The appearance of virtual axis CNC machine tool is considered as the most revolutionary machine tool design breakthrough in this century.If we give full play to the advantages of this new machine tool in structure, it is possible to open up a new way to greatly improve the performance of the machine tool.

Through the analysis found that for general directly based on the principle of Stewart platform of virtual axis machine tool, the motion of rotating coordinates reasonable five coordinate nc machine tools is much smaller than regular (usually only 20 ~ 30 degrees, and five coordinate of machine tool can reach above 90 degrees), and with the increase of rotation Angle will dramatically reduce the size of the effective work of machine tools.Although the compound structure can expand the Angle range, but the structure is complex, it is difficult to ensure high stiffness, therefore, the common virtual axis machine tool is not suitable for processing large range, multi-coordinate motion parts.However, from another point of view, in the actual production of complex parts requiring multi-coordinate processing is a small number, and the dominant position is still the processing of ordinary conventional parts.Therefore, it will be of more practical significance to study how to make use of the structural characteristics of virtual axis machine tool to play its advantages in high-speed and efficient processing of conventional parts.

The basic idea of imitated triaxial control method for virtual axis machine tool is to control the six degrees of freedom movement of virtual axis machine tool by imitating the control method of existing three-coordinate CNC machine tool.In this way, not only the existing mature three coordinate automatic programming system can be directly used for six degrees of freedom of the virtual axis machine tool, but also through the imitation of three axis control can make the spindle unit only carry on the translation movement, greatly expanded the virtual axis machine tool work space, make it play a greater role.In addition, the imitated triaxial control can effectively reduce the complexity of the control system, so as to significantly reduce the cost of the machine tool, which is conducive to the application of this new machine tool in a large range. 

2. Advantages of conventional machining with virtual axis machine tool

A typical structure of a virtual shaft machine tool, which can be summed up as a so-called "six-bar platform structure".Its specific meaning is to fix one end of the six variable length driving rod (short for driving rod) on the static platform (such as foundation or machine tool frame), and the other end of the driving rod is connected with the moving platform, that is, with the spindle unit.In this way, the length of the six-drive rod can be adjusted so that the spindle and cutter can make the required feed motion relative to the workpiece.Through the control system to feed movement for precise control, can be processed to meet the requirements of the workpiece. 

In view of the virtual axis machine tool has the conventional CNC machine incomparable advantages, and these advantages are to achieve high speed, high precision machining is necessary, so it is used as the conventional parts of the efficient processing equipment, in order to maximize its advantages.

The basic principle of three - axis control

Since there is no guide rail along the fixed direction in the virtual axis machine tool, the tool motion axis X, Y and Z required by numerical control machining do not really exist. Therefore, even if only to obtain 3d tool motion (attitude constant only position change), it is necessary to control the moving platform with six degrees of freedom. 

The imitative triaxial control method is a control method to simulate the conventional three coordinate CNC machine tool according to the structure characteristics of the virtual axis machine tool.Its starting point is: when using the virtual axis machine tool to process the conventional parts, the tool installed in the spindle only needs to make a three-dimensional translation movement, its attitude is a fixed value.Thus, although the spindle unit fixed to the moving platform has six degrees of freedom of motion, only three degrees of translation freedom are involved in real-time calculation.In this paper, the tool position is represented by Xm, Ym and Zm coordinates of the tool center or end face center in the machine tool coordinate system, and the displacement is calculated in real time by the three-coordinate interpolation algorithm.At the same time, a cutter coordinate system with the origin at the center of the cutter ball or end face is established, and its coordinate axes Xt, Yt and Zt are parallel to Xm, Ym and Zm axes of the machine tool coordinate system.The rotation Angle of tool coordinate frame around Xm, Ym and Zm axis is used to represent the attitude of the moving platform and set it to a fixed value.In this way, the motion of the moving platform along the three coordinates of Xm, Ym and Zm is calculated and controlled in real time, and the rotation of the moving platform around the axes of Xm, Ym and Zm is controlled in real time with fixed values. Thus, the full degree of freedom of the moving platform can be controlled, and the three-coordinate linkage control of the tool movement can be realized.Because this method does not require real-time calculation of moving platform attitude, in this way, not only can effectively reduce the actual amount of calculation, mapping, and linkage control can also include six degrees of freedom of virtual axis machine tool control in conventional three coordinate number S control machine tool control category, with the aid of mature three coordinate control method to control of this new type of machine tool. 

From the structure of the virtual axis machine tool, it can be known that the directly controllable controlled quantity in the machine tool is the length of the six-drive rod supporting the spindle component Li(I =1,2,..., 6), that is the actual movement of the machine tool spindle (referred to as "real axis), thus to make the degree of freedom of moving platform motion control, thus realize the precise control of tool motion trajectory, the moving platform motion instructions must be (imaginary axis instruction) conversion to real axis space, and through the space to real axis space imaginary axis of inverse mapping to achieve automatically.

