- Email: [email protected]
MicroMet gets small to expand
Combining image analysis and NNs to optimize powder packing density In the last issue the genera/ concepts of neural network (NN) modelling and its application to powder metallurgy (PM) processes were discussed. Here we focus on a specific area of importance to both powder producers and PM parts manufacturers: the prediction of powder packing density using trained networks. Lyndon Smith of the University of the West of England, together with Luiza Dihoru (University of Leicester) and Prof, Radu Orban (Technical University of Cluj Napoca) describe the methodology and its potential to monitor powders on-line.
S
urveys of metal powder and parts manufacturers1,2 have identified packing density as being one of the most important powder characteristics. Despite the importance of powder density the techniques generally employed for determination of tap density are somewhat unsophisticated. Also, relatively few attempts have been made to model the effects of particle irregularity on packing density3. The work described here combines scanning electron microscope (SEM) imaging, vision system analysis, and neural network (NN) modelling, to achieve prediction and control of powder density. Previously reported research into monitoring powder production has concentrated on particle sizing. Particle size measurement is often achieved using laser diffraction, although various alternative methods are also available4. Determination of the particle size distribution (PSD) allows comparison with existing experimental data to arrive at a prediction of powder density5. The main drawback of such a technique is the assumption made during sizing that the particle is spherical. This can lead to appreciable errors in measured particle size, the magnitude of which depends upon the particle type6. Additional difficulties are associated with the method by which the powder density is inferred, i.e. purely by relating PSD to measured density. If, for example, a change in the morphology of the particles occurred during production, then it is not clear how these methods would be able to model the effects on packing density. 28
MPR
March
2000
0026-0657/00/$-
Using image analysis
with NNs
The method described here aims to overcome these difficulties by directly modelling the effect on powder density of particle size and irregularity for individual and blended powders. Samples from a number of powders underwent SEM imaging. A series of experiments were conducted to determine the densities of the individual powders, and a range of powder blends. Vision system analysis of the SEM images was then employed to generate average size and irregularity values for the powder particles. This information, along with proportion by weight (for the blends), was combined with the measured densities and used for training the NN. Once trained, the network was tested using a separate data set. Regression analysis of the predicted and test data for density resulted in a correlation coefficient of 0.98. The reasons for employing an NN for modelling the packing included its ability to easily relate multiple inputs to process outcomes, and the facility provided by the network for rapid updating of the model. The NN models the data directly, without the need for assumptions regarding the form of the model (as is required for curve fitting). Nor is there a requirement to be restricted to previous production procedures. The NN allows the user to investigate the effects on powder density of changes in the particle characteristics. If, for example, production conditions or customer requirements resulted in a new particle size, the NN could easily be trained using this new data. The network would then be immediately available for use in predicting and controlling density. If the powder manufacturer subsequently decided that the powder should be pre-mixed with a lubricant, the NN could be provided with an additional input. The system could then be trained using experimental data for powder with various percentages of lubricant, and would be able to continue providing recommendations. An additional capability of the system is to predict the proportions with which two powders should be combined in order to produce a blend with a specified density. In powder metallurgy (PM) there is a requirement to produce components with high densities, so that strength can be maximized, and distortion minimized. This necessitates a relatively high packing density for the powder. If this is above the densities of the individual powders, it may be attainable by blending two powders
see front matter 0 2000, Elsevier Science Ltd All rights reserved
FIGURE 7: Scanning electron microscope image of high-pressure water atomized 3 161. stainless steel powder particles.
FIGURE 2: Image of 316L stainless steel powder particles in Figure 1 following processing and binarization.
that exhibit differing average particle sizes. The system prompts the user for the required density, and then engages in an iterative process of consulting the NN. If the target density is reached the system advises the user as to the required powder characteristics and proportions by weight. Although training can take an appreciable time (this is dependent upon the network parameters), once trained an NN can provide instant process recommendations. We believe that such a system, when installed in a production environment, could offer potential for realizing considerable productivity gains and cost savings. The current system provides a demonstration of how relevant techniques can be drawn together to provide the required functionality. These techniques (which are described below in more detail), comprise SEM imaging, vision system analysis, and NN programming.
