With the widespread adoption of paperless offices, many workspaces and conference rooms are equipped with computers. However, traditional computer monitors are typically fixed on desktops, which significantly reduces space utilization and makes them prone to dust accumulation. The primary purpose of the hidden computer display lifting mechanism is to save desk space, improve space efficiency, and effectively prevent dust contamination while offering some防盗 benefits. The rapid lifting structure for desktop computer hidden displays has evolved through five generations: the first generation used chain drive, the second employed gear and rack transmission, the third utilized round rod bearing transmission, the fourth adopted ball track structures, and the fifth generation combines linear guides with linear bearings. Currently, various types of lifting mechanisms are in use, with common domestic and international types including rack and pinion gear systems, chain and sprocket systems, and screw-driven systems. This analysis focuses on the rack and pinion gear transmission for lifting, as illustrated below. In rack and pinion gear systems, the rack can be considered a gear with an infinitely large base circle. Rack and pinion transmission offers smooth motion and high transmission efficiency, meeting the requirements for rapid lifting in desktop computer hidden display applications. To achieve cost reduction, preliminary design parameters for the rack and pinion gear are established, followed by finite element analysis to optimize the structure.
In this design, based on usage requirements, the initial parameters for the rack and pinion gear are set as follows: module of 2 mm, pinion teeth count of 25, pressure angle α = 20°, addendum coefficient h*_a = 1, and clearance coefficient C* = 0.25. The pinion material is 40Cr (quenched and tempered), while the rack material is 45 steel (quenched and tempered). Both rack and pinion gear components are selected with a precision grade of 7. The linear velocity of the pinion is 0.1 m/s. The servo motor has a rated torque of 1.27 N·m and a maximum torque of 3.81 N·m. The design process involves calculating surface contact strength, root bending strength, and root fatigue strength to verify that the rack and pinion gear transmission meets operational demands.
The surface contact strength for the rack and pinion gear is calculated using the formula:
$$ \sigma_H = \frac{2K_H T_1}{\phi_d d_1} \cdot \frac{u+1}{u} \cdot Z_H Z_E Z_\epsilon \leq [\sigma_H] $$
where the load factor K_H is selected as 1.3, the face width coefficient φ_d is 0.6, the zone coefficient Z_H is 2.5, and the material elasticity coefficient Z_E is 189.8 MPa^{1/2}. The contact ratio for the rack and pinion gear transmission is determined by:
$$ \epsilon_\alpha = \frac{1}{2\pi} \left[ z_1 (\tan \alpha_{a1} – \tan \alpha’) + \frac{2h^*_a \sin \alpha}{\cos \alpha} \right] $$
with h*_a = 1, α = α’ = 20°, α_{a1} ≈ 22.192°, and z_1 = 25, resulting in ε_α = 1.165. The contact fatigue strength’s contact ratio coefficient Z_ε is:
$$ Z_\epsilon = \sqrt{\frac{4 – \epsilon_\alpha}{3}} = \sqrt{\frac{4 – 1.165}{3}} = 0.972 $$
Substituting into the surface contact strength equation with a torque of 3.81 N·m yields σ_H = 167.6 MPa. The allowable contact fatigue limits are [σ_H]_1 = 600 MPa and [σ_H]_2 = 550 MPa, confirming that σ_H ≤ [σ_H]. For root bending fatigue strength, the calculation focuses on the pinion due to the rack’s infinite diameter approximation:
$$ \sigma_F = \frac{2K_F T_1 Y_{Fa} Y_{Sa} Y_\epsilon}{\phi_d m^3 n_1^2} \leq [\sigma_F] $$
with face width coefficient φ_d = 0.6, trial factor K_F = 1.3, bending strength contact ratio coefficient Y_ε = 0.25 + 0.75/ε_α = 0.894, form factor Y_Fa = 2.65, stress correction factor Y_Sa = 1.59, and allowable bending fatigue limit [σ_F] = 500 MPa. Calculating σ_F gives 12.438 MPa, which is within the allowable limit, indicating the initial rack and pinion gear design meets requirements.
Finite element analysis is conducted to optimize the geometric dimensions, such as face width, for material savings and cost reduction. The continuous body is discretized into small grids, and mathematical models are used for computation. The rack and pinion gear model is simplified to reduce computational load, as shown in the analysis. Material is set as alloy steel, mesh element size is 2 mm, friction coefficient is 0.1, and the applied torque on the pinion is the servo motor’s maximum torque of 3.81 N·m. After meshing, stress analysis reveals that stress is concentrated on the rack, particularly at the root and bolt connection areas, indicating potential failure points. The initial design shows oversized dimensions, allowing for optimization to reduce face width and lower costs.
