Coordinate Metrology
David Flack, James Claverley and Richard Leach, National Physical Laboratory
This chapter discusses coordinate metrology, both macro-scale and micro-scale. Co-ordinate measuring machines, both mechanical and optical are discussed. Different CMM probing systems are addressed along with CMM software and error sources. CMM calibration, performance verification and traceability are also discussed, along with the latest specification standards in this area, and the difference between prismatic and freeform measurements. Micro-CMMs are addressed next: micro-CMM types, probing systems, performance verification and calibration.
Keywords
Coordinate Metrology; Coordinate Measuring Machines; Performance Verification; Micro-CMMs
9.1 Introduction to CMMs
This section gives an overview of coordinate metrology as an introduction to the sections on miniature coordinate measuring machines (CMMs). An understanding of the operation of normal industrial CMMs will help in the understanding of the principles of miniature CMMs (hereafter called micro-CMMs).
A CMM is a measuring system with the means to move a probing system and the capability to determine spatial coordinates on the surface of the part being measured. A photograph of a typical CMM is shown in Figure 9.1. CMMs come in a number of configurations (Figure 9.2) and a range of sizes, from those able to measure something the size of a bus to the miniature versions described in Section 9.4. However, the majority of CMMs fall in the size range 0.5–2 m. Conventional CMMs generally incorporate three linear axes and use Cartesian coordinates, but CMMs are available with four axes, where the fourth axis is generally a rotary axis. The first CMMs became available in the late 1950s and early 1960s (see Ref. [1] for a thorough description of CMMs and some history, and Ref. [2] for an overview of their use).
CMMs measure either by discrete probing, where data from single points on the surface are collected, or by scanning, where data are collected continuously as the stylus tip is dragged across the surface. The stylus tip in contact with the surface is usually a synthetic ruby ball, although other geometries are possible, for example cylindrical stylus tips.
The data collected by the CMM are essentially ball centre data. The stylus in contact with the surface, therefore, needs to be qualified to determine the effective stylus radius and the position of the centre of the tip relative to some reference point. Stylus qualification is carried out by measuring a known artefact, usually a high-quality ceramic reference sphere [3].
The data collected from the part being measured needs to be aligned with either the component drawing or a computer-aided design (CAD) model. This alignment is usually carried out with reference to defined datum features on the drawing. However, for free-form artefacts (see Section 9.1.5), a best-fit alignment may be more appropriate. Once data are collected, they are analysed by a software package. This involves fitting associated features (circles, planes, etc.) to the collected data. The software can then be used to calculate intersection points, distances between features, locations of features in the workpiece coordinate frame, distances between features and form errors such as roundness and cylindricity.
The international specification standard for CMMs is ISO 10360. CMM types are described in ISO 10360 part 1 (2000) and include:
• fixed table cantilever CMMs (Figure 9.2(a));
• moving bridge CMMs (Figure 9.2(b));
• gantry CMMs (Figure 9.2(c));
• L-shaped bridge CMMs (Figure 9.2(d));
• fixed bridge CMMs (Figure 9.2(e));
• moving table cantilever CMMs (Figure 9.2(f));
• column CMMs (Figure 9.2(g));
• moving ram horizontal-arm CMMs (Figure 9.2(h));
• fixed table horizontal-arm CMMs (Figure 9.2(i) and (j)); and
• moving table horizontal-arm CMMs (Figure 9.2(k)).
Moving and fixed bridge-type CMMs are the most common design.
A further type of CMM also encountered is the vision system. A vision or an imaging system CMM is essentially a microscope mounted on one of the CMM arrangements described in this section. It is often referred to as being 2.5D as the range and access in the vertical, z-axis is inferior to that in the x- and y-axes (height is measured by focusing the microscope on the relevant surfaces).
9.1.1 CMM probing systems
The probing system attached to a CMM [3] can be one of the following three types:
An analogue probe is capable of working either in a mode where it collects points from a number of surface contacts or by scanning the component surface. It is a measuring probe, and data are collected from the CMM scales and the probe as it scans along the surface. A touch trigger probe works by recording the machine coordinates when the stylus tip contacts the surface. It is essentially on or off.
Various optical probes can be attached to CMMs, often working on a range of principles, for example triangulation (see Section 6.7.2.1). Optical probes have the advantage of being able to collect data significantly faster than an analogue contacting probe. However, they are generally less accurate than contacting probing systems.
9.1.2 CMM software
An important part of a CMM is its software. The software needs to carry out the following tasks:
• collect data from the CMM (scales, probe, temperature sensors);
• fit associated features to the data;
CMM software needs to be tested, and this is covered in ISO 10360 part 6 [4]. Use is made of reference data sets and reference software to check the ability of the software to calculate the parameters of basic geometric elements.
9.1.3 CMM alignment
To measure a component on a CMM, its alignment relative to the coordinate system of the machine needs to be described. This alignment is usually made using datum features of the part in question.
