Wide Spectra of Quality Control Part 17 ppt

Quality Control and Characterization of Scintillating Crystals for High Energy Physics and Medical Applications 469 42 and 43. The fact that three samples (2865, 2723 and 2699) are close to the line where standard deviation is equal to the average stress value clearly highlights the existence of high stress gradient. In particular the 2723 and 2699 samples are below the curve (eq. 42) but above the line (eq. 43), therefore are not accepted due to the high stress gradient. From this analysis it is possible to conclude that the process 2865 and 2812 have the best production parameter and indicates the development direction to improve the crystals quality. As final analysis it is possible to perform a comparison between the best and worst samples to put in evidence the specific critical points, as shown in the figure 37 (Rinaldi et al., 2010). 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 00,10,20,30,40,50,60,70,8 S(MPa) av (Mpa) 2692 2699 2723 2778 2812 2927 2865 σ Fig. 36. Different samples in the plane S-σ av . Only samples 2865 and 2812 are accepted, meeting the quality requirements Fig. 37 clearly put in evidence that the low quality sample 2692 exhibits high absolute stress values but also high stress variation. On the other hand, the higher level quality sample 2865 has lower absolute stress values and it appears more homogenous. It indicates that the specific production process is well tuned and that probably the production parameter and gradients are well controlled yielding an homogeneous sample. 4. Conclusions Scintillating crystals are widely used in radiographic systems, in computerized axial tomography devices and in calorimeter used in high energy physics. Scintillating crystals are cut to their final shape from an ingot, which is grown by classical crystal growth techniques. From a mechanical point of view, the quality of a crystal is closely related to its Wide Spectra of Quality Control 470 geometry, to the surface finish and moreover to its internal state of residual stresses. In particular an excessive residual stress is a major cause of crystal breakage, which often may occur during crystal cut, during surface finishing or, even worse, only when the crystal is assembled into the detector units. Fig. 37. Comparison between better/worst samples at centre position of the slices (as shown by the inset) as a function of the longitudinal position from the seed The need to produce high-quality crystals is therefore fundamental both to avoid damage during assembly and finishing of crystals. Crystal performance in terms of production of light strongly depends on surface finish, therefore crystal tool machining is a crucial process to achieve the high performance needed in the case of scintillating crystals for high energy physics and medical applications. For optimal crystals performance, attention has therefore to be paid to the mechanical aspects of the production process; from the mechanical point of view this can be guaranteed by adequate quality control methods. If adequate quality inspection of crystals is achieved, this has the potential to prevent breaking during the assembly in an array. The authors have reported the experience which was made within the collaboration with CERN to the development of the electromagnetic calorimeter of the Compact Muon Solenoid (CMS) presently working at CERN. From an industrial point of view, the trend is to use smaller and smaller crystals for biomedical instrumentation; in such crystals the surface plays an even more relevant role in the production of light. For this reason, the final mechanical processing is important for producing high quality crystals. Therefore the experience made for the large crystals of CMS is in general valuable to guide the Quality Control and Characterization of Scintillating Crystals for High Energy Physics and Medical Applications 471 development of suitable quality control methods for scintillating crystals and in particular for biomedical industry. An increasing attention to limit production costs requires an assessment of crystal quality by a fast and possibly non-destructive methodology, finalized to tune and keep under control the crystal growth and finishing processes, and to eliminate from the production process the crystals which are