Optimization involves setting the pinion face width coefficient φ_d to 0.4, resulting in a pinion face width of 20 mm and a rack face width of 15 mm. The optimized rack and pinion gear model undergoes finite element analysis with the same parameters. Results show increased stress on the rack, especially at the root, but within allowable limits. The bolt connection area remains a high-stress zone. The optimized model achieves smaller dimensions, reduced weight, and lower cost while meeting design requirements.
The impact of varying pinion teeth count on maximum stress is analyzed for the optimized model, with teeth counts ranging from 20 to 25. Finite element analysis using SolidWorks Simulation is performed for each case, and results are summarized in the table below:
| Number of Teeth | Maximum Stress (MPa) |
|---|---|
| 20 | 50.76 |
| 21 | 60.21 |
| 22 | 56.72 |
| 23 | 47.14 |
| 24 | 55.09 |
| 25 | 49.81 |
The data shows that maximum stress variations are minimal across teeth counts from 20 to 25, indicating low sensitivity to teeth count changes in this range. Considering potential errors in 3D modeling, finite element analysis positioning, and mesh generation, the teeth count can be reduced slightly to decrease pinion pitch diameter, thus reducing structural volume and manufacturing costs. However, excessive reduction may weaken tooth strength. For this study, a teeth count of 23 is selected as optimal.
In conclusion, through preliminary design calculations, verification, and finite element analysis, the proposed rack and pinion gear solution is theoretically feasible. The optimal parameters for the computer display lifting mechanism’s rack and pinion gear are: module of 2 mm, pinion face width of 20 mm, rack face width of 15 mm, and teeth count of 23. The analysis of teeth count impact demonstrates that maximum stress is insensitive to changes between 20 and 25 teeth, providing a theoretical basis for material savings and cost reduction. Future research could explore the effects of module variations and combined changes in module and teeth count on rack and pinion gear performance to identify optimal combinations for comprehensive study.
The rack and pinion gear system plays a critical role in ensuring smooth and efficient operation of the lifting mechanism. Key advantages of rack and pinion transmission include high precision, reliability, and ability to handle dynamic loads. In this application, the rack and pinion gear must withstand cyclic stresses during frequent lifting operations, necessitating robust design and material selection. The use of finite element analysis allows for virtual testing and optimization, reducing the need for physical prototypes and accelerating development. Further considerations for rack and pinion gear design include lubrication, wear resistance, and noise reduction, which can enhance longevity and user experience. By iterating on design parameters and leveraging computational tools, the rack and pinion gear mechanism can be refined for maximum performance and cost-effectiveness in hidden display systems.
Expanding on the finite element analysis, the mesh generation process involves dividing the rack and pinion gear geometry into tetrahedral elements, with finer meshing at critical areas like tooth roots and contact surfaces. The boundary conditions simulate real-world constraints, such as fixed supports at the rack mounting points and applied torque on the pinion shaft. The solution outputs stress distributions, displacements, and safety factors, guiding design improvements. For instance, stress concentrations at the rack bolt holes may necessitate fillet modifications or material upgrades. The rack and pinion gear’s dynamic behavior under varying loads can also be analyzed to ensure stability during rapid升降.
Material properties significantly influence rack and pinion gear performance. The selected materials, 40Cr for the pinion and 45 steel for the rack, offer good strength and toughness after heat treatment. Alternative materials, such as case-hardened steels or polymers, could be evaluated for specific applications. The rack and pinion gear interface requires precise manufacturing to minimize backlash and ensure smooth engagement. Tolerance analysis and surface finish specifications are essential for optimal rack and pinion operation. Additionally, environmental factors like temperature and humidity may affect material behavior, necessitating protective coatings or seals.
The integration of rack and pinion gear systems with electronic controls enables programmable lifting sequences and position feedback. Sensors can monitor rack displacement and pinion rotation, providing data for closed-loop control. This enhances the reliability and safety of the hidden display mechanism. Maintenance aspects, such as periodic inspection of rack and pinion gear wear and lubrication schedules, should be considered during design to ensure long-term functionality. Cost-benefit analysis of different rack and pinion gear configurations can guide material and manufacturing process selections, balancing performance with economics.
In summary, the rack and pinion gear transmission is a versatile solution for linear motion applications like display lifting. Through systematic design, analysis, and optimization, the rack and pinion gear mechanism can achieve desired performance metrics while minimizing resource usage. The iterative process of parameter adjustment and finite element validation underscores the importance of computational tools in modern engineering. As technology advances, further innovations in rack and pinion gear design, such as composite materials or additive manufacturing, may open new possibilities for enhanced efficiency and customization.