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The paper deals with the numerical stress calculation in the flexspline tooth rim of the harmonic drive. Due to the complex geometry of the toothed ring in the flexspline, the teeth were modeled as a ring, which height corresponded to the particular stress concentration in the teeth. To study the effect of type of wave generator on the stress distr...
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Citations
... Gravagno et al. 9 adopted analytical methods to investigate the effect of the WG profile on the kinematic error and meshing conditions of the harmonic reducer. By modeling the FS teeth as a ring, Pacana et al. 10 analyzed the effect of the type of WG on the FS stress, and Pacana 11 presented a comparative analysis with different models of the FS. Ma et al. 12 proposed a mathematical model to study the meshing characteristics of the harmonic reducer by considering the meshing between the teeth of the CS and FS as a multiple spring compression process. ...
The flexible bearing is usually connected to the cam with an interference fit in harmonic reducers. Studies show that interference fit can cause changes in the structural parameters of the bearing and lead to changes in the service performance of the bearing and its supporting system. This paper proposes a general simulation method to investigate the influence of interference fit in harmonic reducers with the concept of the equivalent interference for non-circular fit between the flexible bearing and cam. Then, the four steps based on the sequential assembling and loading process are designed to ensure assembly concentricity and simulation convergence. The analysis results indicate that appropriately increasing the equivalent interference can improve the service life of the flexspline without degrading the meshing performance and, at the same time, increase the number of loaded balls to make the operation of the harmonic reducer more stable. Moreover, an optimal equivalent interference can be designed to ensure the harmonic reducer operates at its best, where the number of loaded balls and the maximum Mises stress of the inner ring appear inflection point, and the number of meshing tooth pairs reaches the maximum.
... The results demonstrated the excellent suitability and efficacy of the FEM. Pacana et al. [5] calculated the stress distribution in the FS using FEM, and investigated the effects two-roller, four-roller, cam, and disktype wave generators on the stress distribution of the FS. Li [6] employed their FEM software to analyze bending and shear stresses in the FS, and proposed a method for evaluating its fatigue strength failure. ...
The flexspline, as a core component of the harmonic drive, is highly susceptible to fatigue failure due to elastic deformation and alternating stress during operation. Its performance directly affects the working life of the harmonic drive. In this paper, finite element modeling and analysis were carried out on the polyoxymethylene flexspline (POM FS), resulting in stress, displacement, and strain cloud maps. Then, using the control variable method, the influence of structural parameters such as cylinder length L, wall thickness d, and chamfer radius r on the maximum stress of POM FS was studied, and the structural parameters were optimized. Finally, the fatigue life of POM FS was analyzed based on the S-N curve of POM. The results show that the optimized POM FS has a fatigue life of 18,300 hours, which is 24% higher than the original POM FS with the initial parameters. This paper provides a technical reference for the optimization and improvement of the lifespan of POM FS.
... Experiments allow you to verify the previously obtained results of numerical calculations and check the functionality of models made with rapid prototyping methods. Examples of such studies of harmonic drive prototypes can be found in earlier works of the authors [14,17,44,45]. ...
This article includes an analysis of the possibility of using polymer materials for the production of harmonic drive. The use of additive methods greatly eases and accelerates the manufacturing of the flexspline. In the case of gears made of polymeric materials using rapid prototyping (RP) methods, the problem is often with their mechanical strength. In a harmonic drive, the wheel is uniquely exposed to damage, because during work, it deforms and is additionally loaded with torque. Therefore, numerical calculations were conducted using the finite element method (FEM) in the Abaqus program. As a result, information was obtained on the distribution of stresses in the flexspline and their maximum values. On this basis, it was possible to determine whether a flexspline made of specific polymers could be used in commercial harmonic drives or whether they were only adequate for the production of prototypes.
... Improving the quality of products and their occurrence processes is a challenge [51,52], especially in the era of dynamic changes in customer expectations and an increased impact on the natural environment [53][54][55][56]. There is a search for different solutions that support an effective quality management. ...
Improving products and production processes is necessary to ensure the competitiveness of the organisation. As part of these improvements, the popular approach is to use the FMEA method (Failure Mode and Effect Analysis). In the traditional FMEA approach, only the qualitative aspect is included, i.e., the analysis of the quality level of products or processes, its possible incompatibilities, and then proposing improving actions for them. It seems insufficient in times of expansion of the idea of sustainable development and dynamically changing customer requirements. Hence, the purpose of the research is to develop a fuzzy QE-FMEA method to simultaneously analyze hazards for product quality and the natural environment. This method will be based on a fuzzy decision environment. The main elements of originality of the developed method are: (i) extension of the characteristics of the selection of ratings for indicators with triangular fuzzy numbers and the development of a new characteristics of the selection of ratings for the environmental impact indicator, (ii) development of a selection matrix for the qualitative-environmental indicator (QE) according to the rules of triangular fuzzy numbers, (iii) determination of the method of estimating the value of the threat priority, additionally considering the qualitative-environmental indicator (RQE). The complement of research is developed procedure of the Fuzzy QE-FMEA method. It was shown that it is possible to include the effects of incompatibilities (effects of defects occurring in products or processes), which were simultaneously assessed considering the importance and impact on the natural environment. This method will be useful for any company for analysing defects of any products or processes mainly with significant impact on the natural environment.
... The most probable result is that such complicated calculations exceeded the technical possibilities of computers of the time. The computational works in this area were done only by the authors that rejected most of the proposed flexspline shapes as inadvisable due to the risk of cracking [26][27][28]. In view of the complicated shape of the flexible sleeves, the authors also performed the analysis of the flexspline with a welded bottom, which can make it easier to make it out of steel. ...
The unfriendly-for-humans environment of space causes automatic or remotely controlled vehicles and devices to be used for its research. In robot and manipulator control systems, and also in mechanisms adjusting antennas and photovoltaic panels, the hermetic harmonic drive can be used. A special advantage of this type of gear is the ability to transfer power to an isolated space separated by physical barriers from external influences. Therefore, the purpose was to design gears that will allow achieving the highest kinematic precision for control systems by simultaneously maintaining their hermetics. The article presented an analysis of the kinematic accuracy of harmonic hermetic drives powered by four different types of wave generators. The generators used differed in construction but also caused other deformations of the flexspline. The calculation of angular displacement was prepared in the computer program Abaqus. The simulations were performed on virtual models of a complete harmonic hermetic drive using the finite element method (FEM). The results from the analysis allow the most favorable solution to be applied to the Mars rover drive or spacecraft control system. It was determined for which of the wave generators the kinematic accuracy is the highest and how high the backlash exists for the reversing rotation. Finally, the proposed design will allow one to increase the accuracy of the working movements and control of space vehicles while ensuring a minimal influence of the external ambient.
... They are much higher on the bottom side than on the free end of the flexspline. This nature has already been pointed out in previous studies [36,37], and solutions have been proposed, for example, in the form of intermediate rings to improve the cooperation between the flexspline and the wave generator [19,38]. The starting point for the analysis was a flexspline with a bottom modeled with commercial solutions (variant I). ...
Outer space presents construction challenges that are completely different from the terrestrial environment. They should be characterized by high resilience and indefinite durability because there is no possibility of repair during exploitation. There are drives in spacecraft control systems that are necessary to move solar panels, robotic arms, and manipulators, and also to position antennas. In these devices, they have applications where harmonic drives are characterized by high kinematic accuracy but relatively low mechanical strength. The analysis presented in this study is aimed at modifying the shape of the harmonic drive to increase its durability and reliability. In this study, the most vulnerable damage element of the harmonic drive is the flexspline. The calculation was carried out using the finite element method (FEM) in the computer program ABAQUS. A standardized shape was tested as a basic model, and several other design solutions were proposed. For each of them, the mechanical strength was determined, which allowed the selection of the most preferred shape for the flexspline of the harmonic drive. The specific environmental requirements of the expectations for sand for gear used in spacecraft control systems were included in the analysis. The selected construction solutions of the flexspline allow for longer work and transfer of greater loads by the harmonic driver than the solutions currently used. The choice of harmonic driver design shape allows for failure-free and maintenance-free work in space vehicle control systems.
... The experimental method is commonly used for stress testing of HD (Li, 2016;Pacana et al., 2017;Tjahjowidodo et al., 2013). Sticking strain gauges on the FS's surface can measure stress (Guan et al., 2022;İrsel, 2021). ...
