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introduction

NURBS has been widely used in the field of CAD. However, the application in the CAM field is relatively lagging. High-speed and ultra-high-speed machining are characterized by high efficiency, high precision, high flexibility and high quality. They are used not only in aluminum, cast iron and steel, but also in the processing of high-hard materials. It is regarded as a new direction in the field of modern processing technology. Compared with traditional CNC machining, high-speed machining has different requirements for machine tool spindles, tools, CNC systems, servo feed systems and CNC programming methods. The application of NURBS interpolation technology in the field of CNC machining is a supporting technology developed along with high-speed machining, which will greatly improve the overall level of CNC machining technology. Over time, its superior technical performance will be further developed.

With the rapid development of high-speed machining, the application of NURBS in the field of CAM has received widespread attention. Many high-end CAM systems already support NURBS interpolation toolpaths. As part of the CAD/CAM information materialization, some CNC systems such as FANUC, SIEMENS and Mitsubishi have supported NURBS interpolation.
The p-order NURBS curve is defined as

1

Where P i is the control point (forming the control polygon); w i is the weight factor; N ip (u) is the p-order B-spline basis function, and its node vector is U={a,...,q,up+1, ..., um-p-1, b, ..., b} Unless otherwise stated, a = 0, b = 1 is assumed and w i < 0 for all i.
make

1

Then the NURBS curve equation can be written

1

1 NURBS interpolation tool rail

There are two ways to implement NURBS interpolation processing:
1. Through the machine tool numerical control system, the linear interpolation tool path generated by CAM is processed into NURBS interpolation tool path within the given tolerance, so-called “smooth interpolation” (such as GE Fanuc CNC system), and finally by CNC The system performs NURBS interpolation operations (see Figure 1). However, the conversion from the linear tool path of the CAM to the NURBS tool path of the CNC can be done by the CNC system or by special post-processing, in which additional errors are added. However, the smoothness of the machined parts has been improved, so it is called "smooth interpolation".

1

Figure 1 The first NURBS interpolation processing method

1

Figure 2 The second NURBS interpolation processing method

2. The geometric model defined by NURBS in CAD is converted into NURBS tool path by CAM system. The numerical control system performs NURBS interpolation operation by three types of parameters (control point, weight factor and node vector) in the tool path (see Figure 2). . This method does not have the method error of converting the linear tool path into the NURBS tool path, and the precision is higher, which is a more effective method.

Since NURBS interpolation has only been developed in recent years, there is no uniform standard format. Manufacturers develop NURBS format in their own way. CAD/CAM developers, machine tool manufacturers, end users and CNC control system manufacturers need to be unified. The NURBS standard has benefited from it, and the unified NURBS standard is also a sign that NURBS technology is maturing. The typical NURBS interpolation G code format is as follows (such as FANUC):
G06.2 P_K_X_Y_Z_R_F_
K_X_Y_Z_R_
...
K_X_Y_Z_R_
K_
K_
K_
Among them, G06.2 represents NURBS interpolation; P represents NURBS times; K is a node; X, Y, Z represents the coordinates of the control points; R represents the weight factor; F represents the feed rate.
The advantages of the NURBS interpolation tool track are mainly reflected in:
  1. In the high-speed machining of complex-shaped parts, the straight-line segment is used to approximate the shape of the part. In order to ensure the machining accuracy, the displacement defined by each NC code is small, so the NC code becomes very large, and the NC code of the three-dimensional part is generally longer than the NURBS tool path. 10 to 100 times. Due to the limited memory of the CNC system, it is often required to input the NC machining code into the CNC system in batches during the machining process. The DNC implements NC code transmission through serial communication. The transmission speed is generally between 110 and 38,400 baud, and the most common is 9,600 baud. If the average number of characters per NC code is 20 characters and the DNC transmission speed is 960 characters per second, only 48 NC codes can be transmitted per second. The actual transmission speed can only reach about half of the theoretical value. In this case, If the displacement defined by the NC code segment is 0.25mm, the machining feed rate that DNC ​​can satisfy is 360mm/min, which can not meet the requirements of high-speed machining, which affects the machining speed and makes the performance of the machine tool difficult to fully exert. One way to solve this problem is to use the NURBS tool path, and the second is to use the computer numerical control system network (DCN). The DCN transmission speed is about 1,000 times that of the DNC transmission speed.

