The torque coefficient K is defined as K = 12d(P + Ls d² secA' + Lw Dw), where:
- **d** is the nominal diameter of the thread in millimeters,
- **P** is the thread pitch in millimeters,
- **Ls** is the thread friction coefficient, which can be found in literature <6>, typically ranging from 0.1 to 0.2 for steel fasteners without lubrication,
- **dâ‚‚** is the mean diameter of the thread in millimeters,
- **A'** is the thread flank angle,
- **Lw** is the bearing surface friction coefficient, also referenced in literature <6> on page 66, with a value of approximately 0.15 for steel-to-steel contact without lubrication,
- **Dw** is the equivalent diameter of the bearing surface friction torque in millimeters.
When a bolt is installed and connected to a component, it experiences both axial tension and residual preload during operation. The total axial load F acting on the bolt can be expressed as F = F’f + Fc, where Fc represents the centrifugal force generated due to the rotation of the rod and bolt assembly. This force can be calculated using the formula Fc = 2mv²Dz, where:
- **v** is the linear velocity, given by v = PDn / (60 × 1000) in m/s,
- **m** is the total mass of the rod and bolt assembly in kilograms,
- **D** is the drum diameter in millimeters,
- **n** is the roller speed in revolutions per minute,
- **z** is the number of bolts per rod.
The residual preload force F’f is the clamping force remaining between the joint surfaces after the bolt has been subjected to the axial tensile force Fc. It can be calculated as F’f = Ff - (Cm / (Cm + Cb)) * Fc, where Cm/(Cm + Cb) represents the relative stiffness of the connected components. During operation, the joint is also subjected to a lateral force FH caused by the impact of the rod on the material. This force acts perpendicular to the bolt axis and can be measured electrically.
There are three main failure modes for bolted connections between rods:
1. During installation, excessive plastic deformation or fracture may occur due to combined tension and torsion caused by the tightening torque.
2. During operation, the bolt may experience excessive plastic deformation or breakage under axial tensile forces.
3. Sliding between the rod and the drum may occur under lateral loading.
For design calculations, the pre-tightening force Ff and the tightening torque Tf are determined based on the force analysis. A lateral load FH exists during operation, and although the inertial force from the rod assembly has a radial component, it is considered negligible. To prevent joint slippage, the residual preload must satisfy F’f ≥ KsFH/Lz, where:
- **Ks** is the slip resistance coefficient, typically between 1.1 and 1.3 (as per literature <6>),
- **L** is the friction coefficient between the joint faces, which ranges from 0.10 to 0.16 (from literature <6>).
Once F’f is determined, 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 is determined using equations (4) and (5). To ensure the bolt does not fail, the following strength condition must be satisfied: R = 4F / (Ï€d₲q) ≤ [σ], where:
- **dâ‚** is the minor diameter of the bolt in millimeters,
- **R** is the tensile stress in N/mm²,
- **[σ]** is the allowable tensile stress in N/mm².
This leads to the required minimum diameter: d₠≥ √(4F/[σ]).
For installation strength checks, the bolt should be evaluated according to GB/T 16823.2-1997 <5>. The yielding fastening axial force Ffy is calculated using the formula:
Ffy = RyAs + 32dAPn + Ls d₂² secA', 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, calculated as dA = 4As/Ï€.
The safety factor S must satisfy S = Ffy / Ff ≥ [S], where S ≥ 1.2 and [S] is the allowable safety factor.
In conclusion:
1. The appropriate tightening torque for the bolt connection between the threshing drum and the rod should be determined based on operational conditions.
2. The bolt diameter between the drum and the rod should be designed to ensure sufficient strength during operation.
3. To guarantee the strength of the connecting bolts during installation, the design must comply with GB/T 16823.2-1997.
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