*(Student, IV Semester M.Tech (CAD/CAM), Mechanical Engineering Department, Rajiv Gandhi College of Engg. Research & Technology, Chandrapur – 442 403 (Maharashtra) (India)
E-mail: mantopazare@yahoo.com)
Prof.S.D.Khamankar**,
** (Associate Professor, Mechanical Engineering Department, Rajiv Gandhi College of Engg. Research & Technology, Chandrapur – 442 403 (Maharashtra) (India)
E-mail: sudhakarkhamankar@rediffmail.com) ABSTRACT
This paper deals with the stress analysis of bicycle frame by using Finite Element Method. The analysis is carried out in Ansys, The F.E.A. results are compared with theoretical results.
In theoretical analysis the frame is treated as truss like structure and the stresses in various members of frame like top tube, down tube, seat tube, chain stay and seat stay are determined, considering various condition like, static start up, steady state paddling, vertical impact, horizontal impact, rear wheel braking. Also Finite Element Analysis is done considering the above conditions.
From the analysis it is found that there is a good agreement between analytical and F.E.A. results. Result of all the cases reveals that maximum stress is found in top tube of the bicycle frame as compared to other frame members and is equal to 24.84 MPa which is less than yield strength in tension (i.e.Syt = 290 MPa) for the material (aluminum T 6061) selected.
Keywords: Bicycle frame, Stress analysis, FEM.
1. INTRODUCTION
Most modern bicycle frames have the simple form. This shape emerged in about 1895 following several decades of vigorous development and evolution and has remained basically unchanged since that time. The need for low weight coupled with high strength and stiffness has lead to continuing trail and development of high performance material for racing bicycles. Thus in trial and error method is costly and slow, and intuition does not always yield reliable result. A promising solution is to turn a proven tool of structural engineering; the Finite Element Analysis method. The method used for modeling will be described and theoretical predictions of frame stresses will be compared with F.E.A result for some simple loading cases. This design has been the industry standard for bicycle frame design for over one hundred years. The frame consists of a top tube, down tube, head tube, seat tube, seat stays, and chain stays .The head tube of the frame holds the sheerer tube of the fork, which in turn holds the front wheel. The top tube and down tube connect the head tube to the seat tube and bottom bracket. The seat tube holds the seat post, which holds the saddle. The bottom bracket holds the cranks, which hold the pedals. The seat stays and chain stays hold the rear dropouts, which connect the rear wheel to the frame.
2. THEORATICAL ANALYSIS OF BICYCLE FRAME
For the design of Bicycle Frame following data is considered. The problem to be modeled in this example is a simple bicycle frame shown in the following figure. The frame is to be built of hollow aluminum tubing having an outside diameter of 25mm (Seat tube, Top tube, Bottom tube) and 16mm (Seat and chain stay), a wall thickness of 2mm.
Loading conditions,
Following load Cases as part of an Investigation of the frame:
2.1. Static start up: A 700N rider is applying maximum effort to accelerate from a standing stop. Aerodynamic,
2.2. Steady
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2.3. Vertic
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Fig 5.Rear wheel braking
Theoretical stresses on members:
Load case Stresses in members (ANALYTICAL METHOD)
Top tube (AB)
Down tube (AC)
Seat tube (BC)
Seat stays (BD)
Chain stays(CD)
Static start up 2.38 3.05 3.05 3.1 2.95
Steady state pedaling 3.071 3.920 3.770 5.98 3.2327
Vertical impact 5.77 6.110 5.87 6.20 5.200
Rear wheel braking 0 0 0 7.86 5.864
Horizontal impact 21.63 24.85 0 0 0
Table 1: Theoretical Comparisons of Stresses on Members
Fig.6: Theoretical Comparisons of Stresses on Members
3. FINITE ELEMENT ANALYSIS OF BICYCLE FRAME USING ANSYS.
To verify the analytical result of stresses for bicycle frame it is compared with FEA analysis. The problem to be modeled in this example is a simple bicycle frame shown in the following figure. The frame is to be built of hollow aluminum tubing having an outside diameter of 25mm and 16mm and a wall thickness of 2mm.
The material properties specified are as follows.
Young's modulus (E) = 7.2×104 MPa
Poison's ratio (μ)= 0.30
Density(ρ) = 2700×103 MPa
For this analysis, “PIPE 16”element is used which is a uniaxial element with tension, compression, torsion and bending capabilities. It has six degrees of freedom at each node: 3 translations and 3 rotations. It is specialized for symmetrical, circular pipe geometries. Need specifies are the pipe diameter and wall thickness.
3.1. Loading and constraints on the bicycle frame:
The applied loads and constraints should now appear as shown below, 0
5 10 15 20 25 30
Static start up Steady state
pedaling
Vertical impact Rear wheel braking
Horizontal impact
Top tube (AB)
Down tube (AC)
Seat tube (BC)
Seat stays (BD)
4. FINITE ELEMENT ANALYSIS RESULTS
Stress analyses of bicycle frames by considering various type of loading conditions.
Fig.12. Stresses in bicycle frame Static start up Fig.13. Stresses in bicycle frame Steady state pedaling Fig.7. Applying load and constraints to the frame for Static start up Fig.8. Applying load and constraints to the frame for Steady state
pedaling
Fig.9. Applying load and constraints to the frame for Vertical impact Fig.10. Applying load and constraints to the frame for Horizontal Impact
Fig.14. Stresses in bicycle frame Horizontal impact Fig.15. Stresses in bicycle frame Vertical impact
Fig.16. Stresses in bicycle frame Rear wheel braking
4.1 Comparison of Stress on members by F.E.A:
Stresses in members FEA Load case
Top tube (AB)
Down tube (AC)
Seat tube (BC)
Seat stays (BD)
Chain stays(CD)
Static start up 3.1123 4.0175 3.033 3.9649 3.9649
Steady state pedaling 4.2437 4.8885 1.28 5.23 4.1117
Vertical impact(2G) 6.709 7.4814 4.3482 6.1904 7.9029
Rear wheel braking 0 0 0 9.512 6.4698
Horizontal impact 23.942 20.039 0 0 0
Table.3: Comparison of stresses on members FEA
Fig.17. Comparison of stresses on members by FEA 0
5 10 15 20 25 30
Static start up
Steady state pedaling
Vertical impact(2G)
Rear wheel braking
Horizontal impact
Top tube (AB)
Down tube (AC)
Seat tube (BC)
Seat stays (BD)
Table.4: Comparison of stresses on members, Static start up
Fig.18. Comparison of stresses on members, Static start up
5.2 Steady state pedaling:
Top tube (AB)
Down tube (AC)
Seat tube (BC)
Seat stays (BD)
Chain stays(CD)
Steady state pedaling (Analytical ) 3.071 3.92 3.77 5.98 3.23
Steady state pedaling FEA 4.2437 4.8885 3.28 5.23 4.1117
% difference 26.88 % 19.01 % 12.99 % 12.54 % 18.73 %
Table.5: Comparison of stresses on members, Steady state pedaling
Fig.19.Comparison of stresses on members, Steady state pedaling
5.3 Vertical Impact:
Top tube (AB)
Down tube (AC)
Seat tube (BC)
Seat stays (BD)
Chain stays(CD)
Vertical impact (Analytical) 5.77 6.11 5.87 6.2 5.02
Vertical impact FEA 6.709 7.4814 4.3482 6.1904 7.9029
% difference 13.88 % 17.24 % 12.74 % 1.61 % 34.17 %
Table.6: Comparison of stresses on members, Vertical impact 0
2 4 6
Top tube (AB)Down tube (AC)Seat tube (BC)Seat stays (BD)Chain stays(CD)
St
re
ss
Static Start Up
Analytical
FEA
0 5 10
Top tube (AB)
Down tube (AC)
Seat tube (BC)
Seat stays (BD)
Chain stays(CD)
St
re
ss
Steady state padeling
Analytical