produced out of tolerance, thus reducing downtime and waste. Internal residual stress is not only the most important causes of breaking, but may be interpreted as an overall quality indicator. Residual stresses, induced by temperature spatial and temporal distribution during the growth and by complex interaction of the melt material and the growing ingot with the crucible, play an important role in production yield in terms of cracking risk during mechanical processing and heterogeneity in finished crystal properties. A regular production of good crystals requires a quality control plan leading to a fast and easy feed- back on growth parameters, such as temperature distribution and solidification-front velocity. The developed methodology for quality control consists in providing the producer a quality feedback for process control and optimization, obtained by experimental characterization of sample crystals taken from the pre-serial production by photoelasticity. Photoelasticity is a measurement technique aiming to study and evaluate the stress state inside a transparent medium. In traditional photoelasticity a plane stress state distribution is studied, by means of a plane polariscope. Usually it is applied to optically isotropic media, Perspex, glass or optically isotropic crystals, which become birefringent under stress. Referring to naturally anisotropic media, such as uniaxial and biaxial scintillating crystals, the observation of unstressed crystals, by means of a plane polariscope, shows a symmetrical interference pattern due to the symmetry of the lattice. An internal stress state induces a lattice symmetry distortion. The modelling of the interference image obtained from an anisotropic uniaxial crystal when a stress state is present, and the measurement of characteristic parameters of the interference fringe pattern offers a mean for quality control able to provide spatially integrated information on the internal stress. Although a mathematical modelling of the piezo-optical effects is possible, the knowledge of the coefficients of the model is not complete and accurate; therefore a semi-empirical approach is proposed. This leads to the definition of a parameter correlated to the deformation of the fringe pattern of a crystal under stress. The ellipticity, introduced into the fringe pattern is due to the stress state. Linear regression of experimental data of ellipticity vs. stress, collected with crystals undergoing known stress states, allows to build an experimental relationship which can then be used for quality assessment of unknown crystal samples. If the internal stresses are residual stresses, this allows to develop a quality control method to detect the presence of residual stresses non invasively. The method could be applicable on samples taken from the production, for process optimization and control, or it can be applied on the finished crystal as a pass-fail filter for removing from the batch all samples which exceed prescribed limits. The statistical analysis of many data from samples randomly taken from a pre-serial production allows to build a quality index depending on mean stress value and on its standard deviation, which are quantities related to residual stress intensity and gradient. This index can be used as a global indicator of process capacity to produce crystals with acceptable residual stress state. Wide Spectra of Quality Control 472 This method suggests therefore a quality indicator to synthetically evaluate the production by means of a criterion of acceptability, useful in general crystal production. The procedure and the quality index have been validated on PbWO 4 (PWO) uniaxial scintillating crystals; they have been intensively studied owing to the necessity of large amount of them (about 82000 large crystals) for the CMS. In fact the production effort needed a fast and reliable quality control. In that case study, the attention was focused on the measurement of residual stresses over the whole crystal volume, particularly in sections cut perpendicularly to the optical axis. The collected data enabled the construction of a 3-dimensional stress map for each crystal from a pre-serial production. The detection of internal stress and defects, can be related to the corresponding production parameters and may suggest improvements in the production