PATH_IMAGE050
为满足条件的最小值。 Formula (5) obtained
Figure 730386DEST_PATH_IMAGE050
is the minimum value that satisfies the condition.

位置角的最大值即为工件表面形貌残高最高处对应的切削点的位置角，也就是刀具前后两次走刀在垂直进给方向轴向截面内的截交角。图6中进给方向（X轴方向）由O点指向纸面里。 The maximum value of the position angle is the position angle of the cutting point corresponding to the highest residual height on the surface of the workpiece, that is, the interception angle of the two tool passes before and after the tool in the axial section in the vertical feed direction. In Fig. 6, the feed direction (X-axis direction) points to the inside of the paper from point O.

由图6所示可以看出：对于进给方向右侧

Figure 168320DEST_PATH_IMAGE054
这段轨迹来说，
Figure 215036DEST_PATH_IMAGE052
的大小要分两种情况进行讨论。 As shown in Figure 6, it can be seen that for the right side of the feed direction
Figure 168320DEST_PATH_IMAGE054
For this trajectory,
Figure 215036DEST_PATH_IMAGE052
The size of is discussed in two cases.

1)第一次走刀，可以直接根据切削深度

Figure 801055DEST_PATH_IMAGE062
与在此切削深度下的刀具与工件接触点中Z值最大点的几何关系计算得到式（6）： 1) The first knife pass, directly according to the depth of cut
Figure 801055DEST_PATH_IMAGE062
The geometric relationship between the point with the maximum Z value in the contact point between the tool and the workpiece at this depth of cut is calculated to obtain the formula (6):

Figure 726286DEST_PATH_IMAGE064
                     （6）
Figure 726286DEST_PATH_IMAGE064
(6)

2)从第二次走刀开始，

Figure 950594DEST_PATH_IMAGE052
与走刀行距
Figure 136725DEST_PATH_IMAGE058
的大小有直接关系，可以得出它们之间的关系式（7）所示： 2) From the second pass,
Figure 950594DEST_PATH_IMAGE052
and walk distance
Figure 136725DEST_PATH_IMAGE058
There is a direct relationship between the size of them, and the relationship between them can be drawn as shown in (7):

Figure 421075DEST_PATH_IMAGE066
                       （7）
Figure 421075DEST_PATH_IMAGE066
(7)

对于进给方向左侧的

Figure 833602DEST_PATH_IMAGE056
轨迹来说， 
Figure 861601DEST_PATH_IMAGE052
的大小与
Figure 692720DEST_PATH_IMAGE054
存在相对的关系，对于最后一次走刀而言，
Figure 882393DEST_PATH_IMAGE052
大小为式（8）所示： For the left side of the feed direction
Figure 833602DEST_PATH_IMAGE056
In terms of trajectory,
Figure 861601DEST_PATH_IMAGE052
the size of
Figure 692720DEST_PATH_IMAGE054
There is a relative relationship, for the last pass,
Figure 882393DEST_PATH_IMAGE052
The size is shown in formula (8):

Figure 782216DEST_PATH_IMAGE064
                     （8）
Figure 782216DEST_PATH_IMAGE064
(8)

第一次走刀到倒数第二次走刀的过程中，左侧最外面的轨迹线对应的

Figure 348326DEST_PATH_IMAGE052
的值都为式（9）所示： During the process from the first tool pass to the penultimate tool pass, the outermost trajectory line on the left corresponds to
Figure 348326DEST_PATH_IMAGE052
The values of are all shown in formula (9):

Figure 774628DEST_PATH_IMAGE066
                       （9）
Figure 774628DEST_PATH_IMAGE066
(9)

（3）最外侧轨迹线

Figure 135203DEST_PATH_IMAGE054
段和
Figure 522322DEST_PATH_IMAGE056
段区间内刀具运动时间的计算 (3) The outermost trajectory line
Figure 135203DEST_PATH_IMAGE054
paragraph and
Figure 522322DEST_PATH_IMAGE056
Calculation of tool movement time in segment interval