The alignment needs to control the following:
• the part spatial rotation (two degrees of freedom);
As an example, for a rectangular block, the alignment process would typically:
1. measure a plane on the top surface (defines rotation axis and z-zero);
2. measure a line on the side face (defines planar rotation about z-axis and y-zero); and
3. measure a point on a face orthogonal to the side face (x-zero).
Other alignments are possible, for example best-fit alignments and reference point alignments are used for free-form shapes.
9.1.4 CMMs and CAD
Modern CMM software allows programming direct from a CAD model. Furthermore, once data are collected the actual points can be compared to the nominal points and pictorial representations of the errors created. Point clouds can also be best-fitted to the CAD model for alignment purposes.
9.1.5 Prismatic against free form
Artefacts measured on CMMs fall into two categories:
1. purely prismatic components, examples of which include engine blocks, brake components and bearings; and
2. free-form components, examples of which include car doors, body panels, mobile phone covers and IT peripherals.
Prismatic components can be broken down into easily defined elements, for example planes, circles, cylinders, cones and spheres. A measurement will consist of breaking down the component into these geometries and then looking at their interrelationships, for example the distance between two holes or the diameter of a pitch circle.
Free-form components cannot be broken down as with prismatic components. Generally, the surface is contacted at a large number of points and a surface approximated to the data.
If a CAD model exists, then the cloud of data can be compared directly against the CAD model. Having a CAD model is an advantage for free-form surfaces, as the nominal local slope at the contact point is known in advance. The local slope is needed to appropriately correct for the stylus tip radius in a direction normal to the surface. For reverse engineering applications, the local slope needs to be approximated from measurement points adjacent to the target point.
Many real-world components are a mixture of free-form surfaces and geometric features; for example, a mobile phone cover may have location pins that need to be measured.
9.1.6 Other types of CMM
Other types of coordinate measuring systems include articulated-arm CMMs, laser trackers (Flack and Hannaford [2] discuss both types of CMM) and X-ray computed tomography systems [5]. The devices have the advantage that they are generally portable and are better suited to measuring larger items, for example aerospace components. Specification standards applicable to these devices are under development as part of the ISO 10360 series.
9.2 Sources of error on CMMs
Whilst CMM manufacturers aim to build CMMs with small geometric errors, no CMM is constructed perfectly. A typical CMM has 21 sources of geometric error. Each axis has a linear error, three rotation errors and two straightness errors (six per axis gives 18). The final three errors are the orthogonality errors between any two pairs of axes. These errors are also described briefly in Section 7.3.4 for scanning probe microscopes.
Traditionally, these errors were minimised during manufacture of the CMM. However, with the advent of modern computers, CMMs can be error mapped (volumetric error compensation) with corrections to geometric errors made in software [1,6–8].
CMM geometric errors are measured in one of the four following manners:
9.3 Traceability, calibration and performance verification of CMMs
Calibration and performance verification are two issues that are often confused when talking about CMMs [2]. To clarify, CMM calibration is the measurement of the 21 degrees of freedom of a CMM to enable mechanical correction or error mapping of a CMM. Performance verification is a series of tests that allow the manufacturer of the CMM to demonstrate that an individual machine meets the manufacturer’s specification. Note that calibration can be part of the performance verification.
The ISO 10360 series of specification standards defines the procedure for performance verification of CMMs. The series is broken down into seven parts, which are briefly described. In addition, parts 8, 9 and 10 are currently under development.
1. Part 1: Vocabulary. Part 1 [11] describes the terminology used to describe CMMs. It is important when describing CMMs to adhere to this terminology.
2. Part 2: CMMs used for measuring linear dimensions. Part 2 [12] describes how a CMM should be specified and the necessary steps to show that a machine meets specification.
The test detailed in part 2 involves measuring a series of lengths in a number of directions in the machine volume and comparing the machine indication against the known size of the artefact. In addition, part 2 describes how stable artefacts can be used for interim monitoring of the CMM.
3. Part 3: CMMs with the axis of a rotary table as the fourth axis. Part 3 [13] describes the extra steps necessary to performance-verify a CMM, which has a rotary axis as the fourth axis.
4. Part 4: CMMs used in scanning measuring mode. Part 4 [14] contains the tests necessary to demonstrate that the scanning capability of a CMM meets specification.
5. Part 5: CMMs using single- and multiple-stylus contacting probing systems. Part 5 [15] involves measuring a good-quality sphere at a number of positions and examining the variation in indicated radius to cover single- and multiple-stylus probing systems.
6. Part 6: Estimation of errors in computing Gaussian associated features. Part 6 [4] is concerned with assessing the correctness of the parameters of computed associated features as measured by a CMM or other coordinate measuring system.
7. Part 7: CMMs equipped with imaging probing systems. Part 7 [16] is concerned with assessing the error of indication of a calibrated test length (CTL) using an imaging probing system and with testing the errors in the imaging probing system.
9.3.1 Traceability of CMMs
Traceability of CMMs is difficult to demonstrate. One of the problems is associating a measurement uncertainty with a result straight off the CMM. The formulation of a classical uncertainty budget is impracticable for the majority of the measurement tasks for CMMs due to the complexity of the measuring process.
