STATIC ANALYSIS OF MULTI-LEAF SPRING USING ANSYS WORKBENCH 16.0

Transcription

1 International Journal of Mechanical Engineering and Technology (IJMET) Volume 7, Issue 5, September October 2016, pp , Article ID: IJMET_07_05_025 Available online at Journal Impact Factor (2016): (Calculated by GISI) ISSN Print: and ISSN Online: IAEME Publication STATIC ANALYSIS OF MULTI-LEAF SPRING USING ANSYS WORKBENCH 16.0 Rohit Ghosh, Sushovan Ghosh and Shirish Ghimire B. Tech Student, Department of Mechanical Engineering, NIT Durgapur, Durgapur, India Dr. Rabindra Nath Barman Assistant Professor, Department of Mechanical Engineering, NIT Durgapur, Durgapur, India ABSTRACT A multi-leaf spring is one of the most important components of automobile suspension system. Leaves are basically a series of flat plates, usually of semi-elliptical shape. Generally, a multi-leaf spring used in automobile suspension, consists of two types of leaves i.e. graduated-length leaves and full-length leaves. The present work is an attempt to estimate the magnitude of bending stresses in the above mentioned leaves for a semi-elliptic multi-leaf spring made of steel. The present work also validates the concept of cantilever beam employed in the theoretical analysis of multi-leaf spring. A lot of research work has been carried out in the context of leaf spring considering its material and a significant progress has been observed in the field of weight reduction, improvement of load carrying capacity when we replace the material of the spring by any advanced material like composites as E-glass/epoxy, carbon/epoxy etc. Finally referring to the results obtained in these research studies, the present work proposes a new idea regarding the construction of multi-leaf spring based on practical applications and cost analysis. Dimensions of the multi-leaf spring are taken from practical understanding. The multi-leaf spring was modeled in CATIA V5R18 and the same were analyzed under similar conditions using ANSYS (Workbench 16.0) software considering structural-steel as the spring material. Theoretical and software based results are presented and compared for validation. Key words: ANSYS (Workbench 16.0), CATIA V5R18, E-glass/epoxy, Multi-leaf spring, Static analysis. Cite this Article: Rohit Ghosh, Sushovan Ghosh, Shirish Ghimire and Dr. Rabindra Nath Barman, Static Analysis of Multi-Leaf Spring Using Ansys Workbench International Journal of Mechanical Engineering and Technology, 7(5), 2016, pp INTRODUCTION A spring is an elastic machine element which undergoes deflection for the application of any load and intends to regain its original shape depending upon the magnitude of the applied load. The major applications of spring may include its use as a shock and vibration absorber and storing potential energy by its deflection during the application of load. A multi-leaf spring or laminated spring is a very important component in automobile suspension system. It is one of the oldest suspension components too and still 241

2 Rohit Ghosh, Sushovan Ghosh, Shirish Ghimire and Dr. Rabindra Nath Barman today it is extensively used in all the heavy and light duty commercial vehicles, railway wagons and usually in the rear suspension of passenger vehicles. It differs from the conventional helical spring in a way that it can be guided along a definite path and it deflects under the application of load while acting as a structural member. This concept is employed during the analysis of bending stresses in different leaves by consideration of cantilever beam [1]. The present work makes an attempt to validate the above concept by performing static structural analysis using ANSYS software for the evaluation of maximum bending stress and subsequently bending stresses in different leaves, which in all, construct the entire spring. Finally, the reader may get an exposure regarding the bending stress variation for multi-leaf spring, which obviously differs from that of any cantilever beam section. In its construction the leaf spring consists of a series of flat plates or leaves, usually of semi-elliptic shape, which are held together with the help of U-bolts and centre clip. Generally two types of leaves may be observed in a multi-leaf spring i.e. some graduated -length leaves and a few extra full-length leaves. The length of the leaves gradually decreases from top to bottom. The longest leaf in the top is known as master leaf which is bent at both the ends to form spring eyes. The extra full-length leaves are inserted between the master leaf and the graduated-length leaves to support the transverse shear force. In order to maintain proper alignment and to restrict the lateral shifting of leaves, rebound clips are used [2]. In practice, these springs rest on the axle of an automobile. Its front end is connected with the frame by means of a simple pin joint and the rear end is connected with the frame through a flexible link (known as shackle) [3]. A number of research studies have been carried out in this context to replace the material of the leaf spring to enhance its load carrying capability and to reduce the overall weight of an automobile. M.Venkatesan et al.,[4] in their work, have shown the design and experimental analysis of a composite leaf spring made of glass fiber reinforced polymer and compared to steel spring, 67.35% lesser stress and 76.4% weight reduction were found for the composite spring. K.K.Jadhao et al., [5] in their investigation considered glass fiber reinforced plastic (GFRP) and the polyester resin (NETPOL 1011) as the spring material and almost a reduction of 85% in weight was found after performing numerical and finite element analysis for the same. Hence, surely composite materials may be able to provide better performance and efficiency in the practical applications but, from manufacturing point of view we should admit that they are more expensive than that of steel. The present study offers an exclusive idea regarding the construction of multi-leaf spring by combining the advantages associated with both composites and steels, as a leaf material. 2. MATHEMATICAL FORMULATION For the purpose of analysis, the leaves are divided in two groups as master leaf along with graduatedlength leaves forming one group and the extra full-length leaves forming the other group. Let, n f = number of extra full-length leaves, n g = number of graduated-length leaves including the master leaf, n = n f + n g =Total number of leaves present in the multi-leaf spring, b = width of each leaf (mm), t = thickness of each leaf (mm), L = half the length of the semi-elliptic spring or the length of the cantilever (mm), P = force applied at the end of the spring (N), P f = portion of P taken by the extra full-length leaves (N), P g = portion of P taken by the graduated-length leaves (N), So, P = P f + P g. Now, from practical considerations for an automobile leaf spring, that is of semi-elliptical shape usually, for a length of 2L and a load of 2P acting at the centre, the entire beam can be considered as a 242

