Dynamic Analysis of a Straight Bevel Gear Composite Structure Al-Qrimli, Haidar Fadhil Abbas; Almurib, H. A.; Kumar, N.; Mahdi, F. A.

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1 Heriot-Watt University Heriot-Watt University Research Gateway Dynaic Analysis of a Straight Bevel Gear Coposite Structure Al-Qrili, Haidar Fadhil Abbas; Alurib, H. A.; Kuar, N.; Mahdi, F. A. Published in: Journal of Material Sciences and Engineering DOI: / Publication date: 2015 Docuent Version Publisher's PDF, also known as Version of record Link to publication in Heriot-Watt University Research Gateway Citation for published version (APA): Al-Qrili, H. F. A., Alurib, H. A., Kuar, N., & Mahdi, F. A. (2015). Dynaic Analysis of a Straight Bevel Gear Coposite Structure. Journal of Material Sciences and Engineering, 4(1), [ ]. DOI: / General rights Copyright and oral rights for the publications ade accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requireents associated with these rights. If you believe that this docuent breaches copyright please contact us providing details, and we will reove access to the work iediately and investigate your clai.

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3 Material Science & Engineering Research Article Article Al-Qrili et al., 2015, 4:1 Open Open Access Dynaic Analysis of a Straight Bevel Gear Coposite Structure Al-Qrili HF 1 *, Alurib HA 2, Kuar N 2 and Mahdi FA 3 1 Departent of Mechanical Engineering, Curtin University, CDT , Miri, Sarawak, Malaysia 2 Faculty of Electrical Engineering, University of Nottingha, Seenyih, Malaysia 3 Departent of Electrical Engineering, University of Baghdad, Jadriyah, Baghdad, Iraq Abstract In this paper, orthotropic aterials are selected to be used as a straight bevel gear. These aterials have the advantage of being light, are durable in high speeds, require the iniu need for oil, high strengths, and extra loading capacities. Due to these properties, it is highly preferable coparing to conventional aterials. This work deonstrates a standard for of the straight bevel gear, to focus on the study of the behaviour of aterial. Based on the coplex proportional assessent ethod, we selected the woven roving glass fibre as an optiu aterial to be used in the straight bevel gear odel. Fro the results, it was deterined that the coposite gear is better in ters of specific energy absorption and dynaic behaviour copared to steel gears. Fro the results, the jute-epoxy shows a very low value of stiffness and it can be concluded that the natural fibre is not suitable to be used as a aterial for a straight bevel gear. Keywords: Steel; Polyer-atrix coposite; Gears; Finite eleent odelling Noenclature MMC: Metal Matrix Coposite FRP: Fibre Reinforceent Plastic COPRAS: coplex proportional assessent ethod SEA: Specific Energy Absorption S: Stiffness M: Mass of Gear P: Load SE: Stiffness Efficiency C: Cost EM: Easy Manufacturing RS: Relative Significance QU: Quantitative Utility Introduction Recent advances in aterial processing technology have propelled coposite aterials to the forefront of aterial technological developent. Due to advantages such as high specific strength, high specific odulus, and special electrical properties, coposite aterials have attracted considerable attention within the engineering counity, and are touted as potential substitutes for etals in autootive parts, aerospace structural parts, and transportation [1,2]. This is due to the fact that coposites have good properties such as excellent corrosion resistance, high strength to weight ratio, high ipact resistance and possesses design flexibility. These properties ake parts anufactured fro coposite aterials of high-quality, durable and cost-effective products [3]. Coposite are flexible in ters of odifications, fatigue resistance, and the ability to absorb ipact energy, aking the very attractive to current industrial needs. The literature on isotropic etallic gears is assive; however, the author has anaged to locate soe studies regarding gears ade fro coposite aterials. It was started by Ganesan and Vijayarangan, where they conducted an investigation coparing the perforance of a spur gear fabricated using etal atrix coposite (MMC) aterials, to that ade of conventional steel aterials, and analyzed its static behaviour in three diensions using finite eleent analysis [4]. They concluded that the behaviour and perforance of both MMC aterial gears and the ild steel gear are quite siilar, with the safety factor for the etal atrix coposite showing the lowest values relative to other aterials. After that Senthilvelan and Gnanaoorthy reported that gear tooth with less fillet radius fails via crack initiation at its root, while the large fillet radius fails by icro-cracking at the idpoint of the tooth [5]. In response to this