ISO/DIS 16364:2025(en)
ISO TC 156
Secretariat: SAC
Date: 2025-04-13
Corrosion of Metals and Alloys - Guidelines for Galvanic Corrosion Control
© ISO 2025
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
Contents
Annex A (informative) Example schematic diagram of corrosion potential 8
A.1 Corrosion potentials of various practical metals and alloys in seawater 8
Annex B (informative) Example of calculation of galvanic corrosion 11
B.1 Example of calculation of galvanic corrosion in an electrolytic solution 11
B.2 Example of calculation of galvanic corrosion in an atmospheric environment 13
Annex C (informative) Example of galvanic corrosion test method 14
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing International Standards is normally carried out through ISO technical committees. Each member body interested in a subject for which a technical committee has been established has the right to be represented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the different types of ISO documents should be noted. This document was drafted in accordance with the editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of any patent rights identified during the development of the document will be in the Introduction and/or on the ISO list of patent declarations received (see www.iso.org/patents).
Any trade name used in this document is information given for the convenience of users and does not constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and expressions related to conformity assessment, as well as information about ISO's adherence to the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 156, Corrosion of metals and alloys. WG6, General principles of testing and data interpretation.
This is the first edition of guideline for galvanic corrosion suppression.
Any feedback or questions on this document should be directed to the user’s national standards body. A complete listing of these bodies can be found at www.iso.org/members.html.
Introduction
Use of multi-materials, in which not only metal materials but also ceramics, semiconductors, carbon fiber and resins are utilized in structures, is advancing rapidly in many industrial fields such as electronic components, automobiles, aircraft, plant systems and infrastructure, among others. Where corrosion is concerned, this has increased the possibility of galvanic corrosion, heightening the necessity of a comprehensive, cross-sectorial guideline for galvanic corrosion suppression that includes materials and their environments. However, the existing ISO standards do not contain clear provisions concerning galvanic corrosion or standards other than bolting of dissimilar materials. On the other hand, boundary element method (BEM) and finite element method (FEM) are techniques that enable modelling and numerical calculation of galvanic corrosion. Simulations by these techniques have progressed and are already used in practical applications. Moreover, accompanying the application of multi-materials, carbon and other non-metallic materials eluted from ceramics, carbon fibre reinforced plastic (CFRP) or resins are related to galvanic corrosion and have become a critical issue in automobiles, aircraft, etc.
Under these circumstances, a cross-sectorial ISO guideline on galvanic corrosion, with its many inherent issues, is necessary.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights other than those in the patent database. ISO [and/or] IEC shall not be held responsible for identifying any or all such patent rights.
Corrosion of metals and alloys - Guidelines for galvanic corrosion control
1.0 Scope
The primary objectives of this guideline are to present a standard method for avoiding galvanic corrosion in the design stage, to present a standard method for determining whether actual corrosion damage was caused by galvanic corrosion, and to present a guideline for standard methods for suppressing galvanic corrosion.
This guideline includes a method for analysis and prediction of galvanic corrosion in environments, not only solution such as water but also atmospheric and soil, by numerical calculation based on polarization data.
This guideline does not establish the grounds for indexes related to the safety or loss of functions of materials in actual use. However, it is possible to use this guideline to estimate the function maintenance life and safety maintenance life of the said materials in advance; the responsibility for using the guideline rests with the reader.
2.0 Normative references
The following documents are referred to in the text in such a way that some or all of their content constitutes requirements of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 7441, Corrosion of metals and alloys — Determination of bimetallic corrosion in atmospheric exposure corrosion tests
ISO 21746, Composites and metal assemblies — Galvanic corrosion tests of carbon fibre reinforced plastics (CFRPs) related bonded or fastened structures in artificial atmospheres — Salt spray tests
ASTM G71, Standard Guide for Conducting and Evaluating Galvanic Corrosion Tests in Electrolytes
EN 1993‑1-4, Eurocode 3: Design of steel structures: Part 1-4 General rules – Supplementary rules for stainless steels
3.0 Terms and definitions
For the purposes of this document, the following terms and definitions apply.ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https://www.iso.org/obp
— IEC Electropedia: available at https://www.electropedia.org/
3.1
(noble, base) corrosion potential
Corrosion potential (or immersion potential) is the potential measured when materials A and B are immersed individually in the environmental electrolyte concerned. Noble indicates a potential on the positive side, and base potential indicates a potential on the negative side.