shape factor is calculated formula:
Particle characterization was achieved through analysis of SEM images. The samples were prepared by dispersing the particles in on a glass slide. After drying acetone overnight, a layer of particles was transferred onto the copper surface of the SEM stage. The powders consisted of gas atomized, water atomized, and high pressure water atomized 316L stainless steel. Images were generated by connecting the SEM to a PGT - IMIX/IMAGIST (version 8.29) image analysis system (PGT, Princeton, NJ, USA). The images were binarized and processed to achieve separation of the particles that were in contact. Processing techniques included use of ‘cutting’, ‘filling’, and ‘contour processing’ algorithms. 0f the 17 geometrical parameters provided by the system, ‘average diameter’ and ‘shape factor’ were chosen for use in modelling. Between five and seven.images (around 3000 particles) were analysed for each powder. The
using the following
s = 4nAfP” Where: S = shape factor, A = area of particle in 2D, and P = perimeter of particle in 2D. Figure 1 comprises an image from the SEM, and Figure 2 shows the effect of binarization and processing. The data from analysis of the SEM images of the powders were statistically processed. The average diameter was employed for characterization of particle size. The standard deviation of the particle diameter was chosen as a measure of PSD, and ‘shape factor’ was used to quantify the particle morphology. The powder packing (tap) density was measured after 3000 cycles using a tapping machine (‘Dual Autotap’ from Quantachrome Corp, Boynton Beach, FL, USA). The pycnometric density was measured on a helium pycnometer (‘AccuPyc 1330’ from Micromeritics, Norcross, GA, USA).
The statistically processed infi,rmation from the image analysis was collated and combined with the density measurements for the individual powders and the blends. The resulting mat,rix was employed for training an NN that related powder characteristics to packing density. The seven inputs of the NN consisted of Mass percentage of powder 1 Average particle diameter for powder 1 Shape factor of powder 1. Standard deviation of the particle diameter for powder 1 Average diameter of powder 2 Shape factor of powder 2 Standard deviation ofdiameter of powder 2, The output consisted of the fractional density (FD) of the powder blend, where:
Performance
1o-5;;
is 0.00781084,
goal is 1 e-005
500 1000 1500 2000 2500 3000 3500 4000 4500 5’0013 5000epochs
FIGURE 3: Plot of NN error against number of training iterations (epochs). FD = tap densitylpycnometric
density
The NN was developed using the MATLABB (version 5.3) Neural Network Toolbox. A feedforward backpropagation architecture was chosen, since this is generally accepted as useful for statistical modelling problems7, and we have previous experience in this areas. Experiments were performed using various numbers of hidden layers and neurons. Satisfactory responses were obtained with two hidden layers of eight neurons each (with Tansig transfer functions), and one linear output neuron. The gradient descent algorithm was initially employed for training. Subsequent experimentation with other algorithms such as resilient backpropagation was found to decrease training times. Figure 3 is a plot of NN error against number of training iterations, for 5000 epochs. It can be seen that as the number of training epochs increases (particularly above lOOO), the decrease in error becomes increasingly small. Consequently, for this application, 1 Best linear fit: A = (1.02) T + (-0.00827) 0.64,
Measured
density, T
-!
FIGURE 4: Plot of densities predicted by the NN (A) versus measured densities (7J (each point corresponds to a set of test data input parameters).
30 MPR March 2000
training at above 10 000 epochs was not generally considered worthwhile. The NN functions by randomly splitting the data into a training set and a test set. After completing a specified number of epochs using the training set, the test set was used to evaluate the network response. One characteristic of particular interest was the extent to which the NN was able to generalize, in other words how accurately it can predict densities for new input data. Figure 4 shows densities predicted by the NN (A) plotted against measured test densities (T). The line of best fit can be seen to be superimposed on the line A=T, and the correlation coefficient is given as R=0.98. These results show that the NN is able to accurately model the effects of the powder characteristics on the packing density. The final requirement was for the NN to be able to recommend a mass percentage for powder 1, in order to produce a blend with a given density. This is achieved by repeated consultations of the trained network. After the user enters the required density the system initiates an iterative process, which starts by consulting the network for a powder consisting of 100% powder 2. Powder 1 is then considered to be blended with powder 2 in 1% increments, and for each increment the NN is consulted. Figure 5 shows the resulting plot of density versus percentage of powder 1. For example, if the user specified a target density of 61%, the system would recommend a blend of 80% powder 1 and 20% powder 2. If the target density is not reached during the iterative process, the user is advised that the value is out of range.