为了获得各个位置

Figure 892123DEST_PATH_IMAGE026
角对应的切削轨迹线，需要分别得到最外侧轨迹线
Figure 782719DEST_PATH_IMAGE054
段和
Figure 205872DEST_PATH_IMAGE056
段区间内刀具运动时间，通过求出在此区间内P点的转角，再结合刀具的主轴转速求得对应的加工时间，考虑切削微元所在位置处的螺旋滞后角，即可获得最外侧的形貌轨迹，从而得到工件的表面形貌模型。 In order to get the various positions
Figure 892123DEST_PATH_IMAGE026
The cutting trajectory line corresponding to the angle needs to be obtained separately from the outermost trajectory line
Figure 782719DEST_PATH_IMAGE054
paragraph and
Figure 205872DEST_PATH_IMAGE056
The movement time of the tool in the interval, by calculating the rotation angle of point P in this interval, and then combining the spindle speed of the tool to obtain the corresponding processing time, considering the helical lag angle at the position of the cutting element, the outermost The topography trajectory is used to obtain the surface topography model of the workpiece.

为了建立图7中

Figure 814708DEST_PATH_IMAGE068
和
Figure 988200DEST_PATH_IMAGE070
对应的转角
Figure 998882DEST_PATH_IMAGE072
和
Figure 91471DEST_PATH_IMAGE074
的公式，分析
Figure 187603DEST_PATH_IMAGE068
及
Figure 899207DEST_PATH_IMAGE070
点在铣削过程中的转角。 In order to build the Figure 7
Figure 814708DEST_PATH_IMAGE068
and
Figure 988200DEST_PATH_IMAGE070
corresponding corner
Figure 998882DEST_PATH_IMAGE072
and
Figure 91471DEST_PATH_IMAGE074
formula, analysis
Figure 187603DEST_PATH_IMAGE068
and
Figure 899207DEST_PATH_IMAGE070
Point the corner during milling.

对于

Figure 764395DEST_PATH_IMAGE068
点，从起点负y轴，x=0处转到
Figure 903252DEST_PATH_IMAGE068
时，满足下面的式（10）： for
Figure 764395DEST_PATH_IMAGE068
point, from the negative y-axis of the starting point, to x=0
Figure 903252DEST_PATH_IMAGE068
, satisfy the following formula (10):

Figure 112779DEST_PATH_IMAGE076
                         （10）
Figure 112779DEST_PATH_IMAGE076
(10)

即：

Figure 362495DEST_PATH_IMAGE078
                  Right now:
Figure 362495DEST_PATH_IMAGE078

其中，

Figure 347768DEST_PATH_IMAGE012
为球头刀具单位时间的进给量，
Figure 657527DEST_PATH_IMAGE032
为刀具轴旋转速度，R为刀具半径，
Figure 728251DEST_PATH_IMAGE080
为
Figure 906292DEST_PATH_IMAGE068
点的位置角，
Figure 746072DEST_PATH_IMAGE072
为位置角
Figure 226732DEST_PATH_IMAGE080
处对应的刀具转角，且满足
Figure 519173DEST_PATH_IMAGE082
。 in,
Figure 347768DEST_PATH_IMAGE012
is the feed rate per unit time of the ball nose tool,
Figure 657527DEST_PATH_IMAGE032
is the rotational speed of the tool shaft, R is the tool radius,
Figure 728251DEST_PATH_IMAGE080
for
Figure 906292DEST_PATH_IMAGE068
point position angle,
Figure 746072DEST_PATH_IMAGE072
is the position angle
Figure 226732DEST_PATH_IMAGE080
The corresponding tool angle at , and satisfy
Figure 519173DEST_PATH_IMAGE082
.

