Infra-Red and On-Line Testing of Green-State and Sintered P/M Parts

Transcription

1 Infra-Red and On-Line Testing of Green-State and Sintered P/M Parts for Process Control Report No. PR Research Team: Souheil Benzerrouk (508) Prof. Reinhold Ludwig (508) Focus Group members: Ian Donaldson, GKN Worcester, chair Richard Scott, Nichols Portland Michael Krehl, Sinterstahl ABSTRACT The Joule heating of solid materials through direct current excitation can be used to generate a temperature profile throughout the sample under test. When recording this temperature distribution with an infrared (IR) camera focused on the surface, important information regarding the integrity of the material can be gained. This research will concentrate on the formulation of a mathematical model capable of predicting the temperature distribution and heat flow in P/M parts and its relations to the supplied current, injection method, geometry and the thermo-physical properties of these parts. This model will subsequently be employed as a reference to aid in actual measurements of infrared signatures over the surface and its correlation to the detection of surface and subsurface flaws and inhomogeneities. In this progress report we will develop the theoretical background of IR testing of greenstate and sintered P/M compacts in terms of the governing equations, boundary conditions, and analytical and numerical solutions. Our main emphasis is placed on modeling various flaw sizes and orientations in an effort to determine flaw resolution limits as a function of minimum temperature distributions. Preliminary measurements have shown that this IR testing methodology can successfully test both green-state and sintered samples

2 1. Introduction Recent years have seen a rapid growth in the manufacturing of high volume, complex P/M compacts for a wide range of applications. Increasingly, the manufacturing process of compaction in sophisticated mechanical presses followed by sintering is becoming difficult to control in a matter that assures high-quality finished products at competitive cost points. Complex P/M production demands quality assurance throughout the entire manufacturing cycle of the compacts. Ideally, the quality assessment should be conducted in a short period of time with high reliability and at low value-added cost. Since it is desirable to administer these tests as early as possible in the manufacturing cycle, nondestructive evaluation (NDE) has gained an increasingly important role. Unfortunately, a careful review of most currently employed NDE techniques for our membership [1] have shown that most of these techniques cannot directly be applied to the P/M industry without major modifications. For instance, it was found that a generally applicable NDE methodology for both pre- and post-sintered compact inspection simply does not exist at reasonable cost NDE techniques Powder metallurgy is a manufacturing method where parts are created by compacting special metal powders in the presence of lubricants to a predefined composition. This compaction process is carried out under high pressure in a press, before the compacts are sintered at temperatures that approach the melting point of the base material. Due to this particular manufacturing process, conventional NDE techniques are difficult to apply and suffer from a number of disadvantages. Table 1 reviews the most popular NDE methodologies with regards to their relative strengths and weaknesses. As part of our recently completed research project into the electrostatic testing of greenstate compacts [2, 3], it was concluded that an electric measurement methodology has the potential to detect most surface-breaking and sub-surface defects in green state compacts. However, in order to apply this electrostatic crack detection technique for industrial use, a special sensor has to be created that can be fitted to the sample under test. Furthermore, given the extremely high conductivity of the sintered compacts it was concluded that the voltages recorded on the surface are too small to be processed with reasonable equipment expenses. Following discussions within the PMRC membership, a proposal was submitted and funded that embarks on the exploration of infrared imaging as a more generally applicable NDE technique to inspect both green-state and sintered P/M compacts

