Design and Manufacturing of Spur gear tooth: A New Approach Towards Composites

Abstract -Gear is one of the most reliable power transmission systems in modern industry, operates at various speeds and loads. Breakage of gear tooth is a serious issue.Gear manufactured with alternate material can compensate this problem. With the advent of composite materials, it has been possible to reduce the weight of the spur gear without any reduction in the load carrying capacity. Composites are well suited for spur gear applications due to its high strength to weight ratio, fatigue resistance and hence, less chances of failure. All thesehave made composites an excellent replacement for the currently used metallic steel as a gear material. The present work is an attempt to provide an exclusive design technique regardingcomposite spur gear tooth based on an analysis of software affirmation. However, an effort has been taken towards the evaluation of bending stress at the root of the tooth and the total deflection of tooth tip associated with the new construction methodology. The gear tooth ismodelledin CATIA V5R18 and the same areanalysed under similar conditions using ANSYS (Workbench 16.2) software considering composite and structural-steel as the tooth material. Software based results are presented and compared for the two distinct cases mentioned above.

been found for the composite gear.Utkarsh. M. Desai et al., [9] have presented composite spur gear with 70% weight reduction without compromising the strength of the tooth. An overall comparison has been drawn between the existing alloy element (Nickel Chrome Steel) and composite material (GF 30 PEEK) gear. V. Siva Prasad et al. In their paper describes design and analysis of spur gear and it is proposed to substitute the metallic gears of sugarcane juice machine with polymer gears to reduce the weight and noise [10].P.B.Pawara et al., [11] have given a detail comparison of metallic spur gear with the stir casted Al-SiC composite spur gear and an improved hardness, tensile strength has been found with almost 60% weight reduction.Dueto the unique advantages, such as light weight, high strength, higher dimensionalstability and corrosion resistance the metal matrix composite (MMC) is preferred to manufacture different machines components. However, there is a cost problem when this MMC is compared with the polymer based composite [12,13]. Dynamic analysis has been presented using MATLAB and FEA software on composite gear and a study has been carried out for natural frequency with the fibre orientation of the composite gear [14]. In some modern machinery such as textile industries involve oil less transmission in those cases composite gear has no alternative because of its oil less lubrication. From the above course of study one can come in a conclusion that surely composite materials are able to provide a better performance and efficiency in the practical applications but, from manufacturing point of view it leads to expensive cost than that of steel. That's why extending the research work performed by SushovanGhosh et al., [15] the present exertion completely dismisses the proposition associated with manufacturing the complete spur gear by composites; but maintains its intense focus to manufacture those parts which are relatively more critical as well as to maintain conventional materials for the other part to achieve an optimum extent towards the manufacturing costs. In the present work, the tip of the gear toothis modelled separately with composites whereas the root of the same tooth is with conventional steel. Then after the entire system is combined with the proper contact constraints andanalysed under similar conditions in ANSYS software.

II. MATHEMATICAL FORMULATIONS A. Assumption of Lewis equation
The analysis of bending stress in gear tooth was done by Mr. Wilfred Lewis. Gear tooth is considered as a cantilever beam with static normal force F applied at the tip. Assumptions made in the derivation are [16]: 1. The full load is applied to the tip of a single tooth in static condition. 2. The radial component is negligible.
3. The load is distributed uniformly across the full face width. 4. Forces due to tooth sliding friction are negligible. 5. Stress concentration in the tooth fillet is negligible. The Fig.1 shows clearly that the gear tooth is stronger throughout than the inscribed constant strength parabola, except for the section at 'a' where parabola and tooth profile are tangential to each other [16].In the above Fig. 2 the following notations are used: F is the Full load, F r and F t are the Radial and Tangential component of the full load. h, b and t are the height, face-width and thickness of the tooth at critical section respectively.

