Compensating for systematic errors in 5-axis NC machining
Introduction
Five degrees of freedom are the minimum required to obtain maximum flexibility in tool workpiece orientation. This means that the tool and workpiece can be oriented relative to each other under any angle. To orient two rigid bodies in space relative to each other, 6 degrees of freedom are needed for each body (tool and workpiece) or 12 degrees. However, any common translation and rotation which does not change the relative orientation is permitted reducing the number of degrees by 6. The distance between the bodies is prescribed by the toolpath and allows us to eliminate an additional degree of freedom, resulting in a minimum requirement of 5 (rigid) degrees. If a coordinate system is fixed to each of the five bodies implementing the 5 degrees of freedom in the 5-axis machine tool, there can be six errors per body or 30 errors. The errors due to the relative distances between the five bodies must be added to these. Five rigid bodies can be connected rigidly to each other by nine rigid bars. These additional possible degrees of freedom result in nine more error components. So, from the above, it can be seen that there are 39 independent error components in a 5-axis machine or 18 more than in the case of a 3-axis machine. A new general error model based on the kinematics of the 5-axis machine will be developed. To the above errors an additional component due to the interpolation in the CAD/CAM system and the machine control must be added.
Section snippets
Error models
Ramesh et al. [1] reviewed the current state of research in the field of error compensation for machine tools. The sources of errors and the methods to eliminate errors are reviewed. The review focuses in detail on the error measurements and compensation used in the past. From this review it is clear that the first part in error compensation, i.e. modeling, has been very much neglected in past research. Past research focussed on measurement and compensation and not on modeling. This is
Volumetric error concept
Fig. 1 illustrates the concept of closed loop volumetric error. The Cutter Contact point, or CC point, is the point where the tool envelope touches the theoretical surface to be machined. It is represented in Fig. 1 as O and O′. Point O represents the CC point on the tool side. Point O′ represents the corresponding point on the reference surface. Point O and O′ coincide only in discrete locations (Fig. 5). The difference in the locations O and O′ is not shown in Fig. 1. Due to various error
Machine taxonomy and kinematic chain diagram
A 5-axis machine is a milling machine (Fig. 3) with 5 degrees of freedom: three translatory movements X, Y, Z (in general represented by TTT) and two rotational movements AB, AC or BC (in general RR). The kinematic chain can be represented in a simplified way. Fig. 2 is the representation of the axis configuration in Fig. 3.
Inverse kinematics
The CAM system generates a toolpath in a machine independent coordinate system fixed to the workpiece. The transformation from workpiece to machine coordinates is called the
General mathematical model
The approach used by Srivastava et al. [5] can be simplified by total differentiation of the kinematic model of the machine. The volumetric errors can be expressed analytically as the total differential of the inverse geometry transformation equations. This approach is general and applicable to each type of 5-axis kinematics. The workpiece coordinates differentials dx1, dy1, dz1, dI1, dJ1, dK1 from Eq. (1) can be expressed in function of the machine coordinate differentials dx4, dy4, dz4, dA, dB
Case study of a specific 5-axis machine
The general approach will now be demonstrated for a specific 5-axis machine shown in Fig. 3.
Error measurement
A ball bar approach in the case of a 5-axis machine can be adopted. However, the many possible orientations due to the rotations will require avoidance of interference with the machine and result in many reference point changes. Therefore, an approach based on tuning or reference pieces was chosen.
Each of the five rigid bodies in a 5-axis machine has six error components, three translatory and three rotational errors. Each of the errors of these five bodies will influence each other. The
Conclusion
An overview of the systematic error components and their interrelation, influencing the final accuracy of the part, were outlined in the general case of 5-axis machines in a new approach. There are three distinct components in the systematic errors.
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Systematic errors which can be compensated directly in the inverse kinematics relations, mainly reference, positional and angular machine axes errors (nine components).
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Systematic errors which cannot be included in the inverse kinematics, but which
Erik L.J. Bohez is an Associate Professor of Manufacturing Systems Engineering at the Asian Institute of Technology. He graduated in Electromechanical Engineering from the State University of Ghent, Belgium, in 1979. His research interests are CAD/CAM, geometric modeling, 5-axis machining, simulation of metalcutting and CNC.
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Erik L.J. Bohez is an Associate Professor of Manufacturing Systems Engineering at the Asian Institute of Technology. He graduated in Electromechanical Engineering from the State University of Ghent, Belgium, in 1979. His research interests are CAD/CAM, geometric modeling, 5-axis machining, simulation of metalcutting and CNC.