process or highlight criticalities to be solved before a serial production is started. What presented is demonstrated for uniaxial crystals, but the same approach can be extended to all types of crystals, particularly those of a new generation (LYSO, LuYAP) as a function of their applications in high energy physics and for medical diagnostics. As conclusive remarks, we have to consider that other techniques should be taken into account to analyse crystals quality. In particular researchers are paying attention to experimental methods for the assessment of the surface damage, which are not treated in this chapter: X-ray diffraction (XRD), grazing incidence X-ray diffraction (GID) and RX reflectometry (XRR), (Mengucci et al., 2005). 5. Acknowledgment This work has seen the contribution of many colleagues, amongst which we thank prof. Giuseppe Majni and Prof. Fabrizio Davì, who contributed through many fruitful discussions. A relevant part of the work has been developed with the direct contribution of students amongst which we warmly thank Nicola Cocozzella, who was the first to deal with this topic, and PhD candidates, in particular dr. Andrea Ciriaco, whose PhD thesis constitutes a milestone in our work. 6. References Auffray E., Cavallari F., Lebeau M., Lecoq P., Schneegans M., Sempere-Roldan P. (2002). Crystal conditioning for high-energy physics detectors, Nuclear Instruments and Methods in Physics Research Section A (NIM A) 486, pp. 22-34. Baccaro S., Barone L. M., Borgia B., Castelli F., Cavallari F., Dafinei I., de Notaristefani F., Diemoz M., Festinesi A., Leonardi E., Longo E., Montecchi M., Organtini G. (1997). Ordinary and extraordinary complex refractive index of the lead tungstate (PbWO 4 ) crystal. Nuclear Instruments and Methods in Physics Research Section A, 385, pp. 209-214. Born M., Wolf E., (1975). Principles Of Optics, 6 th ed., Pergamon press, New York, USA. Cocozzella N., Lebeau M., Majni G., Paone N., Rinaldi D. (2001). Quality inspection of anisotropic scintillating lead tungstate (PbWO 4 ) crystals through measurement of interferometric fringe pattern parameters. Nuclear Instruments and Methods in Physics Research Section A (NIM A) 469 3 pp.331-339. Quality Control and Characterization of Scintillating Crystals for High Energy Physics and Medical Applications 473 Ciriaco A., Davì F., Lebeau M., Majni G., Paone N., Pietroni P., Rinaldi D. (2007). PWO photo- elastic parameter calibration by laser-based polariscope. Nuclear Instruments and Methods in Physics Research A 570, 55–60 Dally J. W., Riley W. F., (1987). Experimental Stress Analysis, 2 nd ed., McGraw-Hill Book Company, Singapore. Davì F. and Tiero A., (1994). The Saint-Venant's problem with Voigt's hypotheses for anisotropic solids. J. Elasticity 36, pp. 183-199. Frocht, M.M. Photoelasticity, Wiley, New York, 1941. Hodgkinson I. J., Wu Q. H., (1997). Birefringent Thin Films and Polarizing Elements, World Scientific, New Jersey, USA. Hofstadter, R (1949). The detection of gamma-rays with thallium-activated sodium iodide crystals. Phys.Rev. 75, pp. 796-810. Ishii M., Kobayashi M. (1996). Mechanical properties of PWO. Nuclear Instruments and Methods in Physics Research Section A (NIM A) 376, pp. 203-207 Lebeau M. (1985). Monocrystalline bismuth germanate Bi 4 Ge 3 O 12 (BGO) recent results on mechanical properties. J.Mat.Sci.letters 4, 779-782. Lebeau M., Ciriaco A., Gobbi L., Majni G., Paone N., Pietroni P., Rinaldi D. Quality monitoring in PWO scintillating crystal production during R&D phase Proceedings of the 8th International Conference on Inorganic Scintillators and their Use in Scientific and Industrial Applications, Publisher: National Academy of Sciences of Ukraine, Kharkov (2006) 334-337. Lebeau M. (2003). Crystal Growth Technology. In Methods and Tools for Mechanical Processing of Anisotropic Scintillating Crystals, pp.561-586. Wiley and Sons, London. Lebeau M., Pietroni P., Gobbi L., Majni G., Paone N., Rinaldi D. (2005). Mapping residual stresses in PbWO 4 crystals using photoelastic analysis., Proceedings of Scint'03 7 th International Conference on Inorganic Scintillators, September 8-12, 2003, Valencia, Spain. NIM A537 154-158 Lecoq P. et al. (2006). Inorganic Scintillators for Detector Systems. ISBN-10 3-540-27766-8 Springer Berlin Heidelberg New York. Mengucci P., Di Cristoforo