Co-ordinate Measuring Machines (CMM) (Metrology)

17.8.
Three dimensional measurements are essential for various components. CMMs are useful for this purpose. These machines have procise movements in a; -y -z coordinates which
can be easily controlled and measured. Each slide in three directions is equipped with a precision linear measurement transducer which gives digital display and senses + ve/-ve direction. These are manufactured in both manual and computer-controlled models and come in a wide range of sizes to accommodate a variety of applications. The measuring head incorporates a probe tip, which can be of different kinds like taper tip, ball tip etc. Various type of CMMs are shown in Fig. 17.11. All these have very low measuring uncertainty, computer aided measuring runs, vibration free mechanical structure, and high rigidity. In addition all moving parts must be set verv accurately, driven by
(Measuring head movement in plane perpendicular to paper)
(Measuring head movement in plane perpendicular to paper)
Types of CMMs.
Fig. 17.11. Types of CMMs.
fast motors, incorporate sensitive drive unit for fine adjustment of the axis, have rugged and precise probe system to facilitate exact dynamic probing. The cantilever type (CMM—refer Fig. 7.11) is easiest to load and unload, but is most susceptible to mechanical error because of sag or deflection in y-axis beam. Bridge type is more difficult to load but less sensitive to mechanical errors. Horizontal boring mill type is best suited for large heavy workpieces. Vertical bore mill type is highly accurate but usually slower to operate. A floating bridge type machine is also available in which the complete bridge can slide in v-direction on the slides. It has the compromises of both cantilever and bridge type, and is thus fast to operate, simple in alignment, and rugged construction affords consistent accuracy.
For measuring the distance between two holes, the workpiece is clamped to the worktable and aligned with the machine’s three mutually perpendicular*, y and z measuring slides. The tapered-probe tip is then seated in first datum hole and the probe position digital readout is set to zero. The probe is then moved to successive holes, at each of which the digital
readout represents the coordinate part-print hole location with respect to the datum hole. Machine is also equipped with automatic recording and data processing units which are essential when complex geometric and statistical analysis is to be carried out. In fact, in modern machines, automatic on-line processing of measurement data is possible when the part is still on the worktable.
In a special co-ordinate measuring machine, both linear (x and z axes) and rotary axes are incorporated. The machines can measure various features of parts whose shapes are objects of revolutions like cones, cylinders and hemispheres.
R-Q machines having motions of their measuring head in R, 0 and $ direction are used for inspecting parts that are basically spherical.
As it is impossible to manufacture a mechanically perfect machine it is important to be able to analyse the geometry errors associated with each individual CMM and determine their effects on the machine’s measurement accuracy. The result of such analyses can be used to compensate for these effects and thus provide a high degree of accuracy that could not otherwise be achieved.
The prime advantage of co-ordinate measuring machine is the quicker inspection coupled with accurate measurements.
The co-ordinate measuring machine with mechanical gauge makes use of two-axis X and ^positioning tables to bring the work to the probe that engages the holes to the inspected.
Spherical co-ordinate (R-6) Measuring Machine.
Fig. 17.12. Spherical co-ordinate (R-6) Measuring Machine.
Some machines are equipped with an optical comparator as well as travel dial indicator.
Present day co-ordinate measuring machines are three-axis digital read-out type and work up with an accuracy of 10 microns and resolution of 5 microns. These utilise a measuring element called Inductosyn data element which uses inductive coupling between conductors separated by a small air gap. As this element is not subjected to wear, it does not develop inaccuracy. It does not require reference standards or any other external device for its operation. The workpiece is aligned by a probe and by a switching adjustment on the worktable.
Many machines utilize Moire fringe concept for measurement.
Some coordinate measuring machines are available with accessories like optical viewing screen, (optical comparator), microscope attachment for the inspection of thin, soft, or delicate workpieces, and automatic print out. Some machines, in addition to measuring in three axes, are also designed to permit the checking of angularity, roundness, taper, and concentricity. Provision of rotary table makes such co-ordinate measuring machine more versatile because setting of a part need not be changed and all areas can be approached due to positioning of rotary table. The errors likely to occur in multiple set-ups are thus avoided.
Some co-ordinate measuring machines utilise electronic indicator probe (mounted on the end of the spindle) which can reach over and under the workpiece to check squareness in a single set up. Some machines are provided with linear air bearings on the horizontal slide motions to achieve finer slide position resolution.
17.8.1.