discovery, they used injection-olded gear, ade fro Nylon 6/6. Moreover, Cedergren, deonstrated a ethod using a gear wheel to deterine the porosity distribution within a coplex powder copacted 3D structures with a dynaic 3D dilatant finite strain finite eleent progra [6]. The analysis showed that the porosity distribution in the gears is dependent on the nuber of the gear s teeth, thickness of the inner ring, the pressure angle, and is an excessive influence to the values of the porosity, which will induce sall changes in its geoetrical paraeters. They stated that the iniu porosity distribution in the etal atrix coposite gear is 3%, and this is achieved by axiu copaction during olding. However, this ratio is inadequate to prevent the gear s tooth fro the initiation and propagation of cracks. Later on Raesh and Ganesan used etal atrix coposites (MMC) in a railway wheel, and copared the with steel and fibre reinforceent plastic (FRP) wheels fro a static point of view [7]. They concluded that the deflection in MMC is uch lower than that of FRP. Junichi et al. studied the tribology of a etal gear *Corresponding author: Al-Qrili HF, Departent of Mechanical Engineering, Curtin University, CDT , Miri, Sarawak, Malaysia, Tel: ; Fax: ; E-ail: haidar.fa@curtin.edu.y, halqrili@yahoo.co Received Noveber 26, 2014; Accepted January 23, 2015; Published January 31, 2015 Citation: Al-Qrili HF, Alurib HA, Kuar N, Mahdi FA (2015) Dynaic Analysis of a Straight Bevel Gear Coposite Structure. 4: 152. doi: / Copyright: 2015 Al-Qrili HF, et al. This is an open-access article distributed under the ters of the Creative Coons Attribution License, which perits unrestricted use, distribution, and reproduction in any ediu, provided the original author and source are credited.

4 Citation: Al-Qrili HF, Alurib HA, Kuar N, Mahdi FA (2015) Dynaic Analysis of a Straight Bevel Gear Coposite Structure. 4: Page 2 of 8 and a hybrid gear in order to reduce noise with greaseless etal gear and plastic gear, with saller rates of tooth failure [8]. They discovered that the noise is suddenly aplified when a single polyer sheet was spontaneously reoved fro the gear s surface, probably due to its low adhesive strength against shear. Likewise Masaya et al. iproved the perforance of a plastic gear by using five types of carbon fibres blended with poly-ether-ether-ketone (PEEK) [9-11]. They evaluated the load capabilities and the wear properties of the reinforceent aterial used, and the results showed that the carbon fibre reinforced coposite gear have superb affinity with PEEK. Hoskins and his group tested five types of aterials; Polyoxyethylene, Unreinforced polyetheretherketone, fiber reinforced, Polyaide, and Glass fibre reinforced in order to provide the opportunity to iniize transission errors of design developent in gears [12]. Senthilvelan and Gnanaoorthy experientally studied the effect of various rotational speeds and stress on the perforance of unreinforced Nylon 6 spur gears and glass fibre reinforced Nylon 6 spur gears [13]. The result showed that speed has no influence on the gear s life on both under low stress levels. Sion presents an optial tooth odification for a spiral bevel gear that iproves load distribution and decreases the axiu tooth contact pressure, while Yilaz and Cenk investigated the fatigue behaviour at the roots of gear teeth and hardness distribution along the radial direction of the tooth [14,15]. They copared the results with a nuber of experients for odel validation purposes. Mendi et al. anufacture a gear ade fro polypropylene, reinforced with three different etallic springs, and they concluded that the increase in the diaeter of the reinforceent spring will increase the service life of the gear 30 ties ore than gears without etallic springs [16]. Aslantas and Tas carried out a series of experiental and nuerical analysis on a spur gear ade fro austepered ductile iron to predict the pitting occur of the gear teeth [17]. They conclude that the pitting failure tie can be predicted without testing gear. Meanwhile, Hayrettin increased the width of the gear s teeth and studied the theral daage on a single gear tooth surface [18]. He anaged to experientally delay the theral daage of the tooth s surface on axiu Hertzian surface stress. Letzlter et al. anufactured a gear ade fro Polyaide 6.6 aterial, and deonstrated an efficient ethod to predict the echanical behaviour of the gear, while calculating the load sharing with local eshing stiffness over the entire surface of the gear tooth [19]. Toshiki and others looked on the cotton fibre reinforced plastics to be used as an industrial gear aterial. They estiate the gear root stresses under running condition caused by bending consequences [20]. They confired that a plastic gear ade fro cotton fibre is batter in