3 Table 1: Advantages and disadvantages of various NDE techniques applied to P/M inspection. Technique Capabilities Limitations Eddy current Ideal for surface and near surface defects in sintered parts Coil sensor can be adjusted to part under test Depth of penetration limits the usability in green state to surface detection Ultrasonics Can detect deeply embedded defects in sintered parts Cost effective Easy to set up Inefficient in green-state due to high acoustic attenuation of medium Requires a coupling agent (usually a viscous gel). X-Ray Detects defects in both green state and sintered High resolution, deep penetration Established technology for high quality samples (aerospace and military). Not suitable for high volume applications (slow) High ownership cost Not effective in detecting near corner defects Resistivity Resonance Demonstrated performance with green state parts Requires sensor adjustment to compact Simple test method for complex, sintered parts Complex test set-up Generally does not work for sintered parts Cannot provide individual flaw signatures Scientifically unproven in P/M compacts 1.2. Research Objective Goal of this PMRC funded research effort is the design of a new thermo-electric testing methodology of green-state and sintered compacts. We intend to modify and extend the previously developed electrostatic testing methodology in such a way as to use the direct current electric excitation to create Joule heating in the compact. The resulting temperature distribution can then be detected in the sample in the IR spectrum through an infrared camera. Our proposed thermo-electric solution will attempt to overcome the limitations associated with the previous approach. In particular, it is expected that no special sensor development will be required. Furthermore, the technique is expected to equally apply to green-state and sintered compacts

4 This new technique is considered a global area inspection method in that it allows the detection and measurement of absolute temperatures and temperature differences over large surfaces. We intend to use DC current as heating power (Joule heating). As a result, due to the finite conductivity of the compacts a power loss is created. Based on the laws of thermodynamics the power loss can be recorded as IR radiation emanating from the compact. 2. Approach This research is organized as shown in Figure 2.1. Specifically, the electric power deposition is determined through the use of an electrostatic model where the conductivity is calculated from the density through an inverse algorithm developed in the previous research effort. The temperature distribution on the surface of the part can subsequently be detected through an IR camera. DC Current input Electrostatic measurement and power prediction IR detection Signal and image processing Figure 2.1: Block diagram of overall testing approach. The theoretical part will investigate the forward solution, i.e. we will study the energy transfer mechanisms between the electrical and thermal models. This approach will include: Current propagation and potential differences in the part (Electrostatics). Temperature distribution (heat transfer). IR radiation and detection. In addition, due to the complex and multi-disciplinary nature of the thermo-electric phenomena, numerical modeling will be extensively used to study the thermal response of perfect and flawed parts subject to electric excitation. The first phase will involve a steady state approach, followed by a more elaborate transient analysis

5 On the practical side, we intend to procure controlled samples to test and validate the theoretical formulation. Extensive experimentation and signal processing will follow and an effort to obtain quantitative information on flaw sizes and IR signatures. 3. Governing Equations To develop a full theoretical understanding of the IR inspection system, one has to study the following items: A heat source that includes a coupling mechanism, A solver for the heat distribution over the surface, including mechanisms that can take into account effects of the surroundings, and An IR image system that can handle all sources of radiation, optical effects due to the camera and due to the relatively small emissivity of P/M parts. To describe the voltage distribution and the current flow, we have to solve Laplace s equation in the form ( s V ) = 0 (3.1) where s is the electric conductivity of the medium and V is the voltage distribution in the sample. We decided to inject a DC current uniformly through one of the surfaces of the part. The associated boundary conditions involve the inward normal component n of the current density J given as n ( s V ) = -n J (3.2) All remaining boundaries, excluding the ground connection, are set to be insulating boundaries - n J = 0 (3.3) The injected electric current deposits power throughout the part due to the finite conductivity in the sample. The power per unit volume Q is described by the following equations where E is magnitude of the electric field. Q = J 2 / s = se 2 (3.4) 2 Q V = s (3.5) - 5 -