3 Static Analysis of Multi-Leaf Spring Using Ansys Workbench 16.0 double cantilever. If the leaves are cut into two equal halves in longitudinal plane and then combined accordingly, to form almost a triangular plate then, The maximum bending stress is given by [6]. (σ b ) max = 6P.L/n.b.t 2 (1) The bending stress in the graduated-length leaves is given by [3] (σ b ) g = 12P.L/(3. n f +2.n g ).b.t 2 (2) The bending stress in the extra full-length leaves is given by [3] (σ b ) f = 18P.L/(3. n f +2.n g ).b.t 2 (3) It is to be noted that, the maximum bending stress occurs at the supports for such a plate. The above relations hold good for the leaves (or plates), having uniform cross-section. Also, it is seen that the bending stresses in extra full-length leaves are 50% more than that of the graduated length leaves i.e. (σ b ) f = 1.5(σ b ) g [3]. Calculation of length of different leaves: For the calculation of length of different leaves, following relations were used and subsequently, the results were implemented while modeling the multi-leaf spring in CATIA V5R18 software. Length of the smallest leaf = 1*Effective length/ (n-1) + Ineffective length Length of the next leaf = 2*Effective length/ (n-1) + Ineffective length Similarly, Length of the (n-1) th leaf = (n-1)*effective length/ (n-1) + Ineffective length Length of master leaf = 2.L+ 2.Π.(d+t) Ineffective length = Distance between the centres of U-bolts = l Effective length = 2.L 2.l/3 and d = inside diameter of eye[1]. 3. DESIGN SPECIFICATION The objective of the present course of study includes, determination of maximum bending stress for three different loading conditions and to establish the relationship for the magnitude of bending stresses existing in the graduated-length leaves and extra full-length leaves (i.e. (σ b ) f = 1.5(σ b ) g ), with the following dimensional specifications, Table 1 Specification of multi-leaf spring Parameters Value Notation Total length of the semi-elliptic spring (distance between two eyes ) 1243 mm 2L width of each leaf 100 mm b thickness of each leaf 14 mm t number of extra full-length leaves 2 n f number of graduated-length leaves including the master leaf 8 n g Total number of leaves present in the multi-leaf spring 10 n Load acting at the centre of the spring N,10000 N,5000 N 2P The dimensions are taken from practical understanding and the standards available in the market