ters of noise quality. We used the coplex proportional assessent (COPRAS) ethod to deterine the optiu aterial to be used for the gear. This ethod is one of the ost coon ethods in deterining the best designs. It was created by to solve the selection probles of engineering using the stepwise ranking and alternative procedure in ters of their significance [21-23]. Straight bevel gears ade of coposite aterials have been investigated, and the aterials selected are woven fibreglass, carbon-fibres, and natural-fibres (Jute). The reinforceent ixture of the coposite will be epoxy/resin, while the selection of the constituents of the coposite is based on extensive literature review on the subject. In this paper we started with the ethodology, results and discussion and finally the conclusion. The first step of the ethodology is the nuerical procedure by using finite eleent ethod. After that we used COPRASS ethod to select which aterial is the best to be used as a straight bevel gear. The procedure and the equations of this ethod will be discussed. After finding the best aterial we ake an attept to anufacture the straight bevel gear experientally to ensure that the product is successfully working as expected. The anufacturing process and the results will be discussed also. Not to ention, the authors trace scarce literatures on a straight bevel gear. Most of the papers found are on spur gear and using one type of aterial while this study will discuss different type of aterials for a straight bevel gear. Specific Energy Absorption (SEA) The iperative factor in parts design is the specific energy absorption (SEA). This allows deterining the requireents for the weight reduction of ultiple structures such as gears, robotic ars and other echanical coponents. SEA is defined as the total energy absorbed (stiffness) per unit ass of the specien, with an SI unit of kj/ kg. It is represented by equation 1. SEA = S M (1) where S is the total energy absorption and M is the ass of the gear. The total energy absorption (S) is the area under the load strain curve, and it can be nuerically calculated by integrating the load displaceent curve. In this study the post-stage of the aterial developent have been considered due to its iportance copared to the pre-stage. s f S = P ds (2) si where P is the load, S i is the initial displaceent and S f is the final displaceent. Methodology and Procedures There are three ain stages in this investigation. The first stage is dubbed the nuerical stage; the second stage involves the choosing of the optiu aterial, and the final stage involves actual experientation. Figure 1 suarizes the whole procedure that was used in this work to realize the orthotropic straight bevel gear. Nuerical procedure Gear siulation presents itself as one of the ost strenuous proble in echanical design due to the fact that it includes all sources of nonlinearity that has to be incorporated and taken into account during ultiple stages of its developent. A gear s structural is ade up of a coplex geoetrical configuration and different aterials, and experiences high ipact load during operation, which results in high stresses. These high stresses, if they exceed the critical liit of aterial s Idea PRODUCT Design CAD Model Validate Testing Analysis FEA Optiization COPRASS Manufacture Figure 1: Concept and reality flowchart for straight bevel gear design.

5 Citation: Al-Qrili HF, Alurib HA, Kuar N, Mahdi FA (2015) Dynaic Analysis of a Straight Bevel Gear Coposite Structure. 4: Page 3 of 8 yield, will force the structural coponents to undergo large progressive elastic-plastic deforation. This whole process occurs within a very short tie span. As a result in this stage a standard eleent is used with 3D stress for dynaic and explicit test, with triangular eleent types. The global size of the esh is 1.5 in a three connected teeth on the gear and pinion, but on the other surfaces of the gear, a value of 15 is used for the esh of the global size instead, while in the two shafts, a global size of 20 is considered due to the fact that it is assued to be a rigid body and therefore, uniportant. The axiu deviation factor is 0.1, which is a default value for the entire straight bevel gear doain and all the defined parts. The boundary conditions of any finite eleent proble need to be deterined, and in this work, the boundary conditions that are used are siilar to the experiental phase. A torque is applied on one side of the gear, while all the points along the second gear are fixed in every direction, with zero degrees of freedo. For siplicity, the boundaries are shown in Figure 2. The pinion is fixed in all six directions (DoF=0), while the load condition looks to be an external torque, applied on the gear. The agnitude of the applied torque used in the present work is (17640 N.), which results in the tangential force of the gear s tooth surface of (245N). All the standard paraeter used to construct the straight bevel gear is shown in Table 1. The apparent absence of the gear s paraeter effect allows us to focus on the study of the behaviour of aterial. In the odel and within the scope of our work, both the teeth s surface interacts with single surfaceto surface (ASTS) contact between the gear s aterials. A tie constraint was used to bond the rigid shafts to the gears using nodes, as shown in Figure 2. Coplex Proportional Assessent Method Steps (COPRAS) The preliinary developent of anufactured goods depends on the theoretical design of the odel, derived fro the custoer s requireents. To optiize the product s cost, the engineering calculations ust be as precise as possible, with little to no argin of error(s). Material selection and design are iportant factors that Surface to Surface Connection Fixed Shaft Section 2 (Pinion) Fixed Tooth Surface Contact Section 1 (Gear) Rotating Figure 2: Boundary conditions of the straight bevel gear. Applied Torque NO. Design Paraeter Value Options 1. Pressure angle 20 o 2. Module 6 Material odel 3. Face width 28.5 Glasses/Epoxy 4. Addendu 1 /Epoxy 5. Dedendu 1.25 Jute/Epoxy 6. Shaft angle 90 o Chopped/Epoxy 7. Root fillet radius 0.3 Steel 8. Nuber of teeth 24 Table 1: Standard gear paraeters. ust also be taken into account. The coplex proportional assessent ethod (COPRAS) is a suitable ethod that solves the probles of aterial selection for a straight bevel gear. Figure 3 explains the ain steps of this ethod. Step 1: Develop the Initial Matrix (X) and Find the Relative Coefficient (RC) This step contains a atrix with values fro 1 to 3; the decision is in accordance with the significance of the factors; its criteria shown in Table 2. The atrix obtains the positive decision. X = x (3) ij Step-1 Step-2 Step-3 Step-4 Step-5 n where x ij is the perforance value of the i-th alternative on j-th criterion, is the nuber of alternatives copared and n is the nuber of criteria. x ij represents the positives for each criterion. The sybol of the relative coefficient is RC, and it is forulated as RC = r = ij n Copare different profile Find relative coefficients (RC) x ij x i= 1 ij where i = x 1 ij is the suation for a nuber of positives decisions. The iportance of the relative coefficient is that it reduces the values of the criteria to siplify coparisons. Step 2: Deterine the Weighted Noralized Decision Matrix DM DM = y = r w (5) ij n ij j Deterine the noralize decision atrix (DM) Deterine the beneficial and non-beneficial attributes Deterine relative significance or priority (RS) Deterine the quantitative utility (QU) Figure 3: Steps of Coplex Proportional Assessent Method (COPRAS). Material/Criteria Steel Glass/Epoxy /Epoxy Jute/Epoxy S SEA SE FE C EM Table 2: Criteria with profiles used for selecting the best design. (4)

6 Citation: Al-Qrili HF, Alurib HA, Kuar N, Mahdi FA (2015) Dynaic Analysis of a Straight Bevel Gear Coposite Structure. 4: Page 4 of 8 w j is the weight for each criteria; with the suation of the noralized weight for each criteria always equal to the weight of the sae entioned criteria. Step 3: Beneficial and non-beneficial Attributes The values of the noralized decision atrix contain beneficial and non-beneficial attributes. The next step involves division according to their iportance. The cost and anufacturing toughness with lower values are considered non-beneficial attributes, whereas the rest of the criteria are considered beneficial attributes. These two factors are forulated into two equations: S n + 1 y j= 1 + ij = (6) n S 1 = y (7) j= 1 ij where y + ij and y ij are the beneficial and non-beneficial attributes respectively, with the best alternative depending on the greater value that is considered beneficial, and the lower value with non-beneficial attribute. The suation of the inuses also represents the attributes to help find the priorities. = S i = i + = = S i 1 + i S 1 (8) S (9) The su of S and S + are always equal to one, and the separate suation is equal to the sus of the weight of the beneficial and nonbeneficial attributes and this to ensure that the forals used is exact. Step 4: Relative Significance or Priority (RS) The priorities of the alternative have been calculated, and it is surised that the higher the value of RS i, the greater the priority of an alternative will be. The alternative with the axiu relative significance RS ax is considered the best selection for the application design. The relative significance has been forulated below: S in S i= 1 i RSi = S+ i + (10) S S S ( in i) i i= 1 Step 5: Deterine the Quantitative Utility (QU) The value of the quantitative utility is directly related to relative significance; with the values of