#### Transcript Bending

SMC 4133 AUTOMOTIVE STRUCTURES DESIGN FOR BODY BENDING Body bending strength requirement: • To locate and retain the vehicle subsystem in the correct position • Does not fail under static/dynamic loading conditions Shear loads & moments can be identified from the S-BM diagrams All materials in this slide are taken from Donald E Malen. 2011. Fundamentals of Automobile Body Structure Design, SAE International. SMC 4133 AUTOMOTIVE STRUCTURES DESIGN FOR BODY BENDING Severe bending conditions can be occurred due to dynamic loading and jacking/towing A factor of 2-g loading is typically used to represent dynamic condition These two extreme conditions might cause the structure to fail All materials in this slide are taken from Donald E Malen. 2011. Fundamentals of Automobile Body Structure Design, SAE International. SMC 4133 AUTOMOTIVE STRUCTURES DESIGN FOR BODY BENDING The H Point Bending Test is used to approximate bending moment envelope It can be 1 or 2 point loads applied at the seating location The H Point Bending Test: Body is supported at the suspension attachments The loads are increased incrementally and the deflections are recorded until it reachs permanent deformation All materials in this slide are taken from Donald E Malen. 2011. Fundamentals of Automobile Body Structure Design, SAE International. SMC 4133 AUTOMOTIVE STRUCTURES DESIGN FOR BODY BENDING Bending stiffness Can be measured from the load-deflection curve The reason is to cater for body vibration so that it can achieve the feeling of solidness The desired bending frequency is from 22-25 Hz Assume that the structure as a uniform beam; the primary bending frequency is M = wL/g L Now, with a single static load at its center span, the bending resonant frequency is l Simply supported All materials in this slide are taken from Donald E Malen. 2011. Fundamentals of Automobile Body Structure Design, SAE International. SMC 4133 AUTOMOTIVE STRUCTURES DESIGN FOR BODY BENDING Typical values of body strength and stiffness for a mid size vehicle are; 6680 N without permanent deformation 7000 kN/m All materials in this slide are taken from Donald E Malen. 2011. Fundamentals of Automobile Body Structure Design, SAE International. SMC 4133 AUTOMOTIVE STRUCTURES DESIGN FOR BODY BENDING Load Path Analysis o To meet body strength requirement, the structure must be carefully designed o Only end and shear loads are allowed in the structural surface model o The applied load will represent the bending strength requirement o Each surface must be capable of reacting the loads without excessive permanent deformation Example 1 All materials in this slide are taken from Donald E Malen. 2011. Fundamentals of Automobile Body Structure Design, SAE International. SMC 4133 AUTOMOTIVE STRUCTURES DESIGN FOR BODY BENDING All materials in this slide are taken from Donald E Malen. 2011. Fundamentals of Automobile Body Structure Design, SAE International. SMC 4133 AUTOMOTIVE STRUCTURES DESIGN FOR BODY BENDING Analysis of Body Bending Stiffness • • • • Focus on the side frame due to its significant contribution on bending stiffness The model consists of beams, rigid plates and pin connections Applied load acts at the center of rocker/end of B-pillar Approximation of the stiffness is made using finite element method All materials in this slide are taken from Donald E Malen. 2011. Fundamentals of Automobile Body Structure Design, SAE International. SMC 4133 AUTOMOTIVE STRUCTURES DESIGN FOR BODY BENDING • • • • Example of the analysis is given below with the initial guess for beam section size The result shows that the total bending stiffness is 2088 kN/m Only 30% of the target value (7000 kN/m) Change the beams section size/shape. BUT which BEAM? Example 2 All materials in this slide are taken from Donald E Malen. 2011. Fundamentals of Automobile Body Structure Design, SAE International. SMC 4133 AUTOMOTIVE STRUCTURES DESIGN FOR BODY BENDING Finite element analysis SMC 4133 AUTOMOTIVE STRUCTURES DESIGN FOR BODY BENDING Importance of joint flexibility • Previous analysis assumed the beams were rigidly connected • In reality, when two or more thin-walled beams are joined, localized deformation may occur • Thus, it has the effect of a flexible joint and this can be represented by rotational spring • The rotational stiffness can be determined by taking ratio of moment over rotational angle All materials in this slide are taken from Donald E Malen. 2011. Fundamentals of Automobile Body Structure Design, SAE International. SMC 4133 AUTOMOTIVE STRUCTURES DESIGN FOR BODY BENDING Joint Efficiency • To check whether the joint stiffness is a very stiff or very flexible • It can be define as the ratio of the combined stiffness of the beam-joint to the stiffness of the beam alone Example 3 The steel rocker beam has section size of h = 100mm, w = 50mm, t = 1mm L = 1000mm. Compute the joint efficiency for Hinge pillar to rocker joint. All materials in this slide are taken from Donald E Malen. 2011. Fundamentals of Automobile Body Structure Design, SAE International. SMC 4133 AUTOMOTIVE STRUCTURES DESIGN FOR BODY BENDING Solution I = 4.15E+5 mm^4 K = 0.2E+6 Nm/rad from diagram E = 207 GPa Joint efficiency, f = 1/(1 + (2x207000x4.15E5/1000x0.2E6)) = 0.537 The joint reduces ½ of the beam alone All materials in this slide are taken from Donald E Malen. 2011. Fundamentals of Automobile Body Structure Design, SAE International. SMC 4133 AUTOMOTIVE STRUCTURES DESIGN FOR BODY BENDING Example 4 Consider Example 2 with reasonable joint stiffness to three of the joints. Re-run FEA. It is found that the deflection is increased and hence, reduce the bending stiffness to 1735 kN/m; closer to the test data. However, the value is far from the target value. HOW to achieve it? Which beams or joints to adjust? All materials in this slide are taken from Donald E Malen. 2011. Fundamentals of Automobile Body Structure Design, SAE International. SMC 4133 AUTOMOTIVE STRUCTURES DESIGN FOR BODY BENDING Strain energy and stiffness - As the beams deform under load application, strain energy is stored. - The strain energy can be determined as a function of the end moments on the beam - The highest fraction of strain energy will improve stiffness of a structural system All materials in this slide are taken from Donald E Malen. 2011. Fundamentals of Automobile Body Structure Design, SAE International. SMC 4133 AUTOMOTIVE STRUCTURES DESIGN FOR BODY BENDING Example 5 Consider the seat mount system consisting of a beam connected by a Flexible joint to a rocker. The system does not meet the stiffness requirement,. Which element needs to be changed: the beam or the joint? Solution SE beam = 200xM^2/(6x1E10) = 3.33E-9M^2 SE joint = M^2/(2x2E8) = 2.5E-9M^2 The beam stiffness has a larger effect on overall system stiffness All materials in this slide are taken from Donald E Malen. 2011. Fundamentals of Automobile Body Structure Design, SAE International.