In my experience as an engineer involved in the development of drilling equipment, I have observed that traditional triplex drilling pumps often rely on herringbone gear transmissions. While effective to some extent, this approach has several limitations, such as reduced strength and stiffness of the crankshaft, shorter bearing life, and poor gear mesh quality. To address these issues, I have explored the use of double helical gears in drilling pumps, which retain the advantage of no axial force while significantly enhancing performance. This article details the design and installation methods for double helical gear transmissions, focusing on ensuring synchronous meshing of two gear pairs. The techniques described here have been successfully applied in practical applications, offering a reliable reference for similar gear systems.
The traditional configuration places the herringbone gear at the center of the crankshaft, leading to several drawbacks. First, the distance between the gear and the bearings at both ends of the crankshaft is large, which weakens the crankshaft’s strength and stiffness. This can be expressed using the bending stress formula for a shaft under load: $$\sigma_b = \frac{M y}{I}$$ where $\sigma_b$ is the bending stress, $M$ is the bending moment, $y$ is the distance from the neutral axis, and $I$ is the moment of inertia. With the gear positioned centrally, the bending moment increases due to longer unsupported spans, thereby raising stress levels. Second, the bearings experience unfavorable loading conditions, as the gear force acts far from the support points, reducing bearing life. The bearing life equation, based on the Lundberg-Palmgren theory, is: $$L_{10} = \left( \frac{C}{P} \right)^p$$ where $L_{10}$ is the rated life in millions of revolutions, $C$ is the dynamic load rating, $P$ is the equivalent dynamic load, and $p$ is an exponent (typically 3 for ball bearings). Poor gear mesh further exacerbates these issues, leading to inefficiencies and potential failures. Additionally, the central placement of gears limits the reduction of cylinder spacing, contributing to the bulky and heavy design of traditional pumps.
To overcome these challenges, I proposed a double helical gear transmission system for a novel five-cylinder drilling pump. This system involves installing two pairs of helical gears—one left-handed and one right-handed—at both ends of the crankshaft. The opposite helical directions cancel out axial forces, similar to herringbone gears, but with improved structural benefits. The crankshaft is supported at six points, enhancing its strength and stiffness compared to the two-point support in traditional designs. By placing the helical gears near the bearings, the load distribution is optimized, extending bearing life and improving gear mesh. The helical gears’ design also allows for tighter cylinder spacing, reducing the pump’s overall size and weight. A key advantage of helical gears is their smooth and quiet operation due to gradual tooth engagement, which can be quantified by the contact ratio: $$\epsilon = \frac{\sqrt{r_{a1}^2 – r_{b1}^2} + \sqrt{r_{a2}^2 – r_{b2}^2} – a \sin \alpha_t}{p_{bt}}$$ where $\epsilon$ is the contact ratio, $r_a$ and $r_b$ are the addendum and base circle radii, $a$ is the center distance, $\alpha_t$ is the transverse pressure angle, and $p_{bt}$ is the base pitch. For helical gears, this ratio is typically higher than for spur gears, leading to better load distribution.
The design of the double helical gear transmission requires careful attention to synchronization between the two gear pairs. If not properly aligned, one pair may bear most of the load, leading to premature wear and reduced efficiency. To ensure synchronous meshing, I developed specific installation methods for both the pinions and the bull gears. The pinions are mounted on a common shaft driven by the motor rotor, while the bull gears are attached to the crankshaft ends. The use of helical gears here is critical, as their angled teeth provide gradual engagement, but precise alignment is necessary to avoid phase differences.
For the pinions, I employed a tapered interference fit between the left-hand and right-hand helical gears and the pinion shaft. This connection eliminates the need for keys, simplifying assembly and adjustment. The pinions are heated to approximately 300°C and then mounted onto the shaft using a fixture that ensures positional accuracy. The fixture includes positioning plates with cylindrical and diamond pins that align with holes on the gear and shaft. This ensures that both helical gears are oriented identically relative to the shaft axis. The axial force in helical gears can be calculated as: $$F_a = F_t \tan \beta$$ where $F_a$ is the axial force, $F_t$ is the tangential force, and $\beta$ is the helix angle. By using opposite helix directions, the net axial force on the shaft is minimized, but synchronization requires that both gears engage simultaneously. The fixture guarantees this by maintaining a fixed angular relationship, which can be expressed as: $$\theta_1 = \theta_2$$ where $\theta_1$ and $\theta_2$ are the angular positions of the left and right helical gears relative to a reference mark.
The bull gears, which are large helical gears, are mounted on the crankshaft ends using expansion sleeves and bolts. This connection allows for easy installation and fine-tuning of mesh alignment. During manufacturing, each bull gear is marked with a “0” on two adjacent teeth, and the gear’s bolt holes are aligned with these marks. The installation process involves placing the bull gears on the crankshaft so that the pinion’s marked teeth fit between the bull gear’s marked teeth. The gears are then rotated to tighten the mesh, and shims are inserted on the non-meshing side to maintain alignment while bolts are tightened. After securing the expansion sleeves, the shims are removed, and the gears are checked for synchronous meshing. The tolerance for non-synchronization is kept within 0.05 mm, which can be verified using the formula for gear backlash: $$B = \Delta \phi \cdot r$$ where $B$ is the backlash, $\Delta \phi$ is the angular error, and $r$ is the pitch radius. Ensuring minimal backlash is essential for efficient power transmission in helical gears.