the quantitative utility copleting the ranking of the alternatives, denoted by the equation below: QU RS i i = (11) RS ax The axiu value of relative significance is denoted as RS ax. The quantitative utility is directly proportional to the relative significance, and the utility value with a 100 is considered as the best design in this ethod. Experiental gear process As entioned previously, the coposite aterial that will be used is woven fibre and epoxy. The ratio of the ixture of this coposite is 4:1. The first stage of anufacturing involves the preparation of the aterials, along with the equipent, in order to fabricate a circular tube. The fibre is cut into the desired diaeter in order to allow it to cofortably fit into the andrel. After that, a tube was used to arrange the fibre layers until it reaches the desired thickness. While arranging the fibre layers, each layer are carefully brushed. Brushing should be done in equal distribution in order to produce balanced tubes and syetrical diensions for all parts of the tubes. Then, weights are added to the top of the tube to ensure strong adhesion between the layers, and also to ensure that no bubbles are fored in the structure. Upon copletion, the speciens should be left for at least eight hours to ake sure that the epoxy resin is truly dried. In this research, the tubes are exposed to air for ten hours to ensure the copletion of epoxy curing. Moreover, the tubes should be able to vertically stand in order to prevent any of tubes faces fro touching any surfaces. Figure 4 shows the gear anufacturing stages. At this point of the process, the tubes are ready for cutting, and at this stage, the tubes will be turning first, which turns it to a gear blank. The next stage will be the teeth generation by using a gear-cutting achine shown in the Figure 4. In the experient strain gauge test, a steel base was developed to attach the two coposite bevel gears and allow a sall aount of backlash to attach the strain gauge on the gear tooth. The base is ade fro steel, with a square cross-section of 20 thickening, with the two shafts and ball bearing allowing the gears to rotate soothly. The base has a stopper to fix one of the gears in order to perfor the test. Figure 5 shows all the details of the CAD drawing, and the actual prototype. Results and Discussion Force tie history The crash duration is paraount to the gear s tooth surface capacity to withstand loading, as it characterizes the gear s tooth daage. The force-tie curve can deterined the total loading tie of the tooth. Figure 6 shows a copression of the force and the tie curves in the odels of steel, glass, carbon and jute fibre, showing a linear behaviour in the elastic zone, until it reaches the peak force to fall down due to the reaction of the gear tooth surface. This occurs in all the odels. Fro the Figure, it is obvious that the axiu force (peak) is equal to the initial failure force in the four odels. After that, the curves observed a sharp drop, and start fluctuating until it reaches sec, and the curve Coposite Tube Blank Straight Bevel Gear Figure 4: Gear speciens anufacturing process. Figure 5: Straight bevel gear base.

7 Citation: Al-Qrili HF, Alurib HA, Kuar N, Mahdi FA (2015) Dynaic Analysis of a Straight Bevel Gear Coposite Structure. 4: Page 5 of 8 Force (N) Tie (sec) Steel Glass Jute Figure 6: Total contact forces of straight bevel gear ade fro steel Steel Glass Figure 7: Force efficiency of gear tooth with diffrint type of aterail (steel, glass, carbon, jute). Material Paraeter Steel Glass Fibre/ Epoxy Jute Fibre/Epoxy FE Jute Fibre/ Epoxy Stiffness (kj) Max. Force (P ax ) (N) Specific Energy Absorption (SEA) (kj/kg) Force Efficiency (FE) Average Force (P av ) (N) Table 3: Straight bevel gear paraeters for different type of aterials. used in the straight bevel gear, with the perforance of glass fibre gear being ore efficient than the other odels, which proves that it is the best for an energy absorbing syste design that deals with coplex structures and is applicable anywhere. But, as shown in Figure 7, the steel gear shows the lowest value of the force efficiency and all the orthotropic aterials absorb higher values, which ean that using orthotropic aterials iproves the perforance of the gear. In the energy absorbing syste design, it is better to use the glass fibre, as it is ore efficient than other orthotropic aterials as it can be seen in Figure 7. Stiffness tie history By using the finite eleent ethod we applied the explicit dynaic analysis (Structural dynaic analysis) to take into account how the gear s tooth surface responds to the applied toque. This enables us to deterine the odel s analysis in the pre-processing stage. A stress (es) that is observed on the gear s odel is shown in Figure 8. In the Figure, before the