# Best understanding of volume positioning error vol

2022-08-24
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Understand the volume positioning error: Volume diagonal measurement is not sensitive to angular error

in recent years, the volume Diagonal displacement measurement method defined by ASME B5.54 or ISO standards has provided a rapid inspection method of machine tool spatial error, which has been well used in Boeing and many other companies. The first production line in the phase 1 project has been put into trial production. Because these measurements are relatively simple and fast, the measurement cost and downtime are greatly reduced. However, the relationship between body Diagonal displacement error and 21 rigid body errors is not clearly expressed. In addition, the importance of angular error has also been wrongly exaggerated. In order to understand the relationship and importance of angular errors, it is necessary to derive the relationship between 21 rigid body errors and measured Diagonal displacement errors

The 21 rigid body errors derived from the matrix method include the following errors: linear displacement, vertical straightness, horizontal straightness, rolling angle, pitch angle, yaw angle and perpendicularity. The three axes are 21 rigid body errors. It takes expensive time to measure the straightness and perpendicularity errors with traditional laser interferometer, so the volume Diagonal displacement method for rapid detection has been developed, which has been described in detail in ASME B5.54 or ISO standards

body Diagonal displacement error

body Diagonal displacement is a method of measuring volume positioning accuracy with laser interferometer. The laser head is placed on the workbench of the machine tool, and the reflector placed on the spindle reflects the laser beam along the diagonal direction of the machine tool. The diagonal measurement directions of the four bodies are AG, BH, CE and DF (see Figure 1)

the laser beam moves along the diagonal of the body, while the reflector moves along the diagonal of the body in certain increments (see Figure 2). Starting at the origin, each increment along the diagonal reaches a new position, and the displacement error of the three axes is measured. The body diagonal is defined by the positive axis (P) or the negative axis (n)

the last four body diagonals are at the same angle as the first four body diagonals, but the direction is opposite. For this reason, only four body diagonals move forward and backward (bidirectional); The measurement after each simultaneous movement of X, y and Z axes is set only 4 times. The accuracy of each position along the body diagonal depends on the positioning accuracy of all three axes and the geometric error of the machine tool

The theoretical calculation results show that the Diagonal displacement error of the four bodies is sensitive to all nine linear errors and two angular errors. In the body Diagonal displacement error equation, the error term may be positive or negative, or it may cancel each other. Since the error is from a statistical point of view, the probability that the errors at all positions and the diagonals of all four bodies can be offset is theoretically possible, but in fact it is not. Since most of the angle error terms are offset, leaving only two angle error terms, it is concluded that the body Diagonal displacement error, including three displacement errors, six straightness errors and three perpendicularity errors, is insensitive to the angle error. Thus, it is conducive to rapid measurement of volume positioning accuracy

since there are only 4 groups of data and 9 groups of errors, the information to determine the source of the error is still insufficient. This leads to the patented step-by-step diagonal measurement or laser vector measurement technology developed by American optodynamics company

step diagonal measurement

step diagonal measurement method used 4 identical diagonals to collect 12 groups of data. Based on the measured data, all three displacement errors, six straightness errors and three perpendicularity errors can be determined. Therefore, the three-dimensional (volume) positioning error can be measured without a lot of downtime and high cost. Moreover, the measured positioning error can be used to generate a volume compensation table to correct the positioning error, so as to improve the positioning accuracy

the step-by-step diagonal measurement method is different from the body Diagonal displacement measurement. Each axis moves step by step, and the diagonal positioning error is collected after each movement of X axis, Y axis and then Z axis. In this way, three times the amount of data is collected, and the positioning error of each axis moving separately can be measured

in the step-by-step diagonal measurement method, move along the x-axis, Y-axis and then z-axis respectively, and repeat until you reach the opposite corner of the diagonal. The trajectory of the target is not linear, and the lateral movement is large (see Figure 3). The traditional interferometer does not only reflect the parameters, but also can make such measurements, because it is impossible to make a large lateral movement. LDDM single aperture series laser interferometer can be made. With a plane mirror as the target, the parallel movement of the mirror will not transfer the laser beam, nor will it change the distance from the light source. Therefore, the measurement will not be affected