1

Figure 3 Linear interpolation and NURBS interpolation feed rate changes

2. In linear interpolation processing, in order to reduce the speed impact of the linear end, the monitoring function of the CNC system to be processed (ie, the “feedforward” function) is continuously accelerated and decelerated at the straight end, and the NURBS interpolation tool rail is within the allowable machining direction. Internally, no acceleration or deceleration is required, which increases the machining speed (see Figure 3).

3. In the high-speed machining, the NC code block processing capability of the general CNC system often cannot keep up with the high-speed processing speed of the code segment; or the processing speed is reduced; or the high-speed sacrifice accuracy is maintained (increasing the length of the straight line segment to improve the code execution time); The displacement of a section of NURBS interpolation tool often includes the displacement of the linear tool path of 10 to 100 segments, which reduces the requirement for the NC code block processing capability of the CNC, and thus can often meet the requirements of high-speed machining. Table 1 compares the NURBS interpolation and linear interpolation processing of a part. It can be seen from the table that the NURBS interpolation is reduced by more than 30% compared with the linear interpolation processing time.

Table 1 Comparison of NURBS Interpolation and Linear Interpolation Processing
Interpolation method Standard mode Quick mode Finishing mode
NURBS 102min 5s 75min 37s 111min 4s
Linear 141min 56s 124min 54s 157min 38s

4. NURBS interpolation avoids the use of straight lines, thus improving the machining accuracy of the workpiece and improving the surface quality. As shown in Table 2, taking the CNC system of the usual 1ms servo cycle as an example, even if the feed speed is 30m/min, the displacement in the unit servo period is only 0.5mm, that is, in the NURBS interpolation. Approximating with a linear displacement of 0.5 mm. If the linear tool path has a displacement increment of 0.5 mm, the code file becomes large and it is almost impossible to perform economical and reasonable processing.

Table 2 Relationship between feed rate and displacement increment
Servo cycle
Ms 		Incremental displacement at different feedrates during the servo cycle
Mm
2.5 10 18.8 30
20 0.833 3 3.333 3 6.266 6 10.000 0
10 0.416 6 1.666 7 3.133 3 5.000 0
3 0.125 0 0.500 0 0.940 0 1.501 5
1 0.041 6 0.166 7 0.313 4 0.500 0
0.4 0.016 7 0.066 7 0.125 4 0.200 0
0.1 0.004 2 0.016 7 0.031 3 0.050 0
Some high-end CAM software already supports NURBS interpolation toolpath. For example, UG introduces three-coordinate NURBS interpolation from V13, and V16 introduces the first commercial CAM software package that supports five-coordinate NURBS interpolation. The five-coordinate NURBS interpolation high-speed milling can achieve extremely high precision mirror processing, which represents the future development direction of CNC machining.

