Preventing the machine tool from producing errors in the volume positioning is critical for accurately machining contours and other 3D surfaces.
Many machining shops believe that the concepts of 3-axis accuracy and 3-D accuracy are exactly the same. But the actual situation is: 3-axis accuracy only represents 1D dimensional accuracy, because it only explains the tolerance of the linear measurement on each axis. The 3D accuracy refers to the relationship between the linear measurement of each axis and the relationship between the X, Y, and Z axes, that is, the relationship between the flatness and perpendicularity of each axis within a specific work area cube. .
Calibrating 3-axis accuracy is relatively simple and is useful for identifying and solving problems such as pitch/ball screw pitch errors or wear. Calibrating 3D accuracy is relatively complicated, but it does not need to spend more time. However, when cutting contour surfaces and machining 3D parts designed by 3D CAD software, this is the best way to ensure the overall performance of the machine. For the shop floor, it is important to know when to perform these different calibrations, as each calibration will provide different information for the machine's performance.
Before delving into the differences between 3-axis calibration and 3-D calibration, first of all, it should be understood that the positioning system of most machine tools is determined based on the Deckard coordinate system, and the axes of each coordinate are perpendicular to each other. It utilizes a series of axes. Points to represent 3D objects or object properties, so it is helpful to understand this.
Many of the confusions surrounding the 3-axis and 3D calibration problems are related to their terminology. If a shop only calibrates the linear displacement along each axis on the 3-axis, then it can be considered as a 3-axis calibration. However, these three axes are not calibrated for 3D accuracy because the linear displacement does not assume that the axes are perpendicular to each other.
According to the geometry of the rigid body, it is determined by a 90° angle formed by one axis of a particular reference frame, and each axis of a specific machine tool is allowed to have 6 errors for a total of 18 errors. The six errors include three linear errors as well as pitch error, deviation error, and roll angle error. Considering three potential perpendicularity errors, the total number of rigid body errors for a 3-axis machine tool can reach 21. When the displacement error is calibrated along each axis, only 3 errors can be determined, leaving the remaining 18 errors undeterminable.
Figure 1 Measurement of cube diagonal displacement using a laser calibration system is a measure of 3D volumetric accuracy
3-axis calibration
The linear displacement along one axis of a CNC machine tool can be calibrated using a measurement system based on laser Doppler displacement measurement technology (LDDM). This system requires only two optical components and temporarily mounts them on the machine or coordinate measuring machine. This will make the system's debugging settings and laser beam correction relatively easy and fast. The laser used in this application area meets the requirements for standardized tracking, has stable detection characteristics, and has an inspection stability of better than 0.1 ppm, an accuracy of 1.0 ppm, and a resolution of 1 microinches.
The laser readhead is mounted on the bed or table and its retroreflector (also called the light target) is mounted on the spindle. The finely tuned laser beam is parallel to the axis. The operator creates an incremental program for measurement along the axis and the spindle with the retroreflector is started at its original position. The system then begins moving the retroreflectors to each of the specified incremental positions and records the measurements. Incremental positioning and data capture can be done automatically or manually.
By comparing the measurement scale with the measurement position of the calibration system, this process can know the deviation between them. Then use these deviations to calculate and make a compensation table. In some cases, it can be called a single linear correction factor application form. Others require incremental pitch correction coefficients. In other words, errors may occur in certain areas, but are not evenly distributed on the axis.
With linear calibration it can be assumed that the only possible error is the screw/ball screw and thermal expansion error. It is not appropriate to ensure the accuracy of the 3D part along the linear calibration on the 3 axis. Many years ago, German and international standard-setting bodies had realized this, and they introduced ASME B5.54 and ISO 230-6 machine tool performance measurement standards.
Figure 2 The inherent common errors in machine design affect the positioning accuracy of the machine
3D calibration
Two different 3D (volume) calibration methods have been generated from the ASME B5.54 and ISO 230-6 standards. One is called "cube diagonal displacement measurement"; the other unique method is called "sequential step diagonal. Measurement method." For many years, the cube diagonal measurement method determined by the ASME B5.54 and ISO 230-6 standards has provided a rapid measurement method for the detection of volume error, and has obtained very good results. Because the measurement involved is relatively simple and the measurement speed is relatively fast, the cost is very low and the machine tool downtime is very small.
Cube-diagonal displacement measurement uses a laser calibration system to measure the volumetric positioning accuracy of a machine tool. The laser is mounted on the bed of the machine. The retroreflector is mounted on the spindle of the machine and reflects the laser beam. This beam is adjusted according to the machine's diagonal alignment.
When the laser beam is emitted along the diagonal of the cube, the retroreflector starts along the diagonal of the cube and moves in increments specified by the operator. The laser calibration system records the measured values ​​at each position. The measurement of the displacement error starts from the original position and each incremental level on the three axes and moves along the diagonal line until reaching a new position.