4 Rohit Ghosh, Sushovan Ghosh, Shirish Ghimire and Dr. Rabindra Nath Barman Structural steel was considered as the leaf material with an elastic modulus E = 2.1*10 5 MPa, tensile yield strength S yt = 250 MPa and Poisson s ratio=0.3 while performing the analysis in ANSYS (Workbench 16.0) software. 4. ANALYTICAL CALCULATION From the relation of maximum bending stress (σ b ) max and based on the above design specifications, the analytical calculation is carried out for the load of N. From equation (1) the maximum bending stress is given by, (σ b ) max = 6P.L/n.b.t 2 We have, 2P = N, 2L = 1243 mm, n = 10, b = 100, t = 14 mm, then (σ b ) max = {6*(15000/2)*(1243/2)}/(10*100*14 2 ) = MPa Subsequently, the maximum bending stresses were evaluated for the loads of N, 5000 N and presented in TABLE: 2. Table 2 Variation of maximum bending stress with load Load 2P (newton) Maximum Bending stress (σ b ) max (MPa) It is to be noted that, the maximum bending stress occurs at the supports. These theoretical values of (σ b ) max are later compared with the software based results. 5. STATIC ANALYSIS The objective of this analysis is to investigate the stresses in the multi-leaf spring within the desirable limits to obtain a practical validation for the theoretical results. After geometric modeling in CATIA V5R18 software the spring is subjected to static analysis, performed in ANSYS (Workbench 16.0) software. The computer compatible mathematical description of the geometry of the object is called geometric modeling. CATIA is basically CAD (computer-aided design) software that allows the mathematical description of the object to be displayed and manipulated as the image on the monitor of the computer [7], whereas, ANSYS is a engineering simulation software that predicts with confidence about the performance of the product under the real-world environments incorporating all the existing physical phenomena [8]. The layout of static analysis involves meshing, boundary conditions and loading Meshing Meshing is basically the division of the entire model into small elements. In order to maintain the shape, it is convenient to select the free mesh, as the geometry of leaf spring contains sharp curves. Element size of 20 mm with medium smoothing was considered for mesh generation. Minimum edge length of the elements was 14 mm. Within the solution domain under the Adaptive Mesh Refinement segment, Max. Refinement Loops was taken as 3 and Refinement Depth as 2. For the convergence plot, the maximum allowable change was considered as 4%. All the 44 faces were selected for mesh generation and total number of nodes and elements were observed as and 7358 respectively. Figure 1 shows the meshed model of multi-leaf spring

5 Static Analysis of Multi-Leaf Spring Using Ansys Workbench 16.0 Figure 1 Meshed model of multi-leaf spring 5.2. Boundary Conditions The leaf spring is mounted on the axle of an automobile. The frame of the vehicle is connected to the ends of the leaf spring. The ends are constructed in such a way that they form an eye like structure. The front eye of the spring is directly connected with the frame by means of a simple pin joint; hence, it can freely rotate about the pin but is restricted for any kind of translation and rotation in all the other directions. So under the static structural domain of ANSYS software, the Remote Displacement was inserted and except rotation about X- axis, all other motions were constrained to set the above boundary condition. Now, the rear eye of the leaf spring is connected with the frame through a flexible link known as shackle. So, it has the flexibility to slide along length of the spring and also to rotate about the pin. These were again established through Remote Displacement by setting Y- direction as unconstrained for translation according to the geometry, while keeping all other translator y motions restricted and rotation about X- axis was set free as before, keeping all other rotational motions constrained for the rear eye of the spring Load The load is uniformly distributed by all the nodes associated with the bottom surface of the bottom most leaf. The Load is applied along F Z direction as shown in Figure 2. To apply the load, under the static structural domain of ANSYS Software, Force was introduced and the magnitude of load was given for Z- direction. Here, we have considered a load of N is acting on the bottom most leaf. Figure 2 Loading of multi-leaf spring 245

6 Rohit Ghosh, Sushovan Ghosh, Shirish Ghimire and Dr. Rabindra Nath Barman 6. RESULTS AND DISCUSSIONS After associating the real world physics to the CAD generated model in ANSYS software, the solutions were obtained for Equivalent (von-mises) Stress using static structural as the Analysis System. The results obtained after the solution, are presented in the following figures. Figure 3 Distribution of equivalent (von-mises) stresses at a load of 5000 N Figure 4 distribution of equivalent (von-mises) stresses at a load of N Figure 5 distribution of equivalent (von-mises) stresses at a load of N 246

7 Static Analysis of Multi-Leaf Spring Using Ansys Workbench 16.0 Finally, the theoretical results are compared with the above software based solutions for validation and given in the following Table 3. Table 3 Comparison between theoretical and ANSYS based results (Equivalent (von-mises) Stresses) Load 2P (newton) Maximum Bending stress (σ b ) max (MPa) Maximum Equivalent (von-mises) Stress (MPa) Theoretical ANSYS based It is seen that the software based results almost matches with the theoretical solutions and hence, it validates the concept of cantilever beam that was implemented while developing the mathematical formulations for maximum bending stress as well as bending stresses in different leaves. We further conclude that, maximum bending stresses acting on the steel spring for the given loading conditions are well within the safe limits for yield strength of 250 MPa( for steel). For a factor of safety of 1.5 the allowable stress should be within MPa. So with the given design specifications, the multi-leaf spring remains safe. A graph is plotted for the theoretical and ANSYS based results with load on X-axis and stress values on Y-axis, shown in the following Figure Max.Equivalent(von-Mises) Stress or (σ b ) max (MPa) Loads (N) Theoretical ANSYS Based Figure 6 Variation of Stress with different loading conditions It is seen, that the stress values increases almost linearly with the increase in load. Also, we see that the theoretical and ANSYS based results are very close, indicated by brown and black dotted lines respectively in the Figure 6. In order to demonstrate the variation of bending stresses in different leaves at a particular load, we take the help of the following Figure