test case on FANUC 16i CNC vertical machining center

step diagonal measurement was carried out on a vertical machining center (VMC) using FANUC 16i controller. The measured space is x=55 "(1397mm) to 139" (3530.6mm), y=2 "(50.8mm) to 50" (1270mm), z=10.5 "(266.7mm) to 34.5" (876.3mm)

we use the laser calibration system of photodynamic mcv-500 LDDM and step-by-step diagonal measurement accessory sd-500. In order to adjust the laser beam in the diagonal direction of the body conveniently, a universal refractor is used. The laser head is installed on the workbench of the vertical machining center (VMC). The 3 "X4" (75x100mm) plane mirror is installed on the spindle, and its surface is perpendicular to the laser beam. Measure the air temperature and pressure to compensate for the change of laser frequency, and measure the machine temperature to compensate for the thermal expansion of materials

a total of four settings are required, that is, one for PPP, NPP, PNP and NNP in the direction of the four diagonals. The movement of the spindle from one end to the diagonal position is controlled by the program. The measurement data of each step is automatically collected by LDDM software. This software analyzes the data and automatically calculates the error of each axis

in this way, two sets of Diagonal displacement data are collected, one without volume compensation and the other with volume compensation. The linear displacement error of each axis with volume compensation comes out. Based on the measured step diagonal data, the volume positioning error including three displacement errors, six straightness errors and three perpendicularity errors is measured. This automatically generates volume compensation files

the measured Perpendicularity Error is xy=-5.72 arc seconds, yz=1.73 arc seconds, zx=3.47 arc seconds. The linear displacement error of X, y and Z axes, the straightness error of vertical direction and the straightness error of horizontal direction are obtained. For x-axis, the maximum vertical straightness error (deviation in Y direction) is 0.00035 "(0.009mm); the maximum horizontal straightness error (deviation in Z direction) is -0.0005" (-0.0127mm); The maximum displacement error is -0.0005 "(-0.0127mm).

for the Y axis, the maximum vertical straightness error (deviation in the X direction) is 0.0002"/-0.0004 "(0.0051mm/-0.0102mm); the maximum horizontal straightness error (deviation in the Z direction) is 0.0035"/-0.004 "(0.0889mm/-0.0102mm); the maximum displacement error is -0.0013" (-0.0330mm)

for Z axis, the maximum vertical straightness error (deviation in X direction) is 0.0005 "(0.0127mm); the maximum horizontal straightness error (deviation in Y direction) is 0.00055" (0.0140mm); The maximum displacement error is -0.0015 "(-0.0381mm).

according to ASME B5.54 or ISO, the maximum error of the measured body Diagonal displacement without compensation is 1. Here is an introduction to these links. The difference is 0.003" (0.0762mm). Using the step diagonal data and the calculated volume positioning error, a straightness error compensation table is generated for FANUC 16i controller. After using volume compensation, the linear displacement error of each axis is measured. 10. The maximum errors of Y and Z axes are 0.0002 "(0.0051mm), 0.0001" (0.00254mm) and 0.0001 "(0.00254mm) respectively, which are much smaller than those without volume compensation. After volume compensation, the perpendicularity error is xy=-0. The new material can make the display self repair 05 arc seconds, yz=-3.7 arc seconds, zx=-0.32 arc seconds. The perpendicularity error is much smaller than that before volume compensation. After volume compensation, the maximum body Diagonal displacement error is 0.0006" (0.0152mm), There is a 500% improvement

conclusion: since the volume Diagonal displacement measurement method is insensitive to the angle error, it is only a good method for rapid volume positioning error, including three displacement errors, six straightness errors and three perpendicularity errors; The step-by-step diagonal measurement method collected 12 sets of data to solve all 9 straight-line errors and 3 perpendicularity errors. The measured volume positioning error can be used to generate volume compensation files, which can greatly reduce the volume Diagonal displacement error. This method makes the calibration and compensation of CNC machining center or CMM more economical, practical and necessary

Optodyne Inc.

general agent in China: Kewang technology consulting (Shanghai) Co., Ltd.

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