Temperature and Length

Transcription

1 Temperature and Length Speaker / Author: Pieter Greeff NMISA Private Bag X34, Lynnwood Ridge, Pretoria, 0040, RSA pgreeff@nmisa.org Phone: Abstract The environment, especially temperature, affects all length measurements. This paper will consider the effect of temperature variation in context of two measurement systems, namely the gauge block calibration by interferometry system and high accuracy roundness calibration system. The effect of temperature deviation from the reference temperature, as well as temporal and spatial gradients will be experimented with. The results obtained by implementing control or isolation enclosures are detailed. This includes a prototype gauge block temperature control chamber design, which reduced the measurement volume temperature range from ± 1 C to ± 0,1 C and the roundness enclosure which reduced probe drift by 96%. 1. Introduction All dimensional or length measurements must be referenced back to the international standard reference temperature (20 C as defined by ISO 1:2002, Geometrical Product Specifications (GPS) - Standard reference temperature for geometrical product specification and verification), since all physical matter are subject to some degree of dimensional change if exposed to temperature variations. Equation (1) is the first order model for this change, where α is the Coefficient of Thermal Expansion or CTE in ppm/ C, T the temperature difference (equal to material temperature minus 20 C) and L the material length. = (1) Therefore to achieve accurate and comparable results (internally, locally and internationally), temperature effects on length must always be considered [1] and where applicable incorporated in the measurement setup (isolation or control), applied in the measurement result (correction to 20 C) or considered in the measurement uncertainty calculation. There are several other environmental variables that can also be considered (for example: pressure, humidity, ground vibration, dust, electricity supply, electro-magnetic noise, etc.) and the thermal influence on dimensional measurements is also a well-known subject [1, 2], we however focus on how these thermal effects can be reduced passively or controlled actively, with practical implementation and results. Some basic principles involving temperature effects on length measurement are discussed first. Following this the development of a cost effective temperature control system (or an active enclosure) for the calibration of gauge blocks with the Gauge Block Interferometer (GBI) and a passive enclosure for roundness measurements with the Talyrond73 are presented.

2 2 Temperature Effects on Length and Form Measurements CTE as an uncertainty contributor is discussed first and is used for the GBI ECS (Environmental Control System) project motivation, after which form measurements are discussed, in context of the roundness measurement project. Before this however, it is important to deviate shortly to note that highly accurate temperature probes will not necessarily result in highly accurate (temperature corrected) length measurements. It is required to approximate the true value of the UUT (Unit Under Test) temperature, as well as the difference between UUT and probe temperature. Important factors here are: 1. Stabilisation time. Stabilisation time assumes a constant environment and that the actual measurement will not induce a large temperature change of the UUT or reference. It should be long enough to ensure a predictable stable temperature. 2. Temperature Gradient. The temperature gradient can be measured by placing a sufficient number of probes along the measurement axis. 3. Contact Thermal Resistance. The distance between probe and UUT should be minimized, including air or other insulating gaps. This includes taking into consideration contact thermal resistance. 4. Thermometer Calibration. Thermometers are calibrated in ideal laboratory conditions and this is most likely not the same as their operational environment. 2.1 CTE Uncertainty CTE is the parameter which predicts the change in length of the UUT due to temperature change. It is important, though, to remember that thermal expansion not only changes the length (of an end standard such as a gauge block for example), but also the volume, and this can lead to form changes in the UUT or alignment changes in the measurement system, which can affect the result in a non-obvious way. Figure 1. Measurement uncertainty due to different calibration uncertainties of CTE over a (20 ± 1) C temperature range. Based on [3].