8 Rohit Ghosh, Sushovan Ghosh, Shirish Ghimire and Dr. Rabindra Nath Barman Figure 7 Variation of equivalent (von-mises) stresses in different leaves With the help of Probe tool in ANSYS software, the stresses , and (in MPa) in three different points are shown in the above figure for a load of N. It can be clearly observed from the figure that, the stress value of (MPa) associated with the extra full-length of (MPa) corresponding to the graduated-length leaves at a leaves are almost 1.5 times than that of the stress value distance almost equals to the stress value of (MPa) for a given section. This obviously differs from the stress variation that we have observed for any cantilever beam section where the variation is uniform in both the sides of the neutral plane. Here, we observe much higher stresses in the extra full-length leaves. Finally referring to the above results and the research studies associated with the multi-leaf spring with advanced materials like composites, we can propose to manufacture the extra full-length leaves with composite materials instead of the entire spring and to manufacture the graduated-length leaves with steel materials. This will help to reducee the stresses in the extra full-length leaves and also reduces the overall weight of the spring compared to a spring that is completely made of steel. But, composite materials are much expensive than that of steelss from manufacturing point of view. Averagee cost of E-glass (composite) that can be used to manufacture the springs, ranges from USD per square foot [9] whereas, steel ranges from USD per square foot [10]. Hence, if the entire spring is made of composite material then it would not be cost effective at all. So, we propose to manufacture the graduated-length leaves (where the stresses are much lower than that of extra full-length leaves) with steels to reduce the overall cost and for the extra full-length leaves we can use composites to acquire the advantages associated with this advanced materials. 7. CONCLUSIONS AND FUTURE SCOPE OF WORK In the present work, the multi-leaf spring is modeled in CATIA V5R18 and same were analyzed in the Static structural domain of ANSYS software. The results were discussed in the preceding section and it is concluded that, for the given design specifications, the maximum bending stresses for three different loading conditions are well within the safe limits. For the maximum load of N, the stress value was lower than that of the allowable stress of MPa for a factor of safety 1.5. We further concluded that, stresses in the extra full-length leaves were almost 50% more (1.5 times) than that of the graduated-length leaves. Finally, the present work offers an exclusive idea regarding the construction of multi-leaf spring through its proposal for manufacturing the extra full-length leaves with composites, while using steels for the rest of the leaves, to minimize the cost. An extended study can be carried out on the topic in the context of different joining methods for metals with composites if we implement the proposed construction methodology for the spring. Mechanical 248

9 Static Analysis of Multi-Leaf Spring Using Ansys Workbench 16.0 Fasteners, adhesives or both can be used to join composites [12], but to choose the most effective one requires an extensive effort for the same. Also, while modeling the leaf spring, the materials can be applied separately to the graduated-length leaves and extra full-length leaves and the same can be analyzed in a similar fashion like above in the static structural module of ANSYS software. REFERENCE [1] G. Harinath Gowd, E. Venugopal Goud, Static analysis of leaf spring, International Journal of Engineering Science and Technology (IJEST), ISSN: Vol. 4 No.08 August [2] V.B. Bhandari, design of machine elements (McGraw Hill Education, ISBN: , 2014). [3] Preshit. B. Waghmare, Raosaheb. B. Patil, Static and modal analysis of leaf spring using fea, International Journal of Technical Research and Applications e-issn: , Volume3, Jan-Feb [4] M. Venkatesan, D. Helmen. Devaraj (2012), Design and analysis of composite leaf spring in light vehicle, International Journal of modern engineering research Vol.2: pp [5] K. K. Jadhao, DR. R.S. Dalu, Experimental investigation & numerical analysis of composite leaf spring, ISSN: Vol. 3 No. 6 June [6] R.S. Khurmi, J.K. Gupta, a text book of machine design(s. Chand, Eurasia Publishing House (pvt.) ltd., 2005). [7] Retrieved from [8] Retrieved from [9] Retrieved from [10] Retrieved from 8#q=cost%20of%20steel%20per%20square%20foot [11] Retrieved from machinedesign.com/basics-design/joining-composites [12] Prof. N.V. Hargude, Mr. J.G. Herekar and Prof. P.P. Awate, Analysis of Composite Mono Leaf Spring. International Journal of Mechanical Engineering and Technology (IJMET),5(5), 2014, pp [13] Syambabu Nutalapati, Design and Analysis of Leaf Spring by Using Composite Material for Light Vehicles. International Journal of Mechanical Engineering and Technology (IJMET),6(12), 2015, pp