In today’s modern machinery, reducers play a crucial role in matching speeds and transmitting torques between prime movers and working machines or actuators. They are widely used and have been a key research focus for scientists around the world. This article describes the design process of a three-stage involute gear reducer, including the layout design of the transmission structure, the parametric design of the gear transmission system, and the structural optimization design of the reducer housing.
1. Introduction
A reducer is an independent component consisting of gear transmission, worm gear transmission, and gear-worm transmission enclosed in a rigid shell. It is widely used in various fields due to its ability to match the speed and transmit torque between the prime mover and the working machine. The design of a heavy-duty and low-speed reducer is presented in this paper, and the design process includes the layout design of the reducer transmission structure, the parametric design of the gear transmission system, and the topological optimization design of the reducer housing structure using the finite element analysis method. Finally, a professional APP for the parametric mechanical design of the gear transmission system is proposed, and its feasibility is demonstrated through practical operation.
2. Layout Design of the Transmission Structure
The layout of a multi-stage gear transmission system is the study of the relative spatial positions of multiple pairs of gear transmission mechanisms. For a three-stage gear reducer, there are four typical structural layouts based on the position of the axis plane of the secondary gear transmission system relative to the reference axis plane of the primary gear transmission system. In this design, an asymmetrical horizontal layout is chosen for the crane-used heavy-duty reducer, and helical involute gears are used for their advantages of uniform speed and good balance, suitable for high-speed and heavy-duty conditions. The shafts of the reducer adopt a simple support structure and one-way fixation, and the bearing type is a sliding bearing, with tapered roller bearings used for axial fixation.
3. Parametric Design of the Involute Gear Transmission System
The parametric design of the gear transmission system includes determining the technical parameters based on the performance requirements of the reducer. This involves eight aspects: transmission ratio distribution, motion and motion parameter design, mechanical model establishment, gear pair strength design, shaft system structure and strength check, bearing life check, housing structure and strength stiffness design, and reducer lubrication and sealing design.
3.1 Transmission Ratio Distribution
The effective power of the motor is calculated based on the load force and load linear velocity, and the total efficiency is determined by considering the efficiencies of the gears and couplings. The required power of the motor is then calculated, and an appropriate motor is selected based on this power. The working machine speed is calculated based on the diameter of the drum and the load linear velocity, and the total transmission ratio is determined from the motor’s full-load speed and the working machine speed. The transmission ratios for each stage are calculated using specific formulas.
3.2 Motion and Motion Parameter Design
Based on the required power and speed of the motor, as well as the efficiencies of the gears and bearings, the power, speed, and torque of each shaft are calculated using relevant formulas.
3.3 Mechanical Model Establishment
The circumferential force, radial force, and axial force of the gear are calculated based on the known parameters such as power, speed, modulus, number of teeth, pressure angle, and helix angle. These forces are used to calculate the mechanical model of the shaft system.
3.4 Gear Pair Strength Design
3.4.1 Gear Pair Parameter Calculation
In this design, helical cylindrical gears with a 7th precision grade are used. The material for the pinion is 40Cr with surface hardening treatment, and the material for the gear is 20Cr2 with carburizing and surface hardening treatment. The working life is calculated based on the total working time, and the stress cycle numbers for the pinion and gear are calculated based on the pinion speed, the number of meshing times for the same tooth surface, and the number of teeth for the pinion and gear. The contact fatigue life coefficients are obtained from the calculation results.
3.4.2 Gear Strength Check
There are two methods for gear strength check: by tooth surface contact fatigue strength and by tooth root bending fatigue strength. For the contact fatigue strength check, various parameters are calculated using specific formulas, and the actual load factor is calculated. The diameter of the pinion is calculated, and the contact fatigue strength is checked by comparing the calculated stress with the allowable stress. For the bending fatigue strength check, the load factor, the coincidence factor, and the helix angle factor are calculated, and the gear modulus is calculated. Finally, the bending fatigue strength is checked by comparing the calculated stress with the allowable stress.
3.5 Shaft System Structure and Strength Design
3.5.1 Calculation of the Minimum Shaft Diameter
The minimum diameter of the shaft is calculated using a formula that takes into account the power transmitted by the shaft and the speed of the shaft.
3.5.2 Shaft Strength Check
There are two methods for shaft strength check: by the combined stress of bending and torsion and by fatigue strength. For the combined stress check, the bending-torsion synthesis strength condition is calculated, and the stress is compared with the allowable stress. For the fatigue strength check, the safety factor is calculated, and it should be slightly greater than or equal to the design safety factor. The safety factor is calculated based on various factors such as the fatigue limit, the average stress, and the comprehensive influence coefficient.
3.6 Lubrication and Sealing Design of the Reducer
The rolling bearings in the gear reducer system are lubricated with grease, and an oil seal disc is set on the inner side of the bearing to prevent the loss of grease due to the hot oil squeezed out during gear meshing. The sealing of the reducer mainly includes the sealing between the surfaces of the housing and the sealing of the bearing end caps of the outer extension shaft. The transmission system adopts an oil immersion lubrication method, and each shaft is sealed with a sealing ring. A pair of J-type skeleton rubber oil seals is selected to prevent dust from entering the reducer housing and lubricating oil from leaking out.
4. Topological Optimization of the Gear Reducer Housing Structure
To meet the requirements of working strength, stiffness, and casting processability, the housing of the reducer is subjected to topological optimization design. The structural design of the housing is based on the strength and stiffness requirements of the component structure, and the concept unit method for the design of complex component structures is used to analyze the structure from qualitative configuration to quantitative scale.
