The inception of rotary machinery for transmitting the power gears have been used skillful in manner. After that moderation did in wooden gear involute drive trains have been integral to the development of machinery and power control technology. Most modern gearing is conjugate [1], i.e. it is designed to transmit a constant rotational velocity. The involute tooth form [2] is the most common example of conjugate gearing. Ideal involute gears transmit uniform rotational velocities without any error but such gears are practically not possible. The displacement based exciter function known as the transmission error (T.E.) [3] it is the accepted principal source for noise in involute gearing. In most gear systems operating at speed, applied load, inertia forces and relative rotational position error of the meshing gears is directly correlated to any vibration caused by the system. Put another way, an ideal gear pair would be able to transmit a constant rotational velocity perfectly from the drive gear to the driven gear under constant load conditions. The difference in the position of the output gear when compared to its ideal analog is the transmission error. This transmission error can be directly traced to deviations from the perfect involute form due to geometric differences and deformation under load. There are two manifest requirements imposed upon a gearing system (tooth profile) for transmission error fluctuations to be eliminated. One is the transmission error must be constant through the range of the gear rotation for any mesh loading and second one is the gear mesh must transmit a constant loading. The transmission error as experienced in meshing gears arises because of two things one is components geometric deviation and other is deformations under load. Geometric deviations can either be intentional or unintentional. Intentional deviations arise from manufacturing modifications such as crowning or tip relief. Unintentional errors like scalloping or improper finishing are also geometric deviations. Deformation across the loaded tooth mesh also has two components. Both gross body compliance and Hertzian Compliance contributes to deformation under load. These deviations from the ideal involute gear tooth surface for loaded gears are the primary cause of transmission error. Eliminating or compensating for these deviation types can eliminate transmission error. The purpose of this thesis is to reduce noise & vibration by modifying involute profile of gear by minimizing transmission error fluctuations during and the maintenance of constant transmitted gear mesh loading. This method is must accounted for when tooth geometry is modified to achieve the goal. The development of precise compensatory gear geometry that when loaded accounts for all design and compliant variations in the tooth-to-tooth meshing of a rotating gear pair for deformation under load.

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uniformly proportional rotational velocity and thereby no transmission error. The use of finite element analysis (FEA) & numerical optimization.

Gears can be traced to the earliest machines by Greeks [4]. Roman and Chinese [4] first define analytical construction in gear. The mathematical and geometrical tools invented by Renaissance engineers were simply insufficient to solve the problem of the optimal gear tooth profile [8]. Leonhard Euler was the first to successfully attack the problem by showing that uniform transfer of motion can be achieved by a conjugate and specifically, an involute profile [4], in 2003 [5] Invention did on noise of gear. Henry Walker [7] was able to state that the gear noise will primary lead by transmission error. As gear analysis progressed slowly from basics that time author analyzed the transmission error became the accepted cause of gear noise [3]. Before rigorous analysis of involute gearing was available gear noise was addressed during modification of the available gear involute tooth surface by basic principle. This procedure came to be known as crowning [6] or relief. Tip relief made proper tooth clearance and nominal base plane action which are critical to gear noise. In modern crowning is typically combination of single lead and a single profile modification are combined and applied to the gear tooth surface. Axial and profile crowning together have been shown to reduce gear noise but that addressed some issues like addition of load computation, mesh analysis and line of contact constraints [7] after all outcome results was robust and manufacturable. [8] September/October 2002–The author modifies modern gear design is generally based on standard tools reducing tooling expenses and inventory. [9] Bending Stress Minimization (September/October 2003): Author works on Lewis equation and find out the bending stresses developed in the gear. [10] In 2013 author works on high speed non lubricated gear: These type of gear design technique introduce and applied to reduce tooth contact temperature and noise excitation of a high speed spur gear pair running without lubricant.

We can find the solution by two methods they are: A. By using finite element analysis (FEA) software. Before implementing any technique we must have basic information of gear such as material, Number of teeth, face width, pitch radius, helix angle, pressure angle, Young‘s modulus & poison‘s ratio.

1. Make a model for FEA analysis by available input data. 2. Applying meshing on model for analysis.. 3. After applying the load of conjugate teeth we will get the stress affected region it may be line contact type or point contact type. 4. Analysis results we will show maximum stress affected or constant deformation regions exact co-ordinates. Fig.4 shows the stress impact zone.

5. After getting these results we need to modifying stress affected co-ordinates, by making the new model for analysis by removing material from affected stressed zone co-ordinates. 6. Rate of material removing is start from 1micron and gradually increases up to 25 micron. 7. Plot result sheet in the form of length of linearly increment portion of convolution precursor (∆) & Deflection of gear tooth line contact (s). 8. After getting these full results tabulated data now we ready to select optimum solution which will give minimization transmission error, contact loading stress point, vibration excitation and noise. 9. We got these data in form of s & ∆ means actual co-ordinates on gear. Accordingly we will practically remove the material from involute profile by grinding machine.

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geometric accuracy of approximately 1 µm. With a mean step distance on the order of 0.5 mm, it is realistic to attempt to manufacture the negative s portion of contact region for the deformation ranges of 5 µm to 25 µm. Arranging the set up as per below picture on machine Holroyd GTG2 grinding machine. Photo: Gear grinding machine arrangement Before proceeding actual manufacturing the set up approval required by quality assurance person. In that process parameters are verified in case of these grinding of special gear the parameters set as per below, Machine on auto mode inspection Grinding wheel RPM is 1200. Grade of grinding wheel: Fine 2.0 Coolant used which is MMT80. First of all machine operator sets zero – zero value of x and y co-ordinate then as per our resultant value 15 micron set in Y co-ordinate direction and start machine. Due to CNC control machine removed exact 15 micron material from invoute profile of gear. Same was verified by quality inspector which is on video-measuring machine. After that the same modified gear is ready to deliver by production department.