It used to be the case that the only way to demonstrate traceability was to carry out ISO 10360-type tests on the machine. However, if a CMM is performance-verified, this does not automatically mean that measurements carried out with this CMM are calibrated and/or traceable. A performance verification only demonstrates that the machine meets its specification for measuring simple lengths, that is it is not task specific.
This task-specific nature of a CMM can be illustrated with a simple example. Suppose a CMM measures a circle in order to determine its diameter. To do this the CMM measures points on that circle. The points can be measured equally spaced along the circumference but may have to be from a small section only, for example because there is no material present at the rest of the circle. This is illustrated in Figure 9.3, which shows the effect on the diameter and the centre location, if measurements with the same uncertainty are taken in a different manner. This means that, even if the uncertainty for a single coordinate is known, this does not simply correspond to an uncertainty of a feature that is calculated from multiple points.
A better method is described in ISO 15530 part 3 [17]. This specification standard makes use of calibrated artefacts to essentially use the CMM as a comparator. The uncertainty evaluation is based on a sequence of measurements on a calibrated object or objects, performed in the same way and under the same conditions as the actual measurements. The differences between the results obtained from the measurement of the objects and the known calibration values of these calibrated objects are used to estimate the uncertainty of the measurements. However, this method requires independently calibrated artefacts for all its measurements, which is quite contradictory to the universal nature of a CMM.
Alternative methods that are consistent with the Guide to Uncertainty in Measurement (GUM) (see Section 2.8.3) can be used to determine the task-specific uncertainty of coordinate measurements. One such method, that evaluates the uncertainty by numerical simulation of the measuring process, is described in ISO/TS 15530 part 4 [18].
To allow CMM users to easily create uncertainty statements, CMM suppliers and other third-party companies have developed uncertainty-evaluating software, also known as virtual CMMs [19]. Even by adopting ISO 15530 part 4 [14], there are many different approaches to the implementation of a virtual CMM [20–22].
9.4 Micro-CMMs
The advent and adoption of the CMM greatly reduced the complexity, downtime and operator skill required for measurements in a production environment. It is difficult to imagine a modern successful automobile-manufacturing plant that does not employ CMMs. The ‘CMM revolution’ has yet to come to the micro- and nanotechnology (MNT) manufacturing area. Once again, many instruments are employed to measure the dimensions of MNT parts, but there are now additional problems. Despite their tiny size, many of the parts that need measuring are very complex, high-aspect-ratio structures that may be constructed from materials that are difficult to contact with a mechanical probe (e.g. polymers or bio-materials). Also, there is often a need to measure the surface topography of steep walls found in, for example, deep reactive ion etched (DRIE) structures used for microelectromechanical systems (MEMS). The only instruments that are available are those which essentially ‘measure from above’ and were traditionally used to measure surface topography. These instruments often lack traceability for surface topography measurements (although this lack is now being addressed – see Section 6.10). Therefore, it is difficult to measure with any degree of confidence the complex structures that are routinely encountered in MNT products.
In recent years, many groups have developed ‘small CMMs’, typically with ranges of tens of millimetres and tens of nanometres accuracy in the x-, y- and z-directions. These micro-CMMs were developed in two forms: those that are developed as stand-alone CMMs and those that are retrofitted to macro-scale CMMs. One of the first micro-CMMs of the latter form was the compact high-accuracy CMM developed at National Physical Laboratory (NPL) [23]. This CMM used the movement scales of a conventional CMM with a retrofitted high-accuracy probe with six degrees of freedom metrology. This CMM had a working volume of 50 mm×50 mm×50 mm with a volumetric accuracy of 50 nm [24]. Retrofitted CMMs will not be discussed in detail as they are simply a combination of conventional CMMs (see Section 9.1) and micro-CMM probes (see Section 9.5), and they are also now rare, with purpose-built micro-CMMs being more common.
One technical challenge with probing MNT structures arises due to the inability to navigate around the object being measured without some likelihood of a collision between the probe and the part being measured. Typical miniature probing systems are less robust than those on larger CMMs, which incorporate collision protection. Future research should concentrate on these difficult technical issues associated with micro-CMMs if they are to become as widely used as conventional CMMs. However, the technical barriers associated with mechanical contact of probes at the micro-scale may force researchers to look into completely novel approaches such as SEM-based photogrammetry or X-ray computed tomography [25].
9.4.1 Stand-alone micro-CMMs
Several examples of commercially available micro-CMMs are given here. There are a number of instruments that are at the research stage (see, e.g. Refs. [26,27]) and some that were developed, but are not currently commercially available (see, e.g. Refs. [28–31]). The examples of micro-CMMs (and probes) presented below do not form an exhaustive list; rather they are designed to be representative of the different types of system that are available.
9.4.1.1 A linescale-based micro-CMM
The F25 is a micro-CMM based on a design by the Technical University of Eindhoven (TUE) [32] and is available commercially from Carl Zeiss. The F25 has a unique kinematic design that minimises some of the geometric errors inherent in conventional CMMs. The basic kinematic layout is shown schematically in Figure 9.4. The red arms are stationary and firmly attached to the machine. The blue arms form the x- and y-measurement axes and are free to move. The green arms connect the x- and y-axes to the machine and hold them orthogonal to the machine.