4.1 Geometric Model
A three-dimensional geometric model of the reducer housing structure is established, and the housing structure is composed of two completely symmetrical upper and lower parts.
4.2 Physical Parameters
The commonly used steel is selected as the material for the involute gear reducer housing, with an elastic modulus of 210,000 MPa, a Poisson’s ratio of 0.3, and a material density of 7.85 g/cm³.
4.3 Physical Model
The physical model is established by applying load constraints on the geometric model to simulate the real working conditions, and the structural topology optimization is performed using the finite element analysis method. Tetrahedral elements are used for the mesh to ensure the convergence of the calculation results to the real value. The constraints are set on the bottom surface of the fixed reducer housing with full freedom constraints, and the loads are applied at the center positions of the eight shaft holes of the housing. The specific load magnitudes and directions are shown in Table 1.
Table 1: Load Magnitudes and Directions on the Shaft Holes
| Shaft | Magnitude | Direction | Magnitude | Direction | Magnitude | Direction | Magnitude | Direction |
|---|---|---|---|---|---|---|---|---|
| Shaft 1 | 6000 | -x | 5000 | -y | 4000 | -z | 8000 | -y |
| Shaft 2 | 26000 | y | 62000 | -z | 35000 | y | 77000 | -z |
| Shaft 3 | 50000 | y | 120000 | -z | 75000 | y | 170000 | -z |
| Shaft 4 | 64000 | -y | 105000 | -z | 30000 | -y | 70000 | -z |
4.4 Topological Optimization
Using mass as the optimization constraint and overall strain energy as the optimization goal, symmetry constraints and manufacturing process constraints are applied. The Optistruct module solver of the HyperWorks software is used for optimization, and the resulting topological optimization result is shown in Figure 4.
4.5 Optimization Scheme
The topological optimization result clearly describes the force path of the reducer housing. To ensure that the housing has sufficient strength and stiffness, the new structure is optimized by adding ribs inside the housing and reducing the thickness, achieving the requirement of lightweight design. The cross-sectional view of the new structure is shown in Figure 5.
4.6 Housing Performance Analysis
To verify the performance of the new structure, the static performance (displacement, stress) analysis is carried out using the same loading boundary conditions as in Section 4.3. The mesh type and size for the performance analysis are exactly the same as in the physical model. The analysis cloud diagrams are shown in Figures 6 and 7.
Figure 6 shows the displacement analysis cloud diagram result. The maximum displacement area of the housing structure is near the shaft hole of the output shaft, and the maximum displacement is 0.3399 mm, which meets the design requirements. Figure 7 shows the stress analysis cloud diagram result. The maximum stress occurs at the four corners of the bottom surface of the fixed housing, which may be caused by stress concentration. Therefore, in the design process, the four corners of the bottom surface are designed as rounded corners to reduce stress concentration. The maximum stress on the housing is 265 MPa, which is less than the allowable stress of the material, and the design scheme meets the working requirements.
5. Digital Design of the Reducer Transmission System
The calculation of the parameters of the involute gear transmission system in the reducer design is a lengthy and cumbersome process. To improve efficiency, a professional APP is designed to digitize the parameterization process of the involute gear transmission system, which can calculate the various parameters of the involute gear transmission system and perform the checking work.
5.1 APP Digital Design Introduction
The digital design function of the APP is divided into six modules, and each module is operated in a specified sequence. The modules are arranged from left to right, as shown in Figure 8.
5.2 Software Module Function Introduction
This section mainly introduces the function of each module. Due to space limitations, only part of the operation interface is shown.
5.2.1 Motor Selection Module
By inputting the design parameters such as the motor load force and load linear velocity, the various powers of the motor, the transmission ratio, torque, and power of each shaft are calculated. The operation interface is shown in Figure 9.
5.2.2 Gear Transmission Design Module
After completing the motor selection module, the gear design module is run. By inputting the design information such as the desired working life of the gear, the various parameters and coefficients that meet the life of the gear are calculated. Finally, the modulus and number of teeth of the gear are determined by inputting the calculated parameters.
5.2.3 Shaft Structure Design Module
Similar to the gear module, by inputting the desired power and speed of the shaft, the torque, bending and torsion section coefficients, and other parameters of the shaft are calculated, and the fatigue and bending strength checks are performed.
5.2.4 Coupling Design Module
By inputting the power and speed of the coupling and looking up the usage coefficient from the table, the required torque of the coupling is calculated. The operation interface is shown in Figure 10.
5.2.5 Bearing Calculation Module
By inputting the reaction force information of the bearing, the radial load of the bearing is calculated. Finally, by inputting the bearing load, speed, and expected life and other parameters, the bearing life can be calculated.
6. Conclusion
This article describes the overall design process of a high-load and low-speed three-stage asymmetrical involute gear reducer, including the layout design of the reducer transmission structure, the parametric design of the transmission system, and the optimization design of the reducer housing structure. The finite element analysis software is used for the structural topology optimization of the housing to meet the requirements of lightweight while ensuring the normal operation of the housing structure. Finally, a professional APP for calculating the parameters of the involute gear transmission system is developed, and its feasibility is verified through operation.
In summary, the design of the three-stage involute gear reducer takes into account various factors such as the layout of the transmission structure, the parameters of the gear transmission system, and the optimization of the reducer housing structure. The use of digital design and optimization methods can improve the design efficiency and performance of the reducer, making it more suitable for practical applications. Further research and development in this field can lead to more advanced and efficient reducers, contributing to the development of modern machinery.