design for torsion - universiti teknologi malaysiaarahim/skmv 4123 torsion.pdf · design for...

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