Rather than moving orthogonally and independently of each other, as is the case for most bridge-type CMMs, the x- and y-axes are connected together at right angles and move as a single unit. This acts to increase the stiffness and accuracy of the machine. The use of high-quality air bearings to support the xy frame and a large granite base also help to increase the stability of the system.
During the redesign process of the original TUE machine, Zeiss changed many of the component parts so they became serviceable and added a controller and software. The other main additions to the redesign were aimed at increasing the overall stiffness of the system and included the addition of high-quality air bearings and a general increase in the mass of all the major components.
The F25 is subject to only 13 geometric errors and has minimal Abbe error in the horizontal mid-plane. The measurement capacity is 100 mm×100 mm×100 mm. The resolution on the glass-ceramic linescales on all measurement axes is 7.8 nm and the quoted volumetric measurement accuracy is 250 nm. The F25 has a tactile probe based on silicon membrane technology (see Section 9.5) with a minimum commercially available stylus tip diameter of 0.125 mm.
The F25 also includes a camera sensor with an objective lens that is used to make optical 2D measurements. The optics are optimised to exhibit a high depth of field, low distortion and an accuracy of approximately 400 nm [33]. The whole system allows measurements to be taken from the optical sensors and the tactile probe, whilst using the same programmed coordinate system. A second camera is used to aid observation of the probe during manual measurement and programming.
9.4.1.2 A laser interferometer-based micro-CMM
The Isara 400 ultra-precision CMM was developed by IBS Precision Engineering [34]. The Isara 400 was developed to address the problem of off-Abbe measurement (see Section 3.4). To achieve on-Abbe measurements at all positions in the micro-CMM, rather than just the mid-plane (as for the Zeiss F25), three linear interferometers are aligned to orthogonally intersect at the centre of the spherical probe tip. The basic kinematic layout is shown in Figure 9.5.
The mechanical design of the Isara 400 was the subject of extensive research, much of which is publically available. Several design choices are key to the operation of the Isara 400 as an ultra-precision CMM. The product table is an orthogonal mirror block fabricated from a single piece of Zerodur. The three laser interferometer measuring beams are reflected from the outer surfaces of the corner mirror, whereby the virtual extension of the reflected beams intersects at the point of contact between the specimen and the sensor (see Figure 9.5). Because the sample, as opposed to the probe, is scanned in the Isara 400, the Abbe principle is realised over the entire measuring range (there will still be a residual Abbe error due to misalignment of the beams with the probe tip centre).
The measurement volume is 400 mm×400 mm×100 mm, resulting in a measuring volume suitable for large-scale optics. The resolution on the laser interferometer scales on all measurement axes is 1.6 nm and the quoted 3D measurement uncertainty is 109 nm [34,35].
9.4.1.3 A laser interferometer-based nano-CMM
The Nanomeasuring Machine (NMM) was developed by the Ilmenau University of Technology [36,37] and is manufactured commercially by SIOS Messtechnik GmbH. The device implements sample scanning over a range of 25 mm×25 mm×5 mm with a resolution of 0.1 nm. The quoted measurement uncertainty is 3–5 nm and the repeatability is 1–2 nm. Figure 9.6 illustrates the configuration of an NMM, which consists of the following main components:
• traceable linear and angular measurement instruments;
Both the metrology frame, which carries the measuring systems (interferometers), and the 3D stage are arranged on a granite base. The upper Zerodur plate (not shown in Figure 9.6) of the metrology frame is constructed such that various probes can be installed and removed. A corner mirror is moved by the 3D stage, which is built in a stacked arrangement. The separate stages consist of ball-bearing guides and voice coil drives. The corner mirror is measured and controlled by single-, double- and triple-beam plane mirror interferometers that are used to measure and control the six degrees of freedom of the 3D stage.
The operational principle, with respect to ensuring on-Abbe measurements, is similar to that of the Isara 400. Also, angular deviations of the guide systems are detected at the corner mirror by means of a double- and a triple-beam plane mirror interferometers. The detected angular deviations are compensated by a closed-loop control system. The NMM can be used with a range of probes, including both tactile and optical probes [38,39].
9.5 Micro-CMM probes
Certain requirements of micro-coordinate metrology cannot be realised by simply using classical CMM probing systems with suitably small styli. Instead, significant redesign of the probing system is required. Many research groups have developed micro-CMM probes, and a select few probes are now available commercially. A wide range of probing technologies has been developed to enhance the performance of micro-CMMs beyond that of classical CMMs. Four main types of micro-CMM probe have emerged from these developments. These types are mechanical probes, optomechanical probes, silicon-based probes and vibrating probes. Within these groupings, a wide variation of techniques is employed to realise the final working micro-CMM probe. Whilst sometimes referred to as ‘micro-probes’, most micro-CMM probes usually have a standard probe tip of diameter 0.3 mm (although tips with a diameter of 0.125 mm are readily available). This is far too large to measure a typical MEMS structure, for example a deep hole or steep DRIE trench. What are required are smaller, micrometre-scale probe tips that measure in 3D. This is not simply a matter of scaling the size of the probe in direct analogy with probes on conventional CMMs. Several in-depth reviews of micro-CMM probes can be found elsewhere [40–42].
9.5.1 Mechanical micro-CMM probes
At the onset of the development of micro-CMMs, the obvious technology suitable for micro-CMM probes was that which is used for classical CMM probes. These highly refined mechanical probes were based on the same concepts as many classical macro-CMM probes but were optimised for sensitive detection and low force probing.
A mechanical CMM probe head was developed at METAS (the Swiss NMI) which operates with a probing error of 10 nm [30]. This probe has been designed to reduce the probing force and ensure equal probing forces in each measurement axis. The operation of the probe relies on precision flexure hinges and inductive sensors. The mechanical section of the probe is manufactured from a single block of aluminium using electro-discharge machining, which negates the need for assembly. An image of the probe is shown in Figure 9.7.
A mechanical micro-CMM probe was developed at NPL for the small CMM in Section 9.4 [23,24]. The probe had a triskelion (three-legged) design and consisted of three beryllium–copper flexures connecting three tungsten carbide tubes to a central island, which supported the stylus and probing sphere. The flexures were fitted with capacitance sensors. The probe was designed to have near isotropic stiffness. The design of the NPL small-CMM probe is shown in Figure 9.8.
A similar design to that of the NPL probe is used by the Isara 400 ultra-precision CMM (see Section 9.4.1.2). The ‘Triskelion’ probe consists of a triskelion flexure system, with capacitance sensors. The refined flexure body, which is monolithic and includes the capacitance sensor targets, allows for greater control over the geometry and function of the flexures. This technology has resulted in a range of commercially available probes [34].
A 3D mechanical probe design has been developed at the Southern Taiwan University of Technology which uses DVD pickup heads as the sensing element [43]. The DVD pickup heads are intended to be significantly cheaper than any capacitance sensor-based detection system but still maintain a similar level of accuracy. A schematic of the probe is shown in Figure 9.9.
One major area of development in micro-scale probes is the need to reduce the probing force. At the micro-scale, where these probes will be operating, errors due to high probing forces are of the same order of magnitude as the desired probing accuracy. The pressure field generated at the surface when a miniature tip comes into contact may be sufficient to cause plastic deformation [44,45]. Reducing the contact force during measurement will greatly reduce the possible damage caused and increase the accuracy of the measurement.
A reduced stylus diameter results in a more compliant system that requires higher sensitivity detection methods than are used on conventional mechanical probe heads. To address the need for low force probing, a class of probes was developed that rely on precision silicon flexures, membranes or meshes to suspend the stylus, and these are discussed in the following section.
9.5.2 Silicon-based probes
Using silicon to suspend the probe reduces the overall contact force exerted on the measurement surface and serves to make surface contact detection more sensitive. Increased probe sensitivity becomes ever more essential as the stylus diameter is reduced to allow better access to high-aspect-ratio features and micro-structures. The actual detection mechanism can take various forms, either optical or electrical.
Optical detection is employed when the deflection of the stylus alters the orientation of a mirror or prism that in turn alters the position of a reflected laser beam. Alternatively, interferometric measurements can be taken from the top of the stylus. The displacement of the stylus can also be detected by using a capacitor sensor. The top of the stylus may form part of a capacitor whose properties change as contact is made with the measurement surface, and the capacitor plate that the stylus is attached to changes orientation [46].
One of the most promising detection methods for silicon-based probes is the use of piezoresistive sensors on silicon flexures. Several probes have been developed and commercialised using this technology. One such probe was developed at TUE [47] and is now commercially available from Xpress PE [40].
Other silicon-based micro-CMM probes are constructed from a silicon membrane with a micro-stylus suspended from a central locating ‘boss’ structure [48,49]. The silicon membrane has piezoresistive strain sensors etched onto it, which detects deformation of the membrane that results from probe contact with a measurement surface. A schema of a prototype boss-probe, which was developed by PTB, is shown in Figure 9.10. To directly address the anisotropy of the system, several concept probes were designed and modelled [50]. The modelled systems included the prototype single-membrane boss-probe (the original prototype design), two dual-membrane systems (one parallel design, where the two membranes were positioned in the same orientation, and another inverse design, where one membrane was positioned upside down compared to the other) and two flexure systems (one four-beam system and one eight-beam system). The parallel dual-membrane boss-probe exhibited a stiffness ratio of 0.75, where the vertical stiffness was 0.75 times the stiffness of that in the lateral direction. For the single-membrane design, this ratio is usually between 20 and 30 (depending on the geometry) and could be as high as 35.
A commercial collaboration between the University of Freiburg and Carl Zeiss has resulted in a similar three-axis silicon-based micro-CMM probe based on piezoresistive transducers [51]. The probe consists of a flexible cross structure, fabricated through a DRIE technique. The anisotropy of the probe was determined to be close to 4 (stiffness ratio) with the vertical probing force being close to 1 mN. The resolution of measurements taken in the lateral direction is about 10 nm.
