Mechanical Design Thesis
2020-03-16
A STUDY ON INFLUENCE OF
MATERIAL AND CROSS SECTION VARIATION ON HELICAL
COMPRESSION SPRING (DUMP TRUCK, MODEL - ZZ3257N3647C)
KASSA, ESHETU
http://hdl.handle.net/123456789/10423
Downloaded from DSpace Repository, DSpace Institution's institutional repository
BAHIR DAR UNIVERSITY
BAHIR DAR INSTITUTE OF TECHNOLOGY
FACULTY OF MECHANICAL AND INDUSTRIAL ENGINEERING SCHOOL OF RESEARCH AND GRADUATE STUDIES
(MSC. PROGRAM)
A STUDY ON INFLUENCE OF MATERIAL AND CROSS SECTION VARIATION ON HELICAL COMPRESSION SPRING
(DUMP TRUCK, MODEL - ZZ3257N3647C) BY: ESHETU KASSA REDA
PROGRAM: - MSc IN MECHANICAL DESIGN ENGINEERING MAIN ADVISOR: DR. RAMESHBABU SUBRAMANIAN
APRIL, 2019
BAHIR DAR, ETHIOPIA
i A STUDY ON INFLUENCE OF MATERIAL AND CROSS SECTION VARIATION
ON HELICAL COMPRESSION SPRING (DUMP TRUCK, MODEL - ZZ3257N3647C)
By
ESHETU KASSA
A Study on Influence of Material and Cross Section Variation on Helical Compression Spring Submitted to The School of Research and Graduate Studies of Bahir Dar Institute of Technology, BDU in Partial Fulfillment of The Requirements for The Degree of Master’s Science in Mechanical Design in The Faculty of Mechanical and Industrial Engineering.
Advisor Name: Dr. Rameshbabu Subramanian
Bahirdar, Ethiopia May 16, 2019
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© 2018 ESHETU KASSA ALL RIGHTS RESERVED
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Acknowledgment
I express my deep sense of gratitude with sincere acknowledgment to my supervisor, Dr.
Rameshbabu Subrmanian for his invaluable guidance and encouragement throughout this research, and the author wishes to express his gratitude to prof. Rao department of mechanical design for his support, guidance, and patience. The author also wishes to thanks Mohamed dump truck spare-part Sale center for providing information regarding geometries of automotive coil spring.
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ABSTRACT
In this study, the dump truck helical compression spring would be analyzed with different spring materials (namely, chromium vanadium (ASTM A 231), hard drawn (ASTM A 227) and stainless steel (17-7 PH A 313) and cross sections (namely, circular, elliptical, square and rectangular) respectively. It aims to investigate the effects of material as well as the cross section on its mechanical strength specifically stress and stiffness of the spring. The classical theory and finite element simulation result show that, from comparisons of spring materials and cross-sections, chromium vanadium has high stiffness and elliptical cross-section has small in stress compared with a common one.
This study also shows the maximum shear stress distribution and its location as a function of spring index and aspect ratio on an elliptical cross-section which enables to obtaining maximum shear stress theoretically based on the theory of elasticity.
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TABLE OF CONTENT
Contents Page
DECLARATION ... Error! Bookmark not defined.
Acknowledgement ... v
ABSTRACT ... vi
TABLE OF CONTENT ... vii
LIST OF ABBREVIATION ... x
LIST OF SYMBOLE ... xi
LIST OF FIGURES ... xiii
LIST OF TABLES ... xv
1. INTRODUCTION ... 1
1.1 Background ... 1
1.2 Statement of the problem ... 4
1.3 The objective of the study ... 4
1.4 The significance of the Study... 5
2 LITERATURE REVIEW ... 6
2.1 A literature review based on static and fatigue stress analysis ... 6
2.2 A literature review based on optimization ... 9
2.2.1 Static optimization by material substitution ... 9
2.2.2 Optimization based on Geometric Reduction ... 11
3 METHODOLOGY ... 13
3.1 Physical Modeling ... 14
viii
3.1.1 Applied Loads ... 15
3.2 Stress Analysis ... 17
3.2.1 Elastic Stress Analysis of The Spring Through Classical Theory ... 18
3.2.2 Deflection Analysis of Helical Coil Spring ... 21
3.2.3 Critical Frequency of Helical Spring ... 22
3.3 Finite element model ... 23
3.3.1 Static Analysis Through Finite Element Method... 23
3.3.2 Meshing... 23
3.3.3 Boundary Condition ... 23
3.3 Fatigue analysis ... 24
3.3.1 Material fatigue strength ... 24
3.3.2 Fatigue Criteria ... 27
3.3.3 Fatigue failure Analysis ... 30
3.4 Replacement of Existing Spring by Substitution of Material and cross section ... 31
3.4.1 Evaluating Alternatives ... 31
3.4.2 Determination of weighting factor ... 32
3.4.3 Basic Selection Criteria of Spring Materials ... 32
3.5 Analytical Evaluation of The Existing Spring Replaced by Cross Section . 34 4 RESULT AND DISSCATION ... 44
4.1 Maximum shear stress and von-mises stress results of the existing spring through theoretical calculation ... 44
4.2 Stiffness and Deflection results of the existing spring through theoretical calculation ... 45
4.3 Results of stress and deflection analysis through finite element method .... 45
4.4 Stress and Deformation Analysis of Different Spring Materials. ... 47
4.5 Fatigue Life Prediction ... 50
4.6 Stress and Deformation Analysis of Different Cross-Sections of spring. .... 53
ix
4.6.1 Stress and Deflection Analysis Through Classical Theory... 53
4.6.2 Stress and deflection Analysis Through Finite Element Method ... 53
5 CONCLUSION AND RECOMMENDATION ... 58
REFERENCE ... 60
APPENDIX ... 63
Appendix A1 Table: - Tensile strength of spring material depends on wire diameter, material and processing... 63
Appendix A2 Table: - density, modulus of elasticity and modulus of rigidity of different spring materials ... 64
Appendix A3 Table: - chemical composition of spring materials ... 65
x
LIST OF ABBREVIATION
FEA Finite element analysis FEM Finite element method
FRP Fiber reinforced plastic composite material SEM Scanning electron microscope
TEM transmission electron microscope
xi
LIST OF SYMBOLE
D Mean coil diameter d wire diameter p pitch
n number of coils Na number of active coils α helix angle
WG Gross weight FD distributional force P axial load
g Gravitational force Sut ultimate tensile strength Sy yield strength of the material A cross-section area
r radius of the wire J polar moment of inertia.
