Development and evaluation of a non-destructive adhesion test

The object of this work was to further develop the idea introduced by Muaddi et al (1981) which enables some of the disadvantages of earlier destructive adhesion test methods to be overcome. The test is non-destructive in nature but it does need to be calibrated against a destructive method. Adhesion is determined by measuring the effect of plating on internal friction. This is achieved by determining the damping of vibrations of a resonating specimen before and after plating. The level of adhesion was considered by the above authors to influence the degree of damping. In the major portion of the research work the electrodeposited metal was Watt's nickel, which is ductile in nature and is therefore suitable for peel adhesion testing. The base metals chosen were aluminium alloys S1C and HE9 as it is relatively easy to produce varying levels of adhesion between the substrate and electrodeposited coating by choosing the appropriate process sequence. S1C alloy is the commercially pure aluminium and was used to produce good adhesion. HE9 aluminium alloy is a more difficult to plate alloy and was chosen to produce poorer adhesion. The "Modal Testing" method used for studying vibrations was investigated as a possible means of evaluating adhesion but was not successful and so research was concentrated on the "Q" meter. The method based on the use of a "Q" meter involves the principle of exciting vibrations in a sample, interrupting the driving signal and counting the number of oscillations of the freely decaying vibrations between two known preselected amplitudes of oscillations. It was not possible to reconstruct a working instrument using Muaddi's thesis (1982) as it had either a serious error or the information was incomplete. Hence a modified "Q" meter had to be designed and constructed but it was then difficult to resonate non-magnetic materials, such as aluminium, therefore, a comparison before and after plating could not be made. A new "Q" meter was then developed based on an Impulse Technique. A regulated miniature hammer was used to excite the test piece at the fundamental mode instead of an electronic hammer and test pieces were supported at the two predetermined nodal points using nylon threads. This instrument developed was not very successful at detecting changes due to good and poor pretreatments given before plating, however, it was more sensitive to changes at the surface such as room temperature oxidation. Statistical analysis of test results from untreated aluminium alloys show that the instrument is not always consistent, the variation was even bigger when readings were taken on different days. Although aluminium is said to form protective oxides at room temperature there was evidence that the aluminium surface changes continuously due to film formation, growth and breakdown. Nickel plated and zinc alloy immersion coated samples also showed variation in Q with time. In order to prove that the variations in Q were mainly due to surface oxidation, aluminium samples were lacquered and anodised Such treatments enveloped the active surfaces reacting with the environment and the Q variation with time was almost eliminated especially after hard anodising. This instrument detected major differences between different untreated aluminium substrates.Also Q values decreased progressively as coating thicknesses were increased. This instrument was also able to detect changes in Q due to heat-treatment of aluminium alloys.

An investigation of thin amorphous carbon-based sputtered coatings for MEMS and micro-engineering applications

The work presented in this thesis describes an investigation into the production and properties of thin amorphous C films, with and without Cr doping, as a low wear / friction coating applicable to MEMS and other micro- and nano-engineering applications. Firstly, an assessment was made of the available testing techniques. Secondly, the optimised test methods were applied to a series of sputtered films of thickness 10 - 2000 nm in order to: (i) investigate the effect of thickness on the properties of coatingslcoating process (ii) investigate fundamental tribology at the nano-scale and (iii) provide a starting point for nanotribological coating optimisation at ultra low thickness. The use of XPS was investigated for the determination of Sp3/Sp2 carbon bonding. Under C 1s peak analysis, significant errors were identified and this was attributed to the absence of sufficient instrument resolution to guide the component peak structure (even with a high resolution instrument). A simple peak width analysis and correlation work with C KLL D value confirmed the errors. The use of XPS for Sp3/Sp2 was therefore limited to initial tentative estimations. Nanoindentation was shown to provide consistent hardness and reduced modulus results with depth (to < 7nm) when replicate data was suitably statistically processed. No significant pile-up or cracking of the films was identified under nanoindentation. Nanowear experimentation by multiple nanoscratching provided some useful information, however the conditions of test were very different to those expect for MEMS and micro- / nano-engineering systems. A novel 'sample oscillated nanoindentation' system was developed for testing nanowear under more relevant conditions. The films were produced in an industrial production coating line. In order to maximise the available information and to take account of uncontrolled process variation a statistical design of experiment procedure was used to investigate the effect of four key process control parameters. Cr doping was the most significant control parameter at all thicknesses tested and produced a softening effect and thus increased nanowear. Substrate bias voltage was also a significant parameter and produced hardening and a wear reducing effect at all thicknesses tested. The use of a Cr adhesion layer produced beneficial results at 150 nm thickness, but was ineffective at 50 nm. Argon flow to the coating chamber produced a complex effect. All effects reduced significantly with reducing film thickness. Classic fretting wear was produced at low amplitude under nanowear testing. Reciprocating sliding was produced at higher amplitude which generated three body abrasive wear and this was generally consistent with the Archard model. Specific wear rates were very low (typically 10-16 - 10-18 m3N-1m-1). Wear rates reduced exponentially with reduced film thickness and below (approx.) 20 nm, thickness was identified as the most important control of wear.