The harmonic drive (HD) is increasingly used due to its outstanding advantages, especially for equipment requiring high precision and a large gear ratio. This research is based on the Finite Element Method (FEM) and mechanical analysis to investigate stress calculation methods for the flexspline (FS), a significant component of HD transmission, providing a basis for assessing the durability and failure of the FS. First, the FS deformation and stress analysis model based on the FEM is proposed. Since the two boundary elements of the model have the form of a rotation and translational joint, which have not been provided, based on the stiffness matrix of the fixed beam to build the stiffness matrix for these elements, which completes the proposed analytical model. Then, the structures of an HD reduced are designed and applying the proposed force analysis model, the deformation and stress distributions of the FS are obtained. Finally, the theoretical safety factor is calculated and analyzed. The results of the simulation completely coincide with the theoretical calculation and show that the most concentrated stress is at the root of the teeth, which is the leading cause of the FS failure. So, the study as reference material for rapidly evaluating the stress state and calculating the safety when designing and optimizing the FS.
... Liu et al. [8] established a design method for the space tooth profile of CS, which spatially engaged with deformed FS, and a calculation method of backlash between engaged teeth surfaces. To enable more teeth engagement, a complete method to design a tooth profile and its backlash assessment in an HD was presented by Pacana et al. [9]. ...
The flexspline (FS) of the harmonic drive (HD) is subjected to thermal load and force load during operation, leading to the deformation difference between the inner and outer surfaces of the FS. As a result, the transmission performance of the HD assembly decreases. To overcome this problem, the thermal–mechanical coupling deformation mechanism of the FS is analyzed, and then the influence of the deformation difference on the transmission accuracy of the HD is studied in this article. On this basis, the structural parameters of the wave generator are optimized to eliminate actual backlash and to improve the actual transmission accuracy. Finally, the effectiveness of the calculation method proposed in this article was proved by the prototype test.
... Dennis et al. [4] estimated the contact stress and bending stress of flexible gear teeth through the combination of nonlinear dynamic simulation and finite element analysis, and determined the influence of flexible gear tooth shape change on harmonic transmission performance. Li [5] carried out finite element simulation analysis on a cylindrical flexible wheel, cup flexible wheel and top hat flexible wheel; studied the stress characteristics of flexible wheels with different structures; and verified the simulation results with reference manufacturing, and is widely used. This paper studied the involute tooth profile, and its equation can be described by Equation (1). ...
The failure of harmonic gear drive is mainly caused by the fatigue fracture of flexible wheels and the fatigue damage of flexible bearings. In this paper, the stress sensitivity and fatigue life characteristics of flexible wheels with thin-walled vulnerable components are studied. Firstly, the structure of the flexible wheel of a B3-80 general harmonic gear reducer is designed, the finite element model of the flexible wheel is established by using ANSYS finite element software, and the finite element analysis results are compared with the theoretical calculations to verify the correctness of the model. Finally, by changing the cylinder length, smooth cylinder wall thickness and load, the maximum equivalent stress curves of the flexible gear ring, smooth cylinder and flexible wheel bottom are obtained, and the influence law of structural parameters on the stress characteristics of flexible wheel is obtained. At the same time, the influence laws of flexible wheel cylinder length and smooth cylinder wall thickness on the fatigue life of flexible wheel is studied, which provides a theoretical basis for the structural optimization design of the cup flexible wheel.
... As a typical high-performance precision gear drive, harmonic transmission has the characteristics of compact structure, lightweight, and high reduction ratio, which is widely used in aerospace, satellite communications, military weapons, industrial robots, medical equipment and other applications [1,2]. It generally consists of a wave generator, a circular spline and a flexspline. ...
High-performance precision gear drives such as harmonic gear have high requirements on tooth profile accuracy, surface quality, fatigue life and other service performance characteristics, which urgently needs an effective surface strengthening method. This work aims to examine the feasibility and effectiveness of fine particle peening (FPP) treatment on surface integrity of flexspline in harmonic drive precision transmission. To this end, FPP process experiments were carried out, and this process was simulated based on a coupling method of discrete element method and finite element method (DEM-FEM) considering the kinematic hardening behavior of the material. The simulation results were in good agreement with the test results. Effects of shot peening pressure, injection velocity, material properties and tooth profile on surface roughness and induced residual stress of the target flexspline were analyzed. The results reveal that after FPP, the amplitude of residual compressive stress of the flexspline can reach 470 MPa, and the surface roughness Sa becomes approximately 0.5 μm. For precision gears with low hardness such as flexspline in harmonic drive, it is suggested to adopt FPP with low air pressure to achieve both saturated residual compressive stress and lower surface roughness, thus benefitting enhanced fatigue life.
