Arc section starts, then processing 
Straight lines, rough, it seems that there are only two programs on it. But this is not the case, because the first program section processes the arc , tool center along the arc 
movement. At the end, the center of the tool stops at point B'. If you follow the second procedure, you obviously won't get a straight line. The part shape can be machined correctly only if the center of the tool is moved by an additional program from B' to B'' segment. The B'B'' block is called "an additional program for non-smooth transitions." Obviously, in order to make the tool center go from B' to B'', the best way is to take a circle with point B and radius r. Therefore, the additional program is essentially the circular interpolation, B point is the center of the arc, the starting point is B', the end point is B'', the arc radius is the tool radius r.
Figure 2-49
Taking the polar coordinate input method as an example, the input data of this program is cosα, sinα, cosβ, sinβ, and the radius of the arc (equal to r) does not need to be input by the punched tape, and has been dialed out on the tool radius dial. Therefore, the start and end coordinates of the additional block are
The total number of steps that should be taken in both x and y directions is
From the above equation, the additional program is actually a special case of tool offset calculation, that is, R=0.
It can be seen that in the B tool compensation, the sharp corner transition and the same tool offset calculation as the part contour are separated. Especially for the sharp corner transition procedure, the programmer must give enough attention to it and write it carefully.
Figure 2-50B Cross Point and Interruption Point of Tool Compensation Actually, when the programmer compiles the program according to the contour of the part, each program segment is continuously transitioned, there is no break point, and there is no overlap segment. However, after the tool radius compensation (B tool compensation) is performed, discontinuities and intersections may occur in the tool center trajectory between two blocks. As shown in Figure 2-50, the thick line is the programmed contour. When machining the outer contour, the discontinuity A'B' will appear; when the inner contour is processed, the intersection C'' will appear.
For CNC systems with only B tool compensation, the programmer must first estimate the discontinuities and intersections that may occur after tool compensation and perform human processing. If a discontinuity is encountered, a transition arc segment with a radius of tool radius can be added between the two discontinuities. . When crossing points are encountered, a transitional arc segment is added in advance between the two program sections. The radius of the arc must be greater than the radius of the tool used. Obviously, this CNC system with only the B tool compensation function is very inconvenient for programmers.
However, the earliest and most easily thought tool radius compensation method is that the numerical control system calculates the transfer intersection points C' and C'' of the tool center trajectory directly based on the same programming track as the actual contour. The program trajectory is corrected for elongation or shortening.
In the past, C' and C'' points were not easy to obtain, mainly due to the limitation of the speed and hardware structure of the NC device. With the development of CNC technology, the system work method, calculation speed, and storage capacity have greatly improved and increased. Using linear or circular transitions, the tool radius compensation method that directly determines the intersection point of tool center trajectory has been realized. This method is called C function tool radius compensation (referred to as C tool compensation or C tool compensation).
2. The basic design idea of ​​C knife compensation
The main reason that the former tool compensation method (B tool compensation) restricts the programming is to determine the tool center trajectory, and to use a read section, a section, and a section of the control method. In this way, it is impossible to predict the influence of the next machining trajectory caused by the tool radius on the machining trajectory of this section. Thus, for a given machining contour track, when processing the inner contour, in order to avoid tool interference, reasonably selecting the radius of the tool and selecting the appropriate transition arc at the transition of the adjacent machining track, it is necessary to Deal with the programmer.
In order to solve the influence of the next trajectory on the processing trajectory of this section, after the trajectory of this section is calculated, the next section of program is read in advance, and then the trajectory of this section is appropriately modified according to the specific conditions between them. Get the correct processing path for this section.
3, analysis of transfer between blocks
In the CNC system, the most basic contour types that can be controlled are straight segments and circular arc segments. With the different connection modes of the two preceding and following programming trajectories, the corresponding transfer methods are: straight line and straight line transfer; circular arc and arc transfer; straight line and arc transfer. According to the difference between the vector angle α of the two program trajectories and the tool compensation direction, there are the following transitional transition modes: extension type, shortened type, and insert type. The insertion type is divided into two transitional modes, namely the linear transition type and the arc transition type. Introduced separately below.
1) Straight line and straight line transfer
Figure 2-52 shows the situation where the straight line intersects the straight line and left tool compensation is performed. The programming track in the figure is OA→AF.