2 NURBS interpolation of computer numerical control system

It can be seen from Fig. 1 and 2 that in order to realize NURBS curve interpolation, the machine numerical control system must have the function of supporting NURBS interpolation. Currently, some numerical control systems including FANUC, SIEMENS, Mitsubishi, etc. are supported by NURBS interpolation, and most of the control systems The system only supports interpolation such as straight lines and arcs. For linear interpolation, the machining displacement is determined by the displacement defined by the code segment. Because the too small displacement will make the NC code file too long, affecting the processing speed, DNC communication can not meet the transmission requirements of the code, so each NC code is less than 0.25. The displacement of mm is generally difficult to meet the processing requirements. For NURBS interpolation, the CNC system itself calculates and generates an interpolation path for the NURBS curve path based on the interpolation rate. The so-called interpolation rate (or interpolation time, servo period) is a time period in which the index control system measures the actual position of a table and sends a certain number of pulses to the drive axis. During this time, the CNC system is linearly driven. . The shorter the interpolation rate, the smaller the interpolation point distance and the higher the machining accuracy of the part. Table 2 lists the relationship between the interpolation rate, the feed rate and the minimum machining displacement. It can be seen from Table 2 that the commonly used 1 ms interpolation rate can meet the general requirements. The numerical control system of 3D surface high-speed machining of Creative Technology in the United States has an interpolation rate of only 0.11 ms, making it possible to process extremely high precision. The interpolation rate is an important technical parameter of the numerical control system. The numerical control system itself calculates and generates an interpolation path for the NURBS curve path according to its interpolation rate. The shorter the interpolation time (interpolation rate), the smaller the interpolation point distance, and the higher the machining accuracy of the parts.
The relationship between the chord length error D d and the interpolation rate t is as follows
D d = l 2 = v 2· t 2
8 r 8 r
Where: r is the radius of curvature, v is the feed rate, and l is the chord length.
It can be seen that reducing the interpolation rate will improve the machining accuracy by the square relationship. For example, in the shape of curvature radius r = 50mm, processing at 18.8m/min, the numerical control system interpolation rate is 1ms, then the interpolation length is known from Table 2. l =0,313mm, chord length error D d =0.245μm, so even for high-speed machining, the accuracy can be controlled within 1μm. It can be seen that the interpolation rate is an important technical index of the numerical control system. The low interpolation rate and NURBS interpolation are effective ways to improve the machining accuracy. The core of the NURBS curve interpolation on the CNC is the implementation of the interpolator, and the key to the interpolator algorithm is the interpolation speed.
The monitoring of the trajectory to be processed (ie “feedforward”) is a key technology of the numerical control system. The working principle is that the computer control system scans the NC code to be processed while controlling the machining, and dynamically adjusts the feed according to the change of the feed direction. Speed, if the feed direction changes drastically, the trajectory monitoring will be decelerated in some way in advance to avoid overcutting and residual due to machine characteristics. If the feed direction is flat, the feed rate will be increased to the maximum speed quickly. Programming speed, the trajectory monitoring can change the feed rate more than 2,000 times per second to achieve the shortest part processing time, which requires the CNC machine to meet the rapid change of this speed. The linear interpolation tool path is processed by reading in the pre-processing block. The speed change is realized by the displacement of the NC code segment. The NURBS tool path can change the speed with the control point and interpolation rate of the NURBS. The adjustment of the speed is finer, and since the NURBS tool path direction is also smaller than the linear tool path change, the cutting is allowed to be performed at a higher speed. In order to realize the feedforward monitoring of NURBS interpolation, in addition to the higher requirements for the acceleration and deceleration of the machine tool, the key is to realize the intelligent NURBS interpolation based on the continuous dynamic control feed rate, that is, according to the direction change of the NURBS tool path. Feeding speed, this is the direction of future research. In addition, the development of four- and five-axis NURBS interpolation based on three-axis NURBS interpolation is also the focus of future development.
NURBS interpolation achieves high surface cutting speeds, which means that high spindle speeds are required to meet the requirements (especially for small tool machining).
In summary, high-speed spindle systems, rapid feed systems, and high-performance CNC control systems are necessary conditions for high-speed machining of NURBS interpolation.

3 Conclusion

NURBS curve interpolation can provide smooth and stable high-speed, high-precision machining. It is a new interpolation method and is becoming a supporting technology for NC manufacturing technology. CAD/CAM, CNC and tool manufacturers need to work together to solve the key technologies of NURBS interpolation and provide end users with a unified NURBS interpolation standard.

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