In mechanical engineering, the worm gear system is widely recognized for its high transmission ratio, smooth operation, and low noise characteristics. However, in practical applications, failures such as bending deformation of the worm shaft due to seizure and jamming are relatively rare. This article examines a case where a worm gear lifting mechanism experienced catastrophic failure, leading to bending of the worm shaft. We analyze the incident from structural, material, stress, stability, and transmission perspectives, emphasizing the critical role of the worm gear in the system. Through detailed calculations and observations, we identify the root cause as an improper transmission speed ratio and propose countermeasures to prevent similar issues in future designs.
The worm gear mechanism consists of a worm and a worm wheel, where the worm’s helical threads engage with the worm wheel’s teeth to transmit motion and power. This setup offers advantages like self-locking and compact design, but it is prone to overheating and seizure under high loads or improper lubrication. In the studied lifting mechanism, three SWL-25 type worm gear units were arranged in a line on a multi-level platform, driven by a central motor through shafts and universal joints. The worm shafts were connected to a carriage that moved vertically along guides, transporting fermentation tanks between levels. Initially, the system functioned well, but over time, all three worm shafts exhibited bending, with the second shaft showing the most severe deformation.
During on-site inspection, we observed that the lubricating grease in the worm gear boxes had bubbles, darkened color, and reduced quantity, indicating excessive heat generation. The worm wheel teeth showed signs of seizure, and the carriage was misaligned relative to the guide rails. These observations pointed to potential issues in the worm gear transmission, such as inadequate lubrication or overload, which could lead to failure.
To understand the material aspects, we sampled the worm shafts for analysis. The elemental composition of the shafts is summarized in Table 1. According to standards like GB/T 699-2015 for high-quality carbon structural steel, the material met the requirements for Grade 25 steel. However, for shaft components transmitting significant forces, medium-carbon tempered steels like 45 steel or 40Cr are typically preferred due to their higher strength and wear resistance. The use of Grade 25 steel in this worm gear application may have contributed to reduced durability under stress.
| Element | Worm Shaft 2 Sample 1 | Worm Shaft 2 Sample 2 | Worm Shaft 1 Sample | Worm Shaft 3 Sample |
|---|---|---|---|---|
| C | 0.23% | 0.23% | 0.21% | 0.23% |
| Si | 0.21% | 0.22% | 0.21% | 0.21% |
| Mn | 0.55% | 0.55% | 0.55% | 0.54% |
| P | 0.026% | 0.028% | 0.026% | 0.026% |
| S | 0.010% | 0.011% | 0.008% | 0.009% |
| Cr | 0.037% | 0.037% | 0.039% | 0.037% |
| Ni | 0.010% | 0.011% | 0.010% | 0.009% |
| Cu | 0.022% | 0.022% | 0.022% | 0.022% |
Next, we performed strength calculations for the worm shafts under operational conditions. The lifting mechanism handled a carriage weight of 29.4 kN and a满载发酵池 load of 186.2 kN, resulting in a total load Q. Assuming uniform load distribution, the forces on the three worm shafts (F1, F2, F3) were determined using static equilibrium equations for an indeterminate system. The balance equations are:
$$F_1 + F_2 + F_3 = Q_2 + Q_3$$
$$F_2 \cdot g + 2F_3 \cdot g = Q \cdot L$$
$$\frac{2F_2 h}{EA} = \frac{F_1 h}{EA} + \frac{F_3 h}{EA}$$
where E is the elastic modulus, A is the cross-sectional area, h is the worm shaft length, and g is the gravitational acceleration. Solving these, we found F1 = 25.3 kN, F2 = 71.9 kN, and F3 = 118.4 kN. The maximum tensile stress on worm shaft 3 was calculated as:
$$\delta = \frac{F_3}{A} = \frac{4F_3}{\pi d^2}$$
where d is the inner diameter of the worm thread (70 mm). This yielded δ = 30.8 MPa. For Grade 25 steel, the tensile strength is 450 MPa and yield strength is 275 MPa. With a safety factor of 2, the allowable stress is 137.5 MPa, indicating that the worm shaft should withstand normal tensile loads. However, this analysis assumes ideal conditions and does not account for dynamic effects or instability.
