Design of the cylindrical helical compression spring of the towing coupling — example

Design data

Preload pressure of the spherical pair: p₀ = (0.1…0.2) p_max = (0.1…0.2)·1.3 = (0.13…0.26) MPa, with p_max = 1.3 MPa; p₀ = 0.2 MPa is adopted.

Spring preload force: F₀ = 392.7 N.

Spring assembly force: F_a = 252.5 N.

Functional constraints: threaded shank Md = M10 (metric thread of 10 mm diameter); spring stroke between the coupled and uncoupled positions h = 8 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.

Material and heat treatments

The helical spring is made of the special spring steel 56Si17A (0.56% C, 1.7% Si).

Material properties

Heat treatments

Annealing at (680…700) °C before forming.

Quenching at (840…860) °C with oil cooling and tempering at (580…600) °C, HRC 48…50, after forming (coiling into the helical shape).

Sizing and checking

Calculation data

– loading: F_n = 252.5 N, F₁ = 40 N;

– dimensions: D_m = (1.4…1.6)Md = (1.4…1.6)·10 = (14…16) mm; D_m = 15 mm is adopted;

– materials: τ_a = 650 MPa, G = 8.5·10⁴ MPa.

Sizing

Wire diameter

Required wire diameter d_nec = 2.45 mm;

the wire diameter d = 2.5 mm is adopted.

Number of active coils

Required number of coils n_nec = 4.63;

n = 5 active coils are adopted.

Other dimensional parameters

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

– total number of coils n_t = n + n_r = 6.5;

– pitch of the free (unloaded) spring t = 4.8 mm;

– free length of the spring H₀ = n·t + n_r d = 5·4.8 + 1.5·2.5 = 27.8 mm;

– length of the spring under the assembly force F₁ = 40 N and under the nominal force F_n = 252.5 N: H₁ = 26.1 mm and H_n = 17.5 mm respectively;

– spring stroke h = H₁ − H_n = 26.1 − 17.5 = 8.6 mm;

– blank length (developed wire length before coiling) l_s = 308 mm.

Tightening torque of the threaded joint (applied with the wrench)

– parameters of the joint elements: thread M10, d = 10 mm, d₂ = 9.026 mm, p = 1.5 mm; clearance hole diameter D₁ = 11 mm;

– thread torque (friction in the thread), with F_st = 40 N, µ = 0.25 (friction coefficient in the thread), α = 60° (profile angle of the metric thread) and p = 1.5 mm (thread pitch): M_î = 51.9 Nmm;

– friction torque between nut and washer, with F_st = 40 N, µ₂ = 0.2 (friction coefficient between nut and washer) and D₁ = 11 mm (clearance hole diameter): M_p = 56.9 Nmm;

– nut tightening torque (applied with the wrench):

M_c = M_î + M_p = 108.8 Nmm,

which tightens the threaded joint and therefore compresses the spring with the assembly force F₁ = 40 N.

Constructive-technological shape

Constructive-technological drawing (including the spring characteristic)

Adopted dimensions and constructive-technological parameters:

– geometric parameters: d = 2.5 mm, t = 4.8 mm, D_i = 12.5 mm, D_m = 15 mm, D_e = 17.5 mm, n = 5, n_t = 6.5, H₀ = 27.8 mm;

– parameters of the elastic characteristic: H₁ = 26.1 mm, H_n = 17.5 mm, h = 8.6 mm, F₁ = 40 N, F_n = 252.5 N;

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

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

Adopted dimensions of the threaded joint elements (bolt-nut):

– eye bolt with thread M10, d = 10 mm;

– hexagon nut: M10, S = 17 mm, m = 8 mm;

– plain washer: d = 10 mm, d₁ = 10.5 mm, d₂ = 20 mm, h = 2 mm;

– Grower spring washer: MN 10, d = 10 mm, d₁ = 10.2 mm, d₂ = 15.2 mm, g = 2.5 mm.