Application areas Optimized manufacture requires precise control of production parameters in real time. Computerized methods offer an effective means of achieving this through application of relevant models for the generation of timely production advice. Utilization of this information can enable manufacturers to avoid costly secondary processing such as, in the case of powders, additional blending. The neural network modelling described here demonstrates a method for predicting and controlling the packing density of metal powders. A system based on this technology could easily be installed on a PC in a production environment, where it could be consulted for provision of production advice. Both powder manufacturers and parts producers could employ such a system, to help ensure that their production remains within specification. In the case of parts manufacturers, customer performance requirements mean that components generally have to be produced with a high density To reduce distortion during sintering, the manufacturer wishes to produce a green compact with a high density, and is therefore also interested in a high powder packing density in the die (this will tend to minimize the density gradients produced during compaction - thereby minimizing the likelihood of cracking). The target density may
be above that of the powders received from the suppliers. In such a situation the aim is for the system to recommend the proportions of the powders to be blended in order to achieve the desired packing density. For powder manufacturers, it is essential that the powders are shipped with the specified tap density. The system could assist in achieving this by being employed on-line to qnrl rrlorliiul yi*iiidi size End shape, uI u to prediet the tap density. (This would require installation of sampling and microscopy equipment, and application of vision system software capable of real-time particle analysis.) The density data could then be employed in subsequent statistical process control analysis (e.g. computerized control charts or CUSUM diagrams), to identify underlying trends in production. This type of on-line measurement and analysis offers potential to assist in avoidance of expensive out-of-specification production. In conclusion, neural networks can comprise powerful tools for modelling, and thereby optimizing, metal powder production. A major advantage of an NN over conventional statistics is that the modelling is entirely data driven and does not rely on subjective constructs, such as linear, quadratic, or exponential relationships between input and output data. The approach is also flexible, in that additional inputs and outputs can be incorporated, as required. Consequently, if a blend of three or more powders were required, or if apparent density were of interest as well as tap density, then these factors could be included relatively easily. Perhaps most importantly, a neural network represents a method for process modelling that inherently incorporates a facility for machine learning. The difficulties associated with the updating of process modelling tools are a frequently cited reason for their lack of usefulness. In the case of a neural network, updating can be achieved easily, by means of additional network training.
Fraction by weight of powder 1
FIGURE 5. Neural network simulation of blend packing density as a function of the fraction by weight of powder (4) L.N. Smith, ‘A Knowledge Based System for Powder Metallurgy’, (1997), PhD thesis, University of the West of England, Bristol, UK. (5) D.J. Holve and TL. Harvill, ‘Particle Size Distribution Measurements For Inprocess Monitoring and Control’, Particle Size Measurement and Testing, Advances in Powder Metallurgy & Particulate Materials - 1996, Part 4, (1996), Metal Powder Industries Federation, Princeton, NJ, USA. (6) T. Allen, Particle Size Measurement Vol. 1 Powder Sampling and Particle Size Measurement, 5th edition, (1997), Chapman and Hall, London, UK. (7) M. Smith, Neural Networks for Statistical Modeling, Van Nostrand Reinhold, (1993), ISBN 0442013108. (8) L.N. Smith, ‘Modelling PM processes using neural networks’, Metal Powder Report (ZOOO),Vol. 55, No. 2, pp. 30-35. (9) H.B. Demuth and M. Beale, Neural Network Toolbox User’s Guide, (1998), Math Works Inc, Natick, MA, USA.
tact: ~y~~~~ iv. The authors would like to thank Randall M. German, (Brush Chair Professor in Materials, P/M Lab, Penn State University), for authorizing use of SEM images generated in the P/M Lab. MATLAB is a registered trademark of The Math Works Inc (Natick, MA, USA).
Lecturer and Researcher Faculty of Engineering University of the West of England Bristol BS16 l&U, UK. Tel: +44-(0)I 17-9656261. Fax. +44-(0)117-9763873. E-mail: [email protected]
(1) J.M. Capus, Metal Powders: A Global Survey of Production, Applications and Markets, (1996), Elsevier Advanced Technology, Oxford, ISBN 1 8561’7 287 2. (2) SCM, Survey of Parts Manufacturers, (1985), SCM Metal Products Inc, 2601. Week Drive, Box 12166, Research Triangle Park, NC 27709-2166, USA. (3) R.G. Iacocca and R.M. German, “A Comparison of Powder Particle Measuring Instruments~, 7%~ International Journal of Pozuder Metallurgy, (1997), Vol. 33, No. 8.
Researcher, Engineering Dept University of Leicester, University Road, Leicester LEl7RH, UK. ~~a~essa~ Rack @-ban Head of Department of Materials Science and Technology Technical University of Cluj Napoca B-dul Muncii 103-105 Cluj-Napoca, Romania. E-mail: [email protected]
1.
S
urveys of metal powder and parts manufacturers1,2 have identified packing density as being one of the most important powder characteristics. Despite the importance of powder density the techniques generally employed for determination of tap density are somewhat unsophisticated. Also, relatively few attempts have been made to model the effects of particle irregularity on packing density3. The work described here combines scanning electron microscope (SEM) imaging, vision system analysis, and neural network (NN) modelling, to achieve prediction and control of powder density. Previously reported research into monitoring powder production has concentrated on particle sizing. Particle size measurement is often achieved using laser diffraction, although various alternative methods are also available4. Determination of the particle size distribution (PSD) allows comparison with existing experimental data to arrive at a prediction of powder density5. The main drawback of such a technique is the assumption made during sizing that the particle is spherical. This can lead to appreciable errors in measured particle size, the magnitude of which depends upon the particle type6. Additional difficulties are associated with the method by which the powder density is inferred, i.e. purely by relating PSD to measured density. If, for example, a change in the morphology of the particles occurred during production, then it is not clear how these methods would be able to model the effects on packing density. 28
MPR
March
2000
0026-0657/00/$-
Using image analysis
with NNs
The method described here aims to overcome these difficulties by directly modelling the effect on powder density of particle size and irregularity for individual and blended powders. Samples from a number of powders underwent SEM imaging. A series of experiments were conducted to determine the densities of the individual powders, and a range of powder blends. Vision system analysis of the SEM images was then employed to generate average size and irregularity values for the powder particles. This information, along with proportion by weight (for the blends), was combined with the measured densities and used for training the NN. Once trained, the network was tested using a separate data set. Regression analysis of the predicted and test data for density resulted in a correlation coefficient of 0.98. The reasons for employing an NN for modelling the packing included its ability to easily relate multiple inputs to process outcomes, and the facility provided by the network for rapid updating of the model. The NN models the data directly, without the need for assumptions regarding the form of the model (as is required for curve fitting). Nor is there a requirement to be restricted to previous production procedures. The NN allows the user to investigate the effects on powder density of changes in the particle characteristics. If, for example, production conditions or customer requirements resulted in a new particle size, the NN could easily be trained using this new data. The network would then be immediately available for use in predicting and controlling density. If the powder manufacturer subsequently decided that the powder should be pre-mixed with a lubricant, the NN could be provided with an additional input. The system could then be trained using experimental data for powder with various percentages of lubricant, and would be able to continue providing recommendations. An additional capability of the system is to predict the proportions with which two powders should be combined in order to produce a blend with a specified density. In powder metallurgy (PM) there is a requirement to produce components with high densities, so that strength can be maximized, and distortion minimized. This necessitates a relatively high packing density for the powder. If this is above the densities of the individual powders, it may be attainable by blending two powders
see front matter 0 2000, Elsevier Science Ltd All rights reserved
FIGURE 7: Scanning electron microscope image of high-pressure water atomized 3 161. stainless steel powder particles.
FIGURE 2: Image of 316L stainless steel powder particles in Figure 1 following processing and binarization.
that exhibit differing average particle sizes. The system prompts the user for the required density, and then engages in an iterative process of consulting the NN. If the target density is reached the system advises the user as to the required powder characteristics and proportions by weight. Although training can take an appreciable time (this is dependent upon the network parameters), once trained an NN can provide instant process recommendations. We believe that such a system, when installed in a production environment, could offer potential for realizing considerable productivity gains and cost savings. The current system provides a demonstration of how relevant techniques can be drawn together to provide the required functionality. These techniques (which are described below in more detail), comprise SEM imaging, vision system analysis, and NN programming.