Important Features of Co-ordinate Measuring Machines (CMM).

In order to meet the requirement of faster machines with higher accuracies, the stiffness to weight ratio has to be high in order to reduce dynamic forces. To give maximum rigidity to machines without excessive weight, all the moving members, the bridge structure, Z-axis carriage, and Z-column are made of hollow box construction.
Principles of kinematic design are used in the three master guideways and probe location. Even whole machine with its massive granite worktable is supported on a three-point suspension.
A map of systematic errors in machine is build up and fed into the computer system so that error compensation is built up into the software.
All machines are provided with their own computers with interactive dialogue facility and friendly software.
Thermocouples are incorporated throughout the machine and interfaced with the computer to be used for compensation of temperature gradients and thus provide increased accuracy and repeatability.
With the advent of three-axis programming, computers enable CMM to measure three-dimensional object from variable datums.
The real benefit of today’s CMM is its total flexibility and programmability, which makes it capable of handling virtually any measuring requirement within its physical size limit, thus rendering dedicated or specially designed gauging unnecessary.
Design improvements allied to a rapid growth in software for 3 and 4 axis movements enable CMMs to measure straight line relationships between basic features, i.e., hole centre distances, etc. and also a variety of form measurements, such as turbine blades, cam profiles etc.
17.8.2.

Possible Causes of errors in CMM.

The table of CMM may not have perfect geometric form, or the table and probes may not be in perfect alignment. The probes may have a degree of runout, so it should be located at the same rotational position. The probes moving up and down in the z-axis may have some perpendicularity errors. There may be errors in optical readout of the digital system. It is, therefore, very essential that CMM should be calibrated with master plates before using the machine.
The magnitude of dimensional errors of a CMM is influenced by (i) Mechanics-associated with the straightness and perpendicularity of the guideways, {ii) Scale-division and adjustment of scales, (Hi) Probe-form length and structure of probe configuration, (iv) Probe system calibration, repeatability, zero point setting and reversal error, (v) Electronics-interpolation errors due to digitization, (vi) Errors of data feeding by operator into compuer, (vii) Specimen-weight, clamping, surface finish, hardness, and due to (viii) Environment-(temperatures, oscillations, humidity, dirt).
While some conditions may be influenced by the operator/CMM user, other errors can be controlled and ascertained by the manufacturer and minimized by the measuring software. The length of the probe should be minimum and rigid in order to reduce deflection. The weight of the workpiece may change the geometry of the guideways and therefore, the workpiece must not exceed a maximum weight. Variation in temperature of CMM, specimen and measuring lab influence the uncertainty of measurement. Similarly, the smoke particle, a finger print, a dust particle and human hair may introduce uncertainty in measurement.
In addition to above, there can be several errors due to deviations in the guideway of CMM, but these are built in the machine and can not be influenced by the user. There are 21 components of such errors and are identified as translational errors, rotational errors and perpendicularity errors.
Translational errors result from errors in the scale division and errors in straightness perpendicular to the corresponding axis direction. Quite often the errors in scale division are termed as positional errors and are designated as xpx, ypy and zpz. Similarly translational errors due to straightness are termed as xty, xtz, ytx, ytz, ztx and zty. To clarify further it can be said as
Positioning Deviation (denoted byp)
xpx movement in x-axis and positional error in x-axis ypy movement in y-axis and positional error in y-axis zpz movement in z-axis and positional error in z-axis
Straightness Deviation (denoted by t)
xty movement in x-axis and straightness deviation in y-axis xtz movement in x-axis and straightness deviation in z-axis ytz movement in y-axis and straightness deviation in z-axis ytx movement in y-axis and straightness deviation in x-axis ztx movement in z-axis and straightness deviation in x-axis zty movement in z-axis and straightness deviation in y-axis.
Rotational Deviation (denoted by r)
These errors are caused due to twisting deviations in guideways. Depending upon the behaviour of errors these can be split in roll error, pitch error and yaw error. When rolling in x- direction, pitch error is introduced in y-direction and yaw in z-direction. yry movement in y-direction and roll in y-axis yrx movement in y-direction and rotational deviation in x-axis
(also known as pitch error) yrz movement in y-direction and rotational deviation in z-axis
(also known as yaw error) xrx movement in x-direction and roll in x-axis xry movement in x-direction and translational deviation in y-axis
(also known as pitch error) xrz movement in x-direction and translational deviation in z-axis
(also known as yaw error) zrz movement in z-direction and roll in z-axis zrx movement in z-direction and translational deviation in x-axis (also known as pitch error)
zry movement in z-direction and translational deviation in y-axis (also known as yaw error) Perpendicularity Error (denoted byw)
This error is caused if the three axes are not orthogonal and deviation between these are termed as perpendicularity error.
xwy error in squareness between x and y axis
xwz error in squareness between x and z axis
ywz error in squareness between y and z axis 17.8.3. Error reduction and error compensation. In coordinate measuring machine which is not accurate but very repeatable, the inaccuracy can be compensated by error reduction and error compensation. In error reduction, the sources of problem are identified and physically eliminated. In error compensation, the errors are detected and the errors are mathematically eliminated, compensation being done by computers. Thus one by one, all the sources of errors are analysed and treating them as separate entity, all of them are eliminated one by one. In another approach, no attempt is made to separate the sources of errors, but it is assumed that the systems errors are part of an overall problem that can be dealt with as if it were one problem. This method deals with the error sources in combination and bases its
algorithms on this assumption. It uses the smallest number of artifacts, to find the errors. Thus if one finds all the displacement errors existing on the perimeters of the measuring volume, then all errors inside the measuring volume are captured in combination. Since the recommended measurement error is usually no more than 10%, the error compensation should reduce the error to that extent. The data collected in small increments all around the measuring volume allow a grid of data points to be created that no longer has the bar errors.
17.8.4.

