Strain Wave Gearing Research Articles

Stress analysis of strain wave gear drives with four different geometries of wave generator

The comparison of strain wave gear drives with four different geometries of the wave generator is presented. The commonly used elliptical geometry of the wave generator is compared with a simplified geometry based on two rolling elements, a geometry based on four rollers, and a newly proposed parabolic geometry for the wave generator. The comparison will be performed in terms of the average maximum stresses caused in the flexible spline due to the rotation of the wave generator. The finite element method and fully-parameterized automatically-generated two-dimensional finite element models are being used in this work. The flexible spline and the ring gear are considered deformable elements whereas the wave generator is considered as a rigid element in the finite element model. The results show that the best mechanical performance in terms of lower average values of maximum von Mises and tensile stresses is achieved with the simplified and parabolic wave generator geometries. Although yielding slightly higher maximum von Mises and tensile stresses, the elliptical wave generator provides the lowest average maximum absolute compressive stress. The worst mechanical performance was obtained with the four roller wave generator.

High-Performance Positioning using Decoupling Controllers for Flexible Two-Link Robots with Strain Wave Gears

High-Performance Positioning using Decoupling Controllers for Flexible Two-Link Robots with Strain Wave Gears

Effect of tooth profiles on strength of the strain wave gearing

Effect of tooth profiles on strength of the strain wave gearing

Low-Cost, Continuously Variable, Strain Wave Transmission Using Gecko-Inspired Adhesives

In robotics, high gear reductions are often required when using an electromagnetic motor to drive revolute joints, as in a humanoid robot. Strain wave gears (SWGs), also known as harmonic drives, are often used. However, these transmissions are relatively expensive and have a fixed gear ratio. Here, we present a low-cost transmission that maintains the high reduction of the SWG and enables a continuously variable gear ratio. We achieve this by, first, replacing the teeth of an SWG with a smooth frictional contact to enable continuous gear variation and, second, inverting the gear elements to enable high frictional torque transfer with a low preload via the capstan effect. We choose a gecko-inspired dry adhesive as the frictional material because it has high friction at low normal forces, and is not inherently tacky. We present a model describing the transmission, as well as experimental data gathered from a prototype device that verifies this model and establishes a proof of concept. Our transmission expands the possibilities for low-cost robotic systems.

Development of Design Software Used for a New Strain Wave Gearing with Multi-Lobes

In order to develop new Strain-Wave Gearing (SWG) used for next generation robots, a new SWG design with multilobes is studied in this paper. Firstly, software used for designing the new SWG with multi-lobes is developed that can be used in AutoCAD commercial software. Validity of the developed software is also verified with three-dimensional, finite element analysis by calculating deformation of the flex-spline when the multi-lobed wave generator is inserted. Secondly, in order to control tooth thickness of the flex-spline and circular spline during tooth-cutting, a study on how to calculate dimensions over measurement pins (DOP) is conducted in this paper. A formula is proposed to do the calculation of DOP. Also, validity of the formula is verified using the developed design software and AutoCAD software by making an actual measurement of DOP and comparing it with the calculated one. Finally, it is found the developed design software and the proposed formula for DOP calculation are of practical meaning in a real engineering design of the multi-lobed SWG.

Effect of Cam Insertion on Stresses in Harmonic Drive in Industrial Robotic Joints

Stress and strain analysis on flex gear cup of strain wave gearing or harmonic drive due to insertion of conventional cam SWG and split cam SWG is studied without assembling the ring gear. Harmonic Drive is supposed to perform kinematically better with proposed split cam than the conventional cam. However, the stress pattern on the FG changes when HD is assembled with Split cam. The comparison study is carried out using finite element method and experiments. The overall stresses on FG cup with split cam are more and it can be seen with finite element analysis. However, the nodal results show that the strains around the tooth contact between FG teeth and RG teeth is less with split cam. These results are further supported with experiments. The experimental results have good agreement with the FEA results.

Estimation of Power Consumption of Compact Five-Axis-Controlled Machine Tools with Strain Wave Gear Rotary Axes Based on Servo Interior Information

Estimation of Power Consumption of Compact Five-Axis-Controlled Machine Tools with Strain Wave Gear Rotary Axes Based on Servo Interior Information

Castable Bulk Metallic Glass Strain Wave Gears: Towards Decreasing the Cost of High-Performance Robotics.

The use of bulk metallic glasses (BMGs) as the flexspline in strain wave gears (SWGs), also known as harmonic drives, is presented. SWGs are unique, ultra-precision gearboxes that function through the elastic flexing of a thin-walled cup, called a flexspline. The current research demonstrates that BMGs can be cast at extremely low cost relative to machining and can be implemented into SWGs as an alternative to steel. This approach may significantly reduce the cost of SWGs, enabling lower-cost robotics. The attractive properties of BMGs, such as hardness, elastic limit and yield strength, may also be suitable for extreme environment applications in spacecraft.

Diaphragm stress analysis and fatigue strength evaluation of the flex-spline, a very thin-walled spur gear used in the strain wave gearing

This paper deals with diaphragm stress analysis and fatigue strength calculation problems of the flex-spline, a thin-walled spur gear used in the strain wave gearing (SWG). Firstly, a mechanics model and theoretical method used for contact analysis of SWG are presented in this paper. Then finite element method (FEM) software is self-developed through very long time efforts in order to realize the contact analysis and stress calculations of SWG. With the developed FEM software, bending and shear stresses of the diaphragm of the flex-spline are analyzed successfully. Secondly, in order to confirm the FEM software, an experimental method and device are presented in this paper. A three-directional, strain gauge is stuck on a straight surface of the tapered diaphragm of the flex-spline next to the corner of the diaphragm with the boss. Diaphragm strains are measured under the conditions of zero and 110Nm torques respectively and the measured stresses are compared with the calculated ones with the developed FEM software under the same conditions. It is found that the two results are in agreement with each other well. This means that the presented mechanics model and theoretical method are correct and effective. Finally, a method used to evaluate fatigue failure strength of the diaphragm is suggested based on the findings in this paper.