The last four cube diagonals use the same rounded corners as the first four diagonal lines, but their directions are exactly the opposite. For this reason, only four diagonals move in both directions, so only four debugging setups are required, where the measurements are performed after the X, Y, and Z axes are moved simultaneously. The accuracy of each position on the cube diagonal depends on the positioning accuracy of all three axes and the geometric error of the machine tool.
Theoretically, it should be determined by calculations, but these four cube diagonal displacement errors are very sensitive to all nine linear errors. These linear errors may be positive or negative, and these 9 errors may cancel each other out. . Since, by nature, these errors are only statistical errors, theoretically, the probability that these errors are canceled at all positions and in all 4 cube diagonals may exist, but in reality almost It is unlikely.
Figure 3 There may be 6 errors for each axis
However, the cube-diagonal displacement measurement does not clearly illustrate the relationship between the cube-diagonal displacement error and 21 possible rigid-body errors. Another thorny issue caused by this method is its excessive emphasis on angular errors. If you want to understand the relationship and importance of the angle error, it is necessary to understand the relationship between the 21 rigid body errors and the diagonal displacement error of the cube being measured and the root cause. According to the above extended relationship, all angle errors can be eliminated except for two angular errors. Therefore, the cube diagonal displacement error is very sensitive to displacement error, flatness error, and squareness error, but not to the angle error. Because there are only 4 sets of data and 9 sets of errors, the cube-diagonal displacement measurement method does not acquire enough information to determine the source of the error. Optodyne, Inc., a company that develops and markets laser calibration systems, has developed sequential step-diagonal measurements to solve these problems.
The basic concept of this method is that the direction of the laser beam (or measurement direction) is not parallel to the direction of movement of the linear axis. Therefore, the measured displacement error is very sensitive to errors occurring in the parallel and vertical directions of the linear axis. More precisely, the linearity error being measured is the sum of the vectors of all errors projected onto the laser beam, including the displacement error (parallel to the linear axis), the vertical flatness error (perpendicular to the linear axis) and the levelness error (Vertical to the linear axis and vertical flatness error directions).
Using the laser beam to collect data in the diagonal direction of the four cubes, 12 different types of errors can be identified. Since the error on each axis of motion is a vector value containing three vertical error elements, this method is called a vector measurement technique.
During normal cube diagonal measurements, the laser beam moves diagonally along the cube and collects data at preset increments. In the vector detection process, all three axes move in the direction of the diagonal of the cube in order, and the data is acquired after each axis is moved. The number of data collected by this method is more than 3 times higher than that of the conventional cube diagonal measurement method, and it can separate errors according to the motion of each axis.
Sequential step diagonal measurement method is different from the cube diagonal measurement method. Each axis moves in sequence and the diagonal positioning error is acquired after the X, Y, and Z axes are respectively moved. The trajectory of the light target is not a straight line, and its range of lateral movement is quite large. Therefore, a flat mirror must be used as a light target.
Conventional linear displacement measurement techniques only measure along one side, regardless of pitch error, deviation error, and angular error. Sequential step measurement techniques are measured along all four sides. Therefore, the average value of the displacement obtained through the center of the volume is considered to be a more accurate value.
Pitch error, deviation error, and roll angle error affect all measurements, including linear displacements measured by ordinary laser interferometers. Therefore, the linear displacement error measured along the X-axis will be different from the measurement obtained when measuring at different positions on the Y-axis and the Z-axis. This is the result of a different Abbe deviation obtained when moving at different positions, pitch movements, off-motion and roll angles. It is for this reason that the B5.54 standard states that all linear displacement measurements must be measured along three orthogonal lines, that is, they must be parallel to these three axes and pass through the center of the working volume.
The advantage of using a sequential step diagonal measurement technique is that the positioning error caused by angular errors can be measured and can be represented by the average flatness error along the centerline of the working volume. This advantage is critical because most machine tools cannot compensate for angular errors. When the angular error cannot be compensated, the accepted work area will be used to compensate for the average flatness error. Due to Abbe deviations and angular errors, the resulting displacement error and flatness error measured along the working volume will be different from those obtained along the other side of the measurement. It is for this reason that the sequential step diagonal measurement technique can measure four sides and can find the average of the four-sided measurements.
Figure 4: Using the sequential step measurement method developed by Optoyne Corporation to measure all 21 rigid body errors of a 3D stereo calibration
The value of 3D calibration
Each machining shop puts forward specific precision requirements for its customers, machining processes and machine tools. As 3D CAD/CAM systems are increasingly used to design various parts, the importance of ensuring that the machine can accurately machine 3D parts is becoming more and more important. Since the 3-axis calibration does not consider the 3D relationship between each axis, only 3D (volume) calibration can be used to ensure that the machine can precisely machine 3D parts.
Normal 3D calibration and compensation help to shorten the production cycle, improve part quality, reduce maintenance frequency, and reduce warranty costs. The use of dealers' quality control procedures to perform calibrations and make full use of volumetric calibration and compensation capabilities will certainly enable the production process to have a greater competitive advantage and achieve higher profitability.