Ks shear stress augmentation factor C spring index
δ deflection τ shear stress σ* von-mises stress σ m mean stress σ a alternative stress
normal stress n
K stiffness
Se fatigue strength Se *
endurance limit
KL load modification factor KS surface condition process Kg gradient coefficient
xii Wi weighting factor
mi total number of positive decisions for the ith criteria T twisting moment
G modulus of rigidity r aspect ratio
xiii
LIST OF FIGURES
Content Pag
Figure 3.1 Working methodology flow chart ... 13
Figure 3.2 Three-dimensional drawing of compression spring ... 14
Figure 3.3 (a) Cylindrical spring subjected to an axial load P, (b) The diagram of sectioned spring. ... 19
Figure 3.4 Shear stress distribution. ... 20
Figure 3.5 (a) Fixed support and load direction (b) Spring model with mesh ... 24
Figure 3.6 Selection of points to measure the stress components by FEM ... 30
Figure 3. 7 Schematic diagrams of the cylindrical helical spring with a rectangular cross- section. ... 35
Figure 3. 8 Schematic diagrams of the cylindrical helical spring with a square cross- section. ... 36
Figure 3.9 (a) Axially loaded of elliptical spring. (b) Stress components of the elliptical cross section of spring. source: Design formulae for elliptical cross-section helical springs [27]. ... 37
Figure 3. 10 Arbitrary points of the cross-section. ... 41
Figure 3.11 Comparison between second, first and zero order approximation of equivalent shear stress distribution [26] ... 42
Figure 3. 12 Comparison of the maximum resultant shear stress given by the first and the second order approximation. ... 43
Figure 4.1 Total and directional deformation (a, b) and maximum shear stress distribution and von-mises stress distribution (c, d) respectively under astatic loading condition. ... 46
Figure 4. 2 FE simulation results of (a) chrome-vanadium (b) hard drawn (c) stainless steel 17-7 PH materials ... 49
Figure 4. 3 Damage values of spring obtained from the above fatigue criteria ... 50
Figure 4. 4 Illustrates FEA of damage values of different fatigue failure criterion ... 51
Figure 4. 5 Shows the region where the damage values become more, according to the failure criterion... 51
xiv Figure 4. 6 S-N Value for Different Cycle ... 52 Figure 4. 7 Comparison of stress distribution between different cross-sections of helical springs with the same cross-section area. ... 53 Figure 4.8 Shows FEA of an elliptical cross-section with chromium silicon spring material ... 54 Figure 4. 9 FEA of square cross-section with chromium silicon material... 55 Figure 4.10 Illustrates the FEA of rectangular cross-section with chromium silicon spring under static loading condition. ... 56 Figure 4.11 FEA of an elliptical cross-section with chromium vanadium spring steel .... 57
xv
LIST OF TABLES
Content Page
Table 1. 1 Mechanical property of chrome silicon ASTM (55SiCr6) spring ... 2
Table 3.1 Shows the specification of a helical compression spring for a dump truck suspension system ... 15
Table 3.2 Shows the specification of a dump truck ... 16
Table 3.3 Material Properties of the Existing Chrome Silicon (55sicr6) (ASTM) Spring ... 17
Table 3.4 Material Properties of Chrome chromium vanadium Spring steel ... 27
Table 3.5 Stress component in the spring system ... 28
Table 3.6 Stress components of the coil at the fully compressed condition ... 31
Table 3.7 Values of the degree of importance and weighting factor calculation ... 33
Table 3.8 Selection of materials based on the given criteria ... 34
Table 4. 1 Material Properties of the Existing Chrome Silicon (55sicr6) (ASTM) Spring ... 44
Table 4. 2 Maximum and minimum shear stress results for chrome silicon steel spring . 44 Table 4. 3 Von- mises results for chrome silicon steel spring ... 44
Table 4. 4 Classical theory results for chrome silicon steel spring ... 45
Table 4. 5 Classical analysis results for chrome silicon steel spring ... 45
Table 4.6 Results of maximum shear stress, von-mises stress and deflection of spring through FEA... 47
Table 4.7 Comparison of stress and deflection through theoretical calculation and FEA of springs with the same material and geometrical dimension. ... 47
Table 4.8 Stress and stiffness results of selected materials and its comparison through FEA and theoretical calculation. ... 48
Table 4. 9 S-N Value (stress) for Different Cycle ... 52
Table 4.10 Comparison of stress and deflection through FEA of different cross-sectional springs with the same material and cross-sectional area ... 56
xvi Table 4.11 Comparison of stress and deflection through theoretical calculation and FEA of the suitable cross-section with suitable material of present spring analysis and existing springs with the same cross-sectional area. ... 57
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Page 1
1. INTRODUCTION
1.1 BackgroundHelical coil spring for the automobile suspension system
Spring is a component which is an indispensable one for several industrial applications like balances, brakes, vehicle suspensions, and engine valves to satisfy functions like applying forces, storing or absorbing energy, providing the mechanical system with the flexibility and maintaining a force or a pressure. Particularly, the suspension system plays an important role for a comfortable ride for passengers besides protecting the parts from getting damaged due to road shocks. If in a vehicle both front and rear axles are rigidly fixed to the frame, while vehicle is moving on the road, the wheels will be pushed up and down due to the irregularities of road, as such there will be much strain on the component also leads to poor comfortability for the journey of the passengers in the vehicle.
Among several springs, helical spring used to connect the wheel to the body elastically and store the energy to absorb vibrations and smooth out shocks that are received by the wheel from road irregularities to protect structures from damages.
According to the different ways of loading applied, helical springs can be divided into three kinds: compression springs, tension springs, and torsion springs, and they are mainly with a different cross-section. This thesis is focused on the study of stress analysis in helical compression springs, which made of steels. The maximum stress and deflection are majorly affected by the material properties, geometry, manufacturing process, and operating temperatures.