3.2
coupling potential
The potential measured when an electrical short circuit is established between materials A and B which are in contact with the electrolyte concerned.
3.3
electrolyte
An ionically conductive liquid or solid medium covering the surfaces of material A and material B.
3.4
diffusion control
A condition under which the diffusion rate of a dissolved substance in an electrolyte controls the corrosion reaction rate. In many cases, “diffusion control” indicates a condition in which the diffusion rate of dissolved oxygen in a liquid, which supports the cathodic reaction, controls the reaction rate.
3.5
area ratio
The ratio of the area of material A with a base corrosion potential and material B with a noble corrosion potential.
3.6
corrosion accelerate structure
Structures where galvanic corrosion increases the corrosion (corrosion mass loss on the base side due to anodic reaction; usual unit is g/m2), such as when the potential difference between metals is large or the anode area is small compared to the cathode.
4.0 Terms and definitions General Principles
4.1
general
This document provides guidance to minimise galvanic corrosion. Galvanic corrosion is caused by an electric current flow from a material A (Anode) with a base potential to a material B (Cathode) with a noble potential via an electrolyte and then return to the base material A through conductive wiring, conducting body or the material itself. This current causes galvanic corrosion, and as the current becomes larger, the anodic current density on the surface of material A increases and the galvanic corrosion rate becomes larger. This type of corrosion, which is accelerated by electrical contact between materials with different electric potentials, is called galvanic corrosion.
The method is to visualize the process and possible mitigations in accordance with the flowcharts of one or more of the following:
a. Materials designed for avoiding galvanic corrosion
b. Evaluation method for determining whether actual corrosion damage was caused by galvanic corrosion; and
c. Corrosion protection method for suppressing galvanic corrosion
4.2
material design
Figure 1 shows a material design flowchart for avoiding galvanic corrosion. It shows when material selection or, if possible, removal or change in electrolyte should be considered as a design change. It can also be used as an evaluation method for determining whether actual corrosion damage was caused by galvanic corrosion. The process is described below.
4.2.1
conductive dissimilar materials
Verify whether conductive dissimilar materials are in electrical contact. In addition to direct contact, “electrical contact” also includes electrical continuity (conduction) by way of wiring, etc. If electrical continuity does not exist, galvanic corrosion does not occur between those materials.
4.2.2
contact with a common electrolyte
Verify whether the dissimilar materials are in electrical contact, and whether they are also in contact with a common electrolyte. This means verifying whether electrical continuity exists between the two materials, and whether the two materials have also formed an external circuit having electrical conduction by the electrolyte. If an electrolyte is not present, galvanic corrosion is avoided. In case of condensation which can lead to the presence of electrolyte, the presence may only be cyclical and therefore not permanently observable. It will be necessary to ascertain whether or not there is a risk of condensation.
4.2.3
Corrosion accelerate structure
In case the dissimilar materials are in electrical contact and an electrolyte also exists between the materials, verify whether there are factors that accelerate corrosion. Even in the case of dissimilar materials, if the potentials of the two materials are on approximately the same level in the said electrolyte, galvanic corrosion is avoided. If the cathode/anode area ratio of the surfaces in contact with the electrolyte is sufficiently small, galvanic corrosion is suppressed. In addition, if the electrolyte has high resistance, the effective area ratio will differ from the apparent area ratio. Galvanic corrosion can be avoided in structures in which these corrosion-suppressing actions occur. Conversely, if these actions do not occur and a corrosion-accelerating structure is formed, for instance, increase of the potential difference with time, increase of cathode/anode area ratio with time and/or increase of conductivity on electrolyte with time. In such a case it is necessary to change the design of the contacted materials.
