Contact Stress Analysis on Composite Spur Gear using Finite Element Method

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ScienceDirect Materials Today: Proceedings 5 (2018) 13585–13592

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ICMMM - 2017

Contact Stress Analysis on Composite Spur Gear using Finite Element Method Gaurav Mehta1, Mayank Somani2, Narendiranath Babu T3* Tushit Watts4 1,2,3,4

School of Mechanical Engineering, VIT University, Vellore, India.

Abstract

The contact stress in the mating gears is the key parameter in gear design. Deformation of the gear is also another key parameter which is to be considered. Gears generally fail when the working stress exceeds the maximum stress. The study in this paper shows that the complex design problem of spur gear which requires fine software skill for modeling and also for analyzing. The project aims at the minimization of both contact stress as well as deformation to arrive at the best possible combination of driver and driven gear. In this process comparison of Von Mises Stress, Strain and Total Deformation was done of a ceramic (Silicon Nitride) with a conventional steel gear as a substitute in the gear manufacturing industry and the software programmed was performed in SOLIDWORKS and ANSYS Workbench to get the best result possible. © 2017 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of International Conference on Materials Manufacturing and Modeling (ICMMM - 2017).

Keywords:Spur Gear, Contact Stress Analysis, Von Mises Stress, Srain and Total Deformation, Silicon Nitride (Ceramic)

1. Introduction Gears are one of the oldest of humanity’s inventions. Nearly all the devices we think of as machines utilize gearing of one type or another. . Nevertheless, the design or specification of a gear is only part of the overall system design picture. From industry’s standpoint, gear transmission systems are considered one of the critical aspects of Contact Stress Analysis. Investigators analyzing the gear tooth for stresses have done several studies. Spur gears are extremely well known among every other sort of apparatus because of its effortlessness in plan, less support prerequisite and monetary assembling. The gears come up short when the connected load is expanded over specific cutoff points. There are two essential methods of gear tooth disappointment breakage of tooth because of static and

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E-mail address: [email protected] 2214-7853 © 2017 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of International Conference on Materials Manufacturing and Modelling (ICMMM - 2017).

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element loads and surface obliteration. The apparatus material ought to have adequate quality to oppose disappointment because of breakage of tooth [1].According to bar quality hypothesis given by Lewis, goad equip tooth is dealt with as a cantilever pillar to ascertain the twisting anxiety created at base of the tooth. There are many components which are considered while outlining an apparatus like power transmitted, speed proportion, material, adapt tooth geometry (symmetric or potentially awry) and its different parameters like module, addendum, dedendum, confront width ,filet profile and so forth. To outline a legitimate apparatus the accompanying necessities must be satisfied (i) The teeth must be sufficient solid to withstand the static as well as, (ii) Wear opposing properties guarantee the long existence of rigging, (iii) The teeth must have the capacity to oppose tooth avoidance, increasing velocities and stress concentration [2]. The above necessity demonstrates that the material properties assume the real part for adequate quality rigging configuration (bar quality and in addition wear quality). Many research works have been proficient utilizing diverse sorts of materials for gears to build its quality and different parameters. Likewise numerous specialists have proposed a few ideas for gears plan advancement to improve the parameters of apparatus framework. Ceramics provide much improved mechanical properties such as greater strength to weight ratio, increase in hardness, and hence less chances of failure. So this work is concerned with replacing metallic gear with gear of ceramic material of Silicon Nitride so as to improve performance of machine and to have longer working life. To this date, there have only been a few publications on silicon nitride (SixNy) and silicon carbon nitride (SixCyNz) coatings for joint implants (Olofsson et al., 2012; Shi et al., 2011, 2012). Olofsson et al. (2012) used reactive radio frequency (r.f.) sputtering to produce SixNy and SixCyNz coatings that showed a potential for high wear resistance, but issues with coating defects and poor adhesion leading to flaking off of the coatings were reported. Shi et al. (2011) also used different magnetron sputtering methods for fabricating SixNy and SixCyNz coatings; r.f., direct current and unbalanced magnetron sputtering. The transfer of power between gears takes place at the contact between the acting teeth. The stresses at the contact point are computed by means of the theory of Hertz. The theory provides mathematical expressions of stresses and deformations of curved bodies in contact. Fig. 1 shows a model applied to the gear-two parallel cylinders in contact.

