Design of joint 1-4 (threaded joint)

A. Loading diagram and design data

B. Choice of materials and heat treatments

Hook material

C45 (0.45 % C), quenched and tempered (quenching and high tempering), with hardness HB, yield strength σ₀₂ and ultimate tensile strength σ_r (Ex.3.1).

Nut material

Property class x, with x = 6, 8, 10 (σ_r ≈ 600, 800, 1000 MPa).

Note. The usual property class symbols for nuts are 4, 5, 6, 8, 10, 12; meaning: the number × 100 = minimum ultimate tensile strength (σ_rmin) in MPa (e.g. for class 8, σ_r = 8 × 100 = 800 MPa).

Contact properties of the materials

Since all the materials of the elements in contact are steels, the following are adopted: allowable steel-on-steel crushing (bearing) stress σ_as = 60…90 MPa; steel-on-steel friction coefficients μ = 0.15…0.25, μ₁ = 0.15…0.25, μ₂ = 0.15…0.25.

C. Design of the constructive shape

Constructive drawings

Parameters: d – nominal thread diameter, d₁ – minor thread diameter, d₂ – pitch diameter, p – thread pitch; D₁ – clearance hole diameter, D₂ – collar diameter, l₁ – length of the threaded portion, l₂ – length of the joint portion.

Constructive features and constraints

– thickness of element 4, h₄ (Ex.3.2);

– collar diameter, D₂ (Ex.3.1).

D. Calculation model, sizing and checking

Calculation model

Calculation assumptions

– the threaded shank is treated as a straight bar fixed in the body of the towing hook, with a constant circular cross-section of diameter d₁ (the minor thread diameter), loaded in tension by the axial force F_aş;

– the torque that arises when tightening the joint, and therefore the associated shear stresses, are neglected;

– the external force F_Z, which may act in both directions during operation, is assumed for this calculation to act in the positive direction of the Z axis, which places an additional load on the bolted joint;

– the transverse force F_t is transmitted by friction from element 1 to element 4 over a single contact surface.

Calculation data

– loading: F_Z – the vertical force, F_t – the transverse force;

– shape and dimensions: element 4 is a flat bar of thickness h₄;

– material: strength properties: σ₀₂ – the yield strength; σ_at = σ₀₂/c – the allowable tensile stress; c = 2…3 – the safety factor; σ_as = (60…90) MPa – the allowable steel-on-steel crushing stress; μ₁ = 0.15…0.25 – the friction coefficient on the contact surfaces 1-4; μ₂ = 0.15…0.25 – the friction coefficient on the nut–washer contact surfaces; μ = 0.15…0.25 – the friction coefficient in the thread.

Calculation relations for sizing the threaded shank

– the axial force in the bolt F_aș-t, from the condition of transmitting the force F_t by friction,

β_aF_t ≤ F_f,

taking the friction force F_f = μ₁F_aș-t, is given by

F_aș-t = β_a , (Calc.3.3.1)

where β_a = 1.1…1.3 is the safety factor against slipping and μ₁ = 0.15…0.25 is the friction coefficient on the contact surface 1-4;

– the total axial force in the threaded shank (when F_Z acts upwards),

F_aș = F_aș-t + F_Z; (Calc.0)

– sizing: from the tensile strength condition of the threaded shank,

σ_t = ≤ σ_at,

the required minor thread diameter is obtained,

= , (Calc.3.3.2)

where σ_at = σ₀₂/c [MPa] (Calc.0) is the allowable tensile stress, σ₀₂ the yield strength, c = 2…3 the safety factor, and β = 1.1…1.3 a correction factor (it accounts for the additional torsion that arises when the nut is tightened).

Choosing the dimensions of the standard metric thread

From Annex.ST.03 a metric thread with d₁ ≥ is adopted, with the dimensions d₁ (minor diameter), d₂ (pitch diameter), d (nominal diameter), p (pitch); the clearance hole diameter D₁ (medium series), matched to the thread size d, is taken from Annex.ST.05.

Note. It is recommended to adopt coarse-pitch threads (marked in bold), which are the ones most commonly used in practice.

Calculation relations for sizing the collar

From the crushing strength condition of the materials in the contact zone between elements 4 and 1, the contact pressure is

p = = ≤ σ_as,

from which the collar diameter, i.e. the minimum outer diameter of the flat washer, is obtained,

D₂ = , (Calc.3.3.3)

where σ_as is the allowable crushing stress of the materials in contact; the following dimensions are adopted: flat washer d₁, d₂, h (Annex.ST.06); nut d, S, m (Annex.ST.04); Grower washer d₁, g (Annex.ST.07).

Relations for calculating the moments

– the screwing (tightening) moment in the thread,

M_î = F_st tg(arctg + arctg), (Calc.3.3.4)

where d₂ is the pitch diameter of the thread, p the thread pitch, μ the friction coefficient in the thread and α the profile angle of the metric thread (α = 60°).

– the pivoting (friction) moment on the bearing face of the nut,

M_p = F_st μ₂ , (Calc.3.3.5)

where μ₂ = 0.15…0.25 is the friction coefficient on the nut–washer contact surface, S the wrench size of the nut and D₁ the clearance hole diameter.

– the wrench torque for tightening the nut,

M_c = M_î + M_p. (Calc.0)

Checking relations

– checking the threaded shank under combined loading (tension and torsion) at tightening,

σ_e ≤ σ_at,

where

σ_e = (Calc.3.3.6)

and σ_at = σ₀₂/c is the allowable tensile stress, σ₀₂ the yield strength and c = 2…3 the safety factor.

Note. If the inequality above is not satisfied, larger dimensions of the standard metric thread are chosen from Annex.ST.03 and the calculations are repeated from the step Choosing the dimensions of the standard metric thread.

– checking the self-locking condition,

β₂ ≤ φ′,

where β₂ = arctg is the mean helix angle of the thread and φ′ = arctg the reduced friction angle in the thread. (Calc.3.3.7)

E. Design of the constructive-technological shapes

Towing hook, 1

Constructive-technological drawing

Recommendations for choosing the dimensions and technological parameters

– dimensions obtained: D_s, D, l, L_c, l₃ = (0.4…0.6)D, D₂, d, l₁, l₂;

– transition zones are made with fillets R1, R2, R3 (Annex.T.02);

– protective or technological chamfers are adopted: Chamfer1, Chamfer2 (Annex.T.02);

– centre hole (Annex.T.01);

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

– roughness of the spherical surface: R_a1 = 3.2 µm or R_a1 = 1.6 µm; general surface roughness: R_a0 = 6.3 µm (Annex.T.03);

– 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

Recommendations for choosing the dimensions and technological parameters

– dimensions: b₄, h₄, R = b₄/2, L₄ = X₁ + R; D₁ is determined when designing joint 1-4;

– protective chamfers 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).

Fasteners

Recommendations for choosing the dimensions

– nut: d, S, m (Annex.ST.04);

– flat washer: d₁, d₂, h (Annex.ST.06);

– Grower spring washer: d₁, g (Annex.ST.07).