AN OPTIMAL PROFILE AND LEAD MODIFICATION IN CYLINDRICAL
GEAR TOOTH BY REDUCING THE LOAD DISTRIBUTION FACTOR
Balasubramanian Narayanan
Department of Production Engineering, Sathyabama University, Chennai, India E-Mail: [email protected]
ABSTRACT
The face load factor KH, which in rating equations represents the load distribution over the face width in meshing gears is one of the most important parameter for a gear strength calculation. In this study, by implementing various profile and lead modification, the load distribution factor will be calculated to select the optimal profile and lead modification values through KISSsoft machine design software for the same input parameter. Based on the KISSsoft results the optimal profile and lead modification values are taken to avoid gear tooth damage by reducing the load distribution factor. The effects of the profile and lead modifications (Tip and root relief, Helix angle modification, End relief and longitudinal crowning) and corresponding load distribution factors and gear strengths are illustrated with and without profile and lead modification with the same input parameters. By providing optimum lead modifications, KHβ value reduced from 1.80 to 1.1. i.e. 39% load carrying capacity increased and Hertzian stress value reduced from 1860 N/mm² to 1275 N/mm² i.e. 31% stress reduction.
Keywords: cylindrical gear pair, load distribution factor, profile and lead modification, kissSost, Hertzian stress.
1. INTRODUCTION
In general, cylindrical pinion’s tooth without tooth modification shall collide with the gear’s tooth while the tooth pair gets into engagement under load due to deflection in the shaft which makes the Flank (Pitting) and Root (Bending) failures because of uneven load distribution. The result reveals that the selection of optimal Profile and Lead Modifications (Tip and root relief, Helix angle modification, End relief and longitudinal crowning) let to distribute the load at the center of the gear tooth even though if there are any deviations in the manufacturing, bearing and assembly to increase the load carrying capacity. M. S. Tavakoli et al. 1986 [1] A procedure was
used to minimize any combination of the harmonics of gear mesh frequency components of the static transmission error. Different combinations of tip and root relief may be used to achieve optimization. These include varying the starting point of relief and varying the magnitude of relief and selecting the gear and/or the pinion teeth to be tip and/or root-relieved. Xiangfei zhao et al. 2014 [2] the
geometrical shape of gear tooth fillet profile, usually cut out by the cutter tip, plays a significant role in the evaluation of the gear bending stresses. In order to improve the teeth bending strength, the research detailed hereby introduced a novel curve to describe the cutter tip and the gear cut by the optimized cutter exhibits higher bending strength rather than the gear cut by standard cutting tool. Shanmugasundaram Sankar et al. 2011 [3]
This research paper discusses a novel method toprevent the tooth failure in the spur gear by introducing circular
gradient descent algorithm. Some optimum robust linear relief is presented which minimizes transmission error fluctuations over a broad range of loads even in the presence of significant geometrical tolerances. P. Velex et al. 2011 [5] Some Analytical Results on Transmission
Errors in Narrow-Faced Spur and Helical Gears: Influence of Profile Modifications. An original direct solution to the optimum relief minimizing transmission error fluctuations is presented, which is believed to be helpful for designers. The analytical results compare well with the numerical results provided by a variety of models and it is demonstrated that some general laws of evolution for transmission error fluctuations versus profile modifications can be established for spur and helical gears. Yong-jun Wu et al. 2011 [6] in this paper, a precise tooth
profile modification (TPM) approach of the helical gear pairs is presented first. The type and amount of the TPM are accurately determined by the static contact FEA results. Both the simulated and experimental results show that the presented precise TPM of helical gears is effective on vibration reduction around the working load, and the dynamic contact simulation is effective in estimating the effect of the TPM on vibration reduction in the designing stage. I. D. Paul et al. 2010 [7] This Dissertation is a study
profile and lead modification in both pinion and gear tooth. The optimal modifications will reduce the load distribution factor throughout the face width of the matting gear and let to distribute the load at the centre of the gear tooth. By implementing the optimal profile and lead modification we can reduce the load distribution factor to increase root and flank strength.