YouliZhu et.al [1] reported about the spring in dynamic service loading condition, by Visual and scanning electron microscopy (SEM) tools that the surface painting becomes peel out and worn out of the phosphate layer due to the closed ends design. corrosion together with stress singularities at the contact zone of the closed ends that resulted in fatigue crack initiation of the suspension spring. Once the initial crack was formed, it leads to maximum principal tensile stress that forced the crack to propagate along the
Page 2 direction of 450 with the spring wire axis. Raw materials defects, surface imperfections, improper heat treatment, corrosion, surface conditions and decarburization [2] act as stress raiser and lead to failure of spring. Raw material selection for spring manufacturing is the first step where a designer must look for the presence of raw material defects as they play an important role in fatigue failure of spring.
Spring materials
To be effective, a shock absorption material must have the capacity to eliminate or reduce oscillations across a wide range of frequencies. To be effective in an industrial environment, a shock absorption material must perform well in a wide range of temperatures, even changing temperatures, regardless of the source of the shock, over an extended period of time [22]
The most common spring materials are high carbon spring steel, alloy steel wire, stainless steel, and non-ferrous alloy; among those, the previous dump truck company uses Chrome silicon ASTM (55SiCr6) spring materials.
Table 1. 1 Mechanical property of chrome silicon ASTM (55SiCr6) spring Material Ultimate
tensile strength (Mpa)
Tensile yield strength (Mpa)
Density (kg/m3)
Modulus of Elasticity (E) (Gpa)
Modulus of Rigidity (G) (Gpa)
Chrome silicon ASTM
(55SiCr6)
1444.7 1083.5 7850 206 75.8
During static and dynamic loading in service, the plastic deformation was existing on the suspension spring. So, in the spring design consideration, the spring steel has high performance on fatigue strength and sagging resistance. thus, improvement has been achieved by changing the heat treatment process, changing grain size and changing the chemical composition of the spring steel. according to [3] the addition of vanadium V on the spring steel increases the resistance of plastic deformation (sagging) and hardness of the coil through the tempering process which converts carbide to cementite phases.
Hence, the material properties of spring steel at dynamic operation condition leads to
Page 3 fatigue failure of the coil. In order to avoid the earlier failure, it is mandatory to find out the best materials to resist corrosions, high impact load, working temperature, and elasticity. Based on the mechanical properties, the spring materials that could be used for the modified spring to get a good service life are discussed in section (4.4).
Page 4 1.2 Statement of the problem
Due to the road irregularities, Dump truck helical compression springs are subjected to abnormal impact loads. In this case, the stress is uneven and fatigue failure occurs which leads to damages of vehicle structure and uneasiness to the passengers. Majorly the stress in helical compression spring is influenced by the material type and the cross- section of the spring. So, it needs to analyze the stresses and fatigue life of the spring by cross-section and material substitution to have a better service life.
1.3 The objective of the study Main objective
The main objective of this thesis is to study and analyze the stresses influenced by cross-section and material type of the helical compression spring for the dump truck by using classical theory and finite element method (Simulation).
Specific objectives
The specific objectives of the thesis including that;
1. To determine the Von Misses stresses, Shear stresses, Normal stress, Total Deformation and Fatigue Analysis of the coil spring by classical theory and FEM.
2. To calculate the stresses in critical areas and to identify the risk point in coil spring where there are more chances of failure.
3. To evaluate the stress and stiffness of different materials and different cross sections for helical coil spring with designed cross-sectional area.
4. To compare the stresses for the existing and the modified spring and to validate the results obtained from classical theory by FEM simulation.
Page 5 1.4 The significance of the Study
The significance of the study
1. The analysis of material substitution and cross-section variation in the helical compression spring provides knowledge on varying materials and cross-section for the selection of the spring design and the material for a particular vehicular design.
2. It also provides knowledge of the spring behavior for various loading conditions under different cross sections and material types.
Page 6
2 LITERATURE REVIEW
This thesis focuses on a dump truck helical compression spring, which is designed to withstand the shocks elastically. For this absorption of energy, the fatigue failure of the spring occurred is analyzed by approaching in different ways by several types of research in the past decades have been made through classical theories, simulation of software and Experimental tests. A few studies which are pertinent to this work, in specific different of modes of failures and its predictions are discussed herein two categories.
2.1 A literature review based on static and fatigue stress analysis
Won Gong et.al. [3] analyzed the effects of Molybdenum (Mo), Tungsten (W) and Vanadium (V) addition and tempering temperature on the sag resistance of Si-Cr spring steel. The experimental result shows that the sag resistance is influenced by tempering temperature; it increases and decreases after reaching its maximum value at 3500c. he found that the addition of Mo and W do not affect the behavior of carbides at low temperature, but the sag resistance increases at the temperature above 4000c. V addition improves sag resistance as well as hardness due to the precipitation of vanadium carbon- nitrides, regardless of tempering temperature.
K.Michalczyk (2013) calculates the influence of elastomeric layer on stresses as a function of coating parameters in longitudinal resonance vibration conditions [4]. After computed the stress, within and without a coating of spring wire by classical theory and finite element simulation, it has been concluded that a rubber coating material is not good material for coating purpose. It has an impact on the reduction of dynamic stresses in the spring and contributes to lowering of the elastic module and its resonant frequencies. The rubber coating affected also, on increases of mass without any significant increase of a modulus of rigidity.
Youli Zhu et. al. [5] focused on, the failure analysis that why a heavy vehicle suspension springs are mostly fractured at the region of the active coil ends. In order to estimate this problem, the researcher was followed by visual observation, scanning electron microscopy and finite element technique. It has been observed that at the first
Page 7 active coil wear scar is present due to friction and it contacts with the bearing coil under the cyclic axial loading condition.
Also, it was mentioned that, the design of coil spring which is of closed-end type, which collects the fluids. After sometimes corrosion pits are formed and it acts as a stress riser. At service condition, this stress riser leads to the initiation and propagation of cracks. FEA shows that once the crack is initiated, maximum principal stress was formed at a 450 to the wire axis and it forces to the propagation of crack and failures.
