30120140504002
Upcoming SlideShare
Loading in...5
×

Like this? Share it with your network

Share
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Be the first to comment
    Be the first to like this
No Downloads

Views

Total Views
120
On Slideshare
120
From Embeds
0
Number of Embeds
0

Actions

Shares
Downloads
0
Comments
0
Likes
0

Embeds 0

No embeds

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
    No notes for slide

Transcript

  • 1. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online), Volume 5, Issue 4, April (2014), pp. 10-15 © IAEME 10 THE ANALYSIS OF SOME FACTORS FOR THE OPTIMIZATION OF CYLINDRICAL GEAR TRANSMITTERS Dr. sc. NIJAZI IBRAHIMI1 , Dr. sc. SADULLAH AVDIU2 , Msc. RIAD RAMADANI3 , Dr. sc. FATIH KARPAT4 1,2,3 Faculty of Mechanical Engineering, University of Prishtina “Hasan Prishtina”, Prishtina, Kosovo 4 Faculty of Mechanical Engineering, Uludag University, Bursa, Turkey ABSTRACT On the phase of dimensioning of the gear transmitters have influence center distance, gear ratio, material, thermal processing etc. The purpose of this paper is analysis of factors that have influence on the optimization of cylindrical gear transmitters. It is analyzed safety factor for pitting and safety factor for bending for gear transmitters on the dependence of center distance and gear ratio, than it is analyzed safety factor for pitting on dependence on safety factor for bending, gear ratio and material. Through analysis of these factors are defined limits of size that have influence on the optimization of gear transmitters. Keywords: Cylindrical Gear Transmitters, Optimization, Gear Optimization. 1.0 INTRODUCTION Gear power transmitters are part of mechanical group of high importance, which need to fulfill criterion for required performance criteria as: center distance, dimensions, safety factor, efficiency factor, contact ratio etc. Gear power transmitter with multi-stage, represents complex mechanical system that they need to fulfill technical requirement for: - compact design, - gear ratio, - efficiency, - factor of safety INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING AND TECHNOLOGY (IJMET) ISSN 0976 – 6340 (Print) ISSN 0976 – 6359 (Online) Volume 5, Issue 4, April (2014), pp. 10-15 © IAEME: www.iaeme.com/ijmet.asp Journal Impact Factor (2014): 7.5377 (Calculated by GISI) www.jifactor.com IJMET © I A E M E
  • 2. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online), Volume 5, Issue 4, April (2014), pp. 10-15 © IAEME 11 Choosing the best model, which needs to fulfill certain requirements of desired performance, imposes some limitation in the aspect of: assembling of gears pair, gears mesh, roughness of face and flank of gears, surface and volume durability, and other limitations [1]. 2.0 THE ANALYSIS OF FACTORS THAT INFLUENCE ON THE OPTIMIZATION GEAR TRANSMITTERS Many factors influence on the dimensioning of gear power transmitters, therefore it is very important to make the analysis of factors that influence in their optimization. Factors that influence on the optimization of gear transmitters are: center distance, gear radio, contact ration, module of gears, material, safety factors, volume, etc [2]. In order to achieve optimization of each factor mentioned above, a gear pair was analyzed with the following parameters: - Pinion material: steel, type Č.4732, for improvement, - Gear material: steel, type Č.1731 for improvement, - Standard module: mn12 =4.5 mm, - Number of teeth of pinion: z1 =19, - Number of teeth of gear: z2 =80, - Face width: b12 =100 mm, - Helix angle: β12 =14 o , - Center distance a12 =230 mm, - Torque of pinion: T1 =387.324 N· mm, 2.1. Safety factor for pitting on dependence of center distance Factor of safety from Pitting [3]: [ ] H H HS σ σ = (2.1) Where are: Critical contact stress of teeth face [ ] xwVRLNTHH ZZZZZZ⋅= limσσ (2.2) Working stress of teeth face βαβεσ HHvA t EHH KKKK u u bd F ZZZZ ⋅⋅⋅⋅ + ⋅ ⋅ = 1 (2.3) If in the expression (2.1), we substitute expressions (2.2) and (2.3) and expressions below: 1 1 1 2 d T Ft ⋅ = and 1 2 1 + ⋅ = u a d
  • 3. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online), Volume 5, Issue 4, April (2014), pp. 10-15 © IAEME 12 It is obtained expression for calculation of safety factor for pitting on dependency of center distance. βαβε σ HHvABEH xwVRLNTH H KKKK u u ba T ZZZZZ ZZZZZZ S ⋅⋅⋅⋅ + ⋅ ⋅⋅ ⋅⋅ = 3 2 3 1 11lim 1 )1( 4 102 )( (2.4) In the fig. 2.1., are represented curves of safety factor for pitting on dependency of center distance, for some values of gear radio. 220 222 224 226 228 230 232 234 236 238 240 1.05 1.08 1.11 1.14 1.17 1.2 1.23 1.26 1.29 1.32 1.35 SH1 a( ) SH2 a( ) SH3 a( ) SH4 a( ) SH5 a( ) a Fig. 2.1: Safety factor for pitting on dependency of center distance, for some values of gear radio: SH1(a) – u=3.8; SH2(a) – u=4; SH3(a) – u=4.2; SH4(a) – u=4.4; SH5(a) – u=4.6 From the fig. 2.1., it can be seen that with the increase of center distance, for constant gear radio, we have increase of safety factor for pitting. Also, with the increase of gear radio, we have decrease of safety factor for pitting. 2.2. Safety factor for bending on the dependence of center distance Safety factor for bending [3] [ ] F F FS σ σ = (2.5) Where are: Critical stress for bending [ ] xRrelTrelTSTNTFF YYYYY δσσ ⋅= lim (2.6) Working stress for bending βαβεσ FFvA n t saFaF KKKK mb F YYYY ⋅⋅⋅⋅ ⋅ = (2.7)
  • 4. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online), Volume 5, Issue 4, April (2014), pp. 10-15 © IAEME 13 If in the expression (2.5), we substitute expressions (2.6) and (2.7) and expressions below: 1 1 1 2 d T Ft ⋅ = and 1 2 1 + ⋅ = u a d It is obtained expression for calculation of safety factor for bending on the dependency of the center distance βαβε δσ FFvA n saFa xRrelTrelTSTNTF F KKKK amb uT YYYY YYYYY S ⋅⋅⋅⋅ ⋅⋅ ⋅+⋅ = 3 1 11lim 1 10)1( )( (2.8) In the fig. 2.2., are represented curves of safety factor for bending on the dependency of center distance, for some values of gear radio 220 222 224 226 228 230 232 234 236 238 240 4.5 4.65 4.8 4.95 5.1 5.25 5.4 5.55 5.7 5.85 6 SF1 a( ) SF2 a( ) SF3 a( ) SF4 a( ) SF5 a( ) a Fig. 2.2: Safety factor for bending on dependency of center distance, for some values of gear radio: SF1(a) – u=3.8; SF2(a) – u=4; SF3(a) – u=4.2; SF4(a) – u=4.4; SF5(a) – u=4.6 From the fig. 2.2., it can be seen that with the increase of center distance, for constant gear ratio, we have increase of the safety factor for bending. Also, with the increase of gear ratio, we have decrease of safety factor for bending. 2.3. Safety factor for pitting on dependency of safety factor of bending From the expressions (2.4) and (2.8), center distance on the dependency of safety factor for pitting and safety factor for bending is: ( ) xwVRLNTH HHvAHBEH ZZZZZZub KKKKuTSZZZZZ a 1lim 33 11 2 1102 σ βαβε ⋅⋅⋅ ⋅⋅⋅⋅+⋅⋅⋅⋅⋅ = (2.9)