aster surface (gear) touches the slave s surface (pinion), the tooth is blue in colour, signifying a state of zero stress. After that, it s shown that the axiu stress during the entire test occurs in the iddle of the tooth surface. The green colour is to signify the axiu stress. Basically, the weak areas in the odels are in the iddle of the gear tooth surface, as shown in the Figure 8. It can be noticed that the jute fibre/epoxy have higher stress coparing to the other aterials, while the steel shows low effect. The areas under the curves in Figure 9 are divided into two regions; the first region is classified as the pre-crashing region. The value is deterined by calculating the area under the triangle; which is ½, ultiplied by the initial load and the initial displaceent, with an SI unit of kn. (kj). The stiffness can therefore be deterined by suing up two region s absorbed energy (pre and post stages). Fro Table 3, and as shown in the Figure 9, the highest stiffness is produced by steel, followed by carbon fibre, glass fibre and finally, jute fibre. Fro the results, it is clear that the type of aterial affects the stiffness of the tooth gear, the ost effective being steel. However, Table 3 shows a very sall difference. It is surised fro Table 3 that gears ade fro carbon fibres has the highest specific energy absorption, even though the energy absorbed (S) by the steel gear is higher than that of the carbon gear, stops, because it is at the end of the tie step. The fluctuation behaviour in the three coposite odels shows a siilar trend, but in steel the fluctuation is different due to its dissiilar echanical properties. This fluctuation of the curves is due to the atrix deforation and the structure recovery of the aterials. The peak force values occurring by the straight bevel gear ade fro steel shows the highest value, which is N at tie step of sec, while the carbon fibre coes next at N in sec. The glass fibre straight bevel gear shows an interediate result in total, and the value of the force is close to the carbon gear, at N in the sae tie step sec. The jute fibre shows the lowest values, as expected ( N at tie of sec). Force Efficiency (FE) Steel Glass FE serves to evaluate the process s structural perforance, and is defined by average load divided by the produced axiu load. Figure 7 and Table 3 shows all the FE for the different type of aterials Jute Figure 8: Stress distribution of straight bevel gear at tie (t=0.001).

8 Citation: Al-Qrili HF, Alurib HA, Kuar N, Mahdi FA (2015) Dynaic Analysis of a Straight Bevel Gear Coposite Structure. 4: Page 6 of 8 Stiffness (kj) Steel Tie (sec) Figure 9: Tie history of gear tooth stiffniss. Glass Jute Steel Glass Figure 10: Specific energy absorption of steel, glass, carbon, jute straight bevel gear. which incidentally, weighs less than steel. By applying the specific energy equation (equation 1) to deterine SEA, the result of the carbon gear will be highest, followed by the glass fibre, with jute fibre falling behind fibreglass. Steel had the lowest values of SEA, suggesting that weight affects SEA, as the reduction of the gear s weight will increase its reliability. Figure 10 shows the specific energy absorption of all the straight bevel gears. fibres/epoxy sees to have the strongest specific energy absorption, with steel gears having the lowest. Design paraeter selection The SEA is to be the first and ost iportant criteria for design selection. Force Efficiency (FE) is obtained by dividing the average force gathered fro the finite eleent ethod with the axiu force; a value closest to 1 considered the best FE. This paraeter is very iportant due to the fact that it shows the behaviour and the state the aterials are in, and this paraeter is considered beneficial in the design selection criteria. The cost of the raw aterials and the process of the anufacturing of the gear depend ostly on the suppliers of the gear s design. The anufacturing and the achining of the steel straight bevel gear (isotropic) are sipler, and consist of any ethods copared to the coposite aterial. For coposite aterials, it is ore expensive and difficult to achine, and between the coposite constituents, carbon fibre is very expensive, while glass and jute is very cheap. The exact values for the selected aterials and the different criteria that have been chosen for the optiu design are shown in Table 2. Based Jute SEA on Equation 3, the positive decision (x) was calculated, and Equation 4 was used to find the relative coefficient. To find the values of beneficial and non-beneficial paraeters, Equation 6 and 7 are utilised. Then, the results of the suation were deterined by applying Equation 8 and 9. The six entioned criteria include both beneficial and non-beneficial attributes, according to the noralized decision atrix