After the examination of this fatigue failure, they strongly recommended using soil lubrication, to adopt the spring design is a non-closed type, to avoid local hardening and enhance the corrosion and wear of the coil in the vehicle suspension system.
B. Pyttel. [6] Evaluates on an experimental investigation of the influence of shot pining process on the helical compression helical spring at a long-term fatigue behavior.
For experimental work, three materials were selected, which are tempering and oil hardened. They are (Silicon-chromium, silicon chromium-vanadium, and stainless steel).
This experimental study is concerned a various number of springs with different geometrical dimensions is tested at different stress level. The spring is tested before and after the shot pinning process. The result shows that, N= 109 before shot pinning and N=1.5*109 after shot pinning process. Finally, the shot pinning process can improve the fatigue strength of the spring where the springs are made from silicon chromium and silicon chromium vanadium.
Design and failure modes of automotive suspension spring are presented by Y.
Prawoto et.al. [7] pointed out the stress distribution, material characterization and common failure characteristics of helical coil spring in automotive suspension systems.
Specifically, this work is a comparison of the material properties and stress concentration within and without defects. By using x-ray deferred spectroscopy and scanning electron microscopy the surfaces become fracture due to raw material selection (non-metallic inclusion in the spring material), surface imperfection (poor shot pining process, quenching crack), heat treatment (variation of microstructure) and corrosions. After detecting the influencing parameter, FEA also performed to evaluate the local stress within and without defects. The analysis shows that the stress concentration on the local
Page 8 region was observed in the inclusion, corrosion, surface imperfection and decarburization of each model. Finally, the FEA result shows that the stress concentration is large on the defect and causes to the early failure of the coil spring.
L. Del Llano-Vizcaya. et. al [8] presents the failure analysis of AISI MB steel compression spring at fixed mean stress by using multi-axial fatigue criterion and the results are validated by experimental fatigue test. Not only this but also multi-axial fatigue and stress are analyzed by finite element software. From the fatigue failure criteria which uses to evaluate fatigue crack initiation and allocate the most damage zone, Fatemi–Socie critical plane approach gives a good prediction of fatigue life. While the Wang–Brown criterion shows overestimate of fatigue life, and Coffin– Mason criterion gives more conservative results. They also notice that the Universal slopes Mason method to estimate strain-life properties from the monotonic uniaxial tension test gives a better method.
Y.S. Kong et.al. (2017) [9] contributes to the fatigue life of coil spring in three different road missions in Malaysia. These three mission profiling roads are highway, rural and campus roads in Germany. The acceleration signal was collected and analyzed by the shock response spectrum (SRS) and extreme response spectrum (ERS) by time domain and frequency domain analysis respectively. The vibration of the road signal was collected through experimental vehicle testing by using accelerometer and strain-gauge.
The strain gauge was connected to the coil spring and the data accusation connected to a laptop to get real-time data monitoring. shock response spectrum (SRS) and extreme response spectrum (ERS) used to analysis fatigue damages of the coil spring from time- domain and frequency-domain acceleration signals respectively. They found that the campus and rural roads exhibited more response which compared to that of the high way road.
This result demonstrates that less vibrational signals are occurred in the coil spring for high way road profiles due to, the surface roughness and surface conditions. the responses of campus and rural road were higher than that of the high way road profiles.
Generally, the maximum fatigue damage was exhibited for 60 high way road repetitions and 40 rural road repetitions of the vehicle coil spring. Finally, the result shows that the
Page 9 PSD (power spectrum density) fatigue life prediction was more realistic than a single measurement of road load spectrum.
R Bartolozzi and F Frendo* [10] evaluated the Stiffness and strength aspects in the design of automotive coil springs for McPherson front suspensions. The stress analysis and elastic behavior of the suspension spring are analyzed and the result is done by finite element simulation and experimental test. They used to FE simulation for determining elastic stress and X-ray diffraction (XRD) for measuring the residual stress of the spring in different positions. Based on residual stress and elastic stress results, the fatigue strength of the spring is studied theoretically. The result shows that the finite element simulation and analytical analysis of spring stiffness have differences by 2.2 percentage errors. Due to the geometry of spring, orientation, and shape of the seats, the amount of side load is 20 percent times of the axial loads. Therefore, the actual stress developed in the spring is obtained by adding those residual stress and elastic stress contribution. In the stress comparison of finite element and analytical model of sideloaded spring, the error becomes about to arrange of 16 to 26 percent, this error is due to the orientation and location of spring in the analytical determination.
2.2 A literature review based on optimization 2.2.1 Static optimization by material substitution
An experimental investigation into the mechanical behaviors of helical composite springs by Chang-Hsuan Chiu et.al was analyzed [11]. The paper is focused on four different structure of composite spring (unidirectional laminates (AU), rubber core unidirectional laminates (UR), unidirectional laminates with a braided outer layer (BU), and rubber core unidirectional laminates with a braided outer layer (BUR), respectively.
with experimental study. The main goal is to show the effects of the braided outer layer and rubber core on the mechanical properties of unidirectional laminated composite springs.
The result shows, the use of rubber material as a core can increase the failure load by 12% in compression, decreases the prepreg amounts also, and lowers the cost of fibers.
Similarly, the braided outer layer improves the spring constant and increases failure load
Page 10 by 16% and 18% respectively. Finally, the investigation deduces that among the four composite spring a rubber core unidirectional laminated with a braided outer layer have higher mechanical properties. However, it is still limited to lightweight vehicles.
D. Abdul Budan et.al. [12] presents the optimization of steel coil spring by composite materials. The investigation follows an experimental study and testes for its mechanical properties compared with the traditional metal springs. This experimental test is concerned three different composite materials which are Carbone fiber, glass fiber, and high bird. The aims of this study were to reduce the weight of the spring and simultaneously improves the fuel consumption of the automobile. After preparation of the composite spring, it has the same dimension to the steel spring, the experiment has been done. So, the result shows that Carbone fiber has a higher stiffness than the two composites, but it has less stiffness compared with the steel one. Generally, the composite coil spring is limited to lightweight vehicles which require less stiffness (like high bird vehicle and electric vehicles).
