Design of the cylindrical helical compression spring of the towing coupling

A. Loading diagram and design data

Loading diagram

Design data

Preload pressure of the spherical pair: p₀ = (0.1…0.2) p_max, where p_max is the maximum pressure in the spherical pair under load (Ex.8.5).

Spring preload force

With r = D_s/2 and F_r = F₀, the pressure relation from Annex.8.5.1 becomes

p₀ = = ,

from which

F₀ = (Calc.8.6.1),

where D_s is the diameter of the coupling ball.

Spring assembly force

F_a = F₀ sin θ (Calc.8.6.2),

where θ = 35°…45°.

Dimensions: the diameter of the threaded shank of the eye bolt, Md (metric thread), may be M8, M10 or M12; spring stroke between the coupled and uncoupled positions h = 6…10 mm.

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

Design constraints: interchangeability with the coupling systems in use in the EU.

Note. The cylindrical helical compression spring preloads the spherical pair with the pressure p₀, to eliminate any play that could appear in service (especially when switching from pulling to pushing the trailer).

B. Choice of material and heat treatments

The helical spring is made of special spring steel (Annex.M.01; Annex.M.02).

Material properties

Heat treatments

Annealing at (650…700) °C before forming.

Quenching at (820…870) °C with oil cooling and tempering at (550…650) °C, HRC 45…55, after forming (coiling into the helical shape).

C. Design of the constructive shape

D. Calculation models, sizing and checking

Strength calculation model

Key: F – spring load; α – helix angle; T – shear force; M_t – torsional moment; M_î – bending moment; N – axial force; τ_max – maximum shear stress.

Deformation calculation model (displacement, deflection, stroke) and spring characteristic

Calculation assumptions and loads

– since the helix angle is small, α = 6…9°, sin α ≈ 0 and cos α ≈ 1 are assumed, so the shear, compression/tension and bending stresses are neglected;

– the main load on the coil is torsion.

Calculation data

– loading: F_n = F_a – the maximum (nominal) force; F₁ = (0.1…0.2) F_n – the assembly force;

– dimensions: the mean diameter of the spring D_m = (1.4…1.6) Md, where Md may be M8, M10 or M12; spring stroke h = 6…10 mm;

– materials: the allowable stress τ_a (Annex.M.02); G = 8.5·10⁴ MPa – the shear modulus of the spring material.

Calculation relations

– torsional strength condition of the spring coil (strength model):

τ_tmax = K ≤ τ_a,

where K = 1.05…1.2 is the stress concentration factor for torsional shear;

– spring deflection under the load F_n:

δ_n = ,

where n is the number of active coils and G the shear modulus of the spring material;

– spring stroke:

h = ,

where d is the wire diameter.

Sizing

Wire diameter

From the torsional strength condition (see above), the required wire diameter is

d_nec = (Calc.8.6.3).

A wire diameter d ≥ d_nec is adopted from the standard spring-steel wire diameters {… 1.0; 1.2; 1.3; 1.4; 1.5; 1.7; 1.8; 1.9; 2.0; 2.5; 3.0; 3.5; 4.0; 4.5; 5 …} mm.

Number of active coils

From the stroke relation (see above), the required number of active coils is

n_nec = (Calc.8.6.4).

The number of active coils n ≥ n_nec is adopted, rounded up.

Other dimensional parameters

– number of end (seating) coils n_r = 1.5;

– total number of coils n_t = n + n_r;

– pitch of the free (unloaded) spring:

t = d + + 0.1d = 1.1d + (Calc.8.6.5);

– free length of the spring H₀ = n·t + n_r d (Calc.0);

– length of the spring under the assembly force F₁ and under the nominal force F_n:

H₁ = H₀ − δ₁ = H₀ − (Calc.8.6.6),

H_n = H₀ − δ_n = H₀ − (Calc.8.6.6);

– spring stroke h = H₁ − H_n (Calc.0);

– blank length (wire length before coiling):

l_s = (Calc.8.6.7).

Nut tightening torque (applied with the wrench)

– parameters of the joint elements: from Annex.ST.03, the thread dimensions (Md), d, d₂, p; matching the thread size (Md), the clearance hole diameter D₁ (medium series) is taken from Annex.ST.05;

– thread torque (friction in the thread):

M_î = F_st tan(arctan + arctan ) (Calc.3.3.4),

where F_st = F₁, µ = 0.15…0.25 is the friction coefficient in the thread, α = 60° the profile angle of the metric thread and p the thread pitch;

– friction torque between nut and washer:

M_p = F_st μ₂ (Calc.3.3.5),

where µ₂ = 0.15…0.25 is the friction coefficient between nut and washer and D₁ the clearance hole diameter;

– nut tightening torque (applied with the wrench):

M_c = M_î + M_p (Calc.0),

which tightens the threaded joint and therefore compresses the spring with the assembly force F₁.

E. Design of the constructive-technological shape

Constructive-technological drawing (including the spring characteristic)

Recommendations for choosing the dimensions and constructive-technological parameters

– geometric parameters: d, t, D_i, D_m, D_e, n, n_t, H₀;

– parameters of the elastic characteristic: H₁, H_n, h, F₁, F_n;

– the seating faces are ground after heat treatment to a roughness R_a1 = 1.6 μm or R_a1 = 3.2 μm; perpendicularity and parallelism tolerances must be ensured;

– when checking the elastic characteristic, force tolerances of ±10 N are considered.

Recommendations for choosing the dimensions of the threaded joint elements (bolt-nut):

– eye bolt with thread size Md, d;

– hexagon nut (Annex.ST.04): Md, S, m;

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

– Grower spring washer (Annex.ST.07): MN, d, d₁, d₂, g.