B. Methodology identified
Corrective measures are taken to avoid gear tooth damage by selection and implementing the optimum profile and lead modification in the cylindrical gear tooth. The optimized Profile and lead modification value will be given in KISSsoft for comparing the tooth strength and Load distribution factor before and after profile modification.
C. Solution technique
First, Calculate and analysis the tooth strength of the gear with various Profile and Lead modifications for the same input parameters in KISSsoft. Then select optimized Profile and lead modification value to comparing the tooth strength and Load distribution factor before and after profile modification as mentioned below.
a) Stress distribution without modification along the face width.
b) Stress distribution with End relief modifications on pinion along the face width.
c) Stress distribution with End relief and Helix angle modifications on pinion along the face width.
d) Stress distribution with Profile crowning modifications on gear along the face width.
e) Stress distribution with Profile crowning and Pressure angle modification on gear along the face width.
The effects of different Profile modification, such as Load distribution factor and Hertzian stress are addressed, and the most significant Profile modification at which the stresses is minimum are determined by KISSsoft. Finally, the Analysis outcome shows the effect of Profile modification in gear strength calculation.
3. MODELING AND MANUFACTURING OF CYLINDRICAL GEAR PAIR
A. 3D modeling
In this chapter, three dimensional models of cylindrical gears were developed using KISSsoft software. Four modifications are used to investigate the effects of the cylindrical gear which are End relief, helix angle, crowning and pressure angle modification. The following Table-1 shows the material property.
Table-1. Material property.
Descriptions Pinion Wheel
Material 18CrNiMo7-6 18CrNiMo7-6
Surface hardness HRC 61 HRC 61
Fatigue strength. tooth root
stress (N/mm²) [sigFlim] 430 430
Fatigue strength for Hertzian
pressure (N/mm²) [sigHlim] 1500 1500
Tensile strength (N/mm²) [Rm] 1200 1200
Yield point (N/mm²) [Rp] 850 850
Young's modulus (N/mm²) [E] 206000 206000
Poisson's ratio [ny] 0.3 0.3
Mean roughness, Ra, tooth
flank (µm) [RAH] 0.6 0.6
Mean roughness height, Rz,
flank (µm) [RZH] 4.8 4.8
Mean roughness height, Rz,
The following Figure-1 shows the preferred 3D models imported from KISSsoft.
(a) Gear Pinion (b) Gear Wheel
(c) Gear pair
Figure-1. 3D-models of cylindrical gear pair.
The following Table-2 shows the cylindrical gear pair parameters.
Table-2. Cylindrical gear parameter
Centre Distance 320 mm
Module 5mm
No. of. Teeth Z1 25
No. of. Teeth Z2 100
Profile shift coefficient 0.4065
Helix angle 9°
Face width 135mm
Power capacity 325kW
Pinion Speed 375rpm
B. Profile grinding
Modifications of the involute profile are generated on manufacturing grinder by changing the profile of grinding wheel. Machining processes with defined cutting (hobbing) need for any tooth design a specially designed tool, while in process with an undefined cutting edge (tooth grinding) be obtained generally profile
the required modification. With this method only profile crowning is realized practically. Tolerance depends on the type of modification, gear quality and the amount of modification.
Figure-2. Profile grinding machine.
4. ANALYSIS DETAILS
A. Selection of profile and lead modification
In this study, the following profile and lead modification are selected for KISSsoft analysis to compare the load distribution factor and stress distribution along the face width of the cylindrical gear pair.
Figure-3 shows the profile and lead modification types for KISSsoft analysis.
Table-3. Modification types and its values.
Descriptions Cylindrical gear
End Relief Pinion
Helix Angle Modification Pinion
Profile Crowning Wheel
Pressure Angle Modification Wheel
5. RESULTS AND DISCUSSIONS
A. Experimental results
Table-4 shows the variation of load distribution factor and stress distribution. Following results were obtained during analysis for without modification.
Table-4. Stress distribution without modifications on pinion and gear along the face width.