shape factor is calculated formula:
Particle characterization was achieved through analysis of SEM images. The samples were prepared by dispersing the particles in on a glass slide. After drying acetone overnight, a layer of particles was transferred onto the copper surface of the SEM stage. The powders consisted of gas atomized, water atomized, and high pressure water atomized 316L stainless steel. Images were generated by connecting the SEM to a PGT - IMIX/IMAGIST (version 8.29) image analysis system (PGT, Princeton, NJ, USA). The images were binarized and processed to achieve separation of the particles that were in contact. Processing techniques included use of ‘cutting’, ‘filling’, and ‘contour processing’ algorithms. 0f the 17 geometrical parameters provided by the system, ‘average diameter’ and ‘shape factor’ were chosen for use in modelling. Between five and seven.images (around 3000 particles) were analysed for each powder. The
using the following
s = 4nAfP” Where: S = shape factor, A = area of particle in 2D, and P = perimeter of particle in 2D. Figure 1 comprises an image from the SEM, and Figure 2 shows the effect of binarization and processing. The data from analysis of the SEM images of the powders were statistically processed. The average diameter was employed for characterization of particle size. The standard deviation of the particle diameter was chosen as a measure of PSD, and ‘shape factor’ was used to quantify the particle morphology. The powder packing (tap) density was measured after 3000 cycles using a tapping machine (‘Dual Autotap’ from Quantachrome Corp, Boynton Beach, FL, USA). The pycnometric density was measured on a helium pycnometer (‘AccuPyc 1330’ from Micromeritics, Norcross, GA, USA).
The statistically processed infi,rmation from the image analysis was collated and combined with the density measurements for the individual powders and the blends. The resulting mat,rix was employed for training an NN that related powder characteristics to packing density. The seven inputs of the NN consisted of Mass percentage of powder 1 Average particle diameter for powder 1 Shape factor of powder 1. Standard deviation of the particle diameter for powder 1 Average diameter of powder 2 Shape factor of powder 2 Standard deviation ofdiameter of powder 2, The output consisted of the fractional density (FD) of the powder blend, where:
Performance
1o-5;;
is 0.00781084,
goal is 1 e-005
500 1000 1500 2000 2500 3000 3500 4000 4500 5’0013 5000epochs
FIGURE 3: Plot of NN error against number of training iterations (epochs). FD = tap densitylpycnometric
density
The NN was developed using the MATLABB (version 5.3) Neural Network Toolbox. A feedforward backpropagation architecture was chosen, since this is generally accepted as useful for statistical modelling problems7, and we have previous experience in this areas. Experiments were performed using various numbers of hidden layers and neurons. Satisfactory responses were obtained with two hidden layers of eight neurons each (with Tansig transfer functions), and one linear output neuron. The gradient descent algorithm was initially employed for training. Subsequent experimentation with other algorithms such as resilient backpropagation was found to decrease training times. Figure 3 is a plot of NN error against number of training iterations, for 5000 epochs. It can be seen that as the number of training epochs increases (particularly above lOOO), the decrease in error becomes increasingly small. Consequently, for this application, 1 Best linear fit: A = (1.02) T + (-0.00827) 0.64,
Measured
density, T
-!
FIGURE 4: Plot of densities predicted by the NN (A) versus measured densities (7J (each point corresponds to a set of test data input parameters).
30 MPR March 2000
training at above 10 000 epochs was not generally considered worthwhile. The NN functions by randomly splitting the data into a training set and a test set. After completing a specified number of epochs using the training set, the test set was used to evaluate the network response. One characteristic of particular interest was the extent to which the NN was able to generalize, in other words how accurately it can predict densities for new input data. Figure 4 shows densities predicted by the NN (A) plotted against measured test densities (T). The line of best fit can be seen to be superimposed on the line A=T, and the correlation coefficient is given as R=0.98. These results show that the NN is able to accurately model the effects of the powder characteristics on the packing density. The final requirement was for the NN to be able to recommend a mass percentage for powder 1, in order to produce a blend with a given density. This is achieved by repeated consultations of the trained network. After the user enters the required density the system initiates an iterative process, which starts by consulting the network for a powder consisting of 100% powder 2. Powder 1 is then considered to be blended with powder 2 in 1% increments, and for each increment the NN is consulted. Figure 5 shows the resulting plot of density versus percentage of powder 1. For example, if the user specified a target density of 61%, the system would recommend a blend of 80% powder 1 and 20% powder 2. If the target density is not reached during the iterative process, the user is advised that the value is out of range.