4.2.4
design changes
Design changes can be made by applying a data search on galvanic corrosion, and/or predictive calculations for galvanic corrosion and/or accelerated galvanic corrosion testing (ISO 7441). The corrosion rate can be predicted in advance by accelerated testing or predictive calculations. In accelerated testing, evaluate the amount of corrosion and the corrosion rate by preparing galvanic corrosion test specimens and conducting a salt spray test or cyclic corrosion test, or by inducing and accelerating corrosion by atmospheric exposure testing. Alternatively, evaluate the amount of corrosion and the corrosion rate by preparing galvanic corrosion test specimens and measuring the galvanic current using a zero-shunt ammeter or electrochemical testing using the constant potential polarization method set to the coupling potential. In predictive calculations, predict the amount of corrosion and the corrosion rate by using finite element method (FEM: numerical simulation to solve corrosion related equations by dividing the geometry into finite elements) or boundary element method (BEM: numerical simulation to solve corrosion related equations by dividing the boundary into elements). Corrosion can be evaluated quantitatively by either of these methods (see Annex B). In predictive calculations, it is necessary to consider diffusion of dissolved oxygen for cases where the cathodic reaction becomes rate-controlling, and also the effect of corrosion products that are influential to control both (cathodic and anodic) reactions. If the design is changed, re-start the process from the step “Contact of dissimilar materials?”. Finally, when all the judgement items are confirmed as “No”, the design can be fixed.
Figure 1 — Galvanic corrosion – material design flowchart
4.3
suppressing galvanic corrosion
Figure 2 shows a flowchart for the selection of methods for suppressing galvanic corrosion. Some of the methods in Figure 2 should be parallel executed and cannot be arranged in order. For instance, when two or more methods are possible at the same time, which method is preferred should take into account the degree of effect, economy, convenience and practicality. The procedure is described below.
4.3.1
contact structure
Change the contact structure of the dissimilar materials. Provide a structure, for example, with an insulating material between the contact surfaces so that electrical continuity does not exist between the dissimilar materials (EN 1993-1-4). Alternatively, create a structure in which occurrence of the anodic reaction is suppressed by reducing the surface area of the material that forms the cathode with a noble potential. Alternatively, provide a structure that blocks permeation of the electrolyte, so that the electrolyte does not cover the contacting surfaces of the dissimilar materials. Otherwise make contact free structure by total design change such as the omitting relevant parts with alternative structure. Confirm the effect by a corrosion test (ISO 7441, ISO 21746, ASTM G71). If the corrosion protection effect is confirmed, this concludes the problem - solving procedure. In case a corrosion protection effect is not confirmed, or in case structural change is not possible, consider material change.
4.3.2
Material change
Change the combination of dissimilar materials. Make one material into insulator. Otherwise, make generation of a galvanic current difficult by eliminating the combination of materials with base and noble corrosion potentials and using a combination of similar materials or materials with similar corrosion potentials. Confirm the effect by a corrosion test (ISO 7441, ISO 21746, ASTM G71). If the corrosion protection effect is confirmed, this concludes the problem-solving procedure. In case a corrosion protection effect is not confirmed, or in case material change is not possible, consider surface treatment change.
4.3.3
surface treatment
Perform surface treatment of the dissimilar materials. It is recommended that applying coatings for both materials that adds no corrosion reactions as cathodic nor anodic electrodes on the dissimilar materials. The role of coating is to isolate corrosive electrolyte from galvanic couple. When coating, care must be taken not to cause their defects on the anode side. Coating defect on the anode can act as a small anodic area where rapid galvanic corrosion may progress. Alternatively, apply a plating to the surfaces of the dissimilar materials. A galvanic current is suppressed if a combination of similar materials or materials with similar corrosion potentials is used.