D. Ramajogi Naidu (2016) studied on the analysis of coil spring for two and three wheelers by using FEM and classical theory. The coil spring is modeled and analyzed under different loading conditions [13] i.e self-weight of the vehicle, self-weight with one person and self-weight with two persons for two wheelers and three wheelers. This varying load is employed on two spring materials of spring steel and structural steel.
After the analysis, maximum von-mises stress, Maximum strain, and total deformation are obtained from finite element simulation and numerical analysis. The comparison is made and the result shows that the spring steel material has less deformation and less stress concentration, which is best suitable for the production of helical spring.
Vijayeshwar BV [14] focused on the comparative study and analysis of suspension helical coil spring with two different materials (chromium silicon and hard drawn carbon steel) static analysis using FEA to determine the optimum material to reduce the stress and deflection. The Autor provided that through analytical and FEA, chrome silicon spring steel has less shear stress and minimum deflection as compared to hard drawn carbon steel.
Page 11 2.2.2 Optimization based on Geometric Reduction
Byoung-Ho Choi et al (2015) [15] studied, to investigate the minimum wire diameters of carbon fiber/epoxy composite coil springs that have an equal spring rate to the steel wire which have a 10mm diameter. By taking the material properties, the two springs can possible to determine the shear module, after that by equating the shear module ratio to spring rate it can calculate the Carbone spring rates to possess the given applied load. From experimental result the shear modulus for a composite with a 450 ply- angle was a good agreement, to get the suggested mass reduction based on FEA, with an optimized ply angle of 450. But, the wirediameter of a composite coil spring is 17.5mm, and the weight of the spring is reduced by 55%compared with the steel spring.
Dhareshwar S Patil et.al (2016) [16] pointed out on weight optimization of the spring which has a circular helical cross-section with classical theory and validated by finite element simulated software and experimental works. The weight reduction is performed by considering the stress developed on the optimal spring is within the permissible limits.
This optimization technique is compromising the solid wire helical spring redesigning with a hollow section. Both springs had to be evaluated by assuming both are made the same material, have same spring index and stiffness and applied the same load.
After analyzing the static structure (deformation and stress) of the spring, the result shows that, which is gained from classical, FEA and experiment, the maximum shear stress induced in hollow spring is little more than that of a solid one. But it is within that permissible limits. Also, the maximum deflection developed in hollow and solid helical spring is approximately equal. Finally, they conclude that the weight of the material is saved by 22.44% by ANSYS as well as analytical and 24.87% measured by digital weighing instrument.
Arkadeep Narayan et al (2017) presents the analysis of prismatic springs of non- circular coil shape (rectangular and triangular spring) and non-prismatic springs of circular coil shape (volute and conical spring) by classical theory and finite element simulations [17]. In this research, the deflection of prismatic and non-prismatic springs under axial loads was discussed and compared with a common prismatic spring with circular coils. And also, the maximum stresses in the different springs have been
Page 12 presented and compared with FE analyses. The result shows that mass equivalent non- circular springs have more maximum von-Mises stress than the circular coil springs. It is also seen that the deflection of the mass equivalent springs is different with the non- circular springs (across varying coil circularities) deflect more on average while, their circular counterparts are more rigid, with the volute spring being the most rigid and conical spring being the least rigid. It is almost always reasonable to choose springs with circular coil shape for a given design scenario, But the motivation was to cater to design requirements where an elastic element is to be accommodated within a non-circular space and where using more than one cylindrical spring would increase the stiffness of the system.
Generally, researchers had to be done in multi-disciplinary ways of spring design failure analysis within a counter of corrosions, additive materials and coating [3-4]
mechanical and chemical treatment [6-8], stress and deflection of non-circular coil shape with circular springs (based on geometry) [17] and structural materials with the spring material [11-14]. However, there is a gap on material substitution (only spring materials) and analysis of the cross-section of a spring in order to minimize the impacts that developed on the spring.
Page 13
3 METHODOLOGY
In this study, physical modeling, classical theory (theoretical calculation), FE modeling and fatigue analysis would be developed based on the design principle. In this section, three stages would be incorporated to achieve the stresses influenced by cross- section and material substitution. The first stages are to identify and gather the specific geometrical data of the dump-truck compression spring and gross weight of the vehicle (used to evaluate the reaction force on the spring). After that, the spring deflection, maximum stress, and fatigue strength can be evaluated by applying classical theory and FE simulation. In the second stage, the classical theory and finite element analysis have to be done to the modified (present) helical spring by substituting the suitable material and cross section by using material selection criterion with the existing dimension as an input parameter. Finally, the result is discussed in section (4) and the materials, as well as cross-section modifications, has been selected. The general methodology of the study is described in Figure 3.1 as follows:
Figure 3.1 Working methodology flow chart
Page 14 3.1 Physical Modeling
Axial-load helical springs are one of the energy absorber elastic member which, connect the wheel to the body elastically and store the energy to absorb vibrations and smooth out shocks that are received by the wheel from road irregularities to protect structures from damages. So, for this work a front dump truck heavy loaded compression spring was considered. To analyze this model, overall geometrical dimensions of the shock absorber is required which was measured manually. With those dimensions, a solid 3D model was developed with the help of the modeling software.
(a
) Shock absorber (b) helical coil springFigure 3.2 Three-dimensional drawing of compression spring
From the inference of the literature, it is found that the major influencing parameter which affects the behavior of performance of helical compression spring is deflection and maximum shear stress. These influences are basically induced by physical and mechanical properties of the material, the material to be used, cross-section, coil diameter (D), wire diameter (d), pitch (p), number of coils (Na) and the helix angle (α). The basic dimensions of a helical coil spring are given below in Table (3.1).
Page 15 Table 3.1 Shows the specification of a helical compression spring for a dump truck suspension system
Parameters Values
Main coil diameter (D) 70 mm
Wire diameter (d) 18 mm
Pitch (p) 28 mm
Pitch at the end 18.5 mm
Total number of the coil (n) 10
Active coil 8
Solid length LS = d * n 180 mm Free Length LF = p x n 310mm Spring index C = D/d 5
End condition The squared and ground end
The process of analysis of the main load of compression spring is a) curb weight (total weights of the vehicle)
b) loading (luggage) weight or bagging weight c) passenger weight
3.1.1 Applied Loads
To analyze the stress, deflection and fatigue life of the spring first to identify the vehicle specification to determine the force acting on the spring. The specification of a dump truck, (model - ZZ3257N3647C) is mentioned in the table (3.2) and the specifications are as follows.