Accuracy Specifications for Coordinate Measuring Machines.

Two types of accuracies are defined in connection with coordinate measuring machines ; viz geometrical accuracy (determined by independent measurement because they make major contribution to overall accuracy of machine) and (ii) total measuring accuracy (determined by utilising the entire measuring machine system as applied to master gauges).
Geometrical accuracy concerns the straightness of axes, squareness of axes, and position accuracy. Total measuring accuracy concerns axial length measuring accuracy, and volumetric length measuring accuracy.
Straightness of axes. Straightness of axes is defined as deviation from a straight line in two orthogonal planes for each axis of movement, and thus following six measurement parameters need to be considered : Straightness of x-axis measured in y and z directions ; of y-axis in x and z directions ; of z-axis in x andy directions. Measurement is effected against a suitable straightness reference, e.g. laser beam and taking at least 10 readings at different points in each direction over full travel of each axis. Straightness is defined as the distance A (deviation bandwidth) between the two parallel lines containing the two graphs (Refer Fig. 17.14 a).
Error in straightness
(a) Error in straightness
Error in squareness
(b) Error in squareness
Error in position Fig. 17.14
(c) Error in position Fig. 17.14
Fig. 17.13

Squareness of axes.

It is defined as deviation from 90° of the straightness bandwidth lines of two orthogonal axis movements. Three measurement parameters (squareness between x and y axes, between y and z axes, and between x and z axes) are possible. Measurement is effected against a suitable squareness reference, e.g. laser beam, taking at least 10 measurements over full travel of each axis. Squareness is then defined as the deviation from 90° of the angle between the straightness bandwidth lines of two axes and is given as an absolute value in arc seconds (Refer Fig. 17.13 b).

Position accuracy.

