The main requirements for high-speed cutting (HSC) are the ability to machine three-dimensional complex curves and surfaces with high cutting speed, efficiency and machining quality. The so-called complex curves and surfaces mean that they are more complex in shape and cannot be described by quadratic equations, also known as free-form curves and free-form surfaces.
For example, forging dies for the manufacture of insulating parts for the air cable line clamping of urban bus lines are now directly manufactured by high-speed milling using hardened steel (hardness 52HRC). This hard milling process saves a lot of time compared to conventional manufacturing methods that first make graphite electrodes and then use EDM, but require specialized tools and appropriate high-speed milling strategies. Due to the change of the cutting condition, the shape accuracy of the part is required to be within ±0.02mm and the surface roughness Ra < 0.7μm, it puts high demands on the trajectory control quality and adjustment precision of the machine numerical control (CNC) system.
In the process of new product development and manufacturing, firstly, the CAD system is used to draw the sketch of the profile according to the function and design requirements of the product. Then, according to the HSC milling strategy, the coordinates and motion trajectory of the rough finishing are accurately calculated and compiled by the CAM system. CNC machining program. The complex contour curve of the surface of the part is approximated by a segment of a straight line or a quadratic curve such as a circular arc or a parabola. The NC machining program divides the block by the intersection of the approaching line segments. Within the allowable error range, the larger the approximate interval spanning the line segment, the less the number of nodes, and the fewer the corresponding blocks.
The basic task of the CNC system is to calculate the feed command along each axis of the machine according to the programmed part program, and drive each axis to obtain the required trajectory of the tool relative to the workpiece, which needs to be interpolated. Calculation processing. At this time, the simple trajectory description of the CNC is fundamentally different from the mathematical description of the CAD/CAM system.
1 computer numerical control interpolation
The task of interpolation is to calculate the coordinate values ​​of several intermediate points between the start and end points of the trajectory motion specified by each approach line segment according to the required feed speed and tolerance. Since the time required to calculate the coordinates of each intermediate point directly affects the control speed of the CNC, and the calculation accuracy affects the control accuracy, the interpolation algorithm is crucial to the performance of the CNC system.
Linear interpolation
Straight lines and arcs are the basic lines that make up the contours of the parts. Generally, CNC systems have linear and circular interpolation functions. The linear interpolation currently dominant is simple and widely used, but there are a series of problems that need to be solved. In the case of linear interpolation in conventional CNC systems, it is necessary to use a high-precision surface description to make an approximation, that is, to select a small string error. When the surface contour of the part is complex and the curvature of the curve changes greatly, it is necessary to increase the number of intermediate calculation points, which leads to the expansion of the numerical control program and the extension of the execution time, and often there are local programs of several tens of MB scale.
The CNC system has a certain working rhythm, that is, the interpolation period T, which is usually 1 to 10 ms. Its relationship with the interpolation period motion step length L (mm) and the maximum feed speed Fmax (m/min) is Fmax = 60 (L/T).
Figure 1 Interpolation cycle problem in linear interpolation 
Figure 2 Acceleration jump in linear interpolation 
Figure 3 Linear interpolation produces facets and vibrations on the surface of the workpiece 
After the interpolation period T is selected, the short interpolation length L is selected due to the machining accuracy requirement, which not only generates a large amount of calculation data, but also directly limits the maximum feed speed, which is called the interpolation cycle problem, which is required for high-speed cutting. The high trajectory feed rate conflicts, as shown in Figure 1. The result is reduced productivity and machining accuracy, especially for single-piece, low-volume production of models and molds, steam turbine blades or aircraft fuselages.
Linear interpolation forms a polygonal wire. Strict machining along this wire will produce high axial acceleration at the transition of the straight segment, as shown in Figure 2. In theory, this acceleration tends to infinity. The CNC must ensure that the dynamic characteristics of the axes, ie the maximum permissible acceleration, are not exceeded. This can only be achieved by greatly reducing the speed of the trajectory at the sharp corners, with the result that machine productivity is reduced.