对于

Figure 2369DEST_PATH_IMAGE070
点，从起点负y轴，x=0处转到
Figure 696655DEST_PATH_IMAGE070
时，满足下面的式（11）： for
Figure 2369DEST_PATH_IMAGE070
point, from the negative y-axis of the starting point, to x=0
Figure 696655DEST_PATH_IMAGE070
, satisfy the following formula (11):

Figure 348217DEST_PATH_IMAGE084
                      （11）
Figure 348217DEST_PATH_IMAGE084
(11)

即：               Right now:

其中，为球头刀具单位时间的进给量，

Figure 462169DEST_PATH_IMAGE032
为刀具轴旋转速度，R为刀具半径，
Figure 550211DEST_PATH_IMAGE088
为
Figure 817244DEST_PATH_IMAGE070
点的位置角，
Figure 16144DEST_PATH_IMAGE090
为位置角
Figure 45542DEST_PATH_IMAGE088
处对应的刀具转角，且满足
Figure 304485DEST_PATH_IMAGE092
； in, is the feed rate per unit time of the ball nose tool,
Figure 462169DEST_PATH_IMAGE032
is the rotational speed of the tool shaft, R is the tool radius,
Figure 550211DEST_PATH_IMAGE088
for
Figure 817244DEST_PATH_IMAGE070
point position angle,
Figure 16144DEST_PATH_IMAGE090
is the position angle
Figure 45542DEST_PATH_IMAGE088
The corresponding tool angle at , and satisfy
Figure 304485DEST_PATH_IMAGE092
;

运用牛顿迭代法求解非线性方程式(10)与(11)，得到对应位置

Figure 58815DEST_PATH_IMAGE026
角的刀具转角值，结合刀具的旋转角速度，可以求得该切削段内的切削时间
Figure 795827DEST_PATH_IMAGE094
。 Using the Newton iteration method to solve the nonlinear equations (10) and (11), get the corresponding position
Figure 58815DEST_PATH_IMAGE026
The cutting time in the cutting segment can be obtained by combining the tool rotation angle value of the cutting angle with the rotation angular velocity of the tool
Figure 795827DEST_PATH_IMAGE094
.

由于球头铣刀的螺旋切削刃将引起螺旋滞后现象，将对不同位置角处切削点参与切削的时间产生影响，进而影响切削轨迹，各个位置角

Figure 443846DEST_PATH_IMAGE026
对应的刀具螺旋滞后角
Figure 873690DEST_PATH_IMAGE022
可表示为式（12）： Because the helical cutting edge of the ball end milling cutter will cause the helical hysteresis phenomenon, it will affect the cutting time of the cutting point at different position angles, and then affect the cutting trajectory.
Figure 443846DEST_PATH_IMAGE026
Corresponding tool helix lag angle
Figure 873690DEST_PATH_IMAGE022
Can be expressed as formula (12):

Figure 849736DEST_PATH_IMAGE096
                       (12)
Figure 849736DEST_PATH_IMAGE096
(12)

其中，

Figure 390439DEST_PATH_IMAGE098
为刀具的最大螺旋滞后角，为切削点在刀具切削刃上的位置角，螺旋滞后产生的时间影响
Figure 995175DEST_PATH_IMAGE100
。 in,
Figure 390439DEST_PATH_IMAGE098
is the maximum helix lag angle of the tool, is the position angle of the cutting point on the cutting edge of the tool, and the time influence caused by the helical lag
Figure 995175DEST_PATH_IMAGE100
.

将求得的位置角

Figure 724097DEST_PATH_IMAGE026
的范围、刀具在所求得的
Figure 802911DEST_PATH_IMAGE026
的区间内的转角、刀具转过该转角的时间代入到考虑刀具磨损的切削轨迹方程式（2）中，即可得到球头铣刀铣削的工件表面形貌，表示为式（13）； The obtained position angle
Figure 724097DEST_PATH_IMAGE026
The scope of the tool, the obtained
Figure 802911DEST_PATH_IMAGE026
Substituting the rotation angle in the interval and the time when the tool rotates through the rotation angle into the cutting trajectory equation (2) considering tool wear, the surface morphology of the workpiece milled by the ball end milling cutter can be obtained, which is expressed as formula (13);

Figure 300888DEST_PATH_IMAGE102
      （13）
Figure 300888DEST_PATH_IMAGE102
(13)

以上实例仅为说明本发明的技术思想，不能以此限定本发明的保护范围，凡是按照本发明提出的技术思想，在技术方案基础上所做的任何改动，均落入本发明保护范围之内。 The above examples are only to illustrate the technical ideas of the present invention, and cannot limit the protection scope of the present invention with this. All technical ideas proposed in accordance with the present invention, any changes made on the basis of technical solutions, all fall within the protection scope of the present invention .

