Finite element analysis of profile modified spur gear

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1 Finite element analysis of profile modified spur gear Sagar Gaur Mechanical Engineering Department, Institute of Technology, YashluvVirwani Mechanical Engineering Department, Institute of Technology, Rudresh Makwana Assistant profressor, Mechanical Engineering Department, Institute of Technology, Abstract: This paper describes a general Finite Element Analysis of a Spur Gear under desirable loading conditions and the effect of load during the meshing of gear is shown for the fillet foundation. The results are compared with that of various profile modified spur gears. The modified profiles are designed based on the relocation of the Cutting Rack while manufacturing the gear. The designs were confirmed by a number of trials and comparison of their analysis with that of a regular Spur Gear. When the Cutting Rack s axis line or pitch line is moved away from the pitch circle of the gear, the achieved modified gear is known as positively corrected gear, whereas when the same is moved towards the center of the gear, and it intersects with the pitch circle of the gear, the modified gear is known as negatively corrected gear. Spur Gears can be described as the most basic type of gear, largely used in the modern world. Gears were adopted into various mechanism which were earlier attained by use of wheels or belts. The advantage of gears being the teeth of a gear prevent slippage made their value known throughout the globe and their usage along with time increased, efficiency the positive correction makes the teeth of the gear thicker, and improves load carrying capacity and the length of the Addendum increases. But this causes the weight of the equipment to rise, and is also not produced by standard procedures. On the other hand, the negative correction of the gear can be used to avoid unnecessary wear of the gear as it develops a profile that already has an undercut, which in general gear pair occurs as a result of damage due to conjugation of involute profile of a gear with non-involute profile, also called interference. Along with the designs, the Finite Element Analysis on the models are shown for a given required power transmission as a primary requirement, and the results were collected. Keywords Spur gear, profile modification, gear correction I. INTRODUCTION Spur Gears can be described as the most basic type of gear, largely used in the modern world. Gears were adopted into various mechanism which were earlier attained by use of wheels or belts. The advantage of gears being the teeth of a gear prevent slippage made their value known throughout the globe and their usage along with time increased, efficiency improved and more variety of gears came into existence with many different variations. One such variation with respect to spur gears was the Profile Modification of the teeth. The teeth being cut with an involute profile had a lot of advantages, but along with them came some disadvantages which needed improvisation. For instance, at higher speeds the gears have noise related issues and vibrations caused due to conjugation of non-involute profiles and occurrence misalignments. Solution to that came with a type of profile medication known as S- Modification. In the case of S- Gearing Modification, the profile was generated in such a way that the tooth already consisted of an undercut. That is, some material was already removed from the base of the tooth which was the general starting location for all the issues that came with meshing of gears. To achieve this, the cutting rack was placed along the cutting line in such a way that its axis, or its pitch line, intersected with the pitch circle of the required gear. This gave us a tooth profile with an undercut with which there were no more issues related to noise at high speeds, as at the location where the non-involute profiles started to mesh, the respective material was already removed. This also caused reduction in weight of the gear, and thus reducing chances of misalignments greatly. However, the flaw that followed was lowering of power transmission capacity. The other type of modification in the same way was moving away the pitch line of the rack from the pitch circle of the gear, and this was called S+ Modification. As a result, a thicker, stronger tooth profile will be obtained. Even though the weight of the gear box will increase, the power transmitting capacity of the gear will improve appreciably. In this work, such profiles for various factors of modification were generated and analysed on ANSYS

Structural and compared to that of a regular Spur gear with no modification. II.

SPECIFICATIONS Parameters Gear Pinion Pitch circle 500 100 diameter (mm) Number of teeth 100 20 Module

854 (mm) Fillet radius (mm) 2 2 Face width (mm) 50 50 Fig. 3Fixed Support III.

4 Force acting The force acts at the line of contact (during meshing of gears) as shown in fig.4. Fig.

17-7ph Precipitation-Hardenable steel UTS = 1450MPa,Yield Strength = 1310MPa IV.

2 Structural and compared to that of a regular Spur gear with no modification. II. DESIGN SPECIFICATIONS TABLE I. SPECIFICATIONS Parameters Gear Pinion Pitch circle diameter (mm) Number of teeth Module (mm) 5 5 Addendum (mm) 5 5 Dedendum (mm) Clearance (mm) Tooth thickness (mm) Fillet radius (mm) 2 2 Face width (mm) Fig. 3Fixed Support III. FEA ANALYSIS OF STRESSES ON GEAR TOOTH AND MODIFIED GEAR TOOTH PROFILES USING ANSYS Fig. 4 Force acting The force acts at the line of contact (during meshing of gears) as shown in fig.4. Fig. 1 Gear Tooth The material properties are as given below AISI no.17-7ph Precipitation-Hardenable steel UTS = 1450MPa,Yield Strength = 1310MPa IV. TOTAL DEFORMATION AND STRESS IN REGULAR SPUR GEARFIXED SUPPORTS WERE GIVEN AS BOUNDARY CONDITION TO THE SURFACES SHOWN IN FIG. 4. Fig. 2 Meshing of Tooth Mesh details: Number of nodes: Number of elements: Fig. 5 Total deformation Maximum Deformation: mm (At the Tooth Top)

VI. PARAMETERS In a corrected gear, the following parameters remain unaltered: Base circle diameter d, = d cos a [3] Pitch circle diameter d = m z [3] Circular pitch p = (pi)rm [3] The following

3 VI. PARAMETERS In a corrected gear, the following parameters remain unaltered: Base circle diameter d, = d cos a [3] Pitch circle diameter d = m z [3] Circular pitch p = (pi)rm [3] The following parameters change: Fig. 6 Equivalent Stress Maximum Equivalent Stress analyzed: MPa Minimum Equivalent Stress analyzed: MPa V. PROFILE MODIFICATION To avoid undercutting, the practice which is now universally adopted is what is known as the "profile correction" of gear tooth. When a standard, uncorrected pinion is cut by the rack, the pitch line is tangent to the pitch circle of the pinion at the normal pitch point P. When, however, the rack is withdrawn, this situation alters. The rack reference line MM is no longer a tangent to the pitch circle. Instead, it is away by an amount equal to xm millimetres. To effect this, the cutter is withdrawn by a specified distance so that the addendum line of the rack-type cutter or hob just touches the point of tangency when the cutting action begins. [1] Fig. 7 Movement of axis of rack with respect to pitch circle This amount xm is the profile correction of the gear and the coefficient x is known as the correction factor. Positively corrected gear is known as S-plus gear and negatively corrected gear as S-minus gear. x = 14 z/17 [1] Tip circle diameter da becomes bigger by an amount of (+2xm) in case of S-plus gears and smaller by (- 2xm) in case of S-minus gears. [3] [1] Fig. 8 Location of axis of rack with respect to pitch circle (a) Correction factor x= +1.0 (b) Correction factor x= +0.5 (c) Correction factor x= 0 (d) Correction factor x= -0.5 In a positively corrected gear, the addendum is increased by an amount of xm and the dedendum is correspondingly decreased by the same amount. The reverse is true in case of the negatively corrected gears. Normally, the root-fillet becomes smaller in case of positively corrected gears. This has a detrimental effect on stress concentration problems. Negative correction weakens the teeth and the tooth strength decreases. However, this detrimental effect is largely nullified in case of gears with a greater number of teeth. One effect of the positive correction is to make the tooth more and more pointed as the correction factor increases. Consequently, the top land becomes correspondingly smaller and ultimately results in a pointed tip. This phenomenon is termed as peaking. The peaking limit sets a boundary to the amount of positive correction that may be applied. The profile of a positively corrected tooth (i.e. its face and flank) is composed of that portion of the involute which is farther away from the base circle than in case of an

POSITIVE CORRECTION Minimum Deformation: 0mm (In the center of gear) Fig. 11 Deformation (x=-0.25) x = 0.25 Fig. 9 Deformation (x=0.25) Maximum Deformation: 0.0013903 mm Fig.

4 ordinary gear. Moreover, positive correction results in greater tooth thickness at the root. All these aspects combine to make a positively corrected tooth look thicker at the bottom and pointed at the top-more or less like an inverted V. VII. POSITIVE CORRECTION Minimum Deformation: 0mm (In the center of gear) Fig. 11 Deformation (x=-0.25) x = 0.25 Fig. 9 Deformation (x=0.25) Maximum Deformation: mm Fig. 12 Equivalent Stresses (x=-0.25) Maximum Equivalent Stress analyzed: MPa Minimum Equivalent Stress Analyzed: 0 MPa RESULTS TABLE II. Results Fig.10 equivalent stresses Maximum Equivalent Stress analyzed: MPa Minimum Equivalent Stress Analyzed: MPa One effect of the positive correction is to make the tooth more and more pointed as the correction factor increases. Consequently, the top land becomes correspondingly smaller and ultimately results in a pointed tip. This phenomenon is termed as peaking. The peaking limit sets a boundary to the amount of positive correction that may be applied. x = VIII. NEGATIVE CORRECTION Maximum Deformation: mm (At the Tooth Top) Profile Correction Value (mm) Max. Deformation Value (mm) Max. Stress Value (MPa) x = x = (peaking) x = x = CONCLUSION The modifications help in meeting with necessary requirements. The positively corrected profile modify the gear with thicker base, strengthening the gear tooth against undercutting and also improving its load carrying capacity appreciably. That, however, increases the weight of the gearbox. On the other hand, the negatively corrected gear profile have modified pre-existing undercut, due to which any chances of interference and further undercutting can be avoided. In this case, the load carrying capacity reduces, which is a drawback.

5 References [1] Gitin M Maitra, Handbook of Gear Design, Second Edition. [2] V. B. Bhandari, Design of Machine Elements, Third Edition, McGraw Hill. [3] Stephen P. Radzevich, Dudley Handbook of Practical Gear Design and Manufacturing, Third Edition. [4] Bharat Gupta et al, Contact Stress Analysis of Spur Gear, International Journal of Engineering Research & Technology, Vol. 1 Issue 4, June [5] Seok-Chul Hwang et al, Contact Stress Analysis for a pair of mating gears, Mathematical and Computer Modelling 57 (2013), 40-49, Elsevier. [6] M. Divandari et al, Totth Profile Modification and its effect on spur gear pair vibration in presence of localized tooth defect, Journal of Mechanics, Vol. 28, No. 2, June [7] A. Parthiban et al, Profile modfication for increasing the tooth strength in spur gear using CAD & CAE. International Journal of Innovations in Engineering and Technology, Vol. 2, Issue 1, February ELK Asia Pacific Journals

Gear Tooth Geometry - This is determined primarily by pitch, depth and pressure angle

Gear Tooth Geometry - This is determined primarily by pitch, depth and pressure angle Addendum: The radial distance between the top land and the pitch circle. Addendum Circle: The circle defining the outer