Figure 1: SPUR Gear Representation

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The Hertz theory assumes an elliptic stress distribution and the maximum stress is given as below; ∑=[√E(1/T1+1/T2)]/G∏[(1-B12/R1)+(1-B22/R2)] (1) Σ = maximum value of contact stress (N/mm2) E= force pressing the two cylinders together (N) N = half width of deformation (mm) L= axial length of cylinders (mm) d1, d2 = diameters of two cylinders (mm) E1, E2 = modulus of elasticity of two cylinder materials (N/mm2) μ1, μ2= Poisson’s ratio of the two cylinder materials (Unit less) Where E is the load, G is the face width of pinion. Same equation can be apply for teeth, assuming for T1 and T2 the respective radii of the involute curve at the contact point, as shown in Figure. Let us assume that the contact takes place at point 1, and then the respective radii are equal to: T1= tp1sin φ; T2 = tp2sin φ ∑=[√E(1+T1/T2)]/tp1G∏[(1-B12/R1)+(1-B22/R2)sinφ] (2) 2. Methodology: PROCESS FLOW CHART: Table 1. Project development plan as followed while carrying our project

Step 1: Study of alternate materials like ceramics with greater strength to wear ratio, increased hardness and non-magnetic nature Step 2: Study of classifications of ceramics as they have been previously used in engines and cutting tools, with high fracture toughness and strength Step 3: Design of spur gear assembly in Solidworks using parameters like no. of teeth, gear module, pitch circle diameter and pressure angle. Step 4: Finite Element Analysis: Static Structural to evaluate contact stresses in gear assembly using ANSYS Workbench Step 5: Calculation and Verification using available Von-Mises Stress formulas Step 6: Comparative Study of stresses in conventional steel gear and ceramic spur gear Step 7: Results and discussions

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2.1 Design of Gear The material properties of steel and Silicon Nitride composite are given in the table. Table 2. Material Properties

Property

Silicon Nitride

Structural Steel

Density

3310 kg m-3

7850 kg m-3

Young’s Modulus

3.17e+011

2.0e+011

Poisson’s ratio

1.1. 0.23

0.3

The comparative study of steel gear and composite gear is done. So the basic design of spur gear is same for both the gears. 2.2 Proposed Work 2.2.1Design Objectives And Description For the designing of spur gear it was decided that the Silicon Nitride would prove to be a better substitute in industrial applications. The future of industrial usage of Silicon Nitride would result in cost cutting, better or atleast maintained industrial efficiency and dependency. The low density, low coefficient of thermal expansion, high resistance to wear and no response to magnetic field make the ceramic an ideal material for gear manufacture. 2.2.2 Design Specifications The gear assembly was designed on machine designing software SOLIDWORKS using the sketcher module and padding options. Similar gear profiles were used for gear and pinion to maximise the contact areas while performing part assembly. The gear specifications such as gear module, number of teeth, pitch circle diameter, addendum, dedendum and pressure angle were considered and the spur gear was designed. 2.2.3 Static Structural Analysis Finite Element Analysis: Finite Element Method is the easy technique as compared to the theoretical methods to calculate the stressdeveloped in teeth of gears. Therefore FEM is widely used for the stress analysis of mating gears. FE analysis is done to determine the maximum contact stresses for steel and composite material. Also the deformation is found out for both the gears. CAD model of gear is show below. The static structural analysis is one of the most basic types of analysis. It is available as Static Structural analysis system under the Analysis toolbox window. This system analysis the structural components for displacements (deformations), stresses, strains and forces under different loading conditions. The loads under this analysis are assumed to have damping characteristics (time dependent).

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Figure 2: Spur Gear modeling (as rendered in Solidworks 2013)

3. Results and Discussions Contact stress for steel and silicon nitride is calculated in proposed work. Figure 3 shows the contact stress for steel and figure 4 shows the contact stress for ceramic steel. Evaluation of proposed work is being done using following metrics; a. Von Mises Stress Von Mises stress is considered to be a safe haven for design engineers. Using this information an engineer can say his design will fail, if the maximum value of Von Mises stress induced in the material is more than strength of the material. It is written as below; Σ = (σ1-σ2)2- (σ2-σ3)2-(σ3-σ1)2/2

(3)

b. Von Mises Strain It can be calculated as below;  =2/3 3(rxx2+ryy2+rzz2)/2 + 3(rxx2+ryy2+rzz2)/24 c. Strain The strain energy formula is given as, U =Fd/2 Where, δ = compression,F = force applied.When stress σ is proportional to strain ϵ. d. Total Deformation Strain is defined as "deformation of a solid due to stress" and can be expressed as ε = dl/lo σ/E Where dl = change of length (m, in) lo = initial length (m, in) ε = strain – (unitless) E = Young's modulus (Modulus of Elasticity) (N/m2 (Pa), lb/in2 (psi))

(4)

(5)

(6) (7)

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Fig 3: Von-Mises Stress Distribution for Structural Steel