Before putting any values in the equation we consider the face width material reduction which is 15 micron from involute side, Before modification of face width = 10mm After FEA results modified face width is = 10mm – 0.015 x 2 …. (For both sides). Now final face width is 9.97 After addendum module which is 6mm then, Face width, Theoretical Analysis of Contact Stress using Hertz Equations: Earle Buckingham used the Hertz theory to determine the contact stress between a pair of teeth while transmitting power by treating the pair of teeth in contact as cylinders of radii equal to the radii of curvature of the mating involutes at the pitch point. According to Hertz theory as given in when two cylinders are pressed together, the contact stress is given by,

As per mathematical formulae & calculation we found that acting stresses is 205.7387MPa.

Refer below test report table which was conducted at external lab. Refer annexure for testing report.

Gear 1300 N 207.13

After modifying involute profile of spur gear tooth effect as,

Without profile modified earlier gear data Profile modified gear data Noise 15dB 9 dB Vibration 3.2 mm at32 Hz 2.4 mm at 25 Hz Stress 248.453MPa

FEA Analysis : 205.778MPa Mathematical :205.73 MPa Actual on gear stress testing in lab : 207.13 MPa Life of mating gear average 145 days Till 200 days and more no issue Surface finish Ra 1.2 Ra 0.4

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1. Without profile modified : Before modifying involute profile of gear tooth maximum peak value point is 3.2 mm at 32 Hz.

2. After modification of involuteprofile: After modifying involute profile of gear tooth maximum peak value point is 2.4 mm at 25 Hz .

In case of validation the results obtained from software analysis and results from testing are compared and they should be nearly equals and for our case the results are nearly equals. So from above test report it is clear that the method we chose for analysis as well as manufacturing modification is right and gives satisfactory results and can predict the outcomes from software analysis are nearly equivalent to actual results obtained from testing.

1) Young‘s modulus and Poisson‘s ratio adds variability and uncertainty to the full technique. 3) Friction and lubrication properties are small and do not lay in the plane of action.

It is an optimal gear design method by modifications on an involute tooth working surface for minimizing error fluctuation, vibration excitation & nose including all Hertzian contributions. The results of this procedure is most beneficiaries and it is practically possible invention. Hope it‘s real revolution in gear design & manufacturing industries.

I am most grateful and indebted to my thesis advisor Prof. Ganesh A. Kadam for his generosity with guidance, patience, and encouragement that he has shown me. I would also like to thank ME co-ordinating team for her unyielding support over the duration of this work.

J. E. Shigley and J. Uicker, Theory of Machines and Mechanisms, McGraw-Hill Inc., (1980) W. A. Tuplin, Involute Gear Geometry, Chatto and Windus, (1962) ]S. L. Harris, Proceedings of the Institute of Mechanical Engineers (1958). T. Koetsier, Mechanism and machine science, pages 5–26, Norwell, MA, 2000, Kluwer Academic Publishers. W. D. Mark, Journal of the Acoustical Society of America (1978). R. G. Munro, N. Yildirim, and D. M. Hall, Optimum profile relief and transmission error in spur gears, First International Conference: Gearbox Noise and Vibration, pages 35–42, Institution of Mechanical Engineers, (1990). H. Walker, Performance improvement in gear ASME Journal of engineering for industry.(1994) Thomas McNamara Direct Gear Design for Spur and Helical Involute Gears published n SME gear processing and manufacturing journal (September/October 2002). Alexander L. KapelevchDirect Gear Design: Bending Stress Minimization published in Gear technology (2003).

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Optimization for Low Contact Temperature of a High Speed, Non Lubricated Spur Gear Pair (May 2013) Modification of Spur Gear Using Computational Method-Involutes Profile Being Modify by I. D. Paul and G.P. Bhole.Publisher ICIE (2010). L. P. Euler, Noise and Vibration, Marcel Dekker, Inc., New York, NY, second edition, (2003). D. B. Welbourn, Fundamental knowledge of gear noise - a survey, in Noise and Vibrations of Engines and Transmissions, pages 9–14, London, (1979) F.L. Litvin, A. Fuentes, A. Demenego, D. Vecchiato, and Q. Fan, New developments in the design and generation of gear drives, in Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, volume 215, pages 747–757, Professional Engineering Publishing, (2001). P. Wagaj and A. Kahraman, Impact of tooth profile modifications on the transmission error excitation of helical gear pairs, in Proceedings of ESDA2002: 6th Biennial Conference on Engineering Systems Design and Analysis, (2002). A. Andersson and L. Vedmar, Journal of Sound and Vibration 260, 195 (2003). G. Liu and R. G. Parker, Journal of Mechanical Design 130, 121402 (2008). W. B. Rockwood et al., Finite elements applied to the nonlinear calculation of tooth loads and root stresses in high power density gearing, in AIAA/SAE/ASME/ASEE 23rd Joint Propulsion Conference, (1987) W. D. Mark, Gear Noise, chapter 36, pages 36.1–36.22, McGraw-Hill Inc., (1991). G. Liu and R. G. Parker, Journal of Sound and Vibration 320, 1039 (2009). Shanmugasundaram Sankar1, MaasanamuthuSundar Raj, MuthusamyNatarajofile Modification for Increasing the Tooth Strength inSpur Gear Using CAD. Published n scientific research. (2010). Kristina MARKOVIĆ – Marina contact stresses in gear teeth due to tip relief profile modification Published in science journal (2013).

Department of Mechanical Engineering, SKN Sinhgad Institute of Technology and Science, Lonavala, Pune, India