Planetary Reducer Research Articles

Design of Gearings from Involute-Bevel Gears

The article presents formulas for determining the dimensions of involute-bevel gears and the gearings composed of them. It examines the most general cases of gearings formation, consisting of two involute-bevel gears with crossing axes (hyperboloid gearings), with intersecting axes (bevel gearings), and with parallel axes (cylindrical gearings). Gearings composed of involute-bevel gears have design, technological, and operational advantages compared to gearings composed of conventional cylindrical and bevel gears. The use of involute-bevel gearings with crossing axes allows for achieving the required contact character of the teeth from localized contact to linear contact, reducing sensitivity to manufacturing and assembly errors, and increasing the load capacity of the gearing compared to helical gearings from cylindrical gears. Bevel gearings with involute-bevel gears allow for the creation of gearings with any desired small shaft angles, which is difficult to achieve with conventional bevel gears. The use of internal meshing bevel gearings with modified tooth profiles in planetary reducers allows for gearings comparable to harmonic drives in terms of power and kinematic characteristics, but with a higher operational life. The use of involute-bevel gears in cylindrical gearings improves the smoothness of the mechanism and allows for adjusting the center distance and backlash in the meshing, making them suitable for backlash-free drives. By combining the taper angles of the gears and the inclination of the teeth, it is possible to create a one-way rotation mechanism - a freewheel mechanism. Modern CAD systems do not take into account the geometry features of gearings composed of involute-bevel gears, which limits their application in technology. The article proposes an algorithm for calculating the main geometric parameters of gearings composed of involute-bevel gears with arbitrary axis placement in space. Examples of geometric calculations of various types of gearings based on the proposed algorithm are provided.

The new constructive design of the planetary gearbox winches

Although the constructions of planetary reducers are complex, their technical indicators are higher than other gear boxes, and their overall dimensions are smaller. In this article, the constructions of planetary gearboxes were investigated, and an in-depth literature analysis was conducted on their modernization. Application of these gearboxes with high technical indicators and compact dimensions in lifting mechanisms would be suitable for the purpose. Thus, small overall size, large efficiency, and high reliability are the main requirements for winches, and planetary gearboxes can also provide these features. But for some reason, traditionally, geared elevator winches are mainly made with worm gearboxes. This is mainly due to the fact that they provide a high gear ratio in single stage and self-braking. But the efficiency of worm gear box is small, and the friction losses are larger. Therefore, it is time and necessity to replace them with other progressive designed gearboxes in the lifing winches. Taking these into account, in the article, as a result of structural and kinematic analysis and synthesis of planetary gearboxes, new constructions were developed and structural schemes were proposed for their application in the lifting mechanisms. For each of these schemes, the transmission ratio and efficiency were evaluated and compared with each other. The proposed schemes can be applied in the different types of lifting winches. The application fields of winches are different. Winches are more commonly used in drilling equipment and elevators. Winches are the main units of these equipments. Winches and their braking systems must meet operational requirements and operating conditions. Their strength and traction must be sufficient to perform the most demanding technological operations. Lifting and lowering speeds should ensure accident-free operations, be economically efficient and highly productive.

Safety Analysis of the Gear Strength of Differential Compound Planetary Reduction System

Safety Analysis of the Gear Strength of Differential Compound Planetary Reduction System

Transmission efficiency of one tooth difference sine tooth profile planetary reducer

The structural size of space exploration and unmanned aerial vehicle manipulator is required to be as small as possible, and the weight must be as light as possible. However, the existing reducers have difficulties in achieving lightweight robot joint drive systems. For it, this paper proposes a single tooth difference continuous sine tooth profile K–H–V type planetary reducer in which pin type equi-speed output mechanism is used. Concerning the reducer, its structural composition and meshing characteristics are analyzed. Based on the findings, the meshing pair's force, the friction coefficient, and the meshing efficiency are investigated. The force and bearing efficiency of the planetary gear are studied, and the efficiency of the equi-speed output mechanism in addition to the total efficiency of the reducer are determined. Moreover, the efficiency of the reducer prototype is measured and compared to the calculated efficiencies. The results show that the gear modulus, the input speed, the surface roughness, and the lubricating oil viscosity have a significant effect on the meshing efficiency. Furthermore, the efficiency of the eccentric bearings is significantly lower than that of the non-eccentric bearings. Therefore, it can be increased by tuning the pressure angle, the tooth number of planetary gear, the tooth height, and the distribution circle radius of the pinhole. In addition, the power loss of the output mechanism has the greatest effect on transmission efficiency. Reducing the center distance, the inner diameter of the rotating arm bearing, and the tooth number of planetary gear, as well as increasing the outer diameter of the pin shaft can reduce the power loss of the output mechanism. The experimental efficiency of the reducer prototype is 82.47%, its computational efficiency is 83.72%, and its error is 1.25%, verifying the correctness of the efficiency calculation method.

