Lecture 3. Volumetric Positioning Errors

Transcription

1 Lecture 3 Volumetric Calibration and Compensation 3-1 Volumetric Positioning Errors A linear displacement error is the positioning error in the same direction as the axis direction. The volumetric positioning error is the positioning error in a spatial direction not necessarily in the direction of the axis motion. Hence this error is a vector and its three components are the linear displacement error, the vertical straightness and horizontal straightness. Using conventional laser interferometer to measure these errors is very complex, time consuming, and costly. The key is how to measure all these errors accurately and quickly. 3-2

2 Volumetric Positioning Errors 3-3 Volumetric Positioning Errors According to ASME B5.54 and ISO230-6 volumetric machine tool performance measurement standards The rigid body 21 errors include three each of the following errors: linear displacement, vertical straightness, horizontal straightness, roll angular, pitch angular, yaw angular, and squareness. Using a conventional laser interferometer for measuring the straightness and squareness errors requires a prohibitive amount of time, leading to the development of the body diagonal displacement method for a quick check as defined in the ASME B5.54 or ISO standards. 3-4

3 Volumetric Positioning Errors The theoretical results indicate that the four body diagonal displacement errors are sensitive to all nine linear errors and two angular errors. The error terns in the body diagonal displacement error equation may be positive or negative, and they may cancel each other out. Because the errors are statistical in nature, the probability that all of the errors will be cancelled in all of the positions and in all of the four body diagonals is theoretically possible but highly unlikely. Since most of the angular error terms are cancelled and only two angular error terms are left, we concluded the body diagonal displacement errors, including three displacement errors, six straightness errors, and three squareness errors, are not sensitive to angular errors. Accordingly, it is a good and quick measure of the 3D (volumetric) positioning accuracy. 3-5 Machine tool positioning errors For a 3-axis machine, there are 6 errors per axis or a total of 18 errors plus 3 squareness errors. These 21 rigid body errors can be expressed as the followings, Linear displacement errors: Dx(x), Dy(y), and Dz(z) Vertical straightness errors: Dy(x), Dx(y), and Dx(z) Horizontal straightness errors: Dz(x), Dz(y), and Dy(z) Roll angular errors: Ax(x), Ay(y), and Az(z) Pitch angular errors: Ay(x),Ax(y), and Ax(z) Yaw angular errors: Az(x), Az(y), and Ay(z) Squareness errors: Øxy, Øyz, Øzx, where, D is the linear error, subscript is the error direction and the position coordinate is inside the parenthesis, A is the angular error, subscript is the axis of rotation and the position coordinate is inside the parenthesis. 3-6

4 Existing definition of volumetric accuracy For a 3 axes machine, if the dominate positioning errors are the 3 displacement errors of each axis, Dx(x), Dy(y), Dz(z), then the volumetric error is the rootmean-square sum of all these displacement errors. That is. Volumetric error=sqrt {[Max Dx(x)-Min Dx(x)]² + [Max Dy(y)-Min Dy(y)]² + [Max Dz(z)- Min Dz(z)]²}. This definition is okay as long as the dominate errors are the 3 displacement errors (or lead screw pitch errors). However, for current machine tools, the dominate errors are the straightness and squareness errors rather than the linear displacement errors. Hence, the above definition is no longer valid. 3-7 New definition of volumetric accuracy The positioning error in each axis direction, Dx(x,y,z), Dy(x,y,z), and Dx(x,y,z), is the sum of displacement error and straightness errors as the following. Dx(x,y,z) = Dx(x) + Dx(y) + Dx(z), Dy(x,y,z) = Dy(x) + Dy(y) + Dy(z), Dz(x,y,z) = Dz(x) + Dz(y) + Dz(z). 3-8

5 New definition of volumetric accuracy Then the volumetric error is the root-mean-square sum of these total errors. That is, Volumetric error = sqrt {[Max Dx(x,y,z)-Min Dx(x,y,z)]² + [Max Dy(x,y,z)-Min Dy(x,y,z)]² + [Max Dz(x,y,z)- Min Dz(x,y,z)]²}. However, using a conventional laser interferometer, the measurement of these straightness and squareness errors are time consuming. Hence, the body diagonal displacement error measurement in the ASME B5.54 or ISO standard is a good quick check 3-9 of the volumetric error. Machine Tool Need to Calibrate and Compensation at Volumetric Positioning Errors Competition in the global manufacturing market today requires improving the CNC machine tool performance to achieve higher productivity, better quality and less downtime. With the latest generation of CNC controls it is now possible to achieve higher accuracy even on a lower cost machine. To do this it is important to measure the volumetric errors of the machine and to compensate these errors. The key is how to measure all these errors accurately and quickly. Using conventional laser interferometer to measure these errors, it is very complex, time consuming and costly. This is one of the major reasons these errors are not compensated. The other reason is time, with the cost of machine time most companies are not willing to invest the to 20 hours required to measure all these errors.

6 Calibrate Volumetric Positioning Errors 3-11 Volumetric Positioning Errors 3-12

7 Calibrating and Compensating the Displacement Errors is not Enough In general, calibrating the machine displacement accuracy over the 3 axes, or compensating the machine pitch error over 3 axes is not enough. There are many other errors, such as the straightness of the guide way, the squareness of the axes, the effect of weight shifting, counter balancing etc, which cause far larger errors than the 3 pitch errors Body Diagonal Measurement The ASME B5.54 standard section Volumetric Performance Using Diagonal Displacement Measurements section states that The volumetric accuracy may be rapidly estimated by measuring the displacement accuracy of the machine along body diagonals. This is because the diagonal displacement error is sensitive to all the error components. However, if the measured errors are large, there is not enough information to identify the error sources. 3-14

8 Body Diagonal Measurement 3-15 Body Diagonal Measurement The volumetric positioning errors, including 3 displacement errors, 6 straightness errors, squareness errors and some angular errors, will show up as the 4 body diagonal displacement errors [4]. Hence it is a good and efficient measurement of the volumetric error. The volumetric error can be defined as [Max Dr(x,y,z) Min Dr(x,y,z)], where Dr(x,y,z) is the diagonal displacement error. 3-16

9 Compensate Volumetric Positioning Errors Most modern controller have the capability of volumetric compensation (or sometimes called sag compensation, or cross compensation), the measured volumetric positioning errors can be used to generate the volumetric compensation files for the controller to compensate the machine errors and achieve higher volumetric accuracy Compensate Volumetric Positioning Errors 3-18

10 Sequential Step Diagonal Measurement Similar to the diagonal measurement, the laser beam is pointing in the diagonal direction, instead of moving x-, y- and zaxis continuously in the diagonal direction, the machine is now programmed to move x-axis, stop, collect data, then move y-axis, stop, collect data, then move z-axis, stop, collect data. The process is continued till the opposite corner is reached. Hence it is called sequential step diagonal measurement. The major advantages are 1) 3 times more data are collected, 2) x, y, and z motions are separated, and 3) all error components can be measured. With 4 setups (4 body diagonals), all 3 displacement, 6 straightness and 3 squareness errors can be determined. On a machine with a work volume of 1 cubic meter, all four diagonals can be measured in 2 to 4 hours. 3-19