Double-layer multi-strand cable having improved bending endurance

A two-layer multi-strand cord comprising:

• an internal layer of the cord made up of K=1 three-layer internal strand comprising:
• an internal layer made up of Q=1, 2, 3 or 4 internal metallic threads of diameter d1;
• an intermediate layer made up of M intermediate metallic threads of diameter d2 wound around the internal layer;
• and
• an external layer made up of N external metallic threads of diameter d3 wound around the intermediate layer;
• and
• an external layer of the cord made up of L>1 three-layer external strands wound around the internal layer of the cord comprising:
• an internal layer made up of Q′=1, 2, 3 or 4 internal metallic threads of diameter d1′;
• an intermediate layer made up of M′ intermediate metallic threads of diameter d2′ wound around the internal layer;
• and
• an external layer made up of N′ external metallic threads of diameter d3′ wound around the intermediate layer,
• wherein the cord has a bending endurance criterion SL≤40 000 MPa·mm with
• SL
• =
• max
• ⁡
• (
• Δ
• ⁢
• σ
• bending
• ⁢
• _
• ⁢
• CI
• Cp
• ;
• Δ
• ⁢
• σ
• bending
• ⁢
• _
• ⁢
• CE
• C
• r
• ×
• Cp
• )
• ,
• and a size criterion Ec≥0.46 with Ec=Sc/Se, where:
• Δσbending CI=Msteel×Max(d1;
• d1′;
• d2;
• d2′)/2 in MPa·mm is a maximum bending stress per unit curvature seen by the internal threads of the internal and external strands or intermediate threads of the internal and external strands,
• Δσbending_CE=Msteel×Max(d3;
• d3′)/2 in MPa·mm is a maximum bending stress per unit curvature seen by the external metallic threads of the internal and external strands,
• Msteel— 210 000 MPa is the modulus of the steel,
• d1, d1′, d2, d2′, d3 and d3′ are expressed in mm,
• Cp
• =
• CpIT
• +
• CpTE
• 2
• ,
• Cp is a penetration coefficient for the cord with CpIT an inter-strand penetration coefficient and Cp TE a penetration coefficient for the external strands with:
• CpIT=0.4 when the inter-strand distance E of the external strands of the external layer E<30 μm;
• or
• CpIT=1.0 when E>70 μm;
• or
• CPIT=0.015×E−0.05 when 30 μm≤E≤70 μm;
• and
• CpTE
• =
• CpC
• ⁢
• 3
• ′
• +
• min
• ⁡
• (
• CpC
• ⁢
• 2
• ′
• ;
• CpC
• ⁢
• 3
• ′
• )
• 2
• ,
• where CpC2′ is a penetration coefficient for the intermediate layer of the external strand and CpC3′ is a penetration coefficient for the external layer of the external strand such that:
• Cp C2′=0.4 when the inter-thread distance I2′ of the intermediate metallic threads of the intermediate layer I2′<10 μm;
• or
• Cp C2′=1.0 when I2′>40 μm;
• or
• Cp C2′=0.02×I2′+0.2 when 10 μm≤I2′≤40 μm;
• and
• Cp C3′=0.4 when the inter-thread distance I3′ of the external metallic threads of the external layer I3′<10 μm;
• or
• Cp C3′=1.0 when I3′>40 μm;
• or
• Cp C3′=0.02×I3′+0.2 when 10 μm≤I3′≤40 μm;
• Cr is a dimensionless performance coefficient of the cord with
• C
• r
• =
• 1
• -
• (
• sin
• ⁡
• (
• ∝
• f
• )
• d
• ⁢
• 3
• ×
• d
• ⁢
• 3
• ′
• ×
• (
• ∑
• i
• =
• 1
• Q
• ′
• +
• M
• ′
• +
• N
• ′
• ⁢
• F
• mi
• )
• ×
• sin
• ⁡
• (
• α
• ⁢
• t
• )
• N
• ×
• Cste
• )
• where:
• d3 and d3′ are expressed in mm,
• αf is an angle of contact between the external metallic threads of the internal strand and the external metallic threads of the external strands expressed in radians,
• αt is a helix angle of each external strand expressed in radians;
• ∑
• i
• =
• 1
• Q
• ′
• +
• M
• ′
• +
• N
• ⁢
• ′
• ⁢
• F
• mi
• is a sum of forces at break for the Q′+M′+N′ threads of an external strand in Newtons;
• Cste=1500 N·mm−2;
• D is a diameter of the cord in mm;
• and
• Sc is a compacted surface area in mm2 with Sc=[Q×(d1/2)2+M×(d2/2)2+N×(d3/2)2+L×(Q′×(d1′/2)2+M′×(d2′/2)2+N′×(d3′/2)2)]×π and Se is the surface area of the cord in mm2 Se=π×(D/2)2.