In the operation of the double-sided milling machine set, the gear shaft within the gearbox of the nine-roll straightener frequently experiences fracture failures, which disrupts production continuity and necessitates a thorough investigation. This study systematically examines the working mechanism of the straightener, with a particular focus on the bending deformation of the straightening rolls. By selecting and calculating key parameters and performing rigorous checks on the bending deformation of the work rolls, the root causes of the gear shaft fracture are identified. Additionally, this research provides critical guidelines for operational practices to ensure stable and efficient performance of the production equipment. The analysis emphasizes the importance of proper parameter adjustments and load distribution to prevent overloading, which is often linked to the gear shaft failure.
The nine-roll straightener in the double-sided milling machine set comprises several core components, including an electric motor, reduction gearbox, gearbox, connecting shafts, and straightening rolls. The gearbox plays a vital role in distributing torque evenly to each straightening roll via the connecting shafts, ensuring synchronized operation. However, the gear shaft within this assembly is prone to fracture under excessive loads, highlighting the need for a detailed analysis of the system’s mechanics. The straightener’s pressing mechanism, which involves motors, reducers, worm gear reducers, screw-down mechanisms, balance springs, and upper and lower frames, allows for adjustable pressure application on the material. This adjustability is crucial for achieving the desired straightening effect but must be carefully controlled to avoid overstressing components like the gear shaft.
The working principle of the nine-roll straightener involves an alternating arrangement of upper and lower rolls, where the upper rolls are mounted on an adjustable beam that can be tilted. This design enables a gradual reduction in bending deformation from the entry to the exit side, effectively straightening the material. The straightening process relies on applying reverse bending moments to eliminate initial curvature variations in the strip. Specifically, the small deformation straightening scheme progressively reduces residual curvature by controlling the bending at each roll, while the large deformation scheme uses more aggressive bending in the initial rolls to accelerate the process. Both schemes require precise calculation of parameters to prevent issues such as gear shaft overload, which can lead to fracture. The gear shaft is critical in transmitting torque, and any imbalance in load distribution can exacerbate stress concentrations.
To understand the gear shaft fracture, it is essential to analyze the straightener’s design parameters. The roll pitch, roll diameter, number of rolls, and roll length are selected based on material properties and operational requirements. For instance, the maximum roll pitch is determined by straightening quality and bite conditions, while the minimum roll pitch depends on strength constraints like torsional limits of connecting shafts. The gear shaft must withstand the torques involved in these calculations. Key parameters and performance requirements are summarized in the table below:
| Technical Parameter | Performance Requirement |
|---|---|
| Material | Copper and copper alloy hot-rolled strips |
| Strip Thickness (mm) | 8–15 |
| Strip Width (mm) | 600–1050 |
| Line Speed (m/min) | 0–15 |
The roll pitch (t) is calculated considering maximum and minimum limits. The maximum roll pitch is derived from straightening quality and bite conditions. For straightening quality, the formula is:
$$ t_{\text{max}} = \frac{hE}{3\Psi\sigma_S} $$
where h is the strip thickness, E is the elastic modulus (1 × 10^5 N/mm² for copper alloys), Ψ is a coefficient (0.9 for medium-thick plates), and σ_S is the yield strength (250 N/mm²). Substituting values gives t_max ≈ 1185 mm. For bite conditions, the formula is:
$$ t_{\text{max}} = 8r_0\mu_1 $$
where r_0 is the original curvature radius (taken as 30h) and μ_1 is the sliding friction coefficient (0.2). This yields t_max ≈ 384 mm. The minimum roll pitch is based on the strength of connecting shafts, calculated as:
$$ t_{\text{min}} = 2.88h \sqrt[3]{\frac{b}{h}} $$
where b is the strip width (1050 mm). This results in t_min ≈ 178 mm. Thus, a standard roll pitch of t = 200 mm is selected. The roll diameter (D) is determined as D = Ψt = 0.9 × 200 = 180 mm, but standardized to D = 190 mm. The number of rolls (n) is chosen as 9 based on empirical data, and the roll length (L) is set to 1200 mm to accommodate the maximum strip width. The straightening speed (v) is synchronized with the production line at 0–15 m/min.