Claims (1)

1. A modeling method for milling the surface topography of a workpiece is characterized by comprising the following steps:
(1) dispersing a ball head part cutting edge into a series of cutting micro-elements according to a cutting motion track of a milling cutter, wherein the linear velocity of different cutting micro-elements is different during cutting, and linear feed motion and rotation motion of the ball head part cutting edge around a cutter main shaft exist simultaneously in the processing process, so that motion tracks of other points on a ball head cutting edge except a ball head cutter point form a series of trochoids, in order to analyze the appearance formed on a workpiece by the cutting track of the cutter, a dispersed cutting micro-element P point is used as a research object, the motion of a point P in the cutter feeding process is analyzed to obtain the cutting track of the point P finally left on the workpiece after the processing is finished, and the track line cut off in the processing is removed to obtain the track finally forming the appearance of the workpiece; considering the linear motion track and the rotation track, when the tool is not worn, the theoretical cutting track equation of the point P is shown as the formula (1):
Figure 257180DEST_PATH_IMAGE002
(1)
wherein,
Figure 840608DEST_PATH_IMAGE004
、
Figure 90324DEST_PATH_IMAGE006
is the coordinate of the point P after the cutting time,
Figure 200231DEST_PATH_IMAGE008
、
Figure 509990DEST_PATH_IMAGE010
the starting coordinates of the point P are shown,
Figure 580714DEST_PATH_IMAGE012
is the feed speed of the tool per unit time,in order to shorten the machining time, the machining time is shortened,
Figure 473901DEST_PATH_IMAGE016
the influence of the spiral lag angle of the position of the point P on the processing time of the point,，
Figure 873100DEST_PATH_IMAGE020
, is the spiral lag angle of the cutter corresponding to the P point,
Figure 549118DEST_PATH_IMAGE024
is the position angle of the point P
Figure 826778DEST_PATH_IMAGE026
The radial radius of the tool at (a),
Figure 872094DEST_PATH_IMAGE028
，
Figure 267304DEST_PATH_IMAGE030
is the radius of the ball end mill when not worn,
Figure 816097DEST_PATH_IMAGE032
is the angular velocity of rotation of the tool spindle,
Figure 904138DEST_PATH_IMAGE026
the included angle between the connecting line of the point P and the center O of the ball head and the main axis Z of the cutter is called a position angle, namely the angle describing the position of the cutting infinitesimal;
when the influence of tool wear is taken into account, as the tool wears, the radial radius corresponding to a point at the same height on the cutting edge
Figure 295806DEST_PATH_IMAGE024
And the corresponding position angle
Figure 494706DEST_PATH_IMAGE026
Will vary, and therefore, when considering the amount of tool wear during machining, the cutting trajectory of point P can be represented by equation (2):
Figure 898005DEST_PATH_IMAGE034
(2)
wherein,
Figure 156948DEST_PATH_IMAGE036
、
Figure 537376DEST_PATH_IMAGE038
in order to take into account the coordinates of the tool wear point P over the machining time,
Figure 274388DEST_PATH_IMAGE008
、the starting coordinates of the point P are shown,
Figure 227618DEST_PATH_IMAGE012
is the feed speed of the tool per unit time,in order to shorten the machining time, the machining time is shortened,
Figure 869000DEST_PATH_IMAGE016
the influence of the helical lag angle of the position of the point P on the machining time of the point P, and
Figure 512471DEST_PATH_IMAGE018
，
Figure 847638DEST_PATH_IMAGE022
is the spiral lag angle of the cutter corresponding to the P point,
Figure 576559DEST_PATH_IMAGE032
is the rotational angular velocity of the tool spindle;
Figure 281472DEST_PATH_IMAGE040