4.3.4
environmental change
Change the electrolyte covering the contacting parts of the dissimilar materials. Eliminate halogens and other chemical species, dissolved oxygen and electrically conductive ions that accelerate the corrosion reaction. In case of atmospheric, decreasing humidity is one of the possible solutions. Alternatively, perform treatment by adding a corrosion inhibitor to the electrolyte covering the surfaces of the contacting parts of the dissimilar materials. In case a corrosion protection effect is not confirmed, or in case structural change is not possible, continue to electrochemical protection.
4.3.5
electrochemical protection
Provide cathodic protection for the contacting parts of the dissimilar materials. Suppress the occurrence of a galvanic current by continuously applying an electric potential, at which the anode does not dissolve, to either the anodic side or the cathodic side of the combination of dissimilar materials. Alternatively, suppress the occurrence of a galvanic current by electrically connecting a sacrificial anode and/or anode by impressed current protection to the combined part of the dissimilar materials. A cathodic protection system is not suitable for protecting metallic structures in atmospheric against galvanic corrosion. Confirm the effect by a corrosion test. If the corrosion protection effect is confirmed, this concludes the study procedure. Confirm the effect by a corrosion test. If the corrosion protection effect is confirmed, this concludes the study procedure.
Figure 2 — Flowchart of selection of appropriate methods for suppressing galvanic corrosion
5.0 Report
In the report, it is necessary to describe the judgment items for each item in the respective flows obtained by conducting a problem solving in accordance with the flowchart for one or more of the following three items:
a. Material design for avoiding galvanic corrosion;
b. The evaluation method for determining whether actual corrosion damage was caused by galvanic corrosion; and
c. Corrosion protection methods for suppressing galvanic corrosion.
(informative)
Example schematic diagram of corrosion potential- Corrosion potentials of various practical metals and alloys in seawater
Regarding potential difference, which is the main cause of galvanic corrosion, there are examples of potential measurement in cases where the electrolyte is seawater. Figure A.1 shows the corrosion potential region of various materials in seawater at 2,4 to 4,0 m/s for 5 to 15 days (see[1] and[2] in Bibliography). As galvanic corrosion proceeds, there are cases in which the order of noble and base in the corrosion potential series changes with the passage of time. Moreover, there are also cases in which the order changes in electrolytes with different environments.
Key
1 volts versus saturated calomel reference electrode
2 active
3 noble
4 black box shows an active state of metal, see NOTE 1 for more information
5 graphite
6 platinum
7 Ni-Cr-Mo alloy C
8 titanium
9 Ni-Cr-Mo-Cu-Si alloy B
10 Ni-Fe-Cr alloy 825
11 alloy 20 stainless steel cast and wrought
12 stainless steel types 316, 317
13 Ni-Cu alloys 400, K-500
14 stainless steel-types 302, 304, 321, 347
15 silver
16 nickel 200
17 silver braze alloys
18 Ni-Cr alloy 600
19 Ni-Al bronze
20 70-30 copper nickel
21 lead
22 stainless steel type 430
23 80-20 copper nickel
24 90-10 copper nickel
25 nickel silver
26 stainless steel type 410, 416
27 tin bronzes(G&M)
28 silicon bronze
29 manganese bronze
30 admiralty brass, aluminum brass
31 Pb-Sn solder(50/50)
32 copper
33 tin
34 naval brass, yellow brass, red brass
35 aluminum bronze
36 austenitic nickel cast iron
37 low alloy steel
38 mild steel, cast iron
39 cadmium
40 aluminum alloys
41 beryllium
42 zinc
43 magnesium
Figure A.1 — Corrosion potentials of various practical metals and alloys in seawater (2)
NOTE 1 Passive metals, like stainless steel, are naturally protected by a thin oxide layer that resists corrosion. When this oxide layer is removed, through chemical or mechanical means, the metal becomes active and is more prone to corrosion.
- Corrosion potentials of various practical metals and alloys in different electrolytic solutions
According to the electrolyte environment, the order of the corrosion potentials would be changed for most of the materials (see[3] and[4] in Bibliography). In addition, corrosion potentials change over time also occur on some materials that produce protective products on the surface. As the results, the order of noble and base in the corrosion potential series change with not only the environments but also passage of time. It is critical to check the corrosion potentials for each case in the designing of the actual galvanic corrosion suppression method.