Fig.20.Comparison of stresses on members, Vertical impact
5.4 Rear wheel braking:
Top tube (AB)
Down tube (AC)
Seat tube (BC)
Seat stays (BD)
Chain stays(CD)
Rear wheel braking (Analytical) 0 0 0 7.26 5.864
Rear wheel braking FEA 0 0 0 9.512 6.4698
% difference 0 % 0 % 0 % 23.57 % 9.28 %
Table.7: Comparison of stresses on members, Rear wheel braking
Fig 21.Comparison of stresses on members, Rear wheel braking
5.5 Horizontal Impact:
Top tube (AB)
Down tube (AC)
Seat tube (BC)
Seat stays (BD)
Chain stays(CD)
Horizontal impact (Analytical) 21.63 24.85 0 0 0
Horizontal impact FEA 23.942 20.039 0 0 0
% difference 9.64 % 19.39 % 0 % 0 % 0 %
Table.8: Comparison of stresses on members, Horizontal impact
Fig.22.Comparison of stresses on members, Horizontal impact
6. DISCUSSION AND CONCLUSIONS
The discussion and conclusion on the results is as follows:
Static start up: In this analysis the stresses in the top tube, down tube, seat tube, chain stay and seat stay are
varying from 2.91 to 4.10 N/mm2, which is nearly equal in all tubes calculated by analytical and by FEA.
Steady state pedaling: In this analysis the stresses in the top tube, down tube, seat tube, chain stay and seat stay
are varying from 1.28 to 5.98 N/mm2, which is nearly equal in all tubes calculated by analytical and FEA.
Top tube (AB)Down tube (AC)Seat tube (BC)Seat stays (BD)Chain stays(CD)
0 5 10
Top tube (AB) Down tube
(AC)
Seat tube (BC) Seat stays
(BD)
Chain stays(CD)
St
re
ss
Rear wheel bracking
Analytical
FEA
0 20 40
Top tube (AB) Down tube (AC) Seat tube (BC) Seat stays (BD) Chain stays(CD)
Str
ess
Horizontal Impact
In the truss analysis, the assumption was made that all of the frame components were two-force members and that these members were attached at hinge joints that cannot apply any moments. The assumption was held that the material being dealt with was linear elastic and isotropic. Looking at the FEA results, it is observed that the stress distribution was not truly uniform across the cross section of the tube. This invalidates our truss analysis since two-force members can only have uniform stress across the cross section of the component.
The good agreement is found between analytical and FEA results. Results of all case reveals that the maximum stresses in the member of bicycle frame in top tube is 23.94 MPa which is less than yield strength in tension i.e.(Syt = 290 MPa) for the material selected.
7.REFERENCES:
[1] AMOS, A.R., A preliminary investigation into cycle frame design 1977, BSc project report, Department of Engineering, UMIST. [2] ADEYEFA. B. A., 1978 Determination of load and deflections and stresses in bicycle frames, 1978, Msc Dissertation, UMIST. [3] KEISHA A PETERSON & KELLY J. LONDRY, A New Tool for bicycle Frame Design” by “Finite Element Structural Analysis” [4] P.D.SODEN and M.A.MILLRV, Department of Mechanical Engineering, UMIST “Stresses and deflections in bicycle frames”,
Journal of strain analysis, Vol. 21, No.4, Pg. 185-195. [5] PIEPHO BLAKE, Bicycle frame structure evaluation, 2009. [6] RAJPUT, R.K. Strength of Materials, (3rd
edition), 2003 (S.CHAND). [7] SHIGLEY, J .E. Mechanical engineering design, (3rd
edition),1977 (McGraw-hill).