values. These beneficial and non-beneficial attributes should be separated according to the iportance of the affected criteria, as shown in Table 4. The best profile depends on the greater value of the beneficial attribute, and the lower value of the non-beneficial attribute. The relative significance (RS) values depend on Equation 10, as entioned previously. The best choice for the profile is the one with the greater nuber of relative significance, which is ranked accordingly in Table 5. The final step in the process of the COPRAS ethod is to calculate the quantitative utility values by applying Equation 11, with the values shown in Table 5. The values of the quantitative utility are directly related to the relative significance (RS). Both the relative significance and the quantitative utility are responsible for the choice of the optiu straight bevel gear aterial. The Coplex proportional assessent ethod (COPRAS) has been perfored, and the ranking values for six alternatives have been denoted. The RS and QU proved that the carbon/epoxy and glass/epoxy is the optiu aterial for straight bevel gear applications. Based on these results, we decided to anufacture a straight bevel gear ade fro glass-fibres. Coposite straight bevel gear The coposite structure of these gears will contain two distinct aterials, naely the fibre reinforceent aterial and its atrix, in Material Beneficial Non-Beneficial S + i S i S i in S i Steel Glass/Epoxy /Epoxy Jute/Epoxy Attributes S = 0. 8 S = 0. 2 = i i Table 4: Beneficial and non-beneficial values. Gear Material RS QU Ranking Steel Glass/Epoxy /Epoxy Jute/Epoxy Table 5: Relative Significance (RS) and Quantitative Utility (QU) values with ranking. Properties Strain Gear Material Steel Glass Fiber E-200 Gear Weight (Kg) Applied Force (N) Isentropic Table 6: Strain gauge readings.

9 Citation: Al-Qrili HF, Alurib HA, Kuar N, Mahdi FA (2015) Dynaic Analysis of a Straight Bevel Gear Coposite Structure. 4: Page 7 of 8 nuerical results. It is concluded that carbon/epoxy and glass-epoxy perfors better copared to jute/epoxy, and is a viable alternative to steel gears. The reduced weight percentage for the straight bevel gear with glass-epoxy is 80% copared to the steel gear. We applied the COPRASS ethod to deterine the optiu aterial gear, and it turned out to be glass/epoxy. The behaviour of orthotropic aterial gears and isentropic steel gears in ters of stiffness is siilar. The stiffness of the carbon/epoxy gear is very close to the steel gear, in contrast, the jute/epoxy shows very low stiffness, leading us to conclude that natural fibres (jute) are unsuitable to be used as straight bevel gear aterial. In this study we used epoxy-hardener as the atrix while there are other types of atrix that can be used for future work depending on the application needed. Acknowledgeent Mid Point Tooth Surface accordance with the required perforance. Based on the nuerical results fro the previous section, we found that the glass fibre has an interediate level of stress copared to the steel bevel gear, while jute fibres showed high values of stress. The carbon fibre odel showed very good results copared to the other coposite aterials, but if cost is taken into consideration, it will be too expensive. As a result of this, we opted to use the woven roving glass fibre in the fabrication of the straight bevel gear, due its reasonably good results, excellent echanical properties and low costs. In the fabrication process, we used the hand-layup technique, as previously entioned and explained. Figure 11 shows the frontal view and the back view of the fabricated odel, and how we arranged the fibre lainate in the gear s odel. Fro the experiental phase, we cae up with the strain reading on the idpoint section of the tooth surface, as shown in Table 6. In fact, only a few strain gauge readings were used, but it turned out to be very useful for FEA verification, and proved that coposites can be used as a aterial for a straight bevel gear. The percentage of error between the nuerical and experiental values is acceptable, and shown in Table 7. Conclusion Figure 11: Glass fibre straight bevel gear odel. FEA Results of Glass/Epoxy Experiental Results of Glass/ Epoxy Percentage Error EXP to FEA (Glass/ Epoxy) σ 1 (Mpa) σ 2 (Mpa) σ 3 (Mpa) The average of percentage error Table 7: Nuerical and experiental results coparison. The focus in this work is on how uch the divergence in behaviour between orthotropic aterial and isotropic aterial such as steel can be reduced. Three types of orthotropic aterials have been used as a straight bevel gear. Finite eleent ethod has been used in the nuerical stage. After that we used a scientific ethod to select the best aterial to be used as a straight bevel gear. 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