The operation process of the system is as follows: first, the tool movement trajectory is generated in real time according to the input information given by the numerical control program of the part, that is, the expected movement velocity of the tool along the coordinates of Xm, Ym and Zm in the virtual axis space is solved;Then, the expected motion of the virtual axis is converted into the motion instruction value of the six-drive rod by virtual real mapping calculation.Finally, the length of each driving rod is decoupled and servo controlled, so that the actual length is consistent with the desired length, and the inverse mapping from real to virtual is realized implicitly through the structure of the machine tool, so that the tool trajectory that conforms to the command can be obtained, and the tool attitude can be guaranteed to be the given constant value. 

Tool path generation in virtual axis space

The task of tool path generation is to convert the tool path given by the part numerical control program (the geometric curve in the virtual axis space that has nothing to do with time and machine tool characteristics) into the discrete tool path related to time and machine tool characteristics (such as acceleration and deceleration characteristics, etc.).The solution process is as follows:

The establishment of mathematical model

In order to ensure the accuracy of trajectory generation, parametric direct interpolation algorithm is used in the pseudo-triaxial control.The key points are: to establish a parametric mathematical model for the interpolated curve that is easy to calculate:

X = f1 (u)

Y = f2 (u)

Z = f3 (u) (1)

In the formula, u -- parameter, u∈[0,1] requires that no function calculation is involved in the real-time trajectory calculation, and only a few times of addition, subtraction, multiplication and division operations can be completed. 

For circular arc interpolation, for example, type (1) the specific form is: (2) the type of M - constant matrix, when the interpolation points are located in a ~ four quadrant, its values are: r - arc radius in this way, the trajectory, it can be absolute manner, namely each trajectory point coordinate calculation with origin of coordinates for the benchmark model, which can eliminate the accumulated error, effectively guarantee the interpolation calculation speed and precision.

Acceleration and deceleration control

In order to make the generated tool trajectory meet the requirements of the acceleration and deceleration characteristics of the machine tool, the optimal acceleration and deceleration curve can be determined according to the dynamic characteristics of the machine tool and stored in the control system.In the process of system operation, firstly, several program segments are scanned before and after to analyze the variation trend of feed speed and determine the desired feed speed F.Then, the feed speed multiplier K on the operation panel is read, and F is modified with it. The target feed speed Fnew, Fnew=K.F;Further, Fnew is compared with the current feed speed Fold, and the instantaneous feed speed Fk(mm/min) of the current sampling period is calculated according to the acceleration and deceleration characteristic curve of the machine tool. 

Speed and error control

Since interpolation is not a static geometric calculation, it must make the distance between the current interpolation point and the previous interpolation point meet the requirements of feed speed, acceleration and deceleration, and ensure that the error between the interpolation line segment and the interpolated curve between the two points is within the given tolerance range.Therefore, the length Dtk of interpolation line segment should be controlled with the instantaneous feed velocity as the control target and the allowable error as the constraint condition.

The method is as follows:

Firstly, according to the instantaneous feed speed Fk given by acceleration and deceleration calculation, the following formula is used to calculate the desired chord length in the current sampling period (the length of interpolation line segment without constraint) : Dt1 in formula (3) -- desired chord length, mm T -- sampling period, ms

E -- the allowable error between the interpolation trajectory and the desired trajectory

R -- radius of curvature of the desired trajectory at the interpolation point

Finally, the value of Dtk is determined according to the relative sizes of Dt1 and Dt2.In other words, if the string length Dt1 is expected to be less than the constraint string length Dt2, the length of the current interpolation line segment is set to Dtk= Dt1; otherwise, Dtk=Dt2.

Interpolation trajectory calculation

The task of interpolation trajectory calculation is to calculate the coordinate value of the preceding point of interpolation trajectory in real time according to the length Dtk of interpolation line segment obtained above in each sampling period.The calculation process is as follows:

Firstly, according to the following relationship between the variable increment Du and Dt, the Du of the current interpolation period is calculated: in equation (5), Du /ds -- the rate of change of the variable on the curve arc length

Due to the high interpolation frequency, the arc length is very close to the chord length in a sampling period, so du/ds≈ du/ Dt can be made in the actual calculation.So if you take an increment of u, Du, and find the corresponding Dt, then you can get the Du /ds that you need. 

Although this approximation has a slight effect on the feed speed, it does not have any effect on the interpolation trajectory accuracy.In the sampling interpolation, the trajectory accuracy is the main contradiction, the coordinate calculation of the interpolation point must be absolutely accurate, while the accuracy of the interpolation point's motion speed along the trajectory is in a secondary position, and minor errors can be allowed.This result not only guarantees the trajectory accuracy, but also improves the calculation speed. 

Then, calculate the value of the parameter variable of the current sampling period: UK =uk-1+Du (6). Finally, substitute UK into equation (1) to calculate the coordinate values xk, yk and zk of the preceding point of the interpolation trajectory.The entire discretized interpolation trajectory can be obtained by repeating the above process until the end point of interpolation is reached.