solving the radial radius of the ball head at the height of the P point after the cutter is worn by the formula (3);
Figure 779450DEST_PATH_IMAGE042
(4)
in the formula,
Figure 285518DEST_PATH_IMAGE044
is the radius of the ball-end mill when not worn,
Figure 501735DEST_PATH_IMAGE046
to cut the height of the cross-sectional plane where the infinitesimal element is located,
Figure 508874DEST_PATH_IMAGE048
is composed ofThe flank wear of the cutting edge of the tool at the height;
(2) the milling track obtained according to the milling track equation does not completely form the surface appearance of the workpiece, part of the track line can be cut off in the processing, only the outermost track line forms the surface appearance of the workpiece, and in order to determine the outermost track line, the position of the cutting edge of the tool corresponding to the outermost track line needs to be solvedAngle value range [ 2 ]
Figure 867940DEST_PATH_IMAGE050
，]Determining the value of,
Figure 608997DEST_PATH_IMAGE052
]Each within the interval
Figure 658861DEST_PATH_IMAGE026
The cutting trajectory lines of the cutter corresponding to the angles form the surface appearance of the machined workpiece by the collection of the cutting trajectory lines;
knife edgexThe shaft is fed in the feeding direction,ythe final paths left on the workpiece surface on both sides of the shaft are respectively
Figure 883169DEST_PATH_IMAGE054
Andto ensure the existence of the outermost path, the path of the cutting edge must satisfy the condition that the coordinate value of the intersection point of the path line and the feed axis is larger than the linear feed amount of the tool rotating for one circle
Figure 494596DEST_PATH_IMAGE058
Thereby obtaining formula (5):
Figure 533222DEST_PATH_IMAGE060
(5)
obtained by the above formula
Figure 295641DEST_PATH_IMAGE050
Is the minimum value that satisfies the condition;
the maximum value of the position angle is the position angle of the cutting point corresponding to the highest residual height of the surface appearance of the workpiece, namely the intersection angle of the front and back feeding of the cutter in the axial section in the vertical feeding direction;
to the right in the feed direction
Figure 477224DEST_PATH_IMAGE054
In the case of this segment of the trajectory,
Figure 932476DEST_PATH_IMAGE052
the size of (c) is discussed in two cases;
1) the first time of the feeding is carried out,can be directly dependent on the cutting depth
Figure 523043DEST_PATH_IMAGE062
And calculating the geometrical relation of the point with the maximum Z value in the contact points of the tool and the workpiece at the cutting depth to obtain an expression (6):
（6）
2) starting from the second feed of the machine,
Figure 185286DEST_PATH_IMAGE052
distance from feed
Figure 572405DEST_PATH_IMAGE058
The magnitude of (2) has a direct relationship, and the relationship (7) between them can be obtained:
Figure 904242DEST_PATH_IMAGE066
（7）
to the left of the feed direction
Figure 60417DEST_PATH_IMAGE056
In the case of a track, the position of the track,
Figure 857472DEST_PATH_IMAGE052
size and of
Figure 466308DEST_PATH_IMAGE054
There is a relative relationship, for the last feed,
Figure 390532DEST_PATH_IMAGE052
the size is represented by formula (8):
Figure 401214DEST_PATH_IMAGE064
（8）
during the process from the first feed to the penultimate feed, the outermost track line on the left side corresponds to
Figure 369170DEST_PATH_IMAGE052
The values of (A) are all represented by formula (9):
（9）
(3) in order to obtain various positions
Figure 911327DEST_PATH_IMAGE026
The cutting path line corresponding to the corner needs to obtain the outermost path lines respectively
Figure 166727DEST_PATH_IMAGE054
Segment and
Figure 305585DEST_PATH_IMAGE056