It is defined as difference between position readout of machine along an individual axis and value of a reference length measuring system. Following three measurement parameters are needed for position accuracy. Position accuracy of a: axis, of y axis, and of z axis. Meaurement is effected along one measuring line for each machine axis located approximately at centre of measuring travel of remaining two axes. For this purpose, a suitable reference length measuring system, e.g. laser interferometer, is aligned to each machine axis within a permissible deviation of 1 arc minute (minimum 20 points measured over full travel of each axis). Fig. 17.14 shows a typical deviation record in which position accuracy F is defined as the distance between the two parallel lines containing the two graphs for the two directions.

Axial Length Measuring Accuracy.

It is denned as difference between the reference length of gauges, aligned with a machine axis, and the corresponding measurement results from the machine. Three reference gauges are measured in each of the three axes x, y and z, with gauge length approximately 1/3, 1/2 and 3/4 of full travel of respective axis (upto a maximum of 1000 mm). Length measuring accuracy G is denned as the absolute value of the difference between the calibrated length of the gauge block and the actual measured value.

Volumetric Length Measuring Accuracy

It is denned as difference between the reference length of gauges, freely oriented in space, and the corresponding measured results from the machine. Three reference gauges are measured, their lengths corresponding to approximately 1/3, 1/2 and 3/4 of the full travel of the longest axes (upto maximum of 1000 mm). Volumetric length measuring accuracy Mis denned as the absolute value of the difference between the calibrated length of the gauge block and the actual measured values.
17.8.5.

Calibration of Three-Coordinate Measuring Machine (CMM).

The optical set up for the x-axis calibration is shown in Fig. 17.15 (a). The laser head is mounted on the tripod stand and its height is adjusted corresponding to the working table of CMM.
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The interferometer contains a polarized beam splitter, which reflects the Fl component of the laser beam and let the F2 component pass through. The retroreflector is an optically ground and polished glass trihedral (three-surface) prism (sometimes called a “cube corner”). It reflects the laser beam back along a line parallel to the original beam, but offset from it by twice the distance at which the incoming beam is offset from the corner apex. For distance measurement, the Fl and F2 beams that leave the Laser Head are aimed at the Interferometer which splits Fl and F2 via polarizing beam splitter. Component Fl becomes the fixed-distance path, and F2 is sent to a target which reflects it back to the Interferometer. Relative motion between the Interferometer and the remote Retroreflector causes a Doppler shift in the
returned frequency..Therefore, the Measurement Receiver Photo-detector in the Laser Head sees a frequency difference given by Fl – F2 ± AF2.
The Fl – F2 ± AF2 signal that is returned from the external Interferometer is compared in the Measurement Display Unit to the Fl – F2 Reference Signal. The difference, AF2, is related to the velocity and hence to the distance.
Laser head is adjusted for orientation and level so that the reflected beam from the Linear Retroreflector mounted on the working table of CMM gives maximum beam strength for the full range of its movement. The Laser Beam splitter fitted with Reference Retroreflector is mounted on the stationary bed of CMM between the Laser Head and Linear Retroreflector and properly aligned to obtain maximum beam strength.
The longitudinal micrometer microscope of CMM is set at zero and the Laser Display Unit is also set at zero. The CMM microscope is then set at the following points and the corresponding readings of Laser Display Unit are noted :
1 to 10 mm, every mm
10 to 200 mm, in steps of 10 mm
The accuracy of linear displacement measurements is affected by changes in air temperature, pressure and humidity. The refractivity of air and hence the wavelength of light propagating through it is dependent on three parameters. The automatic compensation for wavelength changes is provided by the material sensor attached to the machine.
The temperature is also noted at each reading to apply corrections for the thermal expansion of the standard steel scale with reference to the standard temperature of 20°C.
Similarly the readings fory and z axes are taken. The optical arrangements for y and z axes are shown in Fig. 17.15 (6) and 17.15 (c).
17.8.6.

Performance of CMM.