Many silicon-based micro-CMM probes exhibit considerable anisotropy. Therefore, the design of these probes requires careful consideration of geometry and kinematics. To further address the need for low force probing and anisotropy, a class of probes was developed that rely on optical measurements of the stylus tip being used for contact detection. This grouping of micro-CMM probes is discussed in the following section.
9.5.3 Optomechanical probes
The flexures on most mechanical micro-CMM probes result in probing forces in the millinewton range, which can result in plastic deformation of measurement surfaces [44,45]. Therefore, with the aim of significantly reducing the contact force of probing systems, while still maintaining a similar sensitivity, a new concept was developed that relies on optical detection of the stylus tip, therefore, negating the need for flexure elements. Instead, the stylus tip is suspended by other means.
A micro-CMM probing system was designed at PTB [52,53], where the stylus is an optical fibre and the stylus tip is a sphere. The fibre probe tip is illuminated via a fibre-coupled source and its position is then mapped by the use of a measuring microscope. The microscope is attached to the fibre probe so that the stylus tip is always kept within the field of view. A 10× objective lens is used to identify sensitive movement in the x- and y-axes. A second measuring microscope, with an angled mirror, views a second sphere on the fibre horizontally above the contacting tip. This second sphere is used to measure movement in the z-axis [53]. A schema of the 3D fibre probe from PTB is shown in Figure 9.11.
The sphere tip of the PTB 3D fibre probe is sub-100 µm, and can be as low as 25 µm, allowing it to measure sub-millimetre features with few access problems. However, at this scale, the probe tip is very likely to stick to the measurement surfaces, due to the interaction of the probe tip with the surface. This effect is not helped by the low probing forces exhibited by the 3D fibre probe, which have been measured as being on the order of 10 µN. Also, the 3D fibre probe does not exhibit isotropic probing forces.
The PTB 3D fibre probe relies on optical detection of the illuminated probe tip, and therefore, there are several limitations on the geometries that the probe can measure. Although the probe is able to access high-aspect-ratio structures, such as cylindrical holes 200 µm in diameter and over 1 mm in depth, the ability of the optical system to detect the sphere is severely limited below several hundred micrometres.
A similar probe has been developed at the National Institute for Standards and Technology (NIST), which aims to negate the issue with detecting the illuminated sphere tip when inside a high-aspect-ratio hole. To achieve this, the optical detection system is focused on the stem of the fibre probe rather than its tip [54]. To extend the capabilities of the fibre detection probe into 3D, a concept of ‘buckling’ measurement was developed [55]. This allows the optical system to detect z-axis contact with a measurement surface. The operating principle of the NIST fibre deflection probe is shown graphically in Figure 9.12.
Any probe with a stylus tip with a diameter which is of the order of 100 µm and lower will be affected by surface interaction forces when probing at the micrometre scale. This effect is directly addressed by the fibre deflection probe by the addition of a piezoelectric (PZT) buzzer, which results in the capability to perform pseudo-scanning through acoustic excitation of the fibre. The inclusion of the PZT buzzer has a marked effect on this system when performing scanning measurements by reducing surface stiction.
The simultaneous developments of silicon-based micro-CMM probes and optomechanical systems to address the need for low force contact probing is an indication of the importance of this requirement. However, during their developments, it became apparent that both technologies suffer from problems that require further study. The issue of dealing with the surface interaction forces is only superficially addressed by mechanical, silicon-based and optomechanical probes. The most recent developments in micro-CMM probe research, therefore, tend to focus on surface-force counteraction.
9.5.4 Vibrating probes
The main concept of a vibrating micro-CMM probe is to force the probe tip to vibrate at a frequency and amplitude such that it is not significantly affected by surface interaction forces. Once this is achieved, the probes will neither experience snap-in nor sticking (nor, therefore, snap-back). Subsequently, surface contact is detected through analysis of the detected vibration characteristics.
One of the first commercially available vibrating micro-CMM probes was the UMAP system from Mitutoyo [42]. The UMAP probe has a 30 µm diameter stylus tip and during operation a PZT excitation circuit vibrates the stylus vertically at several kilohertz. When the stylus tip contacts a workpiece surface, the detected waveform changes from that which was generated. The estimated contact force is 1 µN. With an estimated repeatability of about 100 nm, the system is not capable of the high-accuracy measurement common with most micro-CMM probing systems. Also, the probe is only able to vibrate in 1D (vertical direction), therefore an indexing head must be employed [56].
Another vibrating probe has been developed that consists of a high-aspect-ratio probe shank (1:700) attached at one end to a quartz oscillator [57]. When in use, the oscillator causes the free end, or probing end, to vibrate at an amplitude greater than the probe shank diameter, and a ‘virtual tip’ is formed. These oscillations have a frequency of several tens of kilohertz (the quartz oscillators have a resonant frequency of approximately 32 kHz). The virtual tip diameter, equivalent to the vibration amplitude at the free end of the shank, is about 30 µm and is the surface region on the shank for which interaction with the specimen surface alters the vibration response. A schema of the operating principle of the virtual probe is shown in Figure 9.13. When using this probe, a probing force of several micronewtons is imparted onto the measurement surface [58]. Also, the probe can repeatably resolve surface features of 5 nm. However, due to its design, this probe is only capable of detection in 1D.