6 The deposited power will cause the temperature of the part to rise gradually until it reaches equilibrium (known as the Joule effect). This process is influenced by the thermal properties of the part and the atmospheric conditions (ambient temperature). In particular, the thermal behavior is described by the generalized heat equation T 4 4 rc - ( k T ) = Q - h( T - Text ) - C( T - T amb ) t (3.6) where the parameters are given as follows: r - Density of the material. c - Heat capacity. k - Thermal conductivity. h - Convection heat transfer coefficient. Q - Heating power. C - Radiation heat Transfer coefficient. Since the dominant transfer mechanism is heat conduction, we obtain a simplified equation T r c - ( k T ) = Q (3.7) t In this formulation it is assumed that the sample surface is cooled through natural convection, implying a Neumann type boundary of type n ( k T ) = h( Text - T ) (3.8) here T and T ext are sample temperature and external temperature, respectively. Equation (3.7) is a second order PDE that can be solved analytically for canonical geometries by using a number of different methods such as the separation of variables, Fourier series, or Laplace transformation. However, from a practically point of view the numerical methods employing the finite difference (FD) or the finite elements (FE) methods will be our method of choice. As discussed in the next section, we have used the FE method to obtain a solution to the electric and heat equations in a cylindrical coordinate system. For this case, we have with the initial condition and the boundary condition k r Ê T Ár r Ë r ˆ ( r, 0) f ( r) T0 T = r c - Q (3.9) t T = - (3.10) T ( r0, t) k + h. T ( r0, t) = 0 (3.11) r - 6 -

7 4. Modeling Our modeling approach is the solution of the complex thermo-electric equations and predicting the behavior of the compacts when they are subjected to an electrically created heating source. This approach will aid in estimating the sensitivity of the IR technique when used in conjunction with simulating hairline flaws of known dimensions. A parametric model was arranged where parts with surface and subsurface cracks of various sizes, shapes, and orientations can be analyzed. In this section we have investigated the following three situations: Static modeling in 3D o Use simple geometry (cylinder). o Electrostatic - to show the voltage distribution. o Heat transfer local heating and major heat transfer mechanisms. Static modeling in 2D - Sensitivity study o Surface and subsurface defects. o Combination of flaws (various sizes and orientations). Dynamic modeling in 2D - sensitivity study o Extend the 2D model to include the dynamic effects Static Modeling in 3D The electric potential analysis of a 3D cylinder was conducted and the results are shown in Figures 4.1 and 4.2. This study is limited to a steady state situation and is based on the following material parameters and boundary conditions: Uniform source current density: J = A/m 2. Uniform conductivity: s =50000 S / m Part length L= 0.05m. The predicted total voltage drop between top and bottom surface is: LJ V = IR = s resulting in: V = volts

8 Figure 4.1: Voltage distribution for a cylindrical compact. The heat transfer portion utilizes the following approximated parameters: r = 7250 kg/m 3 c =440 W/kg C k =40 W/m C h =10 W/ m 2 C where the boundary condition is set to be of Neumann type. (a) (b) Figure 4.2: Temperature distribution in an unflawed cylindrical compact (a), and surface temperature profile along the z-axis (b) in Kelvin

9 4.2. Static Modeling in 2D A parametric study of a number of simulated defects was next conducted in an effort to estimate the sensitivity of the method (see Figure 4.3). (a) 1mm x 1mm Defect 20mm x 100mm Defects (b) Figure 4.3: Temperature distribution in a flawed compact (a), and surface profile along the z-axis (b). As can be seen, surface cracks are clearly detectable. However, the resulting temperature signature varies with flaw size and orientation. Interestingly, subsurface defects do not produce a detectable temperature gradient on the surface under steady state electric excitation conditions. Consequently we proceed by analyzing the same part when the temperature is changed under transient electric excitation condition Dynamic Modeling Dynamic thermography offers a number of significant advantages, including the possibility to detect subsurface defects and very small surface-breaking defects. The results in Figure 4.4 show a distinguishable signature from a small surface break and a noticeable temperature change, clearing indicating the presence of a defect

10 Figure 4.4: Temperature profile in meter over the surface of a compact recorded at three different time instances. 5. Experimental Study Our preliminary experimental study thus far has focused on static IR imaging and the detection of surface breaks within green-state parts. We have configured a simple IR imaging arrangement (see. Figure 5.1) which includes at its heart a camera with a spectral range of 8-12 mm capable of detecting a minimum temperature difference of 0.1 C. Image Processing laptop Power Supply IR Camera Sample under test Figure 5.1: Experimental test arrangement