If the adjustment system does not have a follow-up function, the jump of the acceleration can also cause the machine to vibrate and cause a great load on the feed axes of the machine. In summary, linear interpolation produces not only facets but also vibration patterns on the surface of the workpiece, see Figure 3.
Spline interpolation
Compared with linear interpolation, quadratic interpolation such as arc, parabola, ellipse and hyperbola is more accurate, and circular interpolation is most commonly used. The NURBS (non-uniform rational B-spline) interpolation method that directly processes spline blocks has many advantages and is increasingly used. As a rule of thumb, a spline block can replace 5 to 10 linear blocks with the same precision. The programming of the popular polygons to date will be a method of transferring spline trajectories directly from the CAM system, or by a geometric transformation inside the CNC, ie, a compressed linear block.
The NURBS function based on the cubic B-spline function has a tunable parameter, the constant weight factor wi, which can flexibly and accurately control the shape of the approximation curve or surface, and can accurately represent all quadratic curves and surfaces, including conic curves, Standard geometry such as balls, columns, cones, etc. With the help of the NURBS function description, all curves and surfaces have a uniform mathematical expression in the CAD/CAM system, thus facilitating the management of data exchange between systems.
The CNC needs to pass the coefficients of the NURBS cubic polynomial for each feed axis, for example x(t)=a·t3+b·t2+c·t+d for the x-axis. These spline data must be able to reduce the total amount of data while providing the necessary tangential and curvature continuous block transitions for smooth machining. The CNC is required to automatically smooth the motion trajectory to achieve a smooth surface of the part by specifying the way to refine the polygon block.
2 Other functions of computer numerical control
Modern CNC systems are based on digital signal processing and bus-connected components and use highly integrated electronic components. One of the most important functions of the CNC for HSC is the precise control of the feed drive and the ball screw. The traditional analog connection between them is now replaced by a drive for digitally regulating and digitizing the bus in parallel.
The digital bus parallel connection drive interface for HSC technology has a series of advantages, such as greatly improving the resolution of the CNC and improving the accuracy, which can weaken the interference in the network, eliminate the drift and its adverse effects, and avoid the analog noise on the surface of the workpiece. The graphic pattern is generated, which enables detailed diagnosis and analysis of numerous driving functions, which is easy to put into operation and parameterization of driving in the CNC.
By compensating for machine stiffness and trajectory errors such as limiting reversal and pre-control of speed and torque, a wide variety of adjustment configurations can increase productivity and part machining accuracy. High-resolution digital speed and position detection with digital drive adjustment enables higher-order adjustment algorithms, especially by pre-controlling the speed and torque to compensate for trajectory errors caused by inertial motion, which is at the path feed rate High, especially when generating drag errors. In addition, it can automatically perform various detections such as frequency and roundness, and can automatically optimize compensation such as quadrant error compensation by means of neural network. It can be connected to a direct linear drive such as a linear motor, which can be doubled with a CNC processor and a drive processor. Guarantee the safety of the machine tool.
CNC function for HSC
When the trajectory movement speed is high, only the adjustment strategy with no drag error can meet the machining accuracy requirement, and the speed gain has no damping at the usual Kv=1~4(m/min)/mm, so the feed axis The interpolation control is significant. In order to meet the special requirements of HSC, it is necessary to research and develop new trajectory interpolation, velocity control and geometric transformation methods.
The previous section describes the high-order interpolation method and the fast interpolation technique that accurately describe the machining path. In addition, the CNC for HSC must meet the following requirements: speed pre-control (forward-looking function) of more than 100 blocks, compensate for mechanical errors; geometric transformation (such as correction during clamping or 5-axis transformation) The feed axis has no adjustment of the drag error to ensure high track accuracy; the reverse direction of the track and the axial limit are used to protect the machine tool, the tool length, radius, and type are compensated; it can be safely operated in the machine tool workspace.
Speed ​​pre-control
The task of speed pre-control (forward-looking) is to identify the block transitions with discontinuous speeds and the acceleration of the feed axis being too high due to the curvature of the path. The execution time of the NC block is shorter than the acceleration and brake gradient times necessary for the cutting speed. The prerequisite for continuous processing of NC blocks is to have a program buffer under pre-monitoring. It should be noted that the technically necessary low acceleration increases the look-ahead distance required for speed pre-control to 50 to 150 blocks when the path feedrate is high and the block is short. If there is only a small look-ahead buffer, the path feedrate must be limited so that the brake gradient time at any point in the program can be observed.