A., Lebeau M., Majni G., Paone N., Pietroni P., Rinaldi D. (2005) Surface quality inspection of PbWO 4 crystals by grazing incidence X-ray diffraction. Nuclear Instruments and Methods in Physics Research Section A (NIM A) 537, 207- 210. Perelomova N. V. and Tagieva N. M., (1983). Problems in Crystal Physics with solutions, Mir Publishers, Moscow, Russia. Pietroni P., Lebeau M., Majni G., Paone N., Rinaldi D. (2005). Development of Young’s modulus non-destructive measurement techniques in non-oriented CeF 3 crystals. Nuclear Instruments and Methods in Physics Research Section A (NIM A) 537, 203-206. Rinaldi D., Lebeau M., Majni G., Paone N. (1997). Photoelasticity for the investigation of internal stress in BGO scintillating crystals. Nuclear Instruments and Methods in Physics Research Section A (NIM A) 317-322. Wide Spectra of Quality Control 474 Rinaldi D., P. Pietroni, F. Davì (2009). Isochromate fringes simulation by Cassini-like curves for photoelastic analysis of birefringent crystals. Nuclear Inst. and Methods in Physics Research, A 603, 294–300 Rinaldi D., Ciriaco A., Lebeau M., Paone N. (2010). Quality control on pre-serial Bridgman production of PbWO 4 scintillating crystals by means of photoelasticity Nuclear Inst. and Methods in Physics Research, A 615, 254–258 Walhstrom E.E., (1960). Optical Crystallography, Wiley, New York, (USA). Weber M., Monchamp R. (1973). Luminescence of Bi 4 Ge 3 O 12 - Journal of Applied Physics 44: 5495-5499. Wood E. A. (1964). Crystal And Light, Van Nostrand Company, New Jersey. Wooster, W. A. (1938). A test-book on Crystal Physics, Cambridge University Press. 24 Effect of Last Generation Additives on the Concrete Durability Ana M. Carvajal, M. Soledad Gómez, Pablo Maturana and Raul Molina Pontificia Universidad Católica de Chile Chile 1. Introduction The influence of carbonation on corrosion of reinforcement depends on the degree of ease of diffusion of CO 2 through the concrete from its surface, also on environmental conditions, on the pore structure of concrete (cement, aggregates, and water (without additives)) and on the W / C, where a high ratio generates porous and permeable mortar and concrete (Duran C., 2003; Troconis O. et al., 2006). Permeability is not necessarily related to porosity, but depends on the geometry of the pores and the distribution of pore sizes: two porous bodies can have similar porosities but different permeability, so it is important to consider the penetration of CO 2 into the concrete. If the concrete is not permeable, the attack will be relatively superficial and limited to the surface. The attack in concrete is governed by molecular diffusion, which is much slower than convection processes. The use of concrete with low permeability is the primary means to prevent or minimize the effects of external attack (Morin et al., 2001; Papadakis et al., 1992). A well-proportioned mix of aggregate, which follows a continuous grading curve will produce concrete of good workability, high cohesion and a reduced tendency to segregation. At the same time it will be slightly porous and therefore possess a prolonged durability. Superplasticizer additives added to the mix, filling the interstitial space between large particles, which can cause a high density, high strength and resilient material, with a smaller amount of mixing water (Erdogdu S., 2000; Morin et al., 2001). The main mechanism for CO 2 transport in concrete is difusion, and with moisture, carbonation leads, a phenomenon to be considered from the viewpoint of durability of reinforced concrete (Carvajal et al., 2006). There are expressions that relate the diffusion coefficient of concrete with compressive strength, where increase of resistance, decrease of diffusion coefficient. Because the phenomenon of diffusion of gases is of long-term, resistance in ancient age must to be taken into account and not the resistance usually specified at 28 days. 1.1 Carbon dioxide The CO 2 could form carbonic acid with water. The entry of CO 2 inside the concrete is produced through the pores and capillaries of the cement paste. As a result, the pH of carbonated concrete decreases and once the carbonation front reaches the armor begins to dissolve the passive film that protects steel from corrosion. Wide Spectra of Quality Control 476 1.2 Carbonation of concrete The importance