the time of tool movement in the interval is determined by determining the time of tool movement in the intervalPThe turning angle of the point is combined with the rotating speed of the main shaft of the cutter to obtain the corresponding processing time, and the spiral lag angle at the position of the cutting infinitesimal is considered, so that the appearance track at the outermost side can be obtained, and the appearance track is obtainedObtaining a surface appearance model of the workpiece;
to build up
Figure 889013DEST_PATH_IMAGE068
And
Figure 138729DEST_PATH_IMAGE070
corresponding corner
Figure 750101DEST_PATH_IMAGE072
Andformula (ii), analysis
Figure 130584DEST_PATH_IMAGE068
And
Figure 183990DEST_PATH_IMAGE070
turning a point in the milling process;
for the
Figure 23770DEST_PATH_IMAGE068
Point, from the starting point negative y-axis, at x =0 to
Figure 629064DEST_PATH_IMAGE068
When the following formula (10) is satisfied:
Figure 921505DEST_PATH_IMAGE076
（10）
namely:
Figure 778603DEST_PATH_IMAGE078
wherein,
Figure 472889DEST_PATH_IMAGE012
the feed amount of the ball head cutter in unit time,
Figure 750549DEST_PATH_IMAGE032
for the rotational speed of the tool shaft,Rwhich is the radius of the cutter,is composed of
Figure 191075DEST_PATH_IMAGE068
The angle of the position of the point or points,
Figure 739868DEST_PATH_IMAGE072
is a position angle
Figure 827909DEST_PATH_IMAGE080
At the corresponding corner of the tool and meet
Figure 219576DEST_PATH_IMAGE082
；
For the
Figure 152897DEST_PATH_IMAGE070
Point, from the starting point negative y-axis, at x =0 toWhen the following formula (11) is satisfied:
Figure 80719DEST_PATH_IMAGE084
（11）
namely:
Figure 195568DEST_PATH_IMAGE086
wherein,
Figure 198159DEST_PATH_IMAGE012
the feed amount of the ball head cutter in unit time,
Figure 721544DEST_PATH_IMAGE032
for the rotational speed of the tool shaft,Rwhich is the radius of the cutter,is composed of
Figure 252069DEST_PATH_IMAGE070
The angle of the position of the point or points,
Figure 792771DEST_PATH_IMAGE090
is a position angle
Figure 170663DEST_PATH_IMAGE088
At the corresponding corner of the tool and meet
Figure 771409DEST_PATH_IMAGE092
；
Solving the non-linear equations (10) and (11) by using a Newton iteration method to obtain corresponding positions
Figure 234751DEST_PATH_IMAGE026
The tool angle value of the angle, combined with the rotational angular velocity of the tool, can be used to determine the cutting time in the cutting section
Figure 205243DEST_PATH_IMAGE094
；
As the spiral cutting edge of the ball end mill causes spiral hysteresis, the spiral hysteresis influences the cutting time of the cutting points at different position angles, and further influences the cutting track, and each position angle
Figure 703221DEST_PATH_IMAGE026
Corresponding helical relief angle of tool
Figure 209288DEST_PATH_IMAGE022
Can be represented by formula (12):
Figure 425506DEST_PATH_IMAGE096
(12)
wherein,
Figure 432645DEST_PATH_IMAGE098
is the maximum helical lag angle of the cutter,time effects of helical lag for the position angle of the cutting point on the cutting edge of the tool
Figure 462098DEST_PATH_IMAGE100
；
The obtained position angle
Figure 900033DEST_PATH_IMAGE026
Range of (1), tool in
Figure 212328DEST_PATH_IMAGE026
Substituting the corner in the interval and the time for the cutter to rotate the corner into a cutting track equation (2) considering the cutter abrasion, so as to obtain the surface appearance of the workpiece milled by the ball-end milling cutter, which is expressed as an equation (13);
Figure 419318DEST_PATH_IMAGE102
（13）
。
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CN103713576A (en) * 2013-12-31 2014-04-09 南京航空航天大学 Modeling method for workpiece surface appearance machined through multi-axis milling
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