Fig 4: Von- Mises Strain Distribution for Structural Steel

Fig 5: Strain Energy Distribution for Structural Steel

Fig 6: Total Deformation for Structural Steel

Fig 7: Von- Mises Stress Distribution for Silicon Nitride

Fig 8: Von- Mises Strain Distribution for Silicon Nitride

Fig 9: Strain Energy Distribution for Silicon Nitride

Fig 10: Total Deformation for Silicon Nitride

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Table 3. Comparison table between structural steel and ceramic silicon nitride

FAILURE THEORIES

STRUCTURAL STEEL

SILICON NITRIDE

% DIFFERENCE

100 Nm

150Nm

200Nm

100Nm

150Nm

200Nm

Von-Mises Stress

1.4225e+008 Pa

2.1338e+008 Pa

2.8451e+008 Pa

1.4228e+008 Pa

2.1342e+008 Pa

2.8456e+008 Pa

0.01874

Von-Mises Strain

7.1239e-004 m/m

1.0686e-003 m/m

1.4248e-003 m/m

4.4971e-004 m/m

6.7457e-004 m/m

8.9943e-004 m/m

-36.8728

Strain Energy

7.5329e-004 J

1.6949e-003 J

3.0132e-003 J

4.512e-004 J

1.0152e-003 J

1.8048e-003 J

-40.10

Total Deformation

1.2819e005m

1.9229e-005 m

2.5639e005m

7.9102e006m

1.1865e-005 m

1.582e005m

-36.950

Frictional Stress

3.8285e+007 Pa

5.7426e+007 Pa

7.6566e+007 Pa

3.6048e+007 Pa

5.4071e+007 Pa

7.2093e+007 Pa

-5.843

0.68562

0.68562

0.28909

0.28909

0.28909

-57.835

0.68562

Comparison Analysis

Accuracy

Mass (kg)

Metrics Figure 11: Comparison Graph between Metrics

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4. Conclusion The use of different materials in gear manufacturing provides a range of contact stresses. This range of contact stresses and deformation is useful in the selection of material in different applications. The use of different materials in gear manufacturing provides a range of contact stresses as in Figure 11. This range of contact stresses and deformation is useful in the selection of material in different applications. From result simulations it has been seen that Silicon nitride yields better results i.e comparative stress and reduced strain and strain energy with respect to conventional steel. Silicon Nitride Manufactured gears also experience less deformations, contributing to greater work life. 5. References [1] Riley, F.L., 2000. Silicon Nitride and Related Materials. Journal of the American Ceramic Society 83(2), 245-265. [2] Mazzocchi, M., Gardini, D., Traverso, P., Faga, M., Bellosi, A., 2008. On the possibility of silicon nitride as a ceramic for structural orthopaedic implants. Part II: chemical stability and wear resistance in body environment. Journal of Materials Science: Materials in Medicine 19(8), 2889-2901. [3] Laarz, E., Zhmud, B.V., Bergström, L., 2000. Dissolution and Deagglomeration of Silicon Nitride in Aqueous Medium. Journal of the American Ceramic Society 83(10), 2394-2400. [4] Olofsson, J., Pettersson, M., Teuscher, N., Heilmann, A., Larsson, K., Grandfield, K., Persson, C., Jacobson, S., Engqvist, H., 2012. Fabrication and evaluation of SixNy coatings for total joint replacements. Journal of Materials Science: Materials in Medicine 23(8), 18791889. [5] Shi, Z., Wang, Y., Du, C., Huang, N., Wang, L., Ning, C., 2011. The structure, surface topography and mechanical properties of Si–C–N films fabricated by RF and DC magnetron sputtering. Applied Surface Science 258(4), 1328-1336. [6] Shi, Z., Wang, Y., Du, C., Huang, N., Wang, L., Ning, C., 2012. Silicon nitride films for the protective functional coating: Blood compatibility and biomechanical property study. Journal of the Mechanical Behavior of Biomedical Materials 16, 9-20. [7] Sonny Bal, B., Khandkar, A., Lakshminarayanan, R., Clarke, I., Hoffman, A.A., Rahaman, M.N., 2008. Testing of silicon nitride ceramic bearings for total hip arthroplasty. Journal of Biomedical Materials Research Part B: Applied Biomaterials 87B(2), 447-454. [8] Chawathe D.D, “Handbook of Gear Technology”, New Age International Publication,(2011) pp 26-89,305-536, 579-706 [2]Chabra Pankaj , Bhatia Amit , [9] Chabra Pankaj , Bhatia Amit “Design and Analysis of Composite Material Gear Box”, International Journal of Mechanical and Civil Engineering, Vol.1(2012), Issue1,pp 15-25.