In evaluating the performance of a coordinate measuring machine, the following major aspects need consideration :
(i) Definition and measurements of “geometrical accuracies”, such as positioning accuracy, straightness and squareness.
(ii) Master gauge measurement methods to define “total measuring accuracy” in terms of “axial length measuring accuracy, volumetric length measuring accuracy, and length measuring repeatability, i.e., the coordinated measuring machine has to be tested as complete system. Measuring systems can be characterised by the combination of “mode of operation” and probe type. Modes include free floating manual, driven manual, and direct computer controlled. Probe types are passive, switching, proportional and nulling. The CMM is tested in each mode and with the probe that is commonly used.
(iii) Since environmental effects have great influence, explicit specifications on environmental conditions for the accuracy testing, including thermal parameters, vibrations and relative humidity are required.
It is usually difficult to establish a quantitative relationship between any particular environmental specification and the effect on machine’s performance. Thus it is better to define what level of environmental influence is acceptable, and maintain those conditions.
The thermal effects dominate the environmental influences affecting a CMM. The sources of thermally induced errors include deviations of surrounding air temperature from 20°C, temperature gradients, radiant energy (e.g. sunlight), utility air temperature, and self-heating in machines with drive motors. Thermal effects may take the form of differential expansion between the workpiece and the machine scale system, drift between a workpiece origin and the machine scale system origin, and distortion of the machine structure leading to significant changes in the calibration and adjustment of the machine. The dominant effect of
vibration is to degrade the repeatability of a machine. If the indicated relative motion between the machine table and the ram exceeds 50% of the working tolerance for repeatability, the vibration environment is deemed unacceptable.
It is important that suitable performance tests capable of testing the machine as a complete system are performed. It may be mentioned that use of parametric testing (straightness, squareness, angular motion) does not test the system performance and it is difficult to relate the results of these tests to expected performance. Performance test is carried out by measuring a mechanical artifact which provides some similarity between the machine testing and actual measurement of workpieces. Such testing must sample throughout the work zone. For performance test, linear displacement accuracy is checked by a step bar or a laser interferometer. These measurements are made along three orthogonal lines through the centre of the work zone to provide a thorough sampling of many combinations of x, y, and z errors that occur throughout the work zone of a machine.
Using the socketed ball bar provides a means of sweeping out the surface of a (nearly) perfect hemisphere with a physical object (ball). The CMM is used to measure the location of the centre of this ball at many locations on the hemisphere. The actual measurement data is compared to an ideal hemisphere simply by recording the range of the length of the ball bar computed from the data. The procedure calls for moving the socket defining the centre of the hemisphere to several locations in the work zone and repeating the meaurements. Three different lengths of the bar also are used. The performance is specified independently for the different lengths.
17.8.7.

Applications of CMM.

CMMs find applications in automobile, machine tool, electronics, space, and many other large companies. These machines are ideally suited for development of new products and construction of prototype because of their maximum accuracy, universatility and ease of operation.
Because of high speed of inspection, precision and reproducibility of coordinate measuring machines, these find application to check the dimensional accuracy of NC produced workpiece in various steps of production.
Regular inspection of workpieces by CMMs provides information on possible trends (due to tool wear, temperature factors and other influences) obtained through a statistical evaluation running simultaneously with production, allows efficient process inspection and control.
For safety components as for aircraft and space vehicles, 100% inspection is carried out and documented using CMM.
CMMs are best suited for the test and inspection of test equipment, gauges and tools.
CMMs can be used for determining dimensional accuracy of the bought in components, variation on same and thus the quality of the supplier.
These are ideal for determination of shape and position, maximum metal condition, linkage of results, etc., which other conventional machines can’t do.
Because of verification facility, these can be assessed for their absolute accuracy, running in characteristics and variation. These make it possible to eliminate human error.
CMMs can also be used for sorting tasks to achieve optimum pairing of components within tolerance limits.
A coordinate measuring machine can replace several single purpose equipment with a low degree of utilisation like gear tester, gauge tester, length measuring machine, measuring microscope, etc.
To test a modified component, only a new component program is required whereas expensive modification of reference gauges is required in conventional machines.
CMMs are also best for ensuring economic viability of NC machines by reducing their downtime for inspection results. They also help in reducing reject costs, rework costs through measurement at the appropriate time with a suitable CMM.
17.8.8.