of considering the carbonation in reinforced concrete structures, increases in holding that causes a chemical imbalance and a decrease in pH of water in the pores of the concrete from 12.6 to 13.5 to values around 9, causing depassivation strengthening reinforcements adverse reactions of chlorides and sulfides, and exposing them to corrosion. Without the passive layer, the steel is corroded as if it were exposed to the environment without any protection, and, the carbonation depends on many factors, but those with a higher incidence are: type of cement, concrete permeability, W/C ratio, concrete curing, relative humidity and CO 2 concentration in the environment (Barrera et al., 2003; Carvajal et al., 2003; da Silva et al., 2002). Carbonation is the process by which atmospheric CO 2 is combined with calcium hydroxide [Ca (OH) 2 ] to form calcium carbonate, losing its alkalinity by decreased pH. Ca (OH) 2 + CO 2 Æ CaCO 3 + H 2 O ↓ Insoluble carbonate In a mass of plain concrete, the carbonation can be beneficial, improving some of its properties, such as breaking loads between 22% to 78% higher, to obtain a denser concrete generated by an open porosity that is closed (5 to 12%). On the other hand, the attack produced by carbonic acid, which reacts with calcium hydroxide released from the hydration process of concrete which promotes its alkalinity, will form acid carbonates or bicarbonates (more soluble than carbonates) that has lower pH. Due to this decrease in alkalinity of the concrete, it loses the passivity of the reinforcement, leaving them prone to corrosion. The CO 2 present in polluted environments produces carbonic acid that diffuses into the concrete mixing with pore water (Knopf et al., 1999). CO 2 + H 2 OÆH 2 CO 3 2H 2 CO 3 + Ca(OH) 2 ÆCa(HCO 3 ) 2 + 2H 2 O ↓ Soluble bicarbonate The water in the atmosphere, rain or fog, contains a slight amount of carbonic acid by absorption of atmospheric CO 2 and are exceptions the industrial areas and cities, where the fumes, especially heating, mixed with steam and the fog for a longer period of time, it depositing on all surfaces. A depth that CO 2 has penetrated and reactions have occurred that has changed the pH, usually it`s called "carbonation front" (Thiery et al., 2007). The alkalinity of concrete is mainly due to calcium hydroxide (Ca(OH) 2 , pH 13 approx.) formed during hydration of cement silicates and alkalis that may be part of the cement. These substances place the pH of the aqueous phase contained in the pores between 12 and 14, most alkaline of pH range. Corrosion will occur in concrete that has a permeability such that allow the carbonation to reach the concrete in contact with steel or soluble chlorides can penetrate to the steel. If the concrete is in a dry atmosphere (below 40% RH) or submerged in water (without air intake), the risk of corrosion to the reinforcement decreases. An optimum for the corrosion process is 50 to 70% RH (Troconis O. & Duracon Collaboration, 2006). Effect of Last Generation Additives on the Concrete Durability 477 Considering the effect of carbonation, the pH decreases to values close to 9, which causes the passive iron oxide layer is destroyed (Duran C., 2003). 1.3 Accelerated carbonation chamber As the carbonation is a long-term process, it was implemented a test system of accelerated carbonation, to attack the concrete more quickly and effectively, obtaining experimental results with more speed than the real time. The accelerated carbonation chamber was designed in many countries for this purpose and in general is to expose the concrete samples and continuous ideal environment for the development of carbonation, where four variables can be controlled: temperature, CO 2 concentration, relative humidity and pressure (Carvajal et al., 2003, 2006; Duran C., 2003). The conditions of T ° and RH ranges are 20 and 25ºC and 50-70% respectively, due to these are the environmental conditions of higher penetration rate of CO 2 . To generate a constant environment in the system, the CO 2 pressure has not changes. Respect to the concentration of CO 2 , the atmosphere of the chamber is saturated with 100% CO 2 (Carvajal et al., 2003, 2006). The carbonation chamber, is in acrylic, 6 mm thickness and dimensions 1.00 x 0.50 x 0.50 m. The addition of pure CO 2 through pipes made of PVC previously adapted. 