Design of joint 1-4 (threaded joint) — example

Design data

Forces: F_X = 1500 N, F_Y = 300 N, F_Z = 700 N; transverse force F_t = 1530 N.

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

Design constraints: type of fit of the threaded shank: clearance fit; fastening thread: metric; nut type: standard hexagon nut; flat washer; Grower spring washer.

Materials and heat treatments

Properties of the hook material (element 1)

Nut material: property class 6 (σ_r ≈ 600 MPa).

Contact properties of the materials

Since all the materials in contact are steels, the following are adopted: allowable steel-on-steel crushing stress σ_as = 70 MPa; steel-on-steel friction coefficients μ = 0.2, μ₁ = 0.2, μ₂ = 0.25.

Sizing and checking

Axial force in the bolt from the condition of transmitting F_t by friction: with F_t = 1530 N, β_a = 1.2 and μ₁ = 0.2 (the friction coefficient on the contact surface 1-4), F_aș-t = 9180 N.

Total axial force in the threaded shank,

F_aș = F_aș-t + F_Z = 9880 N.

Axial tightening force of the joint,

F_st = F_aș-t = 9180 N.

From the tensile strength condition of the threaded shank, with F_aș = 9880 N, β = 1.2, σ_at = σ₀₂/c = (100…150) MPa (σ_at = 120 MPa is adopted), the required minor thread diameter is = 11.21 mm.

Adopted: metric thread M14 with p = 2 mm, d = 14 mm, d₁ = 11.825 mm, d₂ = 12.701 mm; clearance hole diameter D₁ = 16 mm; M14 nut with m = 11 mm, S = 22 mm; flat washer with inner diameter d₁ = 15 mm, outer diameter d₂ = 24 mm and thickness h = 2.5 mm; Grower washer 14 with d₁ = 14.2 mm, g = 3.2 mm.

From the crushing strength condition of the materials in contact, with the tightening force F_st = F_aș-t = 9180 N, D₁ = 16 mm, μ = 0.2 and σ_as = 70 MPa, the collar diameter is D₂ = 20.6 mm (D₂ = 21 mm is adopted).

From the screwing moment relation, with F_st = 9180 N, d₂ = 12.701 mm, p = 2 mm, μ = 0.2 and α = 60°, M_î = 16577.2 Nmm.

From the pivoting moment relation, with F_st = 9180 N, μ₁ = 0.2, S = 24 mm and D₁ = 16 mm, M_p = 18604.8 Nmm.

Wrench torque: M_c = M_î + M_p = 35182 Nmm.

From the check of the threaded shank under combined loading (tension and torsion), with F_aș = 9880 N, d₁ = 11.825 mm and M_î = 16577.2 Nmm, σ_e = 136.1 MPa,

and σ_e ≤ σ_at: 136.1 ≤ max (100…150) MPa (satisfied).

From the self-locking check, with p = 2 mm, d₂ = 12.701 mm, μ = 0.2 and α = 60°:

β₂ = 2.87°, φ′ = 16.1°,

and β₂ ≤ φ′: 2.87° ≤ 16.1° (satisfied).

Constructive-technological shapes

Towing hook, 1

Constructive-technological drawing

Adopted dimensions and technological parameters

– dimensions: D_s = 25 mm, D = 20 mm, l = 60 mm, L_c = 70 mm; l₃ = 10 mm; D₂ = 21 mm, d = 14 mm, l₁ = 36 mm, l₂ = 26 mm;

– transition zones are made with fillets: R1 = 2 mm, R2 = 2 mm, R3 = 0.5 mm;

– a protective chamfer, Chamfer2: 0.5×45°, and a technological chamfer, Chamfer1: 1.5×45°, are adopted;

– centre holes: A2.5/5.3;

– machining involves: turning, drilling, threading and grinding of the spherical surface;

– roughness of the spherical surface, finished by grinding: R_a1 = 3.2 µm; general surface roughness: R_a0 = 6.3 µm;

– since the element works in a corrosive environment, the spherical surface is protected by chrome plating to preserve its quality throughout the service life.

Upper tie rod, 4

Constructive-technological drawing

Adopted dimensions and technological parameters

– dimensions: b₄ = 60 mm, h₄ = 15 mm, R = 30 mm, L₄ = 110 mm, D₁ = 16 mm;

– protective chamfers of 0.5×45° are adopted on sharp edges;

– 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 = 12.5 µm; R_a2 = 6.3 µm.

Fasteners

Adopted dimensions

– nut: M10, d = 10 mm, S = 24 mm, m = 13 mm;

– flat washer: d₁ = 15 mm, d₂ = 24 mm, h = 2.5 mm;

– Grower spring washer: MN 14, d₁ = 14.2 mm, g = 3.2 mm.