  • 5. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online), Volume 5, Issue 4, April (2014), pp. 10-15 © IAEME 14 ( ) xRrelTrelTSTNTFn FFFvAsaFa YYYYYmb SKKKKuTYYYY a δ βαβε σ 1lim 1 3 1 101 ⋅⋅ ⋅⋅⋅⋅⋅⋅+⋅⋅ = (2.10) From equalization of center distance aa = , it is obtained expression of safety factor for pitting on dependency of safety factor of bending: ( ) ( ) 11lim 33 1 111lim 3 1 1 )(1102 )(2101 xRrelTrelTSTNTFnHHvABEH FxwVRLNTHFFvAsaFa H YYYYYmbKKKKuTZZZZZ SZZZZZZubKKKKuTYYYY S δβαβε βαβε σ σ ⋅⋅⋅⋅⋅⋅⋅+⋅⋅⋅⋅ ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅+⋅⋅ = (2.11) In the fig. 2.3., are represented curves of safety factor for pitting on dependency of safety factor for bending, for some values of gear ratio and material steel for improvement. 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 1.1 1.13 1.16 1.19 1.22 1.25 1.28 1.31 1.34 1.37 1.4 SH1SF( ) SH2SF( ) SH3SF( ) SH4SF( ) SH5SF( ) SF Fig. 2.3: Safety factor for pitting on dependency of safety factor for bending, for some values of gear ratio and material steel for improvement: SH1(SF) – u=3.8; SH2(SF) – u=4; SH3(SF) – u=4.2; SH4(SF) – u=4.4; SH5(SF)– u=4.6; From the fig. 2.3., it can be seen that with the increase of safety factor for bending, for constant gear ratio, we have increase of safety factor for pitting. With the increase of gear ratio, we have increase of safety factor for pitting. Also, for the material steel for case-harden it is assigned safety factor for pitting on dependency of safety factor for bending. In the fig. 2.4., are represented curves of safety factor for pitting on dependency of safety factor for bending, for some values of gear ratio and material steel case-harden.
  • 6. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online), Volume 5, Issue 4, April (2014), pp. 10-15 © IAEME 15 3.46 3.56 3.66 3.76 3.87 3.97 4.07 4.18 4.28 4.38 4.49 4.59 4.69 4.79 4.9 5 1.1 1.15 1.19 1.24 1.29 1.33 1.38 1.43 1.47 1.52 1.57 1.61 1.66 1.71 1.75 1.8 SH1SF( ) SH2SF( ) SH3SF( ) SH4SF( ) SH5SF( ) SF Fig. 2.4: Safety factor for pitting on dependency of safety factor for bending, for some values of gear ratio and material steel for case-harden: SH1(SF) – u=3.8; SH2(SF) – u=4; SH3(SF) – u=4.2; SH4(SF) – u=4.4; SH5(SF)– u=4.6; From the fig. 2.4., it can be seen that with the increase of safety factor for bending, for constant gear ratio, we have increase of safety factor for pitting. Also, with the increase of gear ratio, we have increase of safety factor for pitting. For the material steel for case-harden the limit of safety factor for bending is 3.46 against it 5 for material steel for improvement. 3. CONCLUSION Based on the analysis of safety factor on dependency of center distance and gear ration we can conclude: - With the increase of center distance, increases safety factors for pitting and bending. - With the increase of gear ratio, increases safety factor for pitting and bending. - Material of gear has influence on safety factor for pitting and bending. REFERENCES [1] Riad Ramadani: Analiza e faktorëve që ndikojnë në optimizimin e transmetuesve me dhëmbëzorë, Master Work, Prishtinë, 2009. [2] Johannes Jahn: Introduction to the theory of nonlinear optimization, Universität Erlangen- Nürnberg, Germany, 2007. [3] Nijazi Ibrahimi, Detalaet e Makinave II - Libri 1 dhe 2, Prishtinë, 2006. [4] Singiresu Rao: Engineering optimization, theory and practice, Purdue University, West Lafayette, Indiana 2006. [5] P. Alexander, T. Sudha and M. Omamageswari, “Automatic Gear Transmission in Two Wheelers using Embedded System”, International Journal of Advanced Research in Engineering & Technology (IJARET), Volume 3, Issue 2, 2012, pp. 164 - 175, ISSN Print: 0976-6480, ISSN Online: 0976-6499.