3 The uncertainty of the thermal expansion itself, is however also an uncertainty contributor. Figure 1 is an example of the resulting graph of such dependency. The possible deviation of length, for a 100 mm gauge block with a CTE of 11,5 ppm/ C at different uncertainties are plotted over temperature (this assumes a linear CTE over the temperature range, with a rectangular uncertainty distribution). From the figure it is clear how an error of 100 nm or 0,1 µm can easily be made with ±1 ppm/ C CTE uncertainty. This example serves to illustrate that for high accuracy measurement of end standards that minimal deviation from 20 C and low uncertainty of material CTE are critical. Figure 2. Photo of a NPL-TESA Automatic Gauge Block Interferometer, with the gauge block measurement volume on the left and electronics on the right [4]. This impacts on how NMISA Length Laboratory s calibrate gauge blocks. The NPL-TESA Automatic Gauge Block Interferometer (GBI, see Figure 2) is one of our primary methods for providing traceability to industry. Traceable gauge block calibration is ensured by calibrating the GBI laser against the national standard for length. The gauge blocks are wrung on a special platen and placed inside the measurement volume of the GBI. This platen can be rotated via the control instrumentation. The deviation from nominal length of the gauge block is then measured by laser interferometry fringe fraction techniques. Table 1. Source of uncertainty and relative contribution, for a 100 mm gauge block, with a ±1 ppm CTE uncertainty. Index Source of Uncertainty Relative Contribution 1 Laser Frequency 0,0% 2 Fringe Factor 0,3% 3 Gauge Temperature 14,9% 4 CTE 70,4% 5 Temperature (Refractive index of air) 0,0% 6 Pressure (Refractive index of air) 0,0% 7 Humidity (Refractive index of air) 0,0% 8 Parallelism/Flatness 0,2% 9 Optics/Aberrations 1,8% 10 Phase Correction 3,8% 11 Wringing Film 8,5% 12 Repeatability 0,1%

4 Currently NMISA CMC (calibration measurement capability) with the system is accredited as ( L) nm, where L is in mm. The uncertainty sources which are taken into account and the relative contribution can be seen in Table 1. The CTE uncertainty is estimated based on three sources: the manufacturer specification; literature [3, 5, 6] and on a worst case scenario using the current laboratory temperature specification of (20 ± 1) C. From the Table 1 it is clear that temperature has the largest effect on the measurement uncertainty of a 100 mm gauge block in the current Length laboratory environment. This placed the emphasis for the ECS (Environmental Control System) project on the control of temperature closer to 20 C and the future development of a gauge block CTE measuring system. 2.2 Temperature Gradient Effect on Form Measurements If measurement traceability is achieved by using a comparison method, only the difference between the CTE of the two standards will affect the temperature dependent length. That is if the two standards (UUT and calibrated standard) are of the same nominal length, at the same temperature, the temperature deviation from 20 C is not as critical, with regards to thermal expansion, as for example a minimal temperature difference between the two standards. The temperature gradient over space and time (volumetric and temporal), however also has an influence. This gradient is of more concern than the deviation from reference temperature value (assuming that the temperature is sufficiently close to the reference temperature), in context of form measurements. The reason for this is that form measurements are ideally traceable to a mathematically defined form and only the deviation from this non-physical standard is measured traceable to the metre. These deviations and therefore the effect of linear thermal expansion on them are usually small in comparison with other sources, and this is the motivation for the roundness experiments. Figure 3. Photos for the Length Laboratory high accuracy roundness instrument, the TalyRond73, before and after a 10 mm thick Perspex enclosure was placed over it.