1.4 Rate of carbonation A simple model to predict the rate of carbonation of concrete is that which relates the depth of carbonation with the square root of exposure time. XCO 2 = KCO 2 √ t Where: XCO 2 = depth of carbonation, mm KCO 2 = carbonation constant : mm * year -0.5 t = time: years The information obtained can provide the time that is associated with a certain depth of carbonation. Likewise, it can gets the time associated to generate a greaterdamage, that is, reaching the reinforcement of the structure (CYTED, 1998; Carvajal et al., 2006). 1.5 Additives The additives are chemicals added to concrete. Additives are defined as "a material other than water, aggregates and hydraulic cement used as a component of concrete or mortar and added to the mixture immediately before or during mixing" (American Concrete Institute, 1991). 1.5.1 Additives used in the study The additives tested are classified as water-reducing admixtures of high rank. According to ASTM C494 classification are type A and F. Higher Reducing Water- admixtures (HRWR) reduce the water content of concrete between 12 and 25%, which is why they are used to increase strength and reduce permeability of concrete by reducing water content in the mixture, or to greatly increase the settlement and produce a fluid concrete without adding water. Its use is essential for high-strength concrete with high contents of cementitious materials and silica fume mixtures. Wide Spectra of Quality Control 478 1.5.1.1 Polycarboxylate-based additive The polycarboxylate based additive is an additive high water reducing capacity, based on synthetic polymers allows maximum flow, high cohesion and maintain the workability of the mixture for long periods. 1.5.1.2 Nanosilica based additive Nanosilica is a nano additive in liquid silica-based nano-sized particles. It is recommended as much water reducer, high activity. Belongs to a last generation additives, where chemical reactions in the concrete make nanoparticles of silica nanoparticles cement. 1.6 Capillary absorption Capillary absorption is a reaction that has a concrete (porous solid) from having contact with a liquid, which penetrates and goes into their pores as well as the relationship between their section and the surface tension permits. According CYTED (1998), the Manual Inspection Evaluation and Diagnosis of Corrosion in Reinforced Concrete Structures, is defined as follows: "capillary absorption is the mass of water per unit area that can be absorbed into the capillaries when the concrete is in contact with liquid water. Represents the effective porosity or accessible to water and therefore to an aggressive environment. To measure the absorption of concrete, tests performed on samples previously conditioned or witnesses to this effect, to measure the mass absorved for differents times, since it comes in contact with the liquid This test is simple to implement and to determine the absorption coefficient of the material according to the amount of water absorbed per unit area at a given time (root of time). 2. Experimental procedure 2.1 Materials Pozzolanic cement, potable water and crushed gravels were used for the manufacture of concrete with and without additives. The gravels with size range of 6-40 mm were used. The fine aggregate was river sand with a maximum size of 4 mm. Additives: nanosilica and polycarboxylate. The chemical composition of the Pozzolanic cement is shown in Table 1. Com SiO 2 Al 2 O 3 Fe 2 O 3 CaO MgO Na 2 O K 2 O SO 3 % 29.7 4.6 3.3 56.6 1.5 0.2 0.4 2.2 Table 1. Composition of Pozzolanic Cement 2.2 Specimens preparation 2.2.1 Specimens cure Specimens were demounted 2 days after casting, and then they were cured in humid chamber for 28-days, with a 95 + 3 % R H and 20 + 2ºC temperature range. 2.2.2 Grade of concretes The concrete without additives was H25 with w/c 0.60 and a slump cone of 19 cm. The concrete with polycarboxylate was H25 with w/c 0.48 and a slump cone of 19 cm. [...]