Design of element 4 (upper tie rod) — Design of Automotive Towing Devices

A. Loading diagram and design data

External loading diagram

Loading diagram of element 4 (upper tie rod)

Design data

External forces: F_X, F_Y, F_Z act at distance L_c (Sec.3.1, Ex.3.1); the moments at the centre of the clearance hole are calculated (Calc.0):

M_X4 = F_Y L_c,

M_Y4 = F_X L_c.

Dimensional constraints: imposed dimension X₁ (Ex.1.2.2).

Operating constraints: temperature T = (−30…40) °C; outdoor working environment with high humidity.

Design constraints: weldable material.

B. Choice of material and heat treatment

Since the tie rod is a welded part, a weldable steel is adopted (e.g. S185, S235, S275) (Annex.M.01), according to SR EN 10025-2 (STAS 500/2). These steels are not heat-treated before welding; after welding, the subassembly may undergo stress-relief annealing. For the adopted steel, the yield strength σ₀₂ and the ultimate tensile strength σ_r are retained for the calculations.

C. Design of the constructive shape

Constructive model

Constructive features and constraints

– a flat bar semi-finished product with standard cross-section dimensions (b₄ and h₄) is adopted;

– element 4 is joined to element 5 by a fillet weld.

D. Calculation model, sizing and checking

Calculation model

Loads and calculation assumptions

– the calculation model treats element 4 as a straight cantilever bar of rectangular cross-section (dimensions b and h), loaded in tension by F_X, in bending by F_Z, F_Y and M_Y4, in torsion by the moment M_X4 and in shear by F_Z and F_Y;

– elements 4 and 5 are welded together, so for sizing the tie rod 4 it is considered fixed in the section (marked in yellow) at the centre of the weld bead;

– since a sizing model accounting for all loads is quite complex, a simplified model is adopted below, which considers the main bending load given by the force F_Z and the moment M_Y4; once the dimensions have been obtained from the simplified model, they are checked with the MDESIGN package (Guide.3.6).

Calculation data

– loading: F_Z – the vertical force, and M_Y4 – the moment about the Y axis;

– shape and dimensions: rectangular bar with b/h = k (k = 3, 4 or 5 may be adopted);

– material: σ₀₂ – the yield strength; σ_at = σ₀₂/c – the allowable tensile stress; σ_aî = (1.05…1.1)σ_at – the allowable bending stress; c = 2…3 – the safety factor.

Calculation relations

– bending moment in the critical section (simplified model): M_{î max} = M_Y4 + F_Z X₁;

– bending strength condition in the critical section,

σ_îmax = = ≤ σ_aî.

– sizing: from the relation above, with b = k h (k = 3, 4 or 5), the thickness of the tie rod is

h^nec = (Calc.3.2.1)

and its width is b^nec = k h^nec (Calc.0); from Annex.ST.01 a flat bar semi-finished product is chosen with b₄ = b ≥ b^nec and h₄ = h ≥ h^nec.

E. Design of the constructive-technological shape

Constructive-technological drawing

Recommendations for choosing the dimensions and technological parameters

– dimensions: b₄, h₄, R = b₄/2, L₄ = X₁ + R; the hole diameter D₁ is determined when designing joint 1-4 (Sec.3.3, Ex.3.3);

– protective chamfers of 0.5×45° are adopted on sharp edges (Annex.T.02);

– machining involves milling the end portions and drilling; the other surfaces remain unmachined, as indicated by the attached symbol;

– roughness of the machined surfaces: R_a1 = 6.3 µm or R_a1 = 12.5 µm; R_a2 = 6.3 µm or R_a2 = 12.5 µm (Annex.T.03).