Synthesis and characterisation of hydrogel polymers for medical applications

A fundamental if poorly understood problem that hydrogels display is the tendency of these contact lens materials to dehydrate, causing certain complications of the corneal epithelium. However, recent studies have indicated that the evaporation rate of water from different hydrogel lenses is the same and the severity of conditions such as corneal staining is controlled by the states of water in the material. A study was therefore undertaken which concluded that increased corneal desiccating staining occurred as the proportion of water existing in the bound state decreased. The possibility of using dehydrated hydrogels as packaging materials with desiccating properties has also been investigated. As hydrogels have a high affinity for water they have adequate ability to function as a moisture scavenger in an enclosed atmosphere. It was concluded that this ability is maximised by a high total water content and an increase in the proportion of this water existing in the bound state for the material when it is fully hydrated. N-vinyl pyrrolidone has a low reactivity in vinyl polymerisation reactions which results in polymers with local domains of the same chemical type which can lead to deposition. As contact lenses comprising of this monomer are susceptible to deposition, a monomer with a higher reactivity in vinyl polymerisations is acryloylmorpholine and its incorporation in favour of NVP is encouraged. Unfortunately a large proportion of high EWC hydrogels are mechanically weak and attempts to increase this property by increasing hydrophobicity or cross-linking results in a decrease in EWC. Monomers with the potential to carry a positive charge were incorporated into a high EWC, AMO-HEMA copolymer and the physical properties were investigated. Although EWC increased, mechanical properties decreased only slightly. Therefore simultaneous incorporation of a positively charged monomer and a negatively charged monomer was investigated. The resulting copolymers showed increased water content and increased initial modulus. A technique for measuring the coefficient of friction of contact lenses during lubrication has been developed.

Wear and corrosion of mechanical seals

Mechanical seals are used extensively to seal machinery such as pumps, mixers and agitators in the oil, petrochemical and chemical industries. The performance of such machinery is critically dependent on these devices. Seal failures may result in the escape of dangerous chemicals, possibly causing injury or loss of life. Seal performance is limited by the choice of face materials available. These range from cast iron and stellited stainless steel to cemented and silicon carbides. The main factors that affect seal performance are the wear and corrosion of seal faces. This research investigated the feasibility of applying surface coating/treatments to seal materials, in order to provide improved seal performance. Various surface coating/treatment methods were considered; these included electroless nickel plating, ion plating, plasma nitriding, thermal spraying and high temperature diffusion processes. The best wear resistance, as evaluated by the Pin-on-Disc wear test method, was conferred by the sprayed tungsten carbide/nickel/tungsten-chromium carbide deposit, produced by the high energy plasma spraying (Jet-Kote) process. In general, no correlation was found between hardness and wear resistance or surface finish and friction. This is due primarily to the complexity of the wear and frictional oxidation, plastic deformation, ploughing, fracture and delamination. Corrosion resistance was evaluated by Tafel extrapolation, linear polarisation and anodic potentiodynamic polarisation techniques. The best corrosion performance was exhibited by an electroless nickel/titanium nitride duplex coating due to the passivity of the titanium nitride layer in the acidified salt solution. The surface coating/treatments were ranked using a systematic method, which also considered other properties such as adhesion, internal stress and resistance to thermal cracking. The sealing behaviour of surface coated/treated seals was investigated on an industrial seal testing rig. The best sealing performances were exhibited by the Jet-Kote and electroless nickel silicon carbide composite coated seals. The failure of the electroless nickel and electroless nickel/titanium nitride duplex coated seals was due to inadequate adhesion of the deposits to the substrate. Abrasion of the seal faces was the principal wear mechanism. For operation in an environment similar to the experimental system employed (acidified salt solution) the Jet-Kote deposit appears to be the best compromise.

