The fundamental principles and assumptions of "vehicle-orbital vibrancy dynamics" have provided methods for calculating P and ar, but these methods rely heavily on electronic computers and cannot theoretically account for the full impact of P and ar. From a maintenance and repair perspective, if the factors that influence P and ar can be eliminated, the formation of screw hole cracks in rails can be significantly reduced. Therefore, certain assumptions must be made about the orbital system:
1. The track is considered to be rigidly supported, with the wheels acting as "excitation points."
2. The track is only subjected to vertical impacts (since P and ar are primarily influenced by vertical forces). In this case, the wheel acts as the impact load, and the rail is the impacted member. This assumption includes: first, that the impacted member still obeys Hooke’s law under impact; second, that the mass of the impacted component is negligible; and third, that no energy losses are considered.
When conditions (1) and (2) are satisfied, P and ar can be simplified using energy methods, conservation of energy, and the principle of energy conversion. This allows for the calculation of the impact force and the vibration acceleration of the rail under that force. For example, when a wheel applies a vertical impact to the rail joint, the wheel's weight Q (including its own weight and load) and its impact velocity Ur are considered. The rail experiences an impact force PI and a sleeper reaction force Frs. The rail's vibration equation is given by: mr * ar = PI - Frs, where mr represents the rail mass. The calculation of Frs follows the same principles as that of PI. Here, am refers to the mass of the wheel, and Kp represents the stiffness of the underlay cushion, fasteners, and sleepers.
According to "Vehicle-Axis Coordination Dynamics," the rail joints on ordinary tracks are the primary sources of disturbance in the wheel-rail system. When a wheel passes through a rail joint, the sudden change in the wheel center causes an instantaneous vertical impact on the track. Once the wheel leaves the joint area, the impact velocity disappears. The calculation of the joint region's impact velocity uses formulas outlined in "Vehicle-Operational Occurrence Dynamics."
Several factors influence P and ar, as shown in equations (1) and (2):
1. P and ar are strongly correlated with axle weight, speed, and disturbances such as rail joints, misaligned welds, low buckles, and peeling blocks. An increase in P and ar directly increases the likelihood of screw hole cracks in rails. This trend has been confirmed through statistical analysis of various lines.
2. P and ar increase linearly with vehicle speed, which aligns with findings from "Vehicle-Track Accidental Dynamics."
3. Disturbances in the track, such as rail joints, low joints, misaligned welds, and peeling blocks, are the root causes of P and ar. These disturbances cause P and ar to increase proportionally. Without disturbances, there would be no shocks or vibrations, making disturbance control essential in managing P and ar.
4. As rail mass increases slightly, P increases while ar decreases slightly. This is consistent with existing conclusions. Statistical data show that P60 rails have more screw hole cracks than P50 rails.
5. Track system rigidity K has a significant effect on P. A higher K leads to a smaller 6j and a larger impact force. K depends on the stiffness of the pad, track bed, and subgrade. Temperature changes affect K, with winter stiffness being greater than summer stiffness. Consequently, P is higher in winter, leading to a higher probability of screw hole cracks during colder months.
6. The stiffness of the under-slab pad KP greatly influences ar. If the track system is dynamic, and fasteners are loose or broken, or sleepers fail, KP decreases, causing ar to increase and rail vibrations to intensify. This increases the risk of screw hole cracks. For instance, the presence of dark pits or voids can worsen the condition, increasing P and ar values.
7. Traffic volume and wheel radius have a major impact on P and ar. Higher traffic volumes and smaller wheel radii (such as those found in freight vehicles) result in higher P and ar, increasing the chance of screw hole cracks. For example, on the Beijing-Kowloon Railway, the downline has a higher traffic volume than the upline, leading to more cracked rails. Despite lower speeds, the high number of trucks increases the risk of cracks compared to other lines like the Huaihuai or Fuxian lines.
Based on the above analysis, the factors contributing to rail screw hole cracks can be attributed to various aspects of the track structure and operational conditions.
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