Manufacturing and contact characteristics analysis of a novel 2K-H internal meshing planetary reducer with involute-cycloid combined tooth profiles

Rotate Vector (RV) reducer involves multiple crankshafts to drive the cycloidal-pin transmission in parallel, leading to an over-positioning structure and high manufacturing and assembly requirements for the reducer, restricting the development of industrial robots. In view of the above problems, a novel configuration of Abnormal Cycloidal Gear (ACG) reducer with a 2K-H internal meshing planetary transmission is proposed. The design innovatively replaces the multiple crankshafts with a pin mechanism, thereby addressing the over-positioning and simplifying the manufacturing and assembly processes. To improve the performance of the reducer, the “epicycloid-involute-hypocycloid” combined tooth profiles are designed and adopted as the ACG reducer’s drive teeth. The configuration principle of the ACG reducer is conducted. Next, a manufacturing method utilizing a rack cutter to generate the profile of drive teeth is presented. Finally, the meshing performance and mechanical behaviors of the designed internal meshing pair for the ACG reducer are evaluated. Results show that ACG reducer has the advantages of a simple structure and large transmission ratio. The combined tooth profiles can be machined at one time using the designed cutter, simplifying the tooth machining process. The internal meshing pair is linear contact and exhibits an obviously multi-teeth meshing effect, which benefits the carrying capacity and transmission performance of the ACG reducer.

Data Analysis and Traction Performance Evaluation of an Electric All-Wheel Drive Tractor During Agricultural Operation

Highlights The study evaluated the feasibility of using a new type of platform, the electric AWD tractor, for agricultural operations. The data for key components of the electric AWD tractor during plowing were analyzed. The traction performance of the electric AWD tractor was evaluated via tractive efficiency and dynamic ratio. The electric AWD tractor was expected to replace conventional tractors in terms of traction performance. Abstract. Owing to the increasing need for research on electric all-wheel drive (AWD) systems, an investigation on the AWD systems applicable to tractors was conducted in this study. The experimental platform consisted of an electric power transmission system including four sets of electric motors, helical and planetary reducers, wheels, and an electrical system including chargers, batteries (LiFePO4), converters, and inverters. The drive control system of the electric AWD tractor was divided into the AWD and the motor controller. The data measurement system consisted of analog (current and traction force) and digital (battery voltage, current, motor rotational speed, state of charge (SOC) level, and travel speed) components that communicate using a controller area network (CAN) bus. Data measured during plowing were used to calculate motor power, motor torque, traction power, and driving power to analyze the power consumption of an electric AWD tractor. The traction performance of the electric AWD tractor was evaluated using tractive efficiency, calculated values (traction power and driving power), and dynamic ratio. The maximum and minimum average voltage of the electric AWD tractor during plowing were 72.2 and 64.7 V, respectively, and the average value was measured as 68.2 V. The average value of the maximum current applied to the inverter was 362.4 A, and the mean value was measured as 187.5 A. The average value of the maximum rotational speed of the four motors was 2111.5 rpm, while the mean rotational speed during the operation was 1131.9 rpm. The average value of motor torque was 79.4 Nm. The decrease rate of battery SOC level per minute was calculated as an average of 1.4%/min. The maximum values of the traction and driving power during plowing were 42.0 and 73.7 kW. The maximum tractive efficiency (TE) was 0.77, with an average TE of 0.47. The maximum dynamic ratio (DR) was 0.28, with an average DR of 0.18. The TE of a conventional tractor was found to be a maximum of 0.61, with averages of 0.41, respectively. The average TE of the electric AWD tractor was approximately 14% higher than that of the conventional tractor. Data analysis indicates that the electric AWD tractor performing speed control is vulnerable to slip, and further research is necessary to improve AWD system performance through speed and slip control. Keywords: Data analysis, Data measurement system, Electric AWD tractor, Plowing, Traction performance.