Nitrogen implantation of tool steels and engineering coatings

Ion implantation modifies the surface composition and properties of materials by bombardment with high energy ions. The low temperature of the process ensures the avoidance of distortion and degradation of the surface or bulk mechanical properties of components. In the present work nitrogen ion implantation at 90 keV and doses above 1017 ions/cm2 has been carried out on AISI M2, D2 and 420 steels and engineering coatings such as hard chromium, electroless Ni-P and a brush plated Co-W alloy. Evaluation of wear and frictional properties of these materials was performed with a lubricated Falex wear test at high loads up to 900 N and a dry pin-on-disc apparatus at loads up to 40 N. It was found that nitrogen implantation reduced the wear of AISI 420 stainless steel by a factor of 2.5 under high load lubricated conditions and by a factor of 5.5 in low load dry testing. Lower but significant reductions in wear were achieved for AISI M2 and D2 steels. Wear resistance of coating materials was improved by up to 4 times in lubricated wear of hard Cr coatings implanted at the optimum dose but lower improvements were obtained for the Co-W alloy coating. However, hardened electroless Ni-P coatings showed no enhancement in wear properties. The benefits obtained in wear behaviour for the above materials were generally accompanied by a significant decrease in the running-in friction. Nitrogen implantation hardened the surface of steels and Cr and Co-W coatings. An ultra-microhardness technique showed that the true hardness of implanted layers was greater than the values obtained by conventional micro-hardness methods, which often result in penetration below the implanted depth. Scanning electron microscopy revealed that implantation reduced the ploughing effect during wear and a change in wear mechanism from an abrasive-adhesive type to a mild oxidative mode was evident. Retention of nitrogen after implantation was studied by Nuclear Reaction Analysis and Auger Electron Spectroscopy. It was shown that maximum nitrogen retention occurs in hard Cr coatings and AISI 420 stainless steel, which explains the improvements obtained in wear resistance and hardness. X-ray photoelectron spectroscopy on these materials revealed that nitrogen is almost entirely bound to Cr, forming chromium nitrides. It was concluded that nitrogen implantation at 90 keV and doses above 3x1017 ions/cm2 produced the most significant improvements in mechanical properties in materials containing nitride formers by precipitation strengthening, improving the load bearing capacity of the surface and changing the wear mechanism from adhesive-abrasive to oxidative.

Preparation and electrical properties of graphene nanosheet/Al2O3 composites

Fully dense graphene nanosheet(GNS)/Al2O3 composites with homogeneously distributed GNSs of thicknesses ranging from 2.5 to 20 nm have been fabricated from ball milled expanded graphite and Al2O3 by spark plasma sintering. The percolation threshold of electrical conductivity of the as-prepared GNS/Al2O3 composites is around 3 vol.%, and this new composite outperforms most of carbon nanotube/Al2O3 composites in electrical conductivity. The temperature dependence of electrical conductivity indicated that the as-prepared composites behaved as a semimetal in a temperature range from 2 to 300 K.

Isotropic compression of mixtures of hard and soft spheres

The compaction behaviour of powders with soft and hard components is of particular interest to the paint processing industry. Unfortunately, at the present time, very little is known about the internal mechanisms within such systems and therefore suitable tests are required to help in the interpretative process. The TRUBAL, Distinct Element Method (D.E.M.) program was the method of investigation used in this study. Steel (hard) and rubber (soft) particles were used in the randomly-generated, binary assemblies because they provided a sharp contrast in physical properties. For reasons of simplicity, isotropic compression of two-dimensional assemblies was also initially considered. The assemblies were first subject to quasi-static compaction, in order to define their behaviour under equilibrium conditions. The stress-strain behaviour of the assemblies under such conditions was found to be adequately described by a second-order polynomial expansion. The structural evolution of the simulation assemblies was also similar to that observed for real powder systems. Further simulation tests were carried out to investigate the effects of particle size on the compaction behaviour of the two-dimensional, binary assemblies. Later work focused on the quasi-static compaction behaviour of three-dimensional assemblies, because they represented more realistic particle systems. The compaction behaviour of the assemblies during the simulation experiments was considered in terms of percolation theory concepts, as well as more familiar macroscopic and microstructural parameters. Percolation theory, which is based on ideas from statistical physics, has been found to be useful in the interpretation of the mechanical behaviour of simple, elastic lattices. However, from the evidence of this study, percolation theory is also able to offer a useful insight into the compaction behaviour of more realistic particle assemblies.

The development of a testing procedure for dry friction brakes

A description of the background to testing friction materials for automotive brakes explains the need for a rapid, inexpensive means of assessing their behaviour in a way which is both accurate and meaningful. Various methods of controlling inertia dynamometers to simulate road vehicles are rejected in favour of programming by means of a commercially available XY plotter. Investigation of brake service conditions is used to set up test schedules, and a dynamometer programming unit built to enable service conditions on vehicles to be simulated on a full scale dynamometer. A technique is developed by which accelerated testing can be achieved without operating under overload conditions, saving time and cost without sacrificing validity. The development of programming by XY plotter is described, with a method of operating one XY plotter to programme the machine, monitor its own behaviour, and plot its own results in logical sequence. Commissioning trials are described and the generation of reproducible results in frictional behaviour and material durability is discussed. Teclmiques are developed to cross check the operation of the machine in retrospect, and retrospectively correct results in the event of malfunctions. Sensitivity errors in the measuring circuits are displayed between calibrations, whilst leaving the recorded results almost unaffected by error. Typical results of brake lining tests are used to demonstrate the range of performance parameters which can be studied by use of the machine. Successful test investigations completed on the machine are reported, including comments on behaviour of cast iron drums and discs. The machine shows that materials can repeat their complex friction/ temperature/speed/pressure relationships at a reproducibility of the order of +-0.003u and +~ 0.0002 in. thickness loss during wear tests. Discussion of practical and academic implications completes the report with recommendations for further work in both fields.

Prestressed concrete beams with stirrups subjected to torsion, bending and shear

Reported in this thesis are test results of 37 eccentrically prestressed beams with stirrups. Single variable parameters were investigated including the prestressing force, the prestressing steel area, the concrete strength, the aspect ratio h/b and the stirrups size and spacing. Interaction of bending, torsion and shear was also investigated by testing a series of beams subjected to varying bending/torsional moment ratios. For the torsional strength an empirical expression of linear format is proposed and can be rearranged in a non-dimensional interaction form: T/To+V/Vo+M/Mo+Ps/Po+Fs/Fo=Pc2/Fsp. This formula which is based on an average experimental steel stress lower than the yield point is compared with 243 prestressed beams containing ' stirrups, including the author's test beams, and good agreement is obtained. For the theoretical analysis of the problem of torsion combined with bending and shear in concrete beams with stirrups, the method of torque-friction is proposed and developed using an average steel stress. A general linear interaction equation for combined torsion with bending and/or shear is proposed in the following format: (fi) T/Tu=1 where (fi) is a combined loading factor to modify the pure ultimate strength for differing cases of torsion with bending and/or shear. From the analysis of 282 reinforced and prestressed concrete beams containing stirrups, including the present investigation, good agreement is obtained between the method and the test results. It is concluded that the proposed method provides a rational and simple basis for predicting the ultimate torisional strength and may also be developed for design purposes.

Elasto-plastic impact of fine particles and fragmentation of small agglomerates

Surface deposition of dense aerosol particles is of major concern in the nuclear industry for safety assessment. This study presents theoretical investigations and computer simulations of single gas-born U3O8 particles impacting with the in-reactor surface and the fragmentation of small agglomerates. A theoretical model for elasto-plastic spheres has been developed and used to analyse the force-displacement and force-time relationships. The impulse equations, based on Newton's second law, are applied to govern the tangential bouncing behaviour. The theoretical model is then incorporated into the Distinct Element Method code TRUBAL in order to perform computer simulated tests of particle collisions. A comparison of simulated results with both theoretical predictions and experimental measurements is provided. For oblique impacts, the results in terms of the force-displacement relationship, coefficients of restitution, trajectory of the impacting particle, and distribution of kinetic energy and work done during the process of impact are presented. The effects of Poisson's ratio, friction, plastic deformation and initial particle rotation on the bouncing behaviour are also discussed. In the presence of adhesion an elasto-plastic collision model, which is an extension to the JKR theory, is developed. Based on an energy balance equation the critical sticking velocity is obtained. For oblique collisions computer simulated results are used to establish a set of criteria determining whether or not the particle bounces off the target plate. For impact velocities above the critical sticking value, computer simulated results for the coefficients of restitution and rebound angles of the particle are presented. Computer simulations of fracture/fragmentation resulting from agglomerate-wall impact have also been performed, where two randomly generated agglomerates (one monodisperse, the other polydisperse), each consisting of 50 primary particles are used. The effects of impact angle, local structural arrangements close to the impact point, and plastic deformation at the contacts on agglomerate damage are examined. The simulated results show a significant difference in agglomerate strength between the two assemblies. The computer data also shows that agglomerate damage resulting from an oblique impact is determined by the normal velocity component rather than the impact speed.