Page 16 Table 3.2 Shows the specification of a dump truck
Parameters values
Length 8145mm
width 2496mm
height 3170mm
Loading weight 7500 kg
Curb weight 2240 kg
No of passenger 2
In order to determine the force acting on the spring first to determine the gross weight of the vehicle applied on the wheel.
Gross weight = curb weight + loading (luggage) weight + passenger weight (1) WG = 2240 kg +7500 kg
WG = 9740 kg
The ratio of distribution of forces from standard [14] is formulated by the relation of the front and rear wheel which is expressed by
60
= 40
= R
FD F (2)
So, the analysis is involved on the front sides of the vehicle spring which, are two in numbers. The weight acting on each front wheel is determined by the ratio of the front reaction force multiplied by the gross weight of the vehicle and divided by two.
expressed as W =(40%WG)/2 W =0.409740kg/2
W = 1948kg
Page 17 Therefore, the force acting on the front wheel
KN P
kg g
W P
109 . 19
81 . 9 1948
=
=
=
3.2 Stress Analysis
Table 3.3 Material Properties of the Existing Chrome Silicon (55sicr6) (ASTM) Spring Material Ultimate tensile
strength(Mpa)
Tensile yield strength (Mpa)
Density (kg/m3)
Modulus of Elasticity (E) Gpa
Modulus of Rigidity G) Gpa
Chrome silicon ASTM
(55SiCr6)
1444.7 1083.5 7850 206 75.8
spring machine parts are relatively highly stressed and it requires the materials have high tensile, yield strength and sagging resistance, which majorly depends on the wire diameter, material type, and manufacturing processes. Therefore, minimum tensile strength can be estimated by the wire diameter shown the relation as follows [22]
ut m d
S = A (3) where intercept A and slope m are known values in the appendix (A1). Therefore, the estimating minimum tensile and yield strength of the existing spring wire is
0.108 18
.
1974 m
ut
mm
S = Mpa = 1444.7 Mpa
Based on distortion energy theory the torsional yield strength (Sys =0.577 Sy) can be obtained by assuming the tensile yield strength is between 60 to 90 percent of tensile strength.
Sy =0.75 (Sut) (4) Sy = 1083.53Mpa
So, yield strength in shear Sys = 0.577 (0.75Sut) = 0.45Sut. This theory is validated for hard drawn materials and music wire spring steels which, have low-end range. On the other hand, the yield strength in shear Sys = 0.5Sut for Cr-V, Cr- Si valve springs [22].
Page 18 3.2.1 Elastic Stress Analysis of The Spring Through Classical Theory
Elastic stress analysis is the fundamental objective of designing helical springs.
Springs are designed to perform at a high level of stress, this stress produced by the axial load. In this section to analyze the yield criteria of the spring, a particular theory for ductile materials which are maximum distortion energy theory (von-mises theory) and maximum shear stress (Tresca theory) are employed.
To estimate Von Mises and maximum shear stress in the spring system two stress tensors are required to determine the stress components. To get this, let’s assume that the cylindrical spring subjected to a vertical axial load P, as shown in figure 3.4 (a), and consider that, at some region, the spring is cut as shown in figure 3.4 (b). For equilibrium condition, the internal forces are produced to maintain that of the remaining parts of the sectioned spring. Which means at this section direct share stress (τ) and torque (T) appears. Then the maximum shear stress induced on the spring wire can be determined by the following generic equation as follows.
A P Tr +J
max =
(5) Where A is the cross-section area, r is the radius of wire and J is the polar moment of inertia.
Page 19 (a) (b)
Figure 3.3 (a) Cylindrical spring subjected to an axial load P, (b) The diagram of sectioned spring.
The above equation Eq. (5) expresses the contribution of the torsion and direct shear stress on the spring. By considering the cross-section of the spring wire is circular, the equation simplified to
2 3
4 8
d P d
PD
= + = 8 3
d KS PD
= 8 3 d PD
( )
C 5 .
1 + 0 (6)
Ks 0C.5
=1 + , d C = D
Where Ks are shear stress augmentation factor and C is the spring index.
The helix shape or curvature of the wire decreases the induced stresses in the outside and increases the stress on the inside springs due to the contact area of the cross-section.
The shear stress in equation (6) is uncorrected shear stresses. Therefore, the uncorrected shear stresses are opposed by Wahl [23], and proposed the shear stress correction factor KW, and multiply equation (6). this corrected shear stress considers many factors in the stress distribution
Page 20 The shear stress augmentation factor together with curvature (helix) effect depending on the spring index C and can be defined by equation (7) and expressed in [Ref 7]. the corrected and uncorrected shear stress as shown in Figure (3.4) is.
C C
KW C 0.651 4
4 1
4 +
−
= − (7)
(a) uncorrected (b) corrected Figure 3.4 Shear stress distribution.
The maximum shear stress induced in the spring including the various effects can be written as
+
−
= −
C C
C d
PD 0.651 4
4 1 4 8
max 3
(8)
And the minimum shear stresses are
−
−
= −
C C
C d
PD 0.651 4
4 1 4 8
min 3
(9) Eq. (8) and (9) are usually used for designs neglecting the curvature effects, finally
3
8 d KW PD
= (10) After generating the equation of maximum shear stress, the von Mises stress could be determined as follows. The von Mises stress would be estimated by considering the two non-zero stress components due to the applied load on the cross section are x &xz . hence,
Von-mises stress, • = ((x)2 +3xz2) (11)
Page 21 KW
• =
min
max, ((x)2 +3xz2) = ((x)2 +3xz2)
−
−
C C
C 0.651 4
4 1
4 (12)
Where normal stress and normal shear can express the formula
4 2 8 3
d and PD
d P
xz
x
= = (13) 3.2.2 Deflection Analysis of Helical Coil Spring
A helical coil spring considered as a circular elastic beam element that is constrained at one end and subjected to the twisting moment at the other end. Then, the helix angle α is given by the relation
GJ L Mt
= (14) Where Mt is the twisting moment, L length of the spring, J is the polar moment of inertia and G is the modulus of rigidity of the material.
Consider a helical coil spring subjected to an axial compression load P, the spring has a mean coil diameter D, coil wire diameter d, the radius of the mean coil R and the number of coils n then, the twisting moment, length and polar moment of inertia of the spring can be expressed as
Mt = PR L=2nR and
32 d4
J =
(15) By substituting Eq. (15) in to Eq. (14), the helix angle α can be formulated by the given equation as follows.
Gd P nR
4
64 2
= (16) From the above equation (eq.16), the spring deflection (δ) can be determined by the product of the helix angle and spring radius of the spring that is δ= α×R.
Then, the spring deflection under axial compression load can be expressed as
Gd P nD
4
8 3
= (17)
And the stiffness or spring rate of the spring can be evaluated by the following equation
Page 22
K = P = 3
4
8nD
Gd (18) According to the mathematical formulation, the results of stress and stiffness of the springs are discussed in section (4)
3.2.3 Critical Frequency of Helical Spring
Spring surge occurs, when one end of a helical spring is resting on a rigid support and the other end is loaded suddenly, then all the coils of the spring will not suddenly deflect equally. If the applied load is of fluctuating type and the time interval between the load applications is equal to the time required for the wave to travel from one end to the other end, then resonance will occur. This resonance leads to very large deflections of the coils and correspondingly very high stresses, in this case, the spring may a fail.Therefore, the surge should be estimated or the natural frequency for springs clamped between two plates is estimated by
𝑓
𝑛=
12
√
𝑘𝑔𝑊
(19)
But Wolford and Smith proved that the spring ends are always in contact with the plates, then the critical frequency of the spring
𝑓
𝑛=
14
√
𝑘𝑔𝑊
(20)
The weight of the active part of a helical spring is 𝑊 = 𝐴𝐿γ =𝜋𝑑2
4 (
𝜋𝐷𝑁𝑎) (𝛾) =
𝜋2𝑑2𝐷𝑁𝑎 𝛾4
where γ is the specific weight. The fundamental critical frequency should be greater than 15 to 20 times the frequency of the force or motion of the spring in order to avoid resonance with the harmonics. It has been found that the natural frequency of spring should be at least twenty times the frequency of application of a periodic load in order to avoid resonance, otherwise the spring may have to be redesigned.
On the other hand, the spring manufacturer follows, the may be eliminated the surge in springs by using the [22]:
Page 23
• Friction dampers on the Center coil so that the wave propagation dies out.
• Springs have a high natural frequency.
• Springs having a pitch of the coils near the ends different than at the center to have different natural frequencies.
3.3 Finite element model
3.3.1 Static Analysis Through Finite Element Method
The suitable methods of, for evaluation, simplification and identification of errors caused by the classical method is a finite element analysis. So, the FEA CAD model of the existing components of suspension systems is developed by solid work 15 modeling software as shown in Figure (3.7a) with the geometric dimension mentioned in Table (3.1). The spring material (Chrome silicon ASTM (55SiCr6)) with its material composition and their relevant mechanical properties are clearly expressed in Table (4.1) and those properties are loaded in the ANSYS workbench working areas. Then, the IGES file format model saved in solid work is imported to ANSYS 15 for obtaining the spring deflection or axial displacement and maximum von miss stress under a uniform axial loading condition.
3.3.2 Meshing
The helical coil spring finite element was generated by using parabolic elements with a global element length 15 mm, which considering the minimum surface lengths. It is a well-known fact that tetrahedral is constant stress elements and usage of this would result in a highly stiff behavior. Hexahedrons are better suited for structural analyses. But because of the shape complexity, it is tedious and time-consuming to build an FE model of the coil spring with hexahedrons [28]. Hence tetrahedral were used. This resulted in 60,840 nodes and 34,018 elements; the meshed coil spring is shown in Figure (3.7b) 3.3.3 Boundary Condition
To perform static analysis in FEM, it has been applying the constraints in the components. Assuming that, the suspension spring is fixed by zero displacements in Z- direction for the bottom face to prevent the spring from moving vertically. Also, the X and Y-direction displacements are fixed by zero for the side of the top for the reason to
Page 24 prevent the spring from twisting moment. Which means that the spring seats at zero in one end and the load is exerted on the direction of spring axis on the other end. Hence, the gross weight of the vehicle is 9740 kg. According to the front to rear force distribution ration of the vehicles, the vertical force applied on the front spring is 19109N.
(a) (b)
Figure 3.5 (a) Fixed support and load direction (b) Spring model with mesh
The total deformation (axial displacement) and the von-mises stress (equivalent stress) were calculated by ANSYS workbench are presented in Figure 4.1(a) within the applied load of 19109 N as shown in section (4.1)
3.3 Fatigue analysis
3.3.1 Material fatigue strength For chromium silicon spring material
The fatigue strength of the material is determined to start from Sut (ultimate strength mentioned in Table (3.4)), then to follow the typical procedure [22]. With 50 % probability of failure, the fatigue limit of the material in fully axial loading, is determined as
Se = KLKSKgSe* (21)
for estimating of Se* (endurance limit) based on ultimate strength using equation as below Se* = 0.5×Sut (for Sut < 1400Mpa)
Page 25 Se* = 700Mpa (for Sut ≥ 1400Mpa) (21a) Where Se*= 700Mpa since, ultimate strength of steel is approximately equal to 1400MPa for a rotary-beam test specimen endurance limit, KL is load modification factor (KL =0.85 depending on loading is axial), KS is a surface condition process (KS =0.6 for cold-drawn surface finishing process), Kg is a gradient coefficient (Kg =0.9) [20], Se = 321.6Mpa.
The high-cycle fatigue domain extends from 103 cycles for steels to the endurance limit life Se, which is about 105 to 107 cycles [20]. Within the reference of 105 load cycles and at a probability of 90% failure, the previously estimated fatigue limit Se was corrected by evaluating the complete curve [21] and by introducing the new probability coefficient. To estimate the previously computed Se, at 105 life cycles, which is 106 conventional life cycles. But when to consider a 90% failure at 0.9Sut the fatigue life is referred to 103. At the introducing of a new probability coefficient, which is 90 % present reliability (Kr =0.897), a final outcome of the material fatigue strength of Se = 535.3Mpa is obtained.