Dynamic Characteristic Analysis of the Shield Machine Three-Stage Planetary Reducer Considering Tooth Wear

Dynamic Characteristic Analysis of the Shield Machine Three-Stage Planetary Reducer Considering Tooth Wear

Friction power loss of continuous sine tooth profile planetary reducer

In this paper, a sine tooth planetary reducer with one tooth difference is proposed. For the proposed reducer, the equations of the oil film thickness, the meshing sliding and rolling friction power loss, and the friction power loss of the bearings for the reducer are proposed. Using these equations, the oil film thickness distribution, the meshing sliding and rolling friction power loss of the sine gear reducer plus the friction power loss of the bearings on eccentric shaft section are analyzed. The power loss of the reducer is measured and compared to the calculated values. Results show that the measured ratio of the friction power loss to input power is 27.90 %, and the calculated one is 26.53 %. The difference between them is 1.65 %. This illustrates analysis about lubrication and friction power loss of the reducer.

Eagle-inspired manipulator with adaptive grasping and collapsible mechanism and modular DOF for UAV operations

This paper presents an eagle-inspired manipulator designed to enhance the efficiency of medium and large multi-rotor UAVs during contact operations such as picking, obstacle cleaning, and grasping. Drawing inspiration from the skeleton structure and motion law of an eagle’s leg, we propose a prototype design of a large load, wide range of movement, multiple DOF, and collapsible manipulator. The main structure of the manipulator consists of a planetary reducer and a coupled parallel linkage mechanism, which enables it to have greater payload capacity while also increasing its range of motion. The grasping mechanism is based on the motion law of an eagle’s claw, which effectively increases the contact area with targets. To further enhance the DOF of the grasping mechanism, we have designed an ankle mechanism that utilizes a pair of double helical telescopic mechanisms to constrain the DOF of the universal joint, connecting the grasping mechanism to the main structure of the manipulator. Regarding the comparison with existing techniques, our eagle-inspired manipulator has several advantages over previous designs. On one hand, the grasp planning strategy, which is inspired by the motion law of an eagle’s claw, can achieve more reliable and accurate grasping than existing techniques. On the other hand, the manipulator’s collapsible design facilitates easier transportation and storage while maintaining its wide range of motion. What’s more, the modular DOF design allows for greater flexibility in adapting to different payloads and operating environments when compared to existing technologies. We outline the development process of this manipulator, including kinematic modeling and control. The ability of the manipulator system is tested, and flight test experiments are conducted on a UAV carrying the manipulator to demonstrate its practicality and effectiveness.

Dynamic characteristics of the ring gear structure of two-stage plastic planetary reducers

Dynamic characteristics of the ring gear structure of two-stage plastic planetary reducers

Power loss scaling laws of high-speed planetary reducers

Scaling laws are increasingly recognized as an interesting solution to accelerate the early stages of the development of drivetrains. Concerning gearboxes, prior studies focused on geometric scaling to achieve new desired torque and speed values and to predict mass, volume, and inertia. Power loss scaling laws are still lacking in literature. This paper seeks to bridge this gap by proposing scaling laws for the power loss of high-speed planetary reducers. Due to the lack of reliable information on the losses at high-speed, scaling laws are derived from an experimental campaign of 5 commercial planetary speed reducers. The proposed scaling laws are defined based on high-level specifications of the drivetrain, namely the maximal input speed, output torque, and gear ratio. The results suggest that the derived scaling laws can predict the efficiency and power losses with an average error of less than 1%, and 8% respectively relative to the measurements, considering a torque scaling factor of up to 4, speed scaling factor of up to 0.6 and gear ratio scaling factor of up to 2.