5 Roundness, or the measurement of out of roundness, is a critical geometric parameter for most mechanical systems with rotating components. The NMISA Length Laboratory has a Taylor-Hobson Talyrond73 high accuracy roundness machine (see Figure 3) with a current CMC of 27 nm, for high accuracy roundness standards. This instrument has a rotating spindle, which carries a probe and measures the out of roundness, relative to the axis of rotation of this spindle. The UUT, usually a glass hemisphere or sphere is placed on the bench and the probe rotates around the UUT, measuring the deflection caused by the difference in roundness between the UUT surface (at that specific height) and spindle. The temperature deviation does not have a significant contribution, since the PV (Peak to Valley) of the roundness instrument and UUT are typically below 50 nm. For glass (8 ppm/ C) with a 100 nm PV out of roundness at a 10 C deviation from 20 C, will result in thermal expansion of 8 pm (0,008 nm). Secondly, since this is a comparative measurement and only the difference between the CTE s (and resulting deformation) will affect the result. Furthermore, a single rotation takes about 10 seconds. During this period of time the whole measurement system must be very mechanically stable. If this is not the case, then the closure (as determined by comparing the 0 and 360 measurement) will show an unacceptably large deviation. Precise absolute temperature therefore is not the most critical parameter, but rather steady, homogenous temperature and environment. This theory was tested with two experiments: (1) spindle roundness measurements were taken at various temperatures and (2) the probe drift was characterized before and after an enclosure was constructed over the instrument, as strongly motivated by [7] GBI ECS Based on the CTE uncertainty detailed previously, the following requirements were derived for the GBI ECS (Gauge Block Interferometer Environmental Control System, see Figure 4): 1. Design, develop and test a cost effective chamber which can: a. Be temperature controlled from 15 C to 25 C, to within 0.1 C, within an environment of (20 ± 1) C, which can be placed inside the GBI and allow for normal gauge block measurements. b. Measure and log the control volume temperature accurately (±50 mk), c. Heat and cool the control volume effectively. 2. Ensure no thermal short-circuits. Experimentation found that thermal short-circuits are very detrimental to the cooling/heating effectiveness. 3. Precise temperature control and temperature is important: a. The temperature must be as close as possible to the set point. b. There must be a minimal gradient inside the measurement volume, especially within the gauge block 4. The ECS should not affect normal GBI operation. Various concepts were considered and prototypes experimented with, they are however not discussed here for brevity. The final concept is a double walled enclosure with a Peltier (Thermo-Electric Effect) cooled/heated inner wall, with two holes: one for the laser beam (on top) and one for the rotating platen (at the bottom). Furthermore, the inner active heat radiation shield is made from 3 mm aluminium, to improve heat conduction and maintain the cost effectiveness. The outer box is made from normal sheet steel and painted. Packaging material is used for insulation between the two boxes (inner and outer). Finally, the double sided door is held in place with magnetic strips and is made from Perspex.

6 Figure 4. CAD model of the GBI enclosure (left) and photo of completed enclosure with Peltier assembly mounted on the side (right). This design was influenced the realisation that the amount of heat which must be pumped is relatively small, if the volume is insulated sufficiently, since: 1. There is minimal heat generation inside the control volume. 2. The difference between room temperature (20 ± 1) C and target temperature set point range 15 C to 25 C is relatively small (a maximum of 6 C). Figure 5. Schematic diagram of ECS prototype in cooling mode. The amount of heat to be pumped (estimated as 20 W) led to the concept of an active heat radiation shield. Conceptually this shield first removes the latent heat (for example, in cooling mode), then removes the precise amount of heat that will potentially be entering the chamber due to the temperature difference. The shield also surrounds the gauge block with heat radiating/absorbing wall (instead of a single heat sink only on one side), and does not

7 require the pumping of temperature controlled air, which can affect interferometric laser measurements. Figure 5 shows an artist impression of the heat flow in the ECS enclosure. An air-to-plate Peltier (a thermo-electric effect temperature actuator) was selected, since: 1. An air-to-plate Peltier only has one moving component which is a fan on the outside. 2. No liquids are required which necessitate refilling or which can spring a leak. 3. High accuracy solid plate temperature control can be achieved. 4. Bi-directional heat pumping is possible. 5. A simple DC motor driver can be used for control ECS Control Principal Control of the Peltier was realised with a 10 bit 20 khz PWM signal driving a DC motor driver board, which is controlled by an Arduino platform, mounted with an ATMEGA microcontroller. The microcontroller sets the DC motor drive output and direction. It is controlled by a PC application, via a serial communication port. The PC application was developed by the Length laboratory in Python and is open source. The application reads the high accuracy digital thermometer, logs the measurements (both on screen display as well as in a text file), determines the required Peltier control output, based on PID algorithms or other user requirements, and sends the new output value to the microcontroller. Figure 6 visualizes this control concept. 4 Results 4.1 GBI ECS Results Figure 6. Control and component diagram of the ECS. The GBI ECS was tested with a special gauge block which has three holes along its height. Three temperature probes were inserted into the holes (Top, Middle and Bottom) and the gauge block was positioned inside the GBI ECS.