Calculation of factor of safety (n)
=176.5Mpa a
(modified Goodman failure criteria) (21b) n = 1.4
for Sut ≤ 1400Mpa, let f = 0.9
𝑆𝑓= 𝑎𝑁𝑏 (21c) where N is the life-cycles to failure and the constants a and b are defined by the points
103, (Sf)103 and 106, Se with (Sf)103= f Sut. Substituting these two points in Eq.(21c) gives as
(21d) a = 5266.667 Mpa
Where f = 0.9 Sut = 1444.7 Mpa Se* = 321. Mpa
Page 26 (21e) b = - 0.202
If a completely reversed stress is given, setting Sf = a in Eq. (21c), the number a of cycles-to-failure can be expressed as
(21f) By substituting the given value, the fatigue life becomes
N =2.5048109× 107cycles
Fatigue strength at the different life cycle
According to equation (15c) the fatigue strength at N=104 cycles
Sf (N) =5266.667(10000)-0.202 = 816.4MPa N=105 cycles
Sf (N) = 5266.667(100000)-0.202 =512.3MPa N=106 cycles
Sf (N) = 5266.667(1000000)-0.202 = 321.4MPa N=107 cycles
Sf (N) = 5266.667(10000000)-0.202 =201.7MPa
Fatigue strength for chromium vanadium spring material, to create an S-N curve for chromium vanadium, the fatigue strength of chromium-vanadium spring material is a similar procedure to the chromium-silicon with its material properties.
Page 27 Table 3.4 Material Properties of Chrome chromium vanadium Spring steel
Material
Ultimate tensile strength (Mpa)
Tensile yield strength (Mpa)
Density (kg/m3)
Modulus of Elasticity (E) Gpa
Modulus of Rigidity G) Gpa
Chrome vanadium ASTM (A232)
1476.5 1107 7850 203.4 77.2
=167.5Mpa ultimate strength of steel is approximately equal to 1400Mpa since, a
Se*= 700Mpa. based on Eq.21(c) the fatigue strength in different cycles can be evaluated as
a = 5490.8 Mpa b = - 0.206
By substituting the given value to the fatigue life Eq. (21f) becomes N =1.934795× 107cycles
Fatigue strength at different life cycle
According to Eq. (21c) the fatigue strength at N=104 cycles
Sf (N) =5490.8(10000)-0.206 = 824.965MPa N=105 cycles
Sf (N) = 5490.8(100000)-0.206 =513.612MPa N=106 cycles
Sf (N) = 5490.8(1000000)-0.206 =319.768 MPa N=107 cycles
Sf (N) = 5490.8(10000000)-0.206 =201.7MPa 3.3.2 Fatigue Criteria
For evaluation of the fatigue strength of the material, some basic fatigue criteria are proposed. Because of the spring stress distribution condition and a number of cyclic loads, stress-based fatigue criteria are most suitable.
Page 28 Table 3.5 Stress component in the spring system
n
(Mpa)
a
(Mpa)
m
(Mpa)
n
(Mpa)
a
(Mpa)
m
(Mpa)
1014.4 167.5 1262.6 584 95.08 730
The criteria that are used in the analysis of fatigue is based on critical plain (shear stress) approach and static strength, which’s are described briefly in Eq. (22-26). All the criteria can predict the failure, by its own formula, which is one or more damage values is drawn. to characterize fatigue failure for fluctuating stress in the spring, various stress components are defined as shown in Table (3.5).
This stress component (alternative and midrange stress) are derived from von Mises and maximum shear stress theory in section (3.2), which is
2
min
max
a = −
2
min
max
m = + (22)
for a similar fashion
2
min
max
a = − and
2
min
max
m = + (23)
1 McDiarmid Fatigue Criterion
The McDiarmid fatigue criterion is a critical plane-based criterion, in which the critical plane is determined as the plane were the maximum shear stress acts. The criterion is given by the relationship.
2 =1 +
U n F a
S S
(24)
Where and a are the maximum alternative shear stress and normal stresses n respectively, which is developed during the cycle, and S is the parameter of material F fatigue strength. The parameter is evaluated by the given formula with the fatigue strength 105 cycles that previously estimated. The result becomes S = 319.3Mpa (SF U = 0.5 Sut).
Page 29 2 Findley Fatigue Criterion
This criterion also based on a critical plane, in this situation, the critical fatigue strength is identified by the values of maximum normal stress and alternative shear stress.
This criterion is defined by the relationship ) 1
( + =
F Max n a
S k
(25)
where k is constants of material which is assumed value is 0.25 [21]. Hence the fatigue strength is estimated from the reference (105 cycle fatigue strength), the result value is SF
= 348.68Mpa
3 Modified Goodman (Von Mises–Juvinall ) Fatigue Criterion
The von Mises – juvenal criterion is estimated based on von-mises stress together. A known Goodman formula
=1 +
ut m e a
S S
(26)
Where and a are von-mises alternative and equivalent mean stress, obtained from m the principal stresses.
4 Soderberg Criterion
The failure criteria of Soderberg are based on the stress-based criterion, in this case, the strength is evaluated by the midrange von-mises stress and alternative von-mises stress. This equation is given as below
=1 +
y m e a
S S
(27)
5 Von Mises Failure Criteria (DE Elliptic)
(28)
Page 30 This failure criterion also a similar phenomenon with von Mises-juvelly and Soderberg but, a variant [22] is which used to evaluate the mean value of stress according to the von-mises equation formula. Generally, according to all the three-strength based criterion, mean stress has an influencing parameter on the fatigue strength of a given system, but as a general conclusion, this influence is very small which is negligible. Se = 330.4Mpa
3.3.3 Fatigue failure Analysis
In this section failure analysis is present; this analysis is done by purely analytical calculation followed different fatigue failure criteria and additional FEA activity are required to evaluate the analytical result. In order to estimate the value of damage (to identify at what revolution or region of coils are engaged more fatigue and leads to failure) all of the above fatigue criterion in section (4.5) would be applied.
Figure 3.6 Selection of points to measure the stress components by FEM