Analysis and simulation of the influence of initial liquid level on lubricating flow state and oil-churning resistance moment of planetary reducer

In order to study the influences of the initial liquid level on lube characteristics and oil-churning resistance moment of gear reducer, the heat generating power of one special kind of planet gear reducer under the special working condition is calculated. The fluid temperature at different initial liquid levels is calculated by FEA method. According to the relation between the physical parameters of the lube and the fluid temperature, the corresponding relation between the physical parameters of the lube and the initial liquid level is deduced. Based on the FEA results, the physical parameters of the lube are set to conduct the co-simulation of the oil-churning process of the planetary reducer under different initial liquid levels by MPS method. Depend on the simulation results, the influence of initial liquid level on lubricating flow state and oil-churning resistance moment of planetary reducer is analysed, and the initial liquid level is sifted. These studies provide methods and reference for lubrication medium set in transmission boxes, such as planet gear reducer and so on.

Reliability Design of Two-Stage Planetary Gear Wheel Hub Reducer based on Multi-Objective Optimization

The mining dump truck has a large load capacity, low running speed, and the characteristics of low speed and high torque. The planetary wheel reducer can meet this demand, which is widely used in such vehicles. According to the structural characteristics of a 170-ton vehicle two-stage planetary gear reducer, the reliability of planetary gear transmission at all levels was analysed, and the system parameters were optimized on this basis. The multi-objective optimization design method was used to transform the maximum reliability of the system into the maximum reliability of the gears at all levels, and the constraints are established based on the actual processing, operation, installation, assembly and other working conditions. The MATLAB multi-objective optimization module was used to solve the analysis, and the best gear design parameters were obtained after rounding. Under different operating conditions, the planetary reducer before and after optimization was compared and analysed to obtain the reliability and service life of the entire deceleration system after optimization. The analysis results show that: after the parameter optimization of the planetary reducer, the transmission efficiency is 0.946, and the transmission ratio of the system is 30.54, which meets the actual use requirements. The reliability coefficient of the contact strength of the tooth surface of the secondary sun gear is 2.52, the reliability coefficient of the bending fatigue strength of the root of the secondary inner ring gear is 2.59, and the reliability of the secondary gear is 0.989. The reliability is obviously improved. The safety factor of the main parts is high. The service life of each gear of the whole secondary reduction system meets the design requirements. The analysis content and results provide reference for the optimization design and reliability analysis of similar planetary gear systems.

Optimal Design of Planetary Reducer of Electric Actuator base on NSGA-II

To solve the problem of equipment installation space shortage in industrial automation sites, a set of hybrid transmission schemes was designed with a two-stage 2K-H(NGW) planetary reducer as the main transmission mechanism combined with a fixed shaft gear train and worm gear and worm mechanism. At the same time, to obtain the design parameters of the electric actuator more quickly and accurately, with the minimum volume and maximum efficiency of the main transmission mechanism as the design objectives, the multi-objective function mathematical model is established under the conditions of meeting the gear matching, displacement coefficient, strength, and overlap degree, and the non-dominated sorting genetic algorithm II (NSGA-II) is used to solve the mathematical model. The research results show that the volume of the main transmission mechanism is reduced by 13.6%, the transmission ratio is increased by 1.54%, but the transmission efficiency is reduced by 3.32% when the strength and life of the gear are equal.

Design considerations and simulation of a rolling-contact gearless automotive differential

This paper presents the design considerations, the kinematical simulation and the FE analysis of a differential mechanism which involves the rolling contact of two cam-track disks with four equally-spaced spherical rollers sliding in a cage much resembling a rolling bearing. The obvious benefit of this concept in the field of power transmissions is the potential replacement of gears in planetary reducers and differentials by cams. The side gears of a conventional open differential are replaced by two identical cam-track disks, while the spider gears are replaced by rolling elements that is, balls, cylinders or tapered cylinders. Practically, the well-known rolling bearing concept is generalized, where the circular tracks are replaced by wavy curves. In order to assess the performance of the mechanism, the shape of the tracks is considered for two distinct cases and a rigorous mathematical modeling follows regarding the kinematics of the mechanism. The results were validated through kinematical simulations and FE analysis was carried out coupled with fatigue life computation for a typical passenger vehicle differential, indicating that service life in the order of 200,000 km is feasible.

The winter of raw computers: the history of the lunar and planetary reductions of the Royal Observatory, Greenwich.

