design for torsion - universiti teknologi malaysiaarahim/skmv 4123 torsion.pdf · design for...
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DESIGN FOR TORSION
Source: Donald E Malen. 2011. Fundamentals of Automobile Body Structure Design, SAE International.
Body torsion strength requirement
• The body has to recover its shape with little to no permanent deformation
during twist ditch maneuver
• The twist ditch torque can be obtained by multiplying axle load (W) by half of
the wheel track (t) 𝑇𝑚𝑎𝑥 = 𝑊𝑎𝑥𝑙𝑒𝑡
2;
(𝑊𝑎𝑥𝑙𝑒 = axle load, t = wheel track)
• The angle of twist can be determined by 2 x deflection divided by width of the
loaded points (w), ∅ =2𝛿
𝑤;
(𝛿 = deflection at suspension point, w = width at loaded points)
DESIGN FOR TORSION
Source: Donald E Malen. 2011. Fundamentals of Automobile Body Structure Design, SAE International.
Torsion stiffness requirement:
1. To ensure good handling properties
2. To ensure a solid structural feel and minimize relative deformations –
squeaks & rattles
As a vehicle turns a corner, it will roll and causes a weight transfer. It
then can affect steering characteristics
High body torsional stiffness is required to ensure good vehicle handling
For good solid structure feel:
- Vehicle first torsional frequency from 22-25 Hz
- Torsional stiffness = 12000 Nm/degree
- Torsion strength = 6250 Nm
DESIGN FOR TORSION
Source: Donald E Malen. 2011. Fundamentals of Automobile Body Structure Design, SAE International.
Load Path Analysis
Let’s begin with a simple structure i.e. a closed box. The box is loaded by a
twisting couple at the front and rear corners.
Observation: Comparison between bending and torsion load case.1. …………………. (loads on the element?)2. …………………. (critical load case?)3. …………………. (vehicle weight?)
DESIGN FOR TORSION
Source: Donald E Malen. 2011. Fundamentals of Automobile Body Structure Design, SAE International.
Determination of the shear loads
DESIGN FOR TORSION
Source: Donald E Malen. 2011. Fundamentals of Automobile Body Structure Design, SAE International.
Body torsional stiffness for box structure
𝐹𝑟𝑜𝑚 𝑡ℎ𝑒 𝑓𝑖𝑔𝑢𝑟𝑒, 𝑡ℎ𝑒 𝑠ℎ𝑒𝑎𝑟 𝑠𝑡𝑟𝑎𝑖𝑛 𝑒𝑛𝑒𝑟𝑔𝑦, e =
𝑣𝑜𝑙𝑢𝑚𝑒
𝜏𝛾
2𝑑𝑉
𝜏 =𝑞
𝑡, 𝑉 = 𝑎𝑏𝑡, 𝐺 =
𝜏
𝛾, 𝑡ℎ𝑒𝑛 𝑒 =
𝑣𝑜𝑙𝑢𝑚𝑒
𝜏2
2𝐺𝑎𝑏𝑡, 𝑒 = 𝑞2
𝑎𝑏
2𝐺𝑡
1
2𝑇𝜃 =
𝑎𝑙𝑙 𝑠𝑢𝑟𝑓𝑎𝑐𝑒𝑠
1
2𝑞2𝑎𝑏
𝐺𝑡𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑖
𝑞 =𝐹
2ℎ=𝑇
2𝑤ℎ,1
2𝑇𝜃 =
𝑎𝑙𝑙 𝑠𝑢𝑟𝑓𝑎𝑐𝑒𝑠
1
2(𝑇
2𝑤ℎ)2𝑎𝑏
𝐺𝑡𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑖
𝐾 =𝑇
𝜃= (2𝑤ℎ)2
1
𝑎𝑙𝑙 𝑠𝑢𝑟𝑓𝑎𝑐𝑒𝑠𝑎𝑏
𝐺𝑡 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑖
𝜏 = 𝑠ℎ𝑒𝑎𝑟 𝑠𝑡𝑟𝑒𝑠𝑠𝛾 = 𝑠ℎ𝑒𝑎𝑟 𝑠𝑡𝑟𝑎𝑖𝑛q = shear flowK = torsional stiffnessG = shear modulusw = width of boxh = height of boxa, b = dimension of
a side surfacet = thickness of
side surface
DESIGN FOR TORSION
Source: Donald E Malen. 2011. Fundamentals of Automobile Body Structure Design, SAE International.
Effective shear rigidity for flat panel with the bars
𝐺 =𝜏
𝛾, 𝜏 =
𝐹
𝑎𝑡, 𝛾 =
𝛿
𝑏
𝐺𝑡 =𝐹
𝛿
𝑏
𝑎
DESIGN FOR TORSION
Source: Donald E Malen. 2011. Fundamentals of Automobile Body Structure Design, SAE International.
Torsional stiffness of a vehicle cabin with effective shear rigidity of side frame
1
2𝑇𝜃 =
𝑎𝑙𝑙 𝑠𝑢𝑟𝑓𝑎𝑐𝑒𝑠
1
2𝑞2𝑎𝑏
𝐺𝑡𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑖
𝐾 =𝑇
𝜃=
1
𝑞𝑇
2 𝑎𝑙𝑙 𝑠𝑢𝑟𝑓
𝑎𝑟𝑒𝑎 𝑜𝑓 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑖𝐺𝑡 𝑒𝑓𝑓
𝑑𝑖𝑣𝑖𝑑𝑖𝑛𝑔 𝑏𝑦 𝑇2 =𝜃
𝑇
𝐹𝑜𝑟 𝑠𝑖𝑑𝑒 𝑓𝑟𝑎𝑚𝑒,
(𝐺𝑡)𝑒𝑓𝑓 =𝑄
𝛿
𝐻
𝐿
Q = shear load along the roof𝛿 = ℎ𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛H = height of side frameL = length of floor