Advantages of CMM.

As the machined parts are becoming increasingly more complex with more features and tighter tolerances, inspection with surface plate and height gauges is becoming slow, inaccurate and costly. The various advantages of CMM are: increased inspection throughput, improved accuracy, minimisation of operator error, reduced operator skill requirements, reduced inspection fixturing and maintenance costs, uniform inspection quality, reduction of scrap and good part rejection, no need of separate go/no go gauges for each feature, reduction in calculating and recording time and errors, reduction in set-up time and fixturing costs through automatic compensation for misalignment, provision of a permanent record for process control and traceability of compliance to specifications, reduction in off-line analysis time, simplification of inspection procedures, possibility of reduction of total inspection tiire through use of statistical and data analysis techniques.
17.8.9.

Computer Controlled Coordinate Measuring Machine.

Fig. 17.16 shows
the layout of a computer controlled CMM, a flexible measuring centre. The measurements as well as the inspection of parts for dimension, form, surface characteristics and position of geometrical elements are done at the same time in a fully coordinated manner (complete metrological description of a workpiece).
Mechanical systems for the computer controlled CMMs can be subdivided into four basic types as shown in Fig. 17.17. The selection of a particular type depends on the application.
All these machines use probes (which may be trigger type or measuring type) Probe system is connected to the
System components of a computer controlled CMM.
Fig. 17.16. System components of a computer controlled CMM.
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(i) Column type
(ii) Bridge type
{iii) Cantilever type
(iv) Gantry type
Fig. 17.17. Mechanical systems of computer controlled CMMs.

spindle in z-direction.

It establishes the relation between the probing points in the measuring volume and the machine coordinate system. Trigger Type Probe System
The main features of this system are shown in Fig. 17.18 (a) and 17.18 (6). The “buckling mechanism” is a three point bearing, the contacts of which are arranged at 120° around the circumference. These contacts act as electrical micro switches. When being touched in any
Part section of Probe head.
(a) Part section of Probe head.
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(b) Out line of Probe head.
Fig. 17.18. Trigger type Probe system.
probing direction one or more contacts is lifted off and the current is broken, thus generating a pulse. When the circuit is opened, the current co-ordinate positions are read and stored. After probing, a prestressed spring ensures the perfect zero position of the three point bearing. The probing force is determined by the prestressed force of the spring. With this probe system data acquisition is always dynamic and therefore the measuring time is shorter than in static principle.

Measuring Type Probe System

It is a small coordinate measuring machine in itself. The “buckling mechanism” of this system consists of parallel guideways. (Refer Fig. 17.19). At the moment of probing the spring parallelograms are deflected from their intitial position. Since the entire system is free from torsion, play and friction, a defined parallel displacement of probes as compared to their
Schematic of measuring probe head.
Fig. 17.19. Schematic of measuring probe head.
Fig. 17.20. Displacement of parallelogram when probing.
Fig. 17.20. Displacement of parallelogram when probing.

original arrangements can be measured.