In 1839 the working hours of the computers employed on the lunar and planetary reductions of the Royal Observatory, Greenwich were reduced from eleven hours to eight hours. Previous historians have explained this decrease by reference to the generally benevolent nature of the manager of the reductions, George Biddell Airy. By contrast, this article uses the letters and notes exchanged between Airy and the computers to demonstrate that the change in the working hours originated from the computers as a reaction to their poor working conditions. Through the exploration of these archival materials, the article shifts the focus of the analysis to the working experience of the computers, rather than to the administrative history of the project that inevitably tends to highlight Airy's actions. By doing so, the article shows how the computers were treated as a disposable low-skilled workforce, as opposed to aspiring astronomers with considerable mathematical talent. Through this reframing, the article takes a step towards a working history of the observatory.

Optimal allocation of reliability improvement target based on multiple correlation failures and risk uncertainty

Optimal allocation of the reliability improvement target is essential for the system optimization design. In order to solve the problems that the optimization model is with loss of generality and the validity of the optimal solution is weakened, an optimal allocation method is proposed by considering multiple correlation failures and risk uncertainty in this paper. Two new concepts are presented, such as independent failure results in basic risk, and correlation failure leads to disturbance risk. A risk assessment machinery of “actual risk = basic risk + disturbance risk” is proposed. The action mechanisms of the three correlation failures are studied based on the cooperation game theory, and the generalized risk models are given under probability measure. Considering the improvement cost, the expectation and the variance of the reduction of system risk, a multi-objective optimal allocation model is developed, which is solved by using the PSO algorithm. Finally, the proposed optimal allocation is implemented at the 2-stage NGW planetary reducer, and the results show that it is more efficient and feasible for engineering practice.

Design of a High Torque Density Robot Joint and Analysis of Force Control Method Applied for a Light Exoskeleton

In many robotic applications, the joint is required to have a small volume, low weight and high torque output. In this paper, based on the finite element analysis (FEA), a 36-slot 40-pole outer rotor surface-mounted permanent magnet (OR-SPM) motor with concentrated winding is designed for the exoskeleton robot. The fractional slot concentrated winding (FSCW) is employed to reduce end winding height, leading better portability. Since the motor is relatively flat, the 3D end effect is critical to the electromagnetic performances. Special attention is paid to 3D end effect during the multi-objective optimization of the OR–SPM motor. In order to increase the ending torque output, the planetary reducer is located between OR–SPM motor and load, and then system level optimization covering motor and reducer is carried out to achieve best torque output. In addition, the force impendence control method with parameter self-adaptive capability is proposed to improve user experience of the exoskeleton robot, where the key parameters in the algorithm vary according to different actions of the exoskeleton. In addition, the inertia of load is calculated using the parameter identification based on least squares method. Finally, the prototype of the joint is fabricated and tested to validate the above FEA results and control method. The user experience of the exoskeleton robot is also covered.

Development of cycloidal planetary reducer

A cycloidal planetary reducer, which fulfils both high reduction ratio and low vibration in a thin and small body, had been proposed to cope with the further downsizing of DC motors. The reduction mechanism is inspired by the intellectual toy ‘Spirograph’ and structurally based on a planetary reducer. Instead of the internal gear of the planetary reducer, output plate with skid epitrochoid groove is introduced. The sun gear is connected to the input shaft and the planetary carrier works as a stator. The planetary gear has a pin that fits in the groove of the output plate. According to the rotation of the planetary gear, the output plate revolves in the counter direction with a speed in inverse proportional to the number of the skid epitrochoid. The prototype can realize higher reduction ratio compared to the planetary reducer without unpleasant vibration that is unavoidable in the cycloidal reducer. It is confirmed that the idling torque is very small with 0.006Nm, and the torque transmission efficiency is acceptable with 73%. But the torque fluctuation caused by the cam motion by the pin and groove is remarkable, which will be forthcoming challenges.

Design and Kinematics Analysis of the Reduction Mechanism for Hub Drive System

Distributed hub drives electric vehicles highly integrate the drive motor, deceleration mechanism, etc. in the wheel. As a key component of the hub drive system, the structure and performance of the reduction mechanism will directly affect the driving and safety of the vehicle. How to realize the integrated design of the reduction mechanism and other parts of the hub drive system in limited wheel space is one of the basic problems to be solved in hub drive system design. In this paper, the NGW-type planetary mechanism is used as the hub reduction mechanism, combined with other parts of the hub drive system to design the specific structure of the planetary reduction mechanism, establish the kinematic model of the reduction mechanism, and carry out the kinematic simulation analysis.