Methods used to vibrate the probe tip vary greatly. In an attempt to reduce the contact probing force to a very low level, a novel CMM probe has been developed that operates by laser trapping an 8–10 µm diameter silica sphere and optically recording its interactions with the measurement surface [59,60]. By ensuring that there is no mechanical contact between the micro-sphere and the CMM, the contact probing force has been reduced to several nanonewtons. The probe is forced to vibrate in the z-axis at frequencies up to 50 MHz. The point of contact is then detected as a change in the amplitude of the vibrations of the probe. Currently, this probe is unable to measure in the x- or y-axes; however, the addition of off-axis circular motion into the trapping beam has been shown to allow sidewalls to be measured [61]. The probe also have the capability to measure deep holes using an interference technique [62].
One major limitation of the vibrating probes is that the technologies currently used to produce the vibration usually result in only one-dimensional oscillation. In the case of the UMAP system and the (early) laser-trapped probe, this is vertical oscillation, for the virtual probe this is a lateral oscillation (with respect to the axis of the stylus). Therefore, any attempt to use these probing systems on 3D micro-CMMs would rely on rotation axes on the CMM or articulating probe heads to orient the probe. New developments in the use of the virtual probes have included the implementation of precision manipulation and rotation stages and active indexing heads to allow 3D probing [63].
To address the need for 3D counteraction of surface interaction forces, and the need for isotropic operation, a novel vibrating micro-CMM probe has been developed at NPL [64]. The vibrating micro-probe consists of a triskelion flexure and a micro-stylus. The vibrating probe is made to vibrate by using six PZT actuators (two on each flexure). Interaction with the measurement surface produces a change in vibration amplitude and is determined by two PZT sensors on either end of each flexure. The basic design of the vibrating micro-CMM probe is shown in Figure 9.14. The vibration of the probe is controlled so that the stylus tip is always vibrating normal to the measurement surface. The vibration of the probe is also controlled so that the acceleration of the stylus tip is sufficient to counteract the surface interaction forces between the stylus tip and the measurement surface during contact measurement. The contact probing force imparted on the measurement surface can also be reduced, theoretically to zero, as interaction with the measurement surface is registered as a change in vibration amplitude or phase rather than a signal from a static strain gauge, capacitance sensor or optical sensor.
9.6 Verification and calibration of micro-CMMs
Micro-CMMs are subject to the same geometric errors as large-scale CMMs. With accuracy goals being higher for micro-CMMs, the importance of proper verification and calibration of the instrument increases. When verifying a micro-CMM, the user is completing tests that verify that the performance of the micro-CMM is within its specification, as defined by either the manufacturer (in the case of an acceptance test) or the user themselves (in the case of a reverification test). Where verification tests the performance of the micro-CMM, calibration actively determines the magnitude of all systematic or kinematic error sources so that they can be compensated. Calibration of a CMM is often referred to as error mapping a CMM. Some effects will perhaps not be compensated, but they still have to be measured in order to assign an uncertainty contribution to them. If care is taken to ensure that all steps in the calibration are traceable to the metre, this forms the basis for the traceability of the micro-CMM as a whole.
For large CMMs, it is customary for the manufacturer to verify performance using CTLs, according to ISO 10360 part 2 [12]. Several suitable CTLs exist for CMMs, including gauge blocks, step gauges, ball bars and ball plates. The advantages of gauge blocks as CTLs are that they can be calibrated with low uncertainty (around 30 nm). Although the use of gauge blocks in performance verification for CMMs is well established, several issues arise when using them for the verification of micro-CMMs. Due to the short stylus length common to micro-CMM probing systems, it is typically not possible to contact the calibrated length of the gauge block. Probing will be close to the edge of the gauge block, which should be taken into account in the initial gauge block calibration. If the gauge block is rotated out of the horizontal plane, the CMM probe can no longer reach the bottom face of the gauge block, and an auxiliary surface has to be wrung onto the gauge block, as shown in Figure 9.15.
Many of the technical and operational issues associated with the verification of micro-CMMs are addressed in a national guideline from the Association of German Engineers – VDI/VDE 2617 part 12.1 [65]. A full review of all existing specification standards and guidelines associated with the verification of micro-CMMs, including a review of suitable CTLs, is available elsewhere [66].
Some specialised artefacts have also been developed for performance verification of micro-CMMs. For one-dimensional verification measurements, METAS has developed miniature ball bars [67] (see Figure 9.11(a)), consisting of ruby spheres connected by a Zerodur rod. A ball plate, manufactured from ruby spheres held in an Invar plate, has also been developed at METAS [68] (see Figure 9.11(c)). Spheres are widely used in artefacts for performance verification, because measuring the relative position of spheres eliminates effects from the probe diameter, shape and sensitivity, thereby allowing verification of the guidance error correction only. However, the probe-related effects have to be verified in an additional test.