Vibrations of Elliptically Shaped Bearings in Strain Wave Gearings

The bearing of a strain wave gearing and the covering thin-walled cup, i.e., the so-called flexspline, are elliptically deformed. This leads to a characteristic excitation of vibration. In this paper, a model for describing the vibration of elliptically deformed bearings is presented. First, the flexspline stiffness is calculated using an a priori finite element (FE) analysis that is validated with measured data. Second, the deformation of the bearing and the flexspline is calculated by superimposing single loads. A numerical study shows that vibrations are mainly caused by the rotation of the ellipse. Furthermore, two types of impulses, i.e., negative impulses and positive impulses, lead to vibration excitation. The negative impulses are caused by the balls passing the angular position of the contact force maxima, while the positive impulses are caused by the balls impacting the surfaces of the races due to the radial tolerance of the bearing. Both negative and positive impulses coincide with characteristic frequencies of the nondeformed bearing. If the surfaces of the bearing are considered to be rough, the characteristic frequencies are not affected. Therefore, characteristic frequencies of nondeformed bearings can be utilized to describe vibrations of elliptically shaped bearings as well.

Harmonic Drive. Evolution of Wave Gear Design

This paper presents a brief history of wave transmission evolution and Harmonic Drive in particular. The invention became a breakthrough in mechanical design and has been attracting the close interest of scientists and engineers for more than fifty years. Contrary to the traditional gearing systems and the laws of ＂rigid-body mechanics＂, the new «Strain Wave Gearing» (SWG) patented by Walton Musser (1959) was based on the use of flexible gear that became the main idea and the driving force of his invention. Nowadays Harmonic Drive is a brand of strain wave gearing. It took just a few years for the SWG to receive recognition-in 1962 one of wave gears was already used in the sputnik. Over the next years’ studies in the world, including Russia, led to the design of many new wave gear systems which have high performance characteristics: high positioning accuracy, high repeatability, high reduction ratio, high torque capacity and efficiency, compactness and light weight. Due to their advantages the wave gears are widely used in aerospace and military applications worldwide.

S1120201 アクチュエータの小型・軽量化を実現する樹脂波動歯車の開発

In recent years, gear units with high reduction ratios are necessary for the weight reduction of the product. Strain wave gearing is high reduction ratios with few components in coaxial reduction gear. On the other hand, materials of the part composed of plastics instead of metal for lightweight. However, Plastic strain wave gearing is not researched so much. In this study, fatigue strength on plastic strain wave gearing was examined.

波動歯車装置の開発をめぐって(基調講演2)

波動歯車装置の開発をめぐって(基調講演2)

1209 AutoCADに基づいた歯車装置の設計計算・製図ソフトの開発(OS-01 歯車の設計)

Gear design calculation and drawing software have been developed based on AutoCAD Visual Basic language included in AutoCAD. With the developed software, a pair of spur gears, helical gears and internal gears can be calculated simply in AutoCAD surrounding. The software developments have also been made for some special gear devices, such as trochoidal gear reducers and strain-wave gearing. Two-dimensional (2D), exact tooth profile shapes and drawings of the designed gears can be drawn automatically and immediately on the template of AutoCAD when the developed software are run. Then three-dimensional (3D) drawings of the designed gears can be made by 3D commands included in AutoCAD. The developed software can also be used to calculate gear bending and contact strength in AutoCAD surrounding based on the JGMA and ISO standards.

Simulation-Based Design of a Rotatory SMA Drive

The design and optimization of a rotatory drive powered by shape memory alloy (SMA) actuators is described in this paper. SMA actuators used in technical applications are parameterized by the use of trial-and-error methods, because there is a lack of computer-aided design tools for this active material. A numerical modeling approach was developed to design and optimize the geometry and the load and heating conditions of SMA actuators in a technical system to achieve a good dynamic and a high reliability. The shape memory effect used in most technical systems is the extrinsic two way effect (2WE). This effect can be simulated with the numerical model which was implemented in MATLAB/SIMULINK. The focus of the model is on the activation behavior of the SMA actuator, which defines its rate of heating and cooling. Different load conditions and various actuator geometries and shapes, e.g. wire or spring actuator, are simulated by the calculation of the energetic balance of the whole system. The numerical model can be used to simulate time variant heating currents in order to obtain an optimal system performance. The model was used to design a rotatory SMA-drive system, which is based on the moving concept of a wave drive gear set. In contrast to the conventional system, which is driven by an electric motor, the SMA drive consists of a strain wave gear and SMA wire actuators that are applied circularly to generate a rotatory movement. Special characteristics of this drive system are a high torque density and a high positioning accuracy.

Evaluation of Noise of Strain Wave Gearing by Vibration Measurement

This paper deals with the radiated noise of strain wave gearing, which is a kind of K-H-V type planetary gears having features of light weight and high reduction ratio. The vibration of the Flex Spline (F/S), which is an element of strain wave gearing shaped like a thin circular cup, is considered to be a main cause of the noise. Theoretically, the magnitude of sound power is expected to increase in proportion to the square of the amplitude of the displacement of the F/S in the radial direction. The displacements in 3 models are calculated using FEM. The vibration of the F/S and the sound power are measured using the fixed-F/S experimental apparatus. It is confirmed that the relