The accuracy of machine tools is one of the most fundamental requirements for high precision engineering. It is typically milling, grinding and turning operations that produce the most tightly toleranced features within high-value machines and assemblies. An understanding of machine tool error sources is the first step in minimizing and compensating for these errors and therefore achieving high-accuracy machined parts. In my previous articles, I’ve looked at methods of measuring and correcting these errors, such as rapid verification, multi-axis calibration and simultaneous error parameter estimation. This article goes into more depth about what the error sources actually are. The sources of errors in machine tools include kinematic errors that are built into the machine, thermo-mechanical errors that cause distortions with temperature changes, load and dynamic forces that cause further distortions, spindle errors, tool errors, motion control and software errors.
Kinematic Errors
Kinematic errors are those built into the machine due to manufacturing inaccuracies and clearances in its geometry-defining components such as linear slideways and rotary bearings. They are always present regardless of any external factors such as temperature and forces. Many kinematic errors only depend on position, such as the straightness of an axis or the alignment between axes. Play in drives, slideways and rotary bearings results in hysteresis effects, which cause different errors depending on the direction of travel. Examples of these effects include backlash and lateral play.
Because kinematic errors are repeatable, they are relatively easy to compensate using calibration. Traditionally, the emphasis was on making mechanical adjustments to machines to eliminate these errors, for example, by grinding an axis flat. Although a good standard of mechanical alignment is still the foundation for machine tool accuracy, the use of computer numerical control (CNC) now allows much greater use of digital correction. This means that if there is a measured high point on the x-axis, that produces an error in the z-direction. Rrather than attempting to remove the high point on the x-axis, it is easier to introduce a corrective offset in the CNC controller. So, when the x-axis approaches the high point, the z-axis will automatically move in the opposite direction to maintain straight line motion of the tool along the nominal x-axis.
Machine tool errors are the difference between the actual tool path and the desired path. A physical object has 6 degrees of freedom with regard to its motion; 3 translations and 3 rotations. It follows from this that deviation from motion along a straight line also has six components:
- One positional deviation, in the direction of motion.
- Two linear deviations orthogonal to the direction of motion, which may be referred to as straightness of the axis.
- Three angular deviations, which may be identified as pitch, roll and yaw, although the distinction between pitch and yaw is dependent on an arbitrary frame of reference.
Considering the 6 degrees-of-freedom, each linear machine axis has 6 error components at any given position. The ISO 230 standard separates these into component errors, which are a function of position, and location errors, which have a constant value. In commonly used machine tool terminology, rotational component errors (,which vary with location along the axis) are referred to as pitch and roll, while the location errors (which have constant values for the whole machine) are referred to as the squareness of the axis. Although each axis has two squareness angles with respect to the other axes, the first axis defines the first two angles of the machine’s coordinate system, and the second axis then defines the remaining rotation about the first axis. The location errors associated with the translational degrees of freedom are normally ignored since these are effectively eliminated each time the machine datums to the workpiece. There are, therefore, only 3 location errors for a 3-axis machine, giving a total of 21 errors. However, since the component errors are dependent on position, they would each normally be measured in at least 10 different positions meaning that a full error map for a machine will have approximately 180 individual values. The 21 kinematic errors for a 3-axis machine tool are shown in Figure 2.
The 6 degrees of freedom which apply to an object travelling along a linear path also apply to an object rotating around an axis; rotary axes therefore also have kinematic errors associated with them. Four distinct types of error can be identified:
- Radial errors have two degrees of freedom per axis, involving translational errors perpendicular to the axis of rotation.
- Axial errors have a single degree of freedom per axis, a translation along the axis of rotation, this may also be referred to as swash.
- Tilt errors have two degrees of freedom per axis, involving rotational errors in alignment between the actual and theoretical axis of rotation.
- Angular positioning is a single rotational error corresponding to the difference between the encoder reading for angular position and the actual angular position.
It should be noted that each of these errors will have a constant component representing alignment with the parent axis and a position-dependent component which varies as the axis moves through its range of motion.
Thermo-Mechanical Errors
Thermal expansion of machine tool components due to changes in operating temperature will result in distortion of the machine geometry. These effects are caused primarily by heat sources related to the operation of the machine, such as motors and slideways. For this reason, it is standard practice to warm a machine using a pre-defined warmup sequence that exercises motors and axes fully. The machine should only be calibrated and operated in this warmed-up state. However, thermo-mechanical errors remain for a number of reasons. Firstly, the machine may be operated either more intensively or less intensively than the warmup sequence. For this reason, in certain cases where machines receive light intermittent use, improved accuracy may be achieved when the warmup cycle is not used.