- Fe/Al galvanic couple
On the Fe/Al galvanic couple, Zn plating onto Fe surface is effective to eliminate galvanic current by reducing the potential difference between dissimilar materials (by changing from Fe/Al couple to Zn/Al couple). Otherwise, insulate dissimilar materials of the galvanic couple from each other. The application method and/or part of insulation depends on the structure such as bolted fastening, welded adjacent materials and so on. Most effective method is to suppress closed circuit regions between dissimilar materials and electrolyte but if it is not applicable because of the structural limits, coating is available for such parts. Confirm the effect by a corrosion test. If the corrosion protection effect is confirmed, this concludes the study procedure. In case a corrosion protection effect is not confirmed, or in case structural change is not possible, continue to environmental treatment.
(informative)
Example of calculation of galvanic corrosion- Example of calculation of galvanic corrosion in an electrolytic solution
Mass transfer of a chemical species i in an electrolytic solution is shown by the following equation.
(1)
Where Ni is the flow velocity (mol/cm2) of chemical species i, and is a vector quantity expressing the mol number and direction of the transferred chemical species per unit of area. Ni is obtained from the first term (electrophoresis), the second term (diffusion), and the third term (convection), on the right side of the equation. z is the valence of the ion, u is mobility, F is the Faraday constant, c is concentration, Φ is the static field potential, D is the diffusion coefficient, and v is the velocity of the electrolyte.
When the electrolyte is decomposed into elements, the mass balance of the unit elements is given by the following equation, which is the sum total of the flow velocity differences of the chemical species from the respective boundaries, and the sum of the formation and consumption (Ri) of the chemical species by chemical reactions in the electrolyte.
(2)
Because a condition of neutrality is satisfied in the electrolyte, the following equation holds.
(3)
The concentration and potential of each chemical species are obtained from the above three equations. Concretely, infinite points are decomposed into finite elements and boundaries by discretizing the continuum expressed by Eq. (1) and Eq. (2), and the potential and concentration distributions of the chemical species are obtained as an approximate solution by the finite element method (FEM) or the boundary element method (BEM) using the electrochemical characteristics of the interface between the electrolyte and the anode material and cathode material as boundary conditions.
Since Ohm’s law holds in the electrolyte, the relationship between potential and current density is expressed by the following equation as electric conductivity κ.
(4)
Here, assuming the accumulation or loss of ions in the electrolyte is negligible, the current density satisfies the following equation.
(5)
The following Laplace’s equation can be obtained from Eq. (4) and Eq. (5).
(6)
The potential and current density distributions are calculated so as to satisfy Eqs. (1) and (2) when the concentration gradient of a chemical species in an electrolyte is considered, and to satisfy Eq. (6) when the electrolyte has a flow velocity but the concentration gradient is not considered.
Assuming the boundary of a region Ω of the electrolyte is Γ, the following boundary conditions are given in Γ for the boundary conditions of the anode-solution interface and the boundary condition of the cathode-solution interface.
i = fixed value: Neumann type boundary (7)
Φ = fixed value: Dirichlet type boundary (8)
= (E) = fa(i): Anodically polarized material surface (9)
= (E) = fc(i): Cathodically polarized material surface (10)
Eqs. (9) and (10) show polarization curves, and in many cases are defined by the following Butler-Volmer equation.
(11)
where, F is the Faraday constant, R is a gas constant, T is absolute temperature, α is a symmetry factor, i0 is the exchange current density, η is overvoltage (overpotential), defined as the difference between the corrosion potential and the equilibrium potential.
Figure B.1 is an example of the boundary conditions in an analysis of galvanic corrosion in an electrolyte. Experimentally measured polarization curves formulated by parameter fitting are generally used as the polarization curves for the anodic side material and cathodic side material. Because there is no ingress/egress of current at the upper surface or the boundary of the electrolyte, a Neumann boundary condition (i = 0) is assumed.