8 The test results found that the ECS can control the temperature to 20 C (with ambient temperature around 18,9 C) within 0,1 C (see Figure 7). The temperature range or gradient between the three probes was 50 mk (Figure 8). The calibration uncertainty of the probes used are ±25 mk. This uncertainty cannot be used directly for the actual temperature measurement result uncertainty, as other temperature measurement uncertainty contributors must also be included (as mentioned previously). The temperature measurement results however serve as sufficient proof of concept at this stage, but not for actual length corrections. Figure 7. ECS Temperature Control Result at 20 C. Figure 8. Temperature Gradient Over Three Probes at 20 C. The time to achieve the required stability was more than 10h. It is possible to reduce this time significantly by optimizing the control parameters. This waiting period will however not influence calibration efficiency, since longer gauge blocks (75 mm or 100 mm) are left over night in the measurement volume for stabilization. Figure 9 shows the results for ESC temperature control at 15 C and 25 C. This confirms the operational ability of the concept. The gradient however was found to be 0,21 C (heating) and 0,14 C (cooling) over the three probes. This is bigger than what the specification requires. The lower limit also seems to be close the actuator limit. This however can be improved.

9 Figure 9. Temperature Control at 15 C and 25 C. The ECS delay time, stability, efficiency and gradient can be improved by (1) reducing the air gap between gauge block and active heat radiation shield, (2) insulating the laser opening with an optical parallel, (3) replacing the current platen with an insulated one, (4) using copper for the inner wall, (5) implement temperature control of the platen or base and (6) drawing a vacuum, as done by [8, 9]. Additional future work includes the incorporation of more temperature sensors and a special back cover for GBI to remove the Peltier ambient side heat Spindle Roundness and Room Temperature Results Spindle roundness measurements were taken by applying an error separation method, where the UUT is rotated. This method yields both the spindle (instrument) and UUT out of roundness. Figure 10 shows the roundness against the room temperature. Using this data it can be motivated that there is a relationship between roundness and temperature, but that it is indeed small compared to the drift. The error separation measurements has an average closure value of 1,2 nm and roundness range (maximum minimum) of 6,8 nm, over a temperature range of 8 C. The current laboratory specification of (20 ± 1) C therefore further demotivates the development of a high accuracy temperature control system for this instrument. The probe drift during measurement however was comparatively large and is discussed next. Figure 10. Plot of spindle out of roundness (RONt) versus room temperature

10 4.2. Roundness Probe Drift Results The probe drift was characterized in order to better understand the instrument uncertainty. This was done by measuring and filtering the probe output, over time, without rotating the spindle. The environmental factors which are assumed to affect this measurement are: electronic drift and noise, mechanical vibration (due to air or ground movement) and thermal deformation due to temperature gradients over the instrument. The last factor is illustrated in Figure 11. The large metrological frame is depicted with this diagram, since the instrument is approximately 1625 mm tall, a temperature gradient from top to bottom of the instrument can cause a dimensional offset over time between the spindle and the UUT. Figure 11. Artist impression of the thermal gradient in the metrological loop or the roundness machine Figure 12 and Table 2 displays the summary of results of obtained. Measurement sets were taken for a period time in various conditions. Each set was dived up into smaller time steps. Over each of these time steps a range (drift, maximum minus minimum value) was calculated. The average range and maximum for each measurement condition per time step was then calculated and compared with each other. Time steps of 10 seconds were used since it takes approximately that long for one spindle revolution. Time Step (s) Table 2. Effect of the roundness enclosure on probe drift. Average Range of Drift (nm) Enclosure Closed, No Contact Enclosure Closed, Contact Enclosure Open, Contact No Enclosure, Stage On, Contact No Enclosure, Stage Off, Contact 10 0,1 0,2 1,2 4,8 5,6 20 0,1 0,4 2,1 8,3 9,2 30 0,2 0,5 2,9 10,2 11,8 The various conditions were: no enclosure over machine, with horizontal axis stage turned off and on. With an enclosure, while the probe is pressing against the UUT, without pressing