Temperature also varies over time both due to the machine utilization and the ambient environment. Machines may use temperature sensors located on the axes to apply corrections for linear scaling errors. However, this assumes that thermal expansion results in a homogeneous scale error, which is not the case. Temperature varies at different positions on the machine due to changes in localized heat sources, both internal (such as motors) and external (such as direct sunlight from a window aligning with a machine). Temperature gradients are also found in indoor environments, due to warmer air rising to the top of a room and cooler air settling to the bottom, of typically one degree C per m. These effects can be very difficult to predict and compensate.
Considerable work has been done to understand how best to model and compensate for thermal deformation in machine tools. Methods usually involve placing temperature sensors on the major structural elements of a machine and then predicting the deformation using either Finite Element Analysis (FEA) or an empirical model such as deep learning. Achieving accurate predictions remains challenging due to a limited number of temperature sensors giving an incomplete picture of the temperature gradients, uncertainties in the temperature sensors themselves, uncertainties in the coefficient of thermal expansion for the machine tool structure, and uncertainties in the models. These are all areas that require further development in order to advance high precision manufacturing.
Loads and Dynamic Forces
The weight of moving parts of the machine and of the work piece will cause a repeatable displacement of the machine structure, which depends on the combination of axis positions. The standard approach to kinematic calibration assumes that the errors in each axis depend only on position along that axis. This means that each axis can be calibrated in isolation and the resultant errors for any given position calculated by superposition. However, when considering loads acting on the axes, this assumption is not valid since when an axis as the end of the kinematic chain is fully extended, it will exert a larger moment on the axis to which it is attached. For this reason, for the highest accuracy, so called volumetric compensation must be carried out. This means that instead of taking measurements at a number of discrete positions along each independent axis, measurements are taken at grid positions within the volume of the machine. The result is a far lengthier calibration process. The additional controller software required to implement volumetric compensation can also be very expensive, meaning that this is only applied for the most demanding applications. Luckily, the inherent stiffness of machine tools means that these errors are usually very small, probably less than a micron for typical CNC machine tools. However, for large gantry-based machines, operating at scales of several meters, volumetric compensation can eliminate significantly larger errors.
Additional deformations of the machine tool structure, and resulting errors, are caused by acceleration of the machine and workpiece mass, as well as process forces. These can have a significant effect on machine errors. Inertial forces are predictable and could, therefore, be compensated using model-based correction, although this is not thought to be done by any current industrial control systems. Process forces are more difficult to predict, although these forces may be reduced to have a negligible impact on the final form of components by reducing the depth and feed rates for finishing cuts. This involves a compromise between process time and accuracy.
Motion Control & Software Errors
Motion control errors include both physical effects, such as the dragging of cable looms, and control interpolation errors, such as servo mismatch and reversal spikes. Dynamic errors are those which are only present when the machine is in motion. Such errors include controller errors such as reversal spikes, and servo mismatch and vibration.
Spindle and Tool Errors
A spindle is effectively an additional rotary axis with the important difference that rotational positioning about the spindle axis does not need to be accurately controlled. In fact, the spindle may be referred to as the rotary drive axis, however, due to the high speed of operation, entirely different measurement techniques are required to measure spindle errors. Errors associated with this axis are sometimes referred to as runout so that radial errors are referred to as radial runout and axial errors as axial runout. Angular positioning is generally not a consideration since the tool is continuously rotating within the axis rather than being rotated accurately.
Although kinematically identical to any other rotary axis, in practice error sources and detection are very different due to the far greater speed of rotation. Non-contact sensors that provide very high frequency measurements are therefore required, such as proximity sensors that make use of eddy current effects.
Additional errors are associated with the repeatability of the tool change operation (index errors) and tool wear which affects tool length, tool diameter and tool geometry. These may be calibrated using laser tool calibrators that are able to recalibrate the tool position and size rapidly during operation of the machine.
Conclusion
Machine tool calibration, using some form of laser interferometer-based measurement, is typically focused on determining kinematic errors. Ballbar measurement may be used to calibrate some motion control errors and hysteresis. Verification of machine tools has historically been an involved process of either careful alignment using physical gauges or machining test pieces which can then be measured. Modern innovations such as the telescopic ballbar and touch trigger probing of reference artefacts have reduced this to several minutes. The verification of a machine tool generally still requires expensive specialized equipment and a skilled operator meaning that quick verification checks cannot be made before critical machining operations are carried out. Additional sources of error such as thermal deformation and inertial loadings are not currently well-calibrated and may represent the next area for accuracy improvement in machine tools.