Description Cylindrical gear Value Load distribution factor
Stress N/mm² Without
Modification Wheel and Pinion NA 1.8 1860
Table-5 shows the variation of load distribution factor and stress distribution. Following results were obtained during analysis for without modification²
Table-5. Stress distribution with End relief modifications on pinion along the face width.
Description Cylindrical gear Value Load distribution factor
Stress N/mm² End relief
on Pinion Pinion
Length = 47 mm
Value = 43 µm 1.52 1810
Table-6 shows the variation of load distribution factor and stress distribution. Following results were obtained during analysis for without modification.
Table-6. Stress distribution with End relief and Helix angle modifications on pinion along the face width.
Description Cylindrical
gear Value
Load distribution factor
Stress N/mm² Helix angle
on pinion Pinion
75 µm Resulting
helix = 9.033° 1.31 1650
Table-7 shows the variation of load distribution factor and stress distribution. Following results were obtained during analysis for without modification.
Table-7. Stress distribution with Profile crowning modifications on gear along the face width.
Description Cylindrical gear Value Load distribution factor
Stress N/mm²
Profile crowning Wheel 20 µm 1.19 1370
Table-8 shows the variation of load distribution factor and stress distribution. Following results were obtained during analysis for without modification.
Table-8. Stress distribution with Profile crowning and Pressure angle modification on gear along the face width.
Description Cylindrical gear Value Load distribution factor
Stress N/mm² Pressure angle
B. Correlation graphs
The correlation graph shows the relationship between profile modification with Load distribution factor and Hertzian stress. And finally, we optimized the Hertzian stress by controlling the profile modification on cylindrical gear pairs. Stress distribution with Helix angle and end relief modifications along the face width at the beginning to the end of contact and the value of Load distribution for a particular load.
Figure-4. Stress distribution without modifications on pinion and gear along the face width.
Figure-5. Stress distribution with End relief modifications on pinion along the face width.
Figure-6. Stress distribution with End relief and Helix angle modifications on pinion along the face width.
6. CONCLUSIONS
With the help of KISSsoft software, the effects of the profile and lead modifications (Tip and root relief, Helix angle modification, End relief and longitudinal crowning) and corresponding load distribution factors and gear strengths are illustrated with and without profile and lead modification with the same input parameters. By providing optimum lead modifications, KHβ value reduced from 1.80 to 1.1. i.e. 39% load carrying capacity increased and Hertzian stress value reduced from 1860 N/mm² to 1275 N/mm² i.e. 31% stress reduction.
The result of this method is, the line load distribution over the face width can be reduced by identifying a nearly perfect proposition for the best flank line modification. As shown in the example, even for complicated duty cycles, it is possible to find the best modifications, hence it will improve the overall lifetime considerably.
REFERENCES
[1] M. S. Tavakoli et al. 1986 Optimum Profile
Modifications for the Minimization of Static Transmission Errors of Spur Gears. [ELSEVIER]
[2] Xiangfei zhao et al. 2014 increasing bending strength
in spur gears using Shape optimization of cutting tool profile. [ELSEVIER]
[3] Shanmugasundaram Sankar et al. 2011 Profile
modification-a design approach for increasing the tooth strength in spur gear. [ELSEVIER]
[4] D. Ghribi et al. 2012. A Contribution to the Design of
Robust Profile Modifications in Spur and Helical Gears by Combining Analytical Results and Numerical Simulations. [ELSEVIER]
[5] P. Velex et al. 2011 Some Analytical Results on
Transmission Errors in Narrow-Faced Spur and Helical Gears: Influence of Profile Modifications. [ELSEVIER]
[6] Yong-jun Wu et al. 2011. Static/dynamic contact FEA
and experimental study for tooth profile modification of helical gears. [ELSEVIER]
[7] I. D. Paul et al. 2010. Modification of Spur Gear
Using Computational Method-Involutes Profile Being Modify. [ELSEVIER]
[8] M. Divandari et al. 2012. Tooth profile modification
and its effect on spur gear pair vibration in presence of localized tooth defect. [ELSEVIER]
[9] KISSsoft software release 10 (2008), www.KISSsoft.ch
[10]ISO 6336-2:2006 Calculation of load capacity of spur and helical gears