Stability analysis is crucial, as the worm shaft may experience compressive forces during jamming. The worm shaft, with a length of 5550 mm and diameter of 70 mm, was modeled as a column with fixed support at the bottom (bearing connection) and simply supported at the top (worm gear engagement). The slenderness ratio λ is given by:
$$\lambda = \frac{\mu h}{\gamma} = \frac{4\mu h}{d}$$
where μ is the constraint factor (0.7 for fixed-simple support) and γ is the radius of gyration. Calculating λ = 220, which exceeds the characteristic slenderness of 92.6 for Grade 25 steel, classifies the shaft as a long column prone to buckling. The critical stress δ_cr and critical force F_cr for Euler buckling are:
$$\delta_{cr} = \frac{\pi^2 E}{\lambda^2}$$
$$F_{cr} = A \delta_{cr}$$
Using E ≈ 200 GPa for steel, we obtained δ_cr = 40.78 MPa and F_cr = 156.9 kN. In a jamming scenario, such as when the worm gear seizes due to overheating, the worm shaft could be subjected to compressive forces exceeding F_cr. For instance, with a dynamic factor of 3-5 accounting for inertia, the compressive force could reach up to 355.2 kN, far above the critical value, leading to instability and bending deformation. The buckling mode for a fixed-simple support column matches the observed bending pattern, confirming this failure mechanism in the worm gear system.
Transmission speed ratio analysis revealed a significant discrepancy. The SWL-25 worm gear unit is designed for a speed ratio of 32:1, but the installed system had a ratio of 24:1. This change increased the worm wheel speed from 45.9 r/min to 61.3 r/min, a 33.6% rise. In worm gear transmissions, higher speeds exacerbate frictional heating, as the relative sliding motion between worm and worm wheel generates substantial heat. The heat can degrade lubricants, reduce viscosity, and cause seizure. The observed grease condition—bubbled, darkened, and reduced—supports this, indicating inadequate heat dissipation and lubrication failure. The increased speed ratio not only elevated temperatures but also accelerated wear, contributing to the eventual jamming and bending of the worm shaft.
To quantify the thermal effects, consider the power transmission and efficiency. The input power from the 18.5 kW motor at 1470 r/min should be sufficient for the worm gear system, but the altered ratio changes the dynamics. The power loss due to friction in the worm gear can be estimated using efficiency formulas, such as:
$$\eta = \frac{\tan \lambda}{\tan (\lambda + \phi)}$$
where λ is the lead angle and φ is the friction angle. A lower lead angle or higher friction coefficient, common in poorly lubricated worm gear systems, reduces efficiency and increases heat generation. This thermal buildup can lead to thermal expansion and altered clearances, further promoting seizure.
In summary, the failure of the worm shaft bending deformation in this worm gear lifting mechanism stemmed from multiple factors. Primarily, the improper transmission speed ratio increased operational speeds, leading to excessive heating and lubrication breakdown in the worm gear. This caused seizure, which in turn subjected the worm shaft to compressive forces beyond its buckling capacity. Additionally, the use of Grade 25 steel, while meeting basic strength requirements, offered lower resistance to wear and instability compared to recommended materials like 45 steel. Lubrication maintenance was also inadequate, as evidenced by the degraded grease, which failed to mitigate friction and heat in the worm gear system.
To prevent such failures, designers should ensure that worm gear systems use appropriate speed ratios as per specifications, select higher-grade materials for critical components, and implement regular maintenance schedules for lubrication. Furthermore, incorporating stability checks in design calculations can help identify potential buckling risks. By addressing these aspects, the reliability and safety of worm gear lifting mechanisms can be significantly enhanced, reducing the likelihood of catastrophic failures like worm shaft bending.
In conclusion, the worm gear plays a pivotal role in transmission systems, but its performance is highly sensitive to design parameters and operational conditions. Through comprehensive analysis involving material science, mechanics, and thermodynamics, we have highlighted the importance of balanced design in worm gear applications. Future work could explore advanced materials or cooling methods to further improve the durability of worm gear systems in heavy-duty lifting operations.