Two-dimensional artefacts in the form of regular arrays of balls or holes have been developed by PTB (Figure 9.16(b)) [69]. As an option with the F25 micro-CMM, Zeiss supplies a half-sphere plate with seven half spheres on a Zerodur plate (Figure 9.16(e)). The use of half spheres instead of full spheres gives better contrast in optical measurements with a vision system. By measuring a ball or hole plate in different orientations and using error separation techniques, it is possible to obtain the remaining errors of the CMM but not scale, without external calibration of the ball or hole positions.
A considerable range of performance verification artefacts have been developed for micro-CMMs, including gauge blocks manufactured from Zerodur [70], various plate base artefacts [71–73] and several artefacts designed for specific task-based verification [70,74,75].
9.6.1 Calibration of laser interferometer-based micro-CMMs
With the calibration of the laser interferometers on a micro-CMM, the length scale is established. The following geometrical errors have to be characterised in order to establish traceability:
The cosine error is directly related to the quality of the laser alignment relative to the mirror normal (see Section 5.2.8.3). Abbe errors result from parasitic rotations in combination with an offset between the probed position on the object and the position where the measurement is taken. Abbe errors can be minimised by moving the sample instead of the probe and having the virtual intersection of the laser beams coincide with the probe centre (as on the NMM in Section 9.4.1.2). The maximum Abbe offset that remains has to be estimated, in order to quantify the maximum residual Abbe error. The rotational errors can be measured with an autocollimator or a laser interferometer with angular optics (see Section 5.2.9). The NMM (see Section 9.4.1.2) uses double and triple interferometers to measure the angular deviations during operation and actively correct for them – this greatly reduces the Abbe errors.
The mirror flatness can be measured on a Fizeau interferometer (see Section 4.4.2). The angle between the orthogonal mirrors can be measured by removing the mirror block from the instrument and using optical techniques (e.g. by comparison with a calibrated optical square). It is also possible to calibrate the orthogonal mirror block directly, by extending it with two additional mirrors and calibrating it as if it were a four-sided polygon [76]. Alternatively, the squareness can be determined using a suitable calibration artefact on the micro-CMM (see Section 9.6.2).
9.6.2 Calibration of linescale-based micro-CMMs
For a linescale-based micro-CMM, such as the Zeiss F25 (see Section 9.4.1.1), the traceability is indirect via the linescales. The linescales are periodically compared to a laser interferometer in a calibration. The calibrated aspects are the linearity, straightness and rotational errors. The squareness between the axes is determined separately, by a CMM measurement on a dedicated artefact.
For the linearity determination, a cube-corner retro-reflector is mounted in place of, or next to, the probe. The offset between the centre of the retro-reflector and the probe centre is kept as small as possible, in order to minimise the Abbe error in the linearity determination. Care must also be taken to minimise the cosine errors during the linearity calibration. Alignment by eye is good enough for large-scale CMMs, but for micro-CMMs with their increased accuracy goal, special measures have to be taken. For the calibration of the F25, a position-sensitive detector (PSD) has been used for alignment [77]. The return laser beam is directed onto the PSD, and the run-out over the 100 mm stroke reduced to a few micrometres. This translates into less than 1 nm of cosine error over the full travel.
Straightness and rotations can be measured with straightness and rotational optics, respectively. Because of the special construction of the F25, some errors are dependent on more than one coordinate. The platform holding the z-axis moves in two dimensions on a granite table. This means that instead of two separate straightness errors, there is a combined straightness, which is a function of both x and y. The same holds for the rotations around the x- and y-axes. This complicates the calibration, by making it necessary to measure the straightness and rotations of the platform along several lines, divided over the measuring volume.
The results of the laser interferometer calibration can be used to establish what is commonly referred to as a computer-aided accuracy (CAA) correction field. Figure 9.17 shows the results of a laser interferometer measurement of straightness (xTx) on the F25 with the CAA correction enabled [77]. In this case, there was a half-year period between the two measurements. The remaining error is a result of the finite accuracy of the original set of measurements used to calculate the CAA field, the finite accuracy of the second set of measurements and the long-term drift of the instrument. The maximum linearity error is 60 nm.
The squareness calibration of the F25 cannot be carried out with a laser interferometer, so an artefact is used. During this measurement, a partial CAA correction is active, based on the laser interferometer measurements only. The artefact measurement consists of measuring a fixed length in two orientations. For the xy squareness, one of these measurements will be along the xy diagonal, the other in an orientation rotated 180° around the y-axis. The squareness can then be calculated from the apparent length difference between the two orientations. The artefact can be a gauge block, but it is better to use an artefact where the distance is between two spheres, since the probe radius does not affect the measurement. Because the principle of the squareness calibration is based upon two measurements of the same length, it is particularly important that this length does not drift between the measurements. In order to get a squareness value which applies to the whole measurement volume, the two spheres should be as far apart as possible and placed symmetrically within the measurement volume.