In Figure 2-52(a), (b), AB and AD are the tool radius. Corresponding to programming tracks OA and AF, the tool center trajectories JB and DK will intersect at point C. In this way, the length of CB and DC will be shortened relative to OA and AF. Therefore, this transfer is called a shortened transfer.
In Figure 2-52(d), point C will be on the extension of JB and DK, so it is called an elongate transfer.
For Figure 2-52(c) and (e), if the extension type transfer is still used, it is necessary to increase the idle travel time of the non-cutting tool. To solve this problem, you can use two methods:
(1) Insert a straight line. Let BC be equal to C'D and equal to the tool radius lengths AB and AD, and insert the transition straight line CC' in the middle. That is to say, the center of the tool must be extended by one edge in addition to the length of one tool radius along the original programmed path. The movement of line CC'. For the original program segment, it is equivalent to insert a program segment in the middle, saying that this transfer type is an insert type transfer.
(2) Insert an arc. Insert an arc between tool center trajectories JB and DK 
The center of the arc is at point A, and its radius is the tool radius length AB.
Obviously, the arc insertion type switching is simpler than the straight line insertion type switching. However, the arc insertion type also has a disadvantage. When the tool moves from point B to point D along the arc BD, the contour is always in the cutting state at the sharp corners. The craftwork of the sharp angle machining is relatively poor, which is particularly prominent in the grinding process. The required sharp corners are often machined into small rounded corners.
Figure 2-53 shows the case where the right tool compensation is performed with straight lines connected to the straight line.
When the straight line is linear in the same coordinate plane, when the angle α between the first programmed vector counterclockwise and the second programmed vector changes within 0° 360°, the transfer of the corresponding tool center trajectory will be sequentially In the above three types of ways.
In Figure 2-52 and Figure 2-53, 
Programming vector for the first paragraph, 
The second stage programming vector, the angle α is the anti-clockwise turning ∠GAF.
Corresponding to Fig. 2-52 and Fig. 2-53, Table 2-11 lists all the classifications of transfer when the straight line and the straight line are connected.
Table 2-11 Transfer Classification When Rectilinear Straight Lines
Connection of programming tracks
Tool compensation direction
Sina>=0
Cosa>=0
Quadrant
Transfer type
Corresponding figure number
G41G01/G41G01
G41
1
1
I
shorten
2-52(a)
1
0
II
shorten
2-52(b)
0
0
III
insert
2-52(c)
0
1
IV
elongation
2-52(d)
G42G01/G42G01
G42
1
1
I
elongation
2-53(a)
1
0
II
insert
2-53(b)
0
0
III
shorten
2-53(c)
0
1
IV
shorten
2-53(d)
2) arc and arc transfer
In the same way as when a straight line is connected to a straight line, the distinction of the transfer type when the arc is connected to the arc can also be determined by the size of the angle α between the starting point and the end point radius vector of the adjacent two circles. However, arcs are often equivalent to straight lines for ease of analysis.
In Figure 2-54, when the programming path is 
Pick up 
Time, 
with 
The radius vectors are the start and end points respectively. If the left tool is G41, the angle α will still be ∠GAF. Take Figure 2-54(a) as an example:
Comparing Fig. 2-52 and Fig. 2-54, the classification and discrimination of their transfer patterns are exactly the same, that is, when the left tool compensation is rounded to G41G02/G41G02, its transfer type is equivalent to the left. The tool compensation line is connected to the straight line G41G01/G41G01. Transfer
3) Straight lines and arcs
Figure 2-54 can also be seen as a connection between a straight line and an arc, that is, the G41G01/G41G02 connection (OA connection ) and G41G02/G41G01 ( Connect AF). Therefore, the discrimination of their transit types is also equivalent to the straight line G41G01/G41G01.
From the above analysis, it can be seen that, according to the three conditions of the cutter compensation direction, the equivalent law, and the variation of the α angle, the classification of the transfer forms among the various trajectories is not difficult to distinguish.
See related literature. Figure 2-55 is a block diagram of the software implementation to determine the transfer classification when a straight line is connected to a straight line.
Of course, in the actual calculation, the tool radius vector in Figure 2-52 to Figure 2-54 is also 
, 
, and the vector from the straight-line transfer point to the intersection point of the center of the tool 
, 
Etc. The detailed calculation process of these vectors will not be repeated. Readers can refer to relevant literature.
Figure 2-55 Software implementation of straight-line straightforward switching classification
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