Application areas Optimized manufacture requires precise control of production parameters in real time. Computerized methods offer an effective means of achieving this through application of relevant models for the generation of timely production advice. Utilization of this information can enable manufacturers to avoid costly secondary processing such as, in the case of powders, additional blending. The neural network modelling described here demonstrates a method for predicting and controlling the packing density of metal powders. A system based on this technology could easily be installed on a PC in a production environment, where it could be consulted for provision of production advice. Both powder manufacturers and parts producers could employ such a system, to help ensure that their production remains within specification. In the case of parts manufacturers, customer performance requirements mean that components generally have to be produced with a high density To reduce distortion during sintering, the manufacturer wishes to produce a green compact with a high density, and is therefore also interested in a high powder packing density in the die (this will tend to minimize the density gradients produced during compaction - thereby minimizing the likelihood of cracking). The target density may
be above that of the powders received from the suppliers. In such a situation the aim is for the system to recommend the proportions of the powders to be blended in order to achieve the desired packing density. For powder manufacturers, it is essential that the powders are shipped with the specified tap density. The system could assist in achieving this by being employed on-line to qnrl rrlorliiul yi*iiidi size End shape, uI u to prediet the tap density. (This would require installation of sampling and microscopy equipment, and application of vision system software capable of real-time particle analysis.) The density data could then be employed in subsequent statistical process control analysis (e.g. computerized control charts or CUSUM diagrams), to identify underlying trends in production. This type of on-line measurement and analysis offers potential to assist in avoidance of expensive out-of-specification production. In conclusion, neural networks can comprise powerful tools for modelling, and thereby optimizing, metal powder production. A major advantage of an NN over conventional statistics is that the modelling is entirely data driven and does not rely on subjective constructs, such as linear, quadratic, or exponential relationships between input and output data. The approach is also flexible, in that additional inputs and outputs can be incorporated, as required. Consequently, if a blend of three or more powders were required, or if apparent density were of interest as well as tap density, then these factors could be included relatively easily. Perhaps most importantly, a neural network represents a method for process modelling that inherently incorporates a facility for machine learning. The difficulties associated with the updating of process modelling tools are a frequently cited reason for their lack of usefulness. In the case of a neural network, updating can be achieved easily, by means of additional network training.
Fraction by weight of powder 1
FIGURE 5. Neural network simulation of blend packing density as a function of the fraction by weight of powder (4) L.N. Smith, ‘A Knowledge Based System for Powder Metallurgy’, (1997), PhD thesis, University of the West of England, Bristol, UK. (5) D.J. Holve and TL. Harvill, ‘Particle Size Distribution Measurements For Inprocess Monitoring and Control’, Particle Size Measurement and Testing, Advances in Powder Metallurgy & Particulate Materials - 1996, Part 4, (1996), Metal Powder Industries Federation, Princeton, NJ, USA. (6) T. Allen, Particle Size Measurement Vol. 1 Powder Sampling and Particle Size Measurement, 5th edition, (1997), Chapman and Hall, London, UK. (7) M. Smith, Neural Networks for Statistical Modeling, Van Nostrand Reinhold, (1993), ISBN 0442013108. (8) L.N. Smith, ‘Modelling PM processes using neural networks’, Metal Powder Report (ZOOO),Vol. 55, No. 2, pp. 30-35. (9) H.B. Demuth and M. Beale, Neural Network Toolbox User’s Guide, (1998), Math Works Inc, Natick, MA, USA.
tact: ~y~~~~ iv. The authors would like to thank Randall M. German, (Brush Chair Professor in Materials, P/M Lab, Penn State University), for authorizing use of SEM images generated in the P/M Lab. MATLAB is a registered trademark of The Math Works Inc (Natick, MA, USA).
Lecturer and Researcher Faculty of Engineering University of the West of England Bristol BS16 l&U, UK. Tel: +44-(0)I 17-9656261. Fax. +44-(0)117-9763873. E-mail: [email protected]
(1) J.M. Capus, Metal Powders: A Global Survey of Production, Applications and Markets, (1996), Elsevier Advanced Technology, Oxford, ISBN 1 8561’7 287 2. (2) SCM, Survey of Parts Manufacturers, (1985), SCM Metal Products Inc, 2601. Week Drive, Box 12166, Research Triangle Park, NC 27709-2166, USA. (3) R.G. Iacocca and R.M. German, “A Comparison of Powder Particle Measuring Instruments~, 7%~ International Journal of Pozuder Metallurgy, (1997), Vol. 33, No. 8.
Researcher, Engineering Dept University of Leicester, University Road, Leicester LEl7RH, UK. ~~a~essa~ Rack @-ban Head of Department of Materials Science and Technology Technical University of Cluj Napoca B-dul Muncii 103-105 Cluj-Napoca, Romania. E-mail: [email protected]
1.