The key to less axis machining is the limitations of analyzing the results in determining part settings and tool path calculations. Machining environment and machinable conditions 1. Processing environment The machining environment used in this paper consists of a 3-axis vertical milling machine and a pitching indexing table as shown. If the workpiece coordinate system (WCF) turntable coordinate system (ICF) and the machine coordinate system (MCF) are respectively established. The ICF is placed in the center of the turntable and is affected by the pitch angle (1) and the corner (2) of the turntable. The dynamic structure of the configuration can be represented by a transition between the three coordinate systems. For ease of analysis, two additional coordinate systems O 1 and O 2 can be established between the MCF and the ICF, which are determined by the elevation angle (1) and the rotation angle (2) and the associated dimensions (a 1) and (d 2). The coordinate transformation of the MCF via O 1 , O 2, ICF to WCF can be expressed in a matrix as: T MCF, WCF = T MCF, O 1 TO 1, O 2 TO 2, ICF T ICF, WCF = T MCF, O 1 TO 1, ICF(1,2)T ICF, WCF(1) where: T MCF, O 1 represents the transformation from the machine coordinate system to the first coordinate system of the turntable, TO 1, ICF(1,2) represents the turntable The transformation of the 1 coordinate system to the center coordinate system of the turntable is affected by the rotation angles 1 and 2.
Substituting the geometric relationship, the above equation can be further expressed as: T MCF, WCF = 1 0 1 PX 0 1 PY 0 - 1 0 PZ 0 1 C 1 C 2 - C 1 S 2 S 1 d 2 S 1 + a 1 C 1 S 1 C 2 - S 1 C 2 C 1 d 2 C 1 + a 1 S 1 S 2 C 2 0 1 = C 1 C 2 - C 1 S 2 S 1 d 2 S 1 + a 1 C 1 + PXS 2 C 2 0 PY - S 1 C 2 - S 1 S 2 C 1 d 2 C 1 - a 1 S 1 + PZ 0 1 (2) where: C i = cos(i) , S i = sin( i), i = 1, 2, i < - i, + i > and - i, + i are the limit rotation angle of the turntable.
1. 2 Machinable conditions For a tool axis vector (t), the machined surface (S t) refers to the tool at the corner limit (i, i) and the stroke limit (L -, L +, L = X, Y, Z) does not interfere with other surfaces or fixtures within the processing limits given.
If the surface of the ball end mill with a radius of R is S ( u, w ), it should be able to generate a set of tool position ( CL ) data indicating the movement position of the tool center. Assuming that the tool position data is subjected to interference check, the tool position data CL j, j < 1, N > should be able to completely avoid interference within the tool movement range.
Visibility conditions: (a) shows two tool vectors and the corresponding range that can be machined by the two axes. Obviously, the machinability is related to the visibility of the tool axis vector to the tool point. The tool vector starting from CL j is represented by tj, then, if tj does not intersect the part side surface (S( u, w )), CL j can be seen by the tool axis direction tj.
This gives the following visibility conditions: tj S( u, w ) = ( 3) Of course, the actual analysis of the interference problem with CAD also takes into account the influence of the tool diameter. The visibility of the tool path indicated by the tool line connection (CE j = CL j CL j + 1) list data is displayed. Also note that the toolholder will collide with other surfaces and fixtures of the part, as well as the machine's travel limit and the pitch of the pitch turret.
From the view of the machinable conditions, there may be more than one cutter axis vector satisfying the machining conditions, the surface a may be machined by the cutter shaft 1 or the cutter shaft 2, and the surface b may only be machined by the cutter shaft 2. Since the tool axis direction is obtained by the turntable device, the number of tool axis settings should be minimized to reduce the total cycle time. Let S t be the surface that can be machined by the tool axis t, then the entire surface should be covered by the union of S t t < 1, N t > , ie S ( u, w) N tt = 1 S t(4) Medium N t is the number of cutter axes (or the number of surface element settings). 2Division of machining space The tool axis vector is established to analyze the direction of the tool axis corresponding to different surface elements, which can discretize the relative movement range of the tool defined by the rotary table rotation limit. To determine the tool axis vector. To this end, the equidistant point can be used to discretely move the tool on the unit sphere, divide the sphere into strips along the longitude line, and then further decompose the annulus a into a point, taking d = / ( + 1) as the two points For the distance, a = < (2sin( a / ( + 1) ) / (? / ( + 0. 5))) + 0. 5> ( 5) The value should be properly determined so that the spacing satisfies the solution accuracy. The tool axis can then be expressed as: ti = OQ a, ba < 1, > b < 1, a > (6) where: O is the center of the sphere, and a and b are the marks corresponding to the revolution i.
The above formula is only a spatial division considering the accuracy of the solution. In order to finalize the tool vector, the indexing accuracy of the turntable should also be considered. To do this, it is also necessary to modify the tool vector with the angle value obtained by the turntable, ie a) calculate the swivel angle (i1, i 2) according to ti ((6)); b) take the closest value (i2) that can be obtained from the turntable ) Adapt ti to replace ti.
The latter work is to find out all the CL tool edge lines that can be machined by each tool axis ti, and generate tool path by region, which can be easily realized in the general CAM software package. The number of cutter axes may be reduced considering the actual shape of the part.
3 Conclusions This paper describes a method for performing 5-axis machining with a less-axis CNC machine. Less axis machining has its inherent limitations because the tool direction is achieved by the discontinuous motion of the pitch table, which results in an increase in set time and a smooth surface at the tool path where the machining path is discontinuous. Try to limit these problems when doing small-axis machining, which makes the tool path planning problem more complicated than pure 5-axis machining, but its processing environment is easy to implement, so there are certain problems for those small and medium-sized enterprises to solve the 5-axis parts processing problem. D.
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