11 against anything and finally with the enclosure door open and probe pressing against the UUT. The results show the benefit of the roundness machine enclosure. For a 10 second interval it reduced the average range with 4,6 nm. Just closing the door resulted in an improvement of 1.0 nm. Considering the current CMC of 27 nm the improvement is significant. The effect of no-probe contact versus contact results in an average range reduction of about 0,1 nm (over 10 seconds). This difference can be used to quantize the electronic versus the mechanical error contribution to drift over time. Figure 12. Average drift of probe over time period steps, in various conditions. These experiments therefore (1) improved the drift characteristics of the roundness instrument; (2) demonstrated the importance of considering thermal gradients as well air vibration and (3) motivates that relatively large uncertainty contributors can be reduced with small expenses in some cases, and (4) demonstrates the relevance of absolute temperature on roundness measurements. Note that this drastic improvement cannot be exclusively contributed to a more homogenous temperature over the instrument, but could possibly also be influenced by a reduction in air vibration. 6. Conclusion Temperature is length dependent, and must always be considered in any dimensional measurement. This is not only the temperature deviation from the reference temperature, but also the temperature gradient (from beginning to end of measurement and over whole measurement volume) and this effect can be reduced with environmental control, corrected by applying the CTE formula, or compensated for with the uncertainty budget The design of the ECS was presented and shown capable of reducing the current Length GBI laboratory temperature control ability of (20 ± 1) C to (20 ± 0,1) C. The ECS can change the temperature within the measurement volume, but improvements needs to be made with respect to temperature control effectiveness and gradients. Several suggestions were made to facilitate this.

12 Experiments with the roundness measuring system improved the drift characteristics of probe by 96% with the construction of a Plexiglas enclosure. This shows that it is important to consider environmental effects on form measurement and that a cost effective passive enclosure reduced the environmental contribution to the measurement uncertainty. It also found that the spatial and temporal temperature gradient is more critical than the temperature deviation from 20 C, specifically for roundness measurements on the Length Laboratory Roundness System. These experiments and results will be used to develop new uncertainty of measurement estimations for the above mentioned measuring systems. Furthermore, it should encourage industry dimensional laboratories with concepts around temperature effects, which will help to improve measurement accuracy and therefore develop industry. Finally, technology such as this could be developed further for practical application and improvement of industry or Afrimets laboratories. Acknowledgements The authors would like to thank Roko Popich (Mechanical Workshop) for the construction of the roundness enclosure, help with the ESC chamber design and adjustments. Oelof Kruger for expert technical guidance, Faith Hungwe for technical revision, Floris v.d. Walt for CMM temperature related measurements and Hans Liedberg for high accuracy temperature calibrations on short notice. References [1] T. Doiron, Uncertainties Related to Thermal Expansion in Dimensional Metrology, NCSLI MEASURE, [2] J. Bryan, International Status of Thermal Error Research, Annals of the CIRP, vol. 39, no. 2, pp , [3] Mitutoyo, Gauge block with calibrated coefficient of thermal expansion, [4] Hexagonmetrology, [Online]. Available: [Accessed ]. [5] Brown&Sharpe, Technical Reference Manual Automatic Gauge Block Interferometer, Shropshire, [6] J. E. Decker and J. R. Pekelsky, Uncertainty Evaluation of the Measurements of Guage Blocks by Optical Interferometery, NRC, Canada, [7] R. Thalmann and J. Spiller, A primary roundness measuring machine, SPIE Proceedings, Recent Developments in Traceable Dimensional Measurements III, vol. 5879, pp , [8] M. Okaji, N. Yamada and H. Moriyama, Ultra-precise thermal expansion measurements of ceramic and steel gauge blocks with an interferometric dilatometer, Metrologia, no. 37, pp , [9] J. Unkuri, J. Manninen and A. Lassila, Accurate Linear Thermal Expansion Coefficient Determination By Interferometry, in XVII IMEKO World Congress Metrology in the 3rd Millennium, Dubrovnik, Croatia, 2003.