III. DESIGN SPECIFICATIONS
For calculating bending stress and total deformation we have taken a standard model for designing the spur gear tooth [17] and different torque specification from the existing vehicle-models of Maruti Suzuki [18,19,20]. The following data is given for the design of 20° full depth spur gear made of structural steel transmitting torque at different rpm:  [1] In the current analysis of bending stress of tooth we consider the Lewis assumption as discussed above in 2.2. (4) Can be rewritten as m * b * σ * Y ( 5 ) When the tangential force increased the stress also increases. When the stress reaches the permissible magnitude of bending stress the corresponding force F t is known as Beam strength and denoted by S b. So replacing F t in the Eq. (5) we have Formulations of total deformation [17] It is observed that the cross section of the gear tooth varies from free end to the fixed end. Lewis has assumed it as a constant strength parabola. Using Castigliano's Theorem total deformation of the tooth can be found with minor error. For linearly elastic structure, where external forces only cause deformations, the complementary energy is equal to the strain energy. For such structures, the Castigliano's first theorem may be stated as the first partial derivative of the strain energy of the structure with respect to any particular force gives the displacement of the point of application of that force in the direction of its line of action [21]. The theory applies to both linear and rotational deflection, . It should be clear that Castigliano's theorem finds the deflection at the point of application of the load in the direction of the load. Here U is the strain energy given by * * , where M is the moment due to the load. Consider the parabolic tooth of height h and tooth thickness t. The equation of parabola y 4 * a * x. Consider the Fig 2. We have the following boundary condition at x = h, y = t/2. After substituting the equation of the parabolic tooth is * * and * . .Putting the value of F * x, * * , the strain energy * * will be * * * * * from this we have * * * * Again we know deflection is given by . From Eq. (7) we have the * * * * This Eq. (8) is the equation of tooth deflection of spur gear when tangential load F t is applied at the tip of the tooth.

III. SAMPLE CALCULATIONS
From the relation of maximum bending stress (σ b ) and deflection(δ) based on the above design specifications from the Table 1, and considering steel as a tooth material the analytical calculation is carried out for the torque of 132 N-m at 3000 rpm is carried out. = 0.0013 mm (approx.) Subsequently, the root bending stresses and total deflection of the tooth tip are evaluated for the other torque sections and presented in Table II. During composite analysis when a unidirectional continuous-fiber lamina or laminate is loaded in a direction parallel to its fibers (0° or 11-direction), the longitudinal modulus E 11 can be estimated from its constituent properties by using what is known as the rule of mixtures [21]: ; Where,E f is the fiber modulus, V f is the fiber volume percentage, E m is the matrix modulus, and V m is the matrix volume percentage.

IV. MODELLING and SIMULATION
The aim of this analysis is to investigate the stresses in the spur gear tooth within the desirablelimits to obtain a practical understanding for the theoretical ideas associated with composite materials. After geometric modelling in CATIAV5R18 software the gear tooth is subjected to static analysis, performed in ANSYS (Workbench 16.2)software.

A. Modelling
The computer compatible mathematical description of the geometry of the object is calledgeometric modelling. CATIA is basically CAD (computer-aided design) software that allows themathematical description of the object to be displayed and manipulated as the image on the monitor of thecomputer [24,25]. While modelling the spur gear tooth, the root of the tooth and the rest portion are designed separately as two different part bodies shown in Fig. 3 and 4, which are again combined to make a single system in ANSYS software through proper contact constraints (shown in Fig. 5 and 6    with torque t decrease percentage The mass reduction and reduction in total deformation per tooth are depicted in the following Table IV

VI. CONCLUSION
In this work, the spur gear tooth is modelled inCATIA V5R18 and is analysed in theStatic structural domain of ANSYS software. A conclusion can be drawn on the basis of result discussed on the previous sections is that for the standard design specifications the values of maximum stresses at different torque conditions are well within the safe limit. Apart from that, most importantly the new design method has proposed to manufacture the tip of the gear tooth separately with composites in contrast to use of composites for the entire tooth.It has been observed that asubstantial decreasing trend toward the deformation values for composite applications with a negligible increase in maximum stress. This agrees well with the previous works so far done in this context. A reduction in mass of more than 18 % is the one of theprominent benefits with the new method; along with optimum extent towards the manufacturing costs can be achieved as composites being highly expensive [26][27] than that of steels (almost 2-3 times costlier). Therefore, the new method seems to be beneficial exclusively for modern auto industry as it provides an optimum solution towards weight reduction as well as manufacturing costs. The focus can be given to the joining of metal and composites with different fasteners or suitable adhesive [28].