Design of elements 13 and 13′ (left/right tie rod) — Design of Automotive Towing Devices

A. Loading diagram and design data

External loading diagram

Loading diagram of element 13/13′

Design data

External forces: F_X, F_Y, F_Z act at distances L_c (Ex.3.1), X₁, X₂, X₃, Y₁, Z₁ (Ex.1.2.2); the forces and moments at the centre of the welded joint are calculated (Calc.0):

F_Xs = F_Xd = F_X/2,

F_Ys = F_Yd = F_Y/2,

F_Zs = F_Zd = F_Z/2;

M_X13 = F_Y (L_c + Z₁)/2,

M_Y13 = F_X (L_c + Z₁)/2 + F_Z (X₁ + X₂)/2,

M_Z13 = F_X Y₁/2 + F_Y (X₁ + X₂)/2.

Note. Since the external forces may act in either direction in service, the maximum possible loads were determined (the components were added in the moment relations).

Dimensional constraints: the square tube 12, with dimensions h₁₂, t₁₂ (Ex.6.1), will be welded to tie rod 13.

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

Design constraints: weldable materials.

B. Choice of material and heat treatment

Since elements 13 (13′) are welded parts, a weldable steel is adopted (e.g. S185, S235, S275) according to SR EN 10025-2 (STAS 500/2) (Annex.M.01). 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

– the square tube 12 is T-welded onto tie rod 13;

– starting from the outer envelope of the weld contour, and allowing room for the bolt head together with the wrench, the width b₁₃ = h₁₂ + (60…80) mm is adopted; a flat bar of standard width b₁₃ is recommended (Annex.ST.01).

D. Calculation model, sizing and checking

Calculation model

Calculation assumptions and loads

– the calculation model is a straight cantilever bar, loaded in tension by the force F_Xs; in oblique bending by the loads F_Zs, F_Ys and M_Z13, M_Y13; in torsion by the moment M_X13; in shear by the forces F_Ys and F_Zs;

– elements 13/13′ and 2/2′ are connected by bolted joints with clearance-fit bolts;

– since a sizing model taking all loads into account is quite complex, a simplified model is adopted that considers the main bending load given by the force F_Ys and the moment M_Z13.

Calculation data

– loading: F_Ys, M_Z13;

– shape and dimensions: flat bar with dimensions b₁₃, X₃ + b₁₃; the thickness g₁₃ is unknown;

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

– bending moment in the critical section (simplified model): M_îmax = M_Z13 + F_Ys X₃.

Calculation relations

– bending strength condition in the critical section:

σ_îmax = = ≤ σ_aî;

– sizing: from the relation above, the required thickness is

= (Calc.7.1.1);

and from Annex.ST.01 a flat-bar blank of standard thickness g₁₃ ≥ is adopted, with the width b₁₃ adopted earlier (see stage C).

E. Design of the constructive-technological shape

Constructive-technological drawing

Recommendations for choosing the dimensions and constructive-technological parameters:

– dimensions: b₁₃, g₁₃, L₁₃ = X₃ + b₁₃; a = (12…18) mm, L = b₁₃ − 2a; the clearance hole diameter D₁ results from the calculation of the bolted joint (Sec.8.2, Ex.8.2);

– the number of sets of adjustment holes is set when drawing the assembly;

– technological operations: milling the ends and drilling;

– sharp edges are chamfered 1×45°;

– roughness of the surfaces machined by milling or drilling: R_a1 = 6.3 µm or R_a1 = 12.5 µm; R_a2 = 6.3 µm or R_a2 = 12.5 µm.