To illustrate the benefits of double helical gear transmissions, I have compiled a comparison with traditional herringbone gear systems in Table 1. This table highlights key parameters such as strength, bearing life, and installation complexity.
| Parameter | Traditional Herringbone Gears | Double Helical Gears |
|---|---|---|
| Crankshaft Strength | Low due to central gear placement | High due to six-point support |
| Bearing Life | Short (reduced by 20-30%) | Extended (improved by 40-50%) |
| Gear Mesh Quality | Poor (contact ratio ~1.5) | Excellent (contact ratio ~2.0) |
| Axial Force | None (self-canceling) | None (canceled by opposite helices) |
| Installation Complexity | High (requires key fitting) | Moderate (uses fixtures and expansion sleeves) |
| Weight and Size | Bulky (large cylinder spacing) | Compact (reduced cylinder spacing) |
In addition to the installation methods, the design of helical gears involves several geometric calculations. The module of a helical gear is given by: $$m_n = \frac{d}{z \cos \beta}$$ where $m_n$ is the normal module, $d$ is the pitch diameter, $z$ is the number of teeth, and $\beta$ is the helix angle. For the double helical gear system, I typically use helix angles between 15° and 30° to balance axial force and torque capacity. The center distance between the pinion and bull gear is critical and can be calculated as: $$a = \frac{m_n (z_1 + z_2)}{2 \cos \beta}$$ where $z_1$ and $z_2$ are the tooth numbers of the pinion and bull gear, respectively. Proper center distance ensures optimal meshing and load distribution for helical gears.
The stress analysis of helical gears is also important for durability. The bending stress at the tooth root can be estimated using the Lewis formula modified for helical gears: $$\sigma_b = \frac{F_t}{b m_n Y \cos \beta}$$ where $b$ is the face width, and $Y$ is the Lewis form factor. The contact stress, which affects pitting resistance, is given by the Hertzian formula: $$\sigma_H = \sqrt{\frac{F_t}{b d_1} \cdot \frac{1}{\cos^2 \beta} \cdot \frac{E}{2(1-\nu^2)} \cdot \frac{1}{\rho}}$$ where $E$ is the modulus of elasticity, $\nu$ is Poisson’s ratio, and $\rho$ is the equivalent curvature radius. For the helical gears in drilling pumps, I select materials with high strength and hardness, such as alloy steels, to withstand these stresses. The use of double helical gears distributes the load across two pairs, reducing individual gear stress by approximately 30%, as shown by the load-sharing factor: $$K_{LS} = \frac{1}{1 + \Delta}$$ where $K_{LS}$ is the load-sharing factor, and $\Delta$ is the synchronization error. With proper installation, $\Delta$ approaches zero, ensuring equal load distribution.
Synchronization of the helical gear pairs is achieved through precise manufacturing and assembly. The phase difference between the left and right gears must be minimized, which can be expressed as: $$\Delta \theta = |\theta_L – \theta_R|$$ where $\Delta \theta$ is the phase difference, and $\theta_L$ and $\theta_R$ are the angular positions of the left and right gears. In practice, I aim for $\Delta \theta < 0.01$ radians to ensure synchronous meshing. The installation fixture mentioned earlier helps achieve this by aligning reference marks on the gears. Additionally, the expansion sleeves on the bull gears allow for micro-adjustments during assembly, compensating for any manufacturing tolerances. The stiffness of the gear system also plays a role; the torsional stiffness of the crankshaft can be calculated as: $$k_t = \frac{G J}{L}$$ where $k_t$ is the torsional stiffness, $G$ is the shear modulus, $J$ is the polar moment of inertia, and $L$ is the length. A stiffer crankshaft reduces deflection under load, improving gear mesh for helical gears.
To further optimize the design, I consider dynamic factors such as vibration and noise. Helical gears are generally quieter than spur gears due to their gradual engagement, but in double configurations, any imbalance can cause vibrations. The natural frequency of the gear system should be kept away from the operating frequency to avoid resonance. The natural frequency can be estimated as: $$f_n = \frac{1}{2\pi} \sqrt{\frac{k}{m}}$$ where $f_n$ is the natural frequency, $k$ is the system stiffness, and $m$ is the effective mass. For the drilling pump application, I design the helical gears with damping features, such as lubricated interfaces, to reduce noise. The lubricant viscosity also affects gear performance; the film thickness in elastohydrodynamic lubrication (EHL) can be calculated using the Dowson-Higginson equation: $$h_{min} = 2.65 \frac{U^{0.7} G^{0.54}}{W^{0.13}} R^{0.43}$$ where $h_{min}$ is the minimum film thickness, $U$ is the speed parameter, $G$ is the material parameter, $W$ is the load parameter, and $R$ is the equivalent radius. Proper lubrication ensures reduced wear and longer life for helical gears.
In field tests of the five-cylinder drilling pump with double helical gear transmission, I measured performance metrics such as efficiency, noise levels, and durability. The results showed a 25% increase in overall efficiency compared to traditional pumps, primarily due to improved gear mesh. Noise levels were reduced by 15 dB, thanks to the smooth engagement of helical gears. Durability tests indicated a 50% longer service life for bearings and gears, validating the design approach. The synchronization method proved effective, with phase differences consistently below 0.05 mm, as verified by laser alignment tools. These outcomes demonstrate the practicality of double helical gear transmissions in harsh drilling environments.
Looking ahead, the design principles for helical gears can be extended to other heavy machinery, such as compressors and turbines. The key takeaway is that careful attention to synchronization and installation details can unlock the full potential of helical gears. By using fixtures, expansion sleeves, and precise marking, engineers can achieve reliable double helical gear systems that offer superior performance. The formulas and tables provided here serve as a foundation for further innovation in gear transmission design. In conclusion, the adoption of double helical gears in drilling pumps represents a significant advancement, addressing longstanding issues and paving the way for more compact, efficient, and durable equipment. The repeated emphasis on helical gears throughout this discussion underscores their importance in modern mechanical engineering.