... normal-direction errors of disk cam profiles (Chang et al., 2008; Chang & Wu, 2008; Chang et al., 2009) 490 Wide Spectra of Quality Control 3 Conjugate variation measurement and the examination of profile accuracy The measurement of the conjugate variation of the assembled conjugate cam mechanism can indirectly reveal the cam profile errors By applying the analytical approach of the conjugate variation... profile errors of each individual machined cam can be further developed That is, if a pair of master conjugate cams with known profile errors is additionally available, through the measured center distance variations induced by a pair of 488 Wide Spectra of Quality Control assembled conjugate cams that consists of one master cam and the other being the inspected cam, then the profile errors of each inspected... representatives of the experimental data function of angle θ, Δfmea(θ) The experimental data of Δfmea(θ), ΔrA,mea(θ) and ΔrB,mea(θ) were then adopted for examining the cam profile error with the use of the presented method For the profile error examination of cam A, data of Δfmea(θ) and ΔrB,mea(θ) were adopted to calculate ΔrA,est(θ) by using Eq (20) Likewise, for the profile error examination of cam B, data of. .. estimation, it is necessary to have two master cams A(m) and B(m) whose profiles are precisely measured and thus the magnitudes of ΔrA,mea and ΔrB,mea in the above 492 Wide Spectra of Quality Control two equations, respectively, can be known Then, for a conjugate cam mechanism, the profile errors of each cam can be estimated subsequently by means of the conjugate variation measurement The process presented above... nanosilica N2: without additives Numbers: 5, 7, 9 and 11 are days of carbonation The concrete with nanosilica presents an intermediate carbonation; higher than the concrete with polycarboxylate and lesser than the concrete without additive thus it shows coefficients of carbonation 480 Wide Spectra of Quality Control Type of concrete 28 56 58 Age of concretes (days) Carbonated Policarboxilate No Carbonated... be estimated and then examined by an analytical manner For the quality control in mass production of assembled conjugate disk cams, simply a pair of master conjugate cams with known profile errors and a set of conjugation measuring fixture must be prepared The objective of this study is to demonstrate how to examine the profile accuracy of assembled conjugate disk cams by applying the conjugate variation... feasibility of the presented concept, an experiment meant to examine profile errors of a pair of machined conjugate cams was conducted The profile errors of the machined cams estimated by using the presented method were compared with the measuring results obtained by using a CMM 2 Parametric expressions for the conjugate cam profiles In order to evaluate the dimensional variations of the machined cam profiles,... However the decrease of the absorption coefficient for higher time of carbonation that matches with a lesser speed of the advance facing the carbonation depth can be explained if it is accepted that the capillaries can have lesser diameter in the concrete mass, and therefore the capacity of forming carbonates to the inside may be seen as decreased although to be 484 Wide Spectra of Quality Control able to... (16) A Convenient and Inexpensive Quality Control Method for Examining the Accuracy of Conjugate Cam Profiles Δfη = − Δη (lA lB cos φA cos φB ) lA cos φA cosα B + lB cosφB cosα A 491 (17) in which, the correlations of θ5 = αA and θ6 = αB exist as shown in Fig 4 Also, parameters θ2 and β depending on the locations of points KA and KB, which are the centers of curvatures of cams A and B respectively, are... (1993) and further investigated by Chang and Wu (2008), is developed by Chang et al (2009) for indirectly evaluating the profile errors of conjugate disk cams The conjugation measuring fixtures are based on the means of measuring the conjugate variation 486 Wide Spectra of Quality Control of the assembled conjugate cam mechanism According to the concept proposed by Chang et al (2009), for a conjugate cam . mechanical point of view, the quality of a crystal is closely related to its Wide Spectra of Quality Control 470 geometry, to the surface finish and moreover to its internal state of residual. evaluating the profile errors of conjugate disk cams. The conjugation measuring fixtures are based on the means of measuring the conjugate variation Wide Spectra of Quality Control 486 of the assembled. induced by a pair of Wide Spectra of Quality Control 488 assembled conjugate cams that consists of one master cam and the other being the inspected cam, then the profile errors of each inspected