Multi-axis transformation and coordinate transformation for tool compensation
Three-dimensional machining in a rotating coordinate system, such as machining a bevel, requires an increase in the amount of data necessary in an offline calculation program. At the same time, it is necessary to calculate and determine the tool parameters such as the tool type, radius and length in the CNC program. Through the geometric transformation in the CNC, the tool compensation can be performed directly on the machine and the post-processing is omitted.
With the ball-end milling cutter for 3-axis machining, only a small portion of the 5-axis milling machine can be utilized. High cutting efficiency can only be achieved with cylindrical and circular milling cutters. In order to achieve maximum cutting efficiency while machining any contoured surface with high quality, they are required to have a defined spatial orientation with respect to the milling cutter trajectory. In order to ensure that the tool contact point falls on the trajectory, many intermediate steps must be inserted in the conventional 5-axis programming that uses the rotary axis to determine the tool orientation.
The 4-axis and 5-axis transformations take on the task of keeping the spatial position of the tool tip constant when the tool orientation changes. The programmed feed parameters only relate to the spatial path of the tool tip. The direction of the tool can be determined by programming the rotary axis position, tool direction vector or Euler angle. The correction of the spatial geometry of different types of milling cutters (such as cylinders, rings and cones) is complemented directly by the CNC. The result is that different tools can be applied to the same NC program.
Polar coordinate transformation is mainly used for turning machining centers, non-circular grinding and high-speed milling of round or spiral parts. Combining the rotation axis with the linear movement axis avoids changing the direction of each coordinate axis of the Cartesian coordinate system and causing the deviation of the theoretical trajectory. An important advantage of this transformation is that the programming of the feed is only related to the tool path, not to the angular velocity as in the programming of the rotary axis. All interpolation methods (line, arc, spline) can be applied in this transformation. The CNC is responsible for tool compensation calculations and monitors all limits in the direction of the path and the direction of the feed axis.
The cylindrical transformation allows the programmer to view the tool path of the cylindrical surface as a virtual XY plane. At this point all geometric representations and feeds are based on the surface of the part, independent of the size of the cylinder radius.
Error compensation
As long as the cost permits, the CNC system should be required to compensate for the machine's static error, thermal error, and dynamic error of the feed axis adjustment. This can achieve the machining accuracy of the parts, and it takes a high price to achieve mechanical compensation in the past.
The error compensation that is of great significance to the application of HSC technology is to compensate for the thermal error caused by the high temperature of the screw and the high speed of the feed axis, and compensate the friction error (quad error) at the reversal point of the feed axis. Compensate the lead lead lead error and measurement system error, compensate the machine tool angle and deflection deformation error by means of interpolation technology, and compensate the indirect measured shaft slack.
Safety of personnel, machine tools and parts
The current safety regulations that are in force for all types of machine tools require the use of a casing to enclose the machine's working space. This prevents the operator from intervening in the operation of the NC program as necessary in many situations. Especially in large machine tools in the manufacture of models and molds, it is very important that the operator or the machine tool installer and debugger skillfully perform the identification in the automatic operation of the program. For security reasons, this requirement can only be achieved through a large-scale restriction and surveillance system in the CNC. In addition to the machine functions monitored by the hardware, first of all, reliable two-channel monitoring of the screw speed and feed motion is included.
3 Conclusion
NURBS spline interpolation is used in computer numerical control for high-speed machining, which can overcome the lack of control precision and speed during linear interpolation. Through high-speed computer numerical control speed pre-control, multi-axis transformation and coordinate transformation to achieve tool compensation, error compensation, labor safety protection and other functions, not only can improve feed rate and cutting efficiency, but also improve the processing accuracy and personnel of complex contour surfaces Equipment security. The high-tech requirements for high-speed machining on computer numerical control systems can only be realized by applying digital drive regulation and bus technology.
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