Bolt-type tension clamps work by gripping the conductor or ground wire through clamping force. This gripping force comes from two aspects:
① The friction force generated by the compression block pressure at the rear part of the clamp and the arc surface friction formed by many small waves;
② The friction force generated by the arc surface at the front part of the clamp, which can also be said to be the friction effect produced by the vertical pressure of several U-bolts (2, 3, 4, or 5 bolts depending on structural design) and the wave-shaped clamp to fix the conductor. Its advantages are simple structure, no need to disconnect the conductor for non-terminal towers during line usage, reducing line joints, facilitating construction, and benefiting the safe operation of the line.
Conductor Tension Calculation
According to the working principle of bolt-type tension clamps, the gripping force of the clamp relies on tightening several U-bolts to compress the conductor and generate tail tension, while generating greater friction force at the front arc section to grip the conductor. The magnitude of friction force on the arc surface depends on the friction coefficient and the angle encompassed by the arc. Figure 3-7 shows the force analysis diagram of the bolt-type tension clamp and the stress analysis of the clamp arc surface.
Figure 3-7 Schematic Diagram of Force Analysis for Bolt-Type Tension Clamp and Stress Analysis Diagram of Clamp Arc Surface
(a) Force analysis intent for bolt-type tension clamp; (b) Stress analysis diagram of clamp arc surface
As shown in Figure 3-7 (b), taking a micro-segment dl on the clamp as an isolated body:
dN = Tsin(dθ/2) + (T + dT)sin(dθ/2)
Since dθ is very small, we can take sin(dθ/2)≈dθ/2, and neglecting the second-order infinitesimal dTsin(dθ/2), we get dN=Tdθ.
Also, since fdN+Tcos(θ/2)=(T+dT)cos(dθ/2), taking cos(dθ/2)≈1, we obtain fdN=dT, therefore:
dN=Tdθ=dT/f or fdθ=dT/T
Integrating both sides:
we get ln(T₁/T₂) = fα, which gives:
(3-1)
Where:
T₁ - Conductor tension, N
T₂ - Groove tail tension, N
e - Base of natural logarithm, e = 2.718
f - Sliding friction coefficient
α - Arc angle, rad
From equation (3-1), it can be seen that increasing angle α can increase friction force. However, the additional bending stress on the conductor is inversely proportional to the curvature radius R. To avoid excessive additional stress on the conductor at the clamp exit, the curvature radius of the clamp must be increased. For ordinary bolt-type tension clamps, there is a certain limit to increasing arc angle α and curvature radius R; excessive increase will lead to oversized dimensions, excessive weight, and impracticality.
To overcome the "certain limit" problem, the general practice is to make the tail of the clamp with wave-shaped small grooves (too deep waves are not suitable for aluminum conductor steel reinforced - ACSR), and use U-bolts to press the conductor into the grooves to increase arc surface friction. However, because the conductor has a certain stiffness (larger conductors have greater stiffness), bending the conductor requires certain pressure. Therefore, the tightening force of installing U-bolts must first overcome the conductor stiffness. After the conductor is pressed against the groove bottom, the remaining force can be used to compress the conductor (importantly, compressing the aluminum strands). Often, due to insufficient force compressing the conductor, the arc surface friction mainly occurs between the aluminum strands and the clamp, causing the aluminum strands to break and the steel core to be pulled out, forming a "core extraction" phenomenon. Therefore, arc surface compressive stress must be considered. As shown in Figure 3-7, the calculation method is as follows:
(3-2)
(3-3)
Where:
φ - Arc angle, rad
R - Curvature radius, m
q - Pressure per unit length, N/cm
τ - Friction force per unit length, N/cm
According to force balance conditions, ΣTᵧ = 0, then:
Therefore, we can solve:
Substituting into equation (3-3), the pressure per unit length L on the groove arc surface is:
q = (T₁ + T₂)/[2Rtan(φ/2)] (3-4)
Bolt-type Tension Clamp Gripping Pressure Calculation
The purpose of calculating bolt pressure is to ensure sufficient static friction force after tension clamp installation.
For M10~M60 coarse thread, tightening torque M=0.2pd (where p is bolt preload force, d is nominal diameter of bolt). For convenience in analyzing bolt preload force and ensuring reliable preload, it should reach 50%~70% of material yield limit. At this time, the bolt preload force can be deduced as:
p = M/(0.2d) = 5(M/d) (3-5)
For convenience of analysis and estimation, assume that the gripping force of the tension clamp groove profile on the conductor consists of four bolt pressures p₁, p₂, p₃, p₄, three small arc friction forces Δt₁, Δt₂, Δt₃ (as shown in Figure 3-8), and large arc friction force ΔT.
Figure 3-8 Schematic Diagram of Force Distribution in the Cable Channel of a Bolt-Type Tension Clamp
According to material mechanics theory, understanding the arrangement of two bolt nuts as a simple beam structure (as shown in Figure 3-9),
Figure 3-9 Simply Supported Beam
and assuming the total pressure of two bolt nuts is p', beam deformation is δ, and EJ is bending strength, then the total pressure of the simple beam formed by two bolt nuts is:
p' = (48EJδ)/L³ (3-6)
The force p₁ used to compress the conductor is:
p₁ = 2p - p' (3-7)
If the friction coefficient between steel clamp and aluminum strands is f (generally f=0.25), then friction force T₂ is:
T₂ = T₁f = 0.25T₁ (3-8)
From equation (3-1), the friction force calculation formulas for three small arcs are:
Large arc friction force ΔT is:
ΔT = (T₁ + Δt₁ + Δt₂ + Δt₃)(e^(fα) - 1) (3-9)
Total gripping force T of the clamp is:
T = T₁ + Δt₁ + Δt₂ + Δt₃ + ΔT (3-10)
The conductor breaking force can be calculated by the following formula:
(3-11)
Where:
σAB - Aluminum strand breaking stress, N/mm²
σSB - Steel strand breaking stress, N/mm²
FA - Aluminum strand cross-sectional area, mm²
FS - Steel strand cross-sectional area, mm²
Stress Calculation of Aluminum Wire on Arc Surface
The stresses on aluminum wire of conductor on arc surface include transverse compression stress, longitudinal tensile force, and bending stress, calculated by equation (3-1). The pressure q per unit length on arc surface is:
q = (T₁ + T₂)/[2Rtan(φ/2)] (3-12)
Where:
φ - Arc angle of large arc surface, rad
R - Large arc radius, mm
The compressive stress σN per unit area on aluminum wire of conductor on arc surface, according to overhead line mechanical calculation principles:
σN = q/D (3-13)
Where:
D - Conductor outer diameter, mm
q - Pressure per unit length on arc surface, N/mm
The additional stress σ caused by conductor bending in the sheave is:
σ = (3/8) × (d/D)EA = 0.375(d/D)EA(3-14)
According to material mechanics theory on two-dimensional stress calculation, the combined stress σ_s is:
(3-15)
In fact, the arc surface compressive stress σ_N has little effect on total stress σ_s and can be neglected.
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