The displacement of parallelogram is shown in Fig. 17.20.
In static operation the electronic position regulating mechanism on probing of the specimen moves the slide of the probe axes till the inductive measuring systems of the probes
are in their corresponding zero positions. After this the machine coordinates are automatically transferred to the computer.
The accuracy of such machines can be improved by in-process correction of the sys tematical deviations using powerful data processing systems.
Numerical error correction is accomplished by developing a mathematical model anc defining a software program, measuring the systematic deviations of the CMM components and storing the deviations, and on-line correction of the measurement values.
The mathematical model of the mechanical system describes the spatial interaction o the systematic deviations of the CMM components. It also forms the basis for the computatior
of error propagation and final estimation of the overall accuracy concerning a specified measuring task.
If the components of the CMM are assumed as rigid bodies, the position deviations of a carriage can be described by three displacement deviations parallel to the axes (1), (2) and (3) and by three rotational deviations about the axes (4), (5) and (6) (Refer Fig. 17.21).
Similarly deviations (7)—(12) occur for X-carriage and (13) to (18) for z-carriage. Thus 18 path-dependent deviations and three squareness deviations (19), (20) and (21) are to be measured and to be treated in the mathematical model.
1. Positioning Deviation Straightness Deviation
2. horizontal
3. vertical
Rotational Deviations Rotational about
4. Moving Axis
5. Horizontal Axis
6. Vertical Axis
1—6. Deviation ot Y-carriage
7—12 and 13—18 for deviations of other X and Z carriages
Squareness Deviations
19. Plane XY
20. Plane XZ
21. Plane YZ
Deviations of a Carriage
Deviations of the Y-carriage of a CMM, squareness deviations
Fig. 17.21. Deviations of the Y-carriage of a CMM, squareness deviations.
The geometrical relationships of the spatial interaction of the deviation components in y-carriage (1) to (6) are shown in Fig. 17.19 in exhagrated form. It is assumed that the other two guideways are perfect, the squareness deviations and the lengths of the probe stylii are not considered. It is also assumed that the systematic deviations, in the y-measuring line are passing through the origin of the coordinate system.
Moving the probe stylus in the y-direction on a line passing through the origin of the coordinate system (line L{) in Fig. 17.22) is not a straight line but a curved one due to errors in the guide. Because of the three displacement deviations, the coordinates x, y, z have to be corrected.
If moving on measuring line L2, further corrections are required due to the offsets x and z from curve L\ resulting from the pitch angle 5, the roll angle 4 and the yaw angle 6. (Refer Fig. 17.22)
Similarly the deviations of all three carriages and the squareness errors can be taken into account.
The treatment of all measured deviations is for (a) improvement of the accuracy by numerical’error correction, and (b) computation of measurement uncertainty.
The effect of the error correction can be tested by means of calibrated step gauges.
Effects of systematic deviations of the Y-carriage
Fig. 17.22. Effects of systematic deviations of the Y-carriage.
In this way, on the basis of the mathematical model, a realistic estimation for the three dimensional length measurement uncertainty can be made.
For simple structured measuring instruments the relationship between accuracy and temperature is well known in contrary to CMMs with their high complexity and flexibility.
It is found that majority of the deviations can be corrected, if the temperatures of the scales are correctly taken into consideration. Thus one temperature sensor per scale should be the absolute minimum requirement for temperature measurements.
It has also been found that deformations of the CMM components (leading e.g. to straightness and squareness deviations) are caused by the changes of the spatial temperature gradients in the environment and by change of the spatial average temperature. The latter becomes obvious by the different thermal time constants of the CMM components, being lower for steel and higher for granite. Consequently one has to take into consideration the distortion of the CMM components caused by temperature influences, in order to guarantee the stated accuracy specifications even under poor environmental conditions.
The users of CMMs must always be sure that the measuring machine used complies with the specified uncertainty of measurement. This requirement can be met over a prolonged period of time only if the machines are re-verified at regular intervals. Several techniques are used to verify and improve the performance of CMMs.

The following accuracy/test items are carried out for CMM :

1. Measurement Accuracy
(a) Axial length measuring accuracy
(6) Volumetric length measuring accuracy
2. Axial Motion Accuracy
(a) Linear displacement accuracy
(b) Straightness
(c) Perpendicularity
(d) Pitch, yaw and roll
The axial length measuring
accuracy is tested at the lowest position of the z-axis on the opposite side of the main axial guide of CMM. The length tested are approximately 1/10, 1/5, 2/5, 3/5, and 4/5 of the measuring range of each axis of CMM. The test is repeated five times for each measuring length and results plotted and permissible value of measuring accuracy is derived.
Volumetric Length Measuring Accuracy
The Volumetric length measuring accuracy is tested by measuring artefacts at two points on a spatial axis at 45° to the x or y axis and about 30° to the x-y plant. Measurments are made as in case of axial length measuring machine.

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