Key
1 electrolytic solution(Ω) (∇2Φ = 0)
2 i= 0
3 anode material (-Φ = fA(i))
4 cathode material ( -Φ = fC(i))
Figure B.1 — Example of boundary conditions used in analysis of galvanic corrosion
Using the above-mentioned equations and boundary conditions, the potential and current density are obtained by repeat calculation by discretization by element decomposition, and a convergent solution is obtained. Analysis methods include the finite difference method (FDM), finite element method (FEM), boundary element method (BEM), etc. Important job in each analysis method is to adopt simplification and optimization for geometric factors shown in Figure B.1.
- Example of calculation of galvanic corrosion in an atmospheric environment
Because galvanic corrosion can also proceed in atmospheric environments if the material surface is covered with an electrolyte film, galvanic corrosion can be calculated by the same method as in the calculation for galvanic corrosion in an electrolytic solution. The thickness and ion concentration of the water film are determined from the relative humidity and amount of adhering salt as the electrolyte, and the analysis is carried out assuming polarization characteristics corresponding to the concentration of the electrolyte as the boundary condition. Because the potential distribution and current density at the material surface are obtained, the amount of corrosion and corrosion range can be predicted (see[5] and[6] in Bibliography). The corrosion and corrosion range are difficult to predict and frequently lack accuracy, correct prediction could be achievable with appropriate parameters (see[7] in Bibliography) and optimum divisions on FDM, FEM or BEM.
(informative)
Example of galvanic corrosion test method
Table C.1 shows typical examples of galvanic corrosion test method. These test methods are useful for estimating the likelihood of galvanic corrosion and how fast it will progress.
Table C.1 — Typical examples of galvanic corrosion test method
Standard | 1. Galvanic couple | 2. Test conditions | 3. Test procedure | 4. Evaluation | |||||
Material | Shape | Area ratio of anode and cathode | Coupling | Surface preparation | Temp. | Duration | |||
ISO7441 | Metals with or without coating | Plates | Const. | Bolting | Atmospheric | As produced commercially | Outside temp. | > 2 years | — Mass loss — Mechanical property |
Washers | Const. | ≥ 1 year | |||||||
Wire on bolt |
| Wrapping | ≥ 90 days | ||||||
ISO21746 | CFRPs and metal | Plate | 1 | Rivet | 3 salt spray tests (NSS, AASS, CASS) (see NOTE 2) |
|
|
| Mass loss |
ASTM G71 | Metals | Plates |
| Electrically conductive | Electrolyte solution | Polished and cleaned | — Lab. temp. — Field temp. | Service period | — Couple current — Metallographic obs. |
NOTE 2 NSS: Neutral salt spray test, AASS: Acetic acid salt spray test, CASS: Copper-accelerated acetic acid salt-spray test
Bibliography
[1] F. L. LaQue, “Marine Corrosion,” John Wiley & Sons, Inc.,1975, p. 179
[2] ASTM G82, Standard Guide for Development and Use of a Galvanic Series for Predicting Galvanic Corrosion Performance
[3] Uhlig’s Corrosion Handbook, Third Edition, Edited by R. Winston Revie, John Wiley & Sons, Inc., 2011, pp123-143.
[4] N. R. Smart and D. J. Blackwood, An Investigation of the Effects of Galvanic Coupling on the Corrosion of Container and Waste Metals in Cementitious Environments, AEA Technology Report AEAT-0251, issue C, 1998.
[5] Mizuno D., Shil Y., Kelly R.G. Modelling of Galvanic Interactions between AA5083 and Steel Atmospheric Condition, Proceedings of the 2011 COMSOL Conference in Boston, 2011
[6] Vit Jenicek, Martina Pazderova, Linda Diblikova, Computational Simulation of Galvanic Corrosion under the Thin Film of Electrolyte, MM Science Journal, 2012, pp 370-373.
[7] Olga Dolgikh, Hans Simillion, Nils Van den Steen, Johan Deconinck, Steps Towards Atmospheric Corrosion Modelling, Chemical Engineering Transactions, Vol. 41, 2014, pp 283-288.