11 A number of flaws were artificially created to help evaluate the effects of flaw size, shape and orientation. In particular, we created the following flaws: Flaw 1: o Horizontal orientation at ~1cm from the top. o Dimensions (length x width x depth): 1cm x (<20_m) x (<20 _m) Flaw 2: o Horizontal orientation at ~2cm from the top. o Dimensions (length x width x depth): 1mm x (~20_m) x (~20 _m). Flaw 3: o Vertical orientation at ~3cm from the top. o Dimensions (length x width x depth): 2mm x (~20_m) x (~20 _m). Flaw 4: o Vertical orientation at ~5cm from the top. o Dimensions (length x width x depth): 1cm x (<20_m) x (<20 _m) Profile Line (a) (b) Figure 5.2: IR image recording from a cylindrical part (powder: 1000B, non-lubricated) and subjected to 20A current excitation: (a) surface profile, and b) line profile along the dotted line. The data was post-processed in Matlab. The next step involved the IR image acquisition, storage in a PC, and Matlab postprocessing by setting a threshold. The idea is to selectively eliminate areas with temperatures below a preset value. A program was written that utilizes a simple image processing algorithm that evaluates all pixels and sets an intensity threshold

12 (a) (b) Figure 5.3: IR Images after thresholding of a cylindrical part (1000B non-lubricated) subjected to 20A of electric current excitation: (a) surface temperature distribution, and (b) temperature profile along the center line of image (a) Discussion In the above plots we can easily distinguish the defects that were artificially embedded into the part. Applying simple image processing techniques it is shown that good qualitative flaw information can be gained. The algorithmic post-processing is rapid, ultimately allowing an automated on-line processing. We also noticed the higher temperature in the contact areas at disproportionately high levels. Investigating the behavior more closely revealed that the electric conductivity itself is highest in this region, resulting in a higher power deposition. We also speculate that density distributions can be detected as the single-punch compacted green-state compacts in Figure 5.4 indicate

13 (a) (b) Figure 5.4: IR Images of two cylindrical compacts of pure 1000B iron compacted to (a) 25tsi, and (b) to 45Tsi. 6. Conclusions The objective of this first progress report is to present our preliminary modeling efforts and practical measurements of green-state compacts. The basic idea is to inject direct current through the compact and observe the energy/ sample interaction. In this first phase we successfully modeled and measured the effects of direct current in terms of creating temperature increases that can be recorded with an IR imaging system. All theoretical solutions were conducted with our own 2D and 3D FEM tools under both steady state and transient conditions. The ability to simulate various flaw configurations clearly demonstrates the potential usefulness of our research efforts. IR imaging has its own limitations where the emissivity plays a major role in recording temperature. Initial tests revealed that P/M parts appear to possess low emissivity. This fact implies long wavelength detectors (8~14_m or higher). Further research is needed to explore the emissivity in complex sintered parts such as gears where reflections between the individual tooth elements can trigger false alarms

14 7. Future Milestones 1. The theoretical model built so far lacks the ability to account for radiative effects such as reflections from other sources, and optical effects from the camera and its filters. It may therefore be necessary to complete the theoretical modeling in an effort to completely characterization the testing environment. 2. Material properties are required to help establish the model. We will need to set up a parallel experimentation to determine: the electrical conductivity, and the specific heat and the thermal conductivity. 3. The acquisition of controlled samples, with surface and subsurface defects are needed to practically validate the testing methodology. 4. A more detailed analysis of transient testing will require an IR camera that can at least capture 50 frames per minute. 5. Additional signal and image processing is required to assist in quantitative sample evaluation. 8. References

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16 13. Logan, D A First Course in Finite Elements Method PWS Publishing Company German, R.M. Powder Metallurgy Science Metal Powder Industries Federation, Princeton, New Jersey, Clark, F. Advanced Techniques in Powder Metallurgy Rowmann and Littlefield Inc. New York, NY