Study of the deposition, properties and applications of electroless deposits containing particles

The deposition efficiencies of a number of electroless nickel and cobalt plating solutions were studied and in the case of nickel compared with a commercial plating solution Nifoss 80. At the optimum plating conditions (92ºC and pH 4.5) Nifoss 80 produced nickel layers most efficiently, the alkaline cobalt solution operated most efficiently at 90ºC and pH 9. The methods of producing compostte layers containing 2-3 µm carbide particles and chromium powder is described. Nickel and cobalt layers containing approximately 27% carbide particles, or 40% (Ni) and 30% (Co) chromium particles by volume were obtained. This value is independent of the particle concentration in the plating solution within the range (20~200 g/l). Hardness of the nickel. as deposited was 515 Hv, this was increased to a maximum of 1155 Hv by heat treatment at 200ºC for 5 hours in vacuum. Incorporation. of .chromium carbide particles resulted in a maximum hardness of 1225 Hv after heating at 500ºC for 5 hours in vacuum and chromium particles resulted in a maximum hardness of 16S0 Hv after heat treatment at 400ºC for 2 hours in vacuum. Similarly the hardness of cobalt as deposited was 600 Hv, this was increased to a maximum of 1300 Hv after heat treatment at 400ºC for 1 hour. Incorporation of chromium carbide particles resulted jn a maximum hardness of 1405 Hv after heating at 400ºC for 5 hours in vacuum and chromium particles resulted in a maximum hardness of 1440 Hv after. heat treating for 2 hours at 400ºC in vacuum. The structure of the deposits was studied by optical and scanning electron microscopy. The wear rate and coefficient of friction was determined by a pin and disc method. Wear rate and coefficient of friction decreased with increase in hardness. The wear resistance of the materials was also determined using a simulated forging test. Dies made of standard die steel were coated and the wear rates of the layers as deposited and after heat treatment were compared with those of uncoated tools. The wear resistance generally increased with hardness, it was 50-75% more than the uncoated die steel. Acetic acid salt spray test and outdoor exposure for six months was used to study the corrosion behaviour of the deposits and potentiodynamic curves plotted to find their corrosion potential. Nickel deposit exhibited less staining than carbide composite deposits and nickel-chromium deposits had the most noble corrosion potential.

The mechanical and wear behaviour of B(SiC) fibre-reinforced composite materials

The mechanical properties and wear behaviour of B(SiC) fibre-reinforced metal matrix composites (MMCs) and aluminium alloy (2014) produced by metal infiltration technique were determined. Tensile tests were peliormed at different conditions on both the alloy matrix and its composite, and the tensile fracture surfaces were also examined by Scanning Electron Microscopy (SEM). Dry wear of the composite materials sliding on hardened steel was studied using a pin-on-disc type machine. The effect of fibre orientation on wear rate was studied to provide wear resistance engineering data on the MMCs. Tests were carried out with the wear surface sliding direction set normal, parallel and anti-parallel to the fibre axis. Experiments were perfonned for sliding speeds of 0.6, 1.0 and 1.6 m/s for a load range from 12 N to 60 N. A number of sensitive techniques were used to examine worn surface and debris, i.e: Scanning Electron Microscopy (SEM), Backscattered Electron Microscopy (BSEM) and X-ray Photoelectron Spectroscopy (XPS). Finally, the effect of fibre orientation on the wear rate of the Borsic-reinforced plastic matrix composites (PMCs) produced by hot pressing technique was also investigated under identical test conditions. It was found that the composite had a markedly increased tensile strength compared with the matrix. The wear results also showed that the composite exhibited extremely low wear rates compared to the matrix material and the wear rate increased with increasing sliding speed and normal load. The effect of fibre orientation was marked, the lowest wear rates were obtained by arranging the fibre perpendicular to the sliding surface, while the highest wear was obtained for the parallel orientation. The coefficient of friction was found to be lowest in the parallel orientation than the others. Wear of PMCs were influenced to the greatest extent by these test parameters although similar findings were obtained for both composites. Based on the results of analyses using SEM, BSED and XPS, possible wear mechanisms are suggested to explain the wear of these materials.

Zwitterionic and charge-balanced (polyampholyte) copolymer hydrogels

Zwitterionic compounds, or zwitterions, are electrically neutral compounds having an equal number of formal unit charges of opposite sign. In common polyzwitterions the zwitterionic groups are usually located in pendent groups rather than the backbone of the macromolecule. Polyzwitterions contain both the anion and cation in the same monomeric unit, unlike polyampholytes which can contain the anion and cation in different monomeric units. The use of cationic and anionic monomers (or monomers capable of becoming charged) in stoichiometric equivalent proportions produces charge-balanced polyampholyte copolymers. Hydrogel materials produced from zwitterionic monomers have been proposed for use and are used in many biomaterial applications but synthetic charge-balanced polyampholyte are less common. Certain properties of hydrogels which are important for their successful use as biomaterials, these include the equilibrium water content, mechanical, surface energy, oxygen permeability, swelling and the coefficient of friction. The zwitterionic monomer N,N-dimethyl-N-(2-acryloylethyl)-N-(3-sulfopropyl) ammonium betaine (SPDA) was synthesized with 2-hydroxyethly acrylate (HEMA) as the comonomer to produce a series of polyzwitterion hydrogels. To produce charged-balanced copolymer hydrogels two “cationic” monomers were selected; 2-(diethylamino) ethyl methacrylate (DMAEMA) and 3-(dimethylamino) propyl methacrylamide (DMAPMA) and an anionic monomer; 2-acrylamido 2,2 methylpropane sulphonic acid (AMPS). Two series’ of charge-balanced copolymers were synthesized from stoichiometric equivalent ratios of DMAEMA or DMAPMA and AMPS with HEMA as a terpolymer. The zwitterionic copolymer and both charge-balanced copolymers produced clear, cohesive hydrogels. The zwitterionic and charge-balanced copolymers displayed similar EWC’s along with similar mechanical and surface energy properties. The swelling of the zwitterionic copolymer displayed antipolyelectrolyte behavior whereas the charge-balanced copolymers displayed behaviour somewhere between this and a typical polyelectrolyte. This work describes some aspects of the polymerisation and properties of SPDA copolymers and charge-balanced (polyampholyte) copolymers relevant to their potential as biomedical / bioresponsive materials. The biomimetic nature of SPDA together with its compatibility with other monomers makes it a useful and complimentary addition to the building blocks of biomaterials.

The study and measurements of the behaviour and characteristics of electromagnetic relays

The thesis presents a theoretical and practical study of the dynamic behaviour of electromagnetic relays. After discussing the problem of solving the dynamicc equations analytically and presenting a historical survey of the earlier works in the relay and its dynamics, the simulation of a relay on the analogue computer is discussed. It is shown that the simulation may be used to obtain specific solutions to the dynamic equations. The computer analysis provides the dynamic characteristics for design purposes and may be used in the study of bouncing, rebound oscillations and stability of the armature motion. An approximate analytical solution to the two dynamic equations is given based on the assumption that the dynamic variation of the pull with the position of the armature is linear. The assumption is supported by the Computer-aided analysis and experimental results. The solution is intended to provide a basis for a rational design. A rigorous method of analysing the dynamic performance by using Ahlberg's theory is also presented. This method may be justified to be the extension of Ahlberg's theory by taking the mass and frictional damping forces into account. While calculating the armature motion mathematically, Ahlberg considers the equilibrium of two kinds of forces, namely pull and load, and disregards the mass and friction forces, whereas the present method deals with the equilibrium of all four kinds of forces. It is shown how this can be utilised to calculate the dynamic characteristics for a specific design. The utility of this method also extends to the study of stability, contact bounce and armature rebound. The magnetic circuit and other related topics which are essential to the study of relay dynamics are discussed and some necessary experimental results are given.