The torque coefficient, denoted as K, is calculated using the formula:
K = 12d(P + Ls d² secA′ + Lw Dw), where:
- d is the nominal diameter of the thread in mm,
- P is the pitch of the thread in mm,
- Ls is the thread friction coefficient, typically ranging from 0.1 to 0.2 for steel fasteners without lubrication (as referenced in literature <6>),
- dâ‚‚ is the mean diameter of the thread in mm,
- A′ is the thread flank angle,
- Lw is the friction coefficient of the bearing surface, which is approximately 0.15 for steel-to-steel contact under dry conditions (also from literature <6>, page 66),
- Dw is the equivalent diameter of the bearing surface friction torque in mm.
When a bolt is connected and in operation, it experiences both axial tension and residual preload. The total axial load on the bolt, F, can be expressed as:
F = F′f + Fc, where Fc is the centrifugal force generated by the rotating assembly. This force is calculated as:
Fc = 2mv²Dz, with v being the linear velocity, given by v = PDn/(60×1000) in m/s, m as the mass of the rod and bolt assembly in kg, D as the drum diameter in mm, n as the roller speed in rpm, and z as the number of bolts per rod.
The residual preload force, F′f, is the clamping force remaining after the bolt is subjected to axial tension. It can be calculated using:
F′f = Ff - Cm/(Cm + Cb) × Fc, where Cm/(Cm + Cb) represents the relative stiffness of the joint components. During operation, the joint is also exposed to a lateral force FH, which results from the impact of the rod against the material. This force acts perpendicular to the bolt axis and is measured electrically.
There are three main failure modes for bolts connecting the rods: during installation, excessive plastic deformation or fracture may occur due to combined tension and torsion caused by the tightening torque; during operation, the bolts may fail under axial tensile forces; and slippage between the rod and drum may occur under lateral loading.
For design calculations, the pre-tightening force Ff and the tightening torque Tf are determined based on the forces acting on the system. Considering the presence of a lateral load FH, the condition that the joint does not slip must be satisfied:
F′f ≥ KsFH/Lz, where Ks is the slip resistance factor (ranging from 1.1 to 1.3, as per literature <6>), L is the friction coefficient between the joint surfaces (typically 0.10–0.16), and z is the number of bolts. Once F′f is known, the pre-tightening force Ff can be calculated using equation (6), and the tightening torque can be derived from equation (1).
During operation, the tensile force F on the bolt should be determined using equations (4) and (5). To ensure no failure occurs, the following strength condition must be met:
R = 4F / (Ï€d₲q) ≤ [σ], where dâ‚ is the bolt diameter in mm, R is the tensile stress in N/mm², and [σ] is the allowable tensile stress. From this, the minimum required diameter can be calculated as:
d₠≥ √(4F / [σ]).
For the installation phase, the bolt must be checked according to GB/T 16823.2-1997. The yielding fastening axial force Ffy is calculated using:
Ffy = RyAs + 3/2 * dA * Pn + Ls d₂² secA′², where Ry is the yield limit of the bolt in N/mm², As is the nominal stress area of the thread in mm², dA is the equivalent diameter of the thread cross-section in mm, and Pn is the nominal pitch. The safety factor S must satisfy:
S = Ffy / Ff ≥ [S], where [S] is the allowable safety factor, typically greater than 1.2.
In conclusion:
(1) The optimal tightening torque for the bolt connection between the threshing drum and the rod should be determined based on specific operating conditions.
(2) The bolt diameter between the drum and the rod should be designed to ensure sufficient strength during operation.
(3) To guarantee adequate strength during installation, the bolts must be checked according to GB/T 16823.2-1997.
80G Fm Radar Level Meter,80G Liquid Level Sensor,Level Monitoring Gauge,Anti-Corrosion High Precision Radar Level Gauge
Jiangsu Pinpai Technology Co., Ltd. , https://www.jspingpa.com