The force and energy parameters are critical for assessing the gear shaft load. The total straightening force (ΣP) is calculated using the formula:
$$ \Sigma P = \frac{4}{t} (1 + m)(n – 2)M_S $$
where m = M_W / M_S, M_S is the plastic bending moment, and M_W is the elastic bending moment. Specifically, M_S and M_W are given by:
$$ M_S = \frac{b h^2}{4} \sigma_S $$
$$ M_W = \frac{b h^2}{6} \sigma_S $$
Substituting values (b = 1050 mm, h = 15 mm, σ_S = 250 N/mm²) yields M_S ≈ 14.8 kN·m and M_W ≈ 9.875 kN·m. Thus, m ≈ 0.667, and ΣP ≈ 3460 kN. The force on each work roll (P) is then P = ΣP / 9 ≈ 384 kN. To check work roll bending deformation, the load per unit length (q) is q = P / l, where l is the bearing span (1450 mm), giving q ≈ 265 N/mm. The maximum deflection (y_max) and end rotation (θ_A, θ_B) are calculated as:
$$ \theta_A = -\theta_B = -\frac{q l^3}{24EI} $$
$$ y_{\text{max}} = -\frac{5q l^4}{384EI} $$
where E is the elastic modulus of the roll material (2 × 10^5 N/mm²) and I is the moment of inertia of the roll cross-section. For a roll diameter of 190 mm, I = πd^4 / 64 ≈ 6.4 × 10^7 mm⁴. Substituting values gives θ_A ≈ -0.0026 rad and y_max ≈ 1.19 mm. The allowable deflection [y] is (0.0003–0.0005)l ≈ 0.435–0.725 mm, and allowable rotation [θ] is 0.001–0.005 rad. Since y_max exceeds [y], the work roll stiffness is insufficient, necessitating support rolls to mitigate bending and reduce stress on the gear shaft.
The total drive torque (M) on the rolls is composed of bending deformation torque (M_b), rolling friction torque (M_k), and mechanical friction torque (M_m). The formula is:
$$ M = M_b + M_k + M_m $$
M_b is calculated as:
$$ M_b = \frac{D}{2} M_S \left[ \frac{1}{r_0} + \frac{K_n}{(n-2)\sigma_S} \right] \frac{h}{E} $$
where D = 190 mm, r_0 is the minimum original curvature radius, and K_n is a straightening scheme coefficient (1.7). This gives M_b ≈ 17.88 kN·m. M_k is given by:
$$ M_k = f \Sigma P $$
where f is the rolling friction coefficient (0.2 mm), resulting in M_k ≈ 0.692 kN·m. M_m, for a system with support rolls, is:
$$ M_m = \left[ C \mu_1 \frac{d_1}{2} + \frac{2f_1}{\cos \phi} + (1 – C) \mu \frac{d}{2} \right] \Sigma P $$
where C is the pressure distribution coefficient (0.7), μ and μ_1 are friction coefficients (0.005), d and d_1 are neck diameters (100 mm and 80 mm), f_1 is the rolling friction coefficient (0.05 mm), and φ is the contact angle (cos φ ≈ 0.85). This yields M_m ≈ 1.03 kN·m. Thus, M ≈ 19.60 kN·m. The straightening power (N) is then:
$$ N = \frac{M \cdot 2V}{D \eta} $$
where V = 0.25 m/s and η = 0.86, giving N ≈ 60 kW. The screw-down power is also calculated to ensure the pressing mechanism does not contribute excessively to gear shaft stress. For each screw, the power is derived from the friction torque (M), motor speed (n = 960 rpm), total reduction ratio (i = 759.5), and efficiency (η = 0.78). The formula is:
$$ N = \frac{M n}{9550 i \eta} $$
resulting in N ≈ 1.32 kW per screw, so the total motor power is 2.8 kW for two screws.
The fracture of the gear shaft is primarily attributed to uneven load distribution within the gearbox, especially when using a single reduction distributor for more than seven rolls. This design flaw causes overloading on specific rolls, particularly the third roll, leading to stress concentration and eventual gear shaft failure. The analysis shows that under large deformation straightening schemes, the initial rolls experience higher pressures, exacerbating the load on the gear shaft. To prevent this, operational practices must ensure that the screw-down adjustments match the strip thickness, avoiding excessive bending moments. Additionally, the use of support rolls in a staggered arrangement helps distribute loads more evenly, reducing the risk of gear shaft fracture. The table below summarizes the roll selection based on material thickness, emphasizing the importance of proper configuration:
| Straightener Type | Material Type | Number of Rolls (n) |
|---|---|---|
| Roller Plate Straightener | Plate Thickness 0.25–1.5 mm | 19–29 |
| Roller Plate Straightener | Plate Thickness 1.5–6 mm | 11–17 |
| Roller Plate Straightener | Plate Thickness >6 mm | 7–9 |
| Roller Section Straightener | Small-Medium Sections | 11–13 |
| Roller Section Straightener | Large Sections | 7–9 |
In conclusion, the gear shaft fracture in the nine-roll straightener is a result of design limitations and operational misalignments. By recalculating parameters and implementing balanced load distribution, the stress on the gear shaft can be mitigated. This study underscores the need for comprehensive design checks and adherence to operational guidelines to enhance the durability of critical components like the gear shaft. Future designs should incorporate multi-branch reduction distributors to improve load sharing and prevent similar failures. The insights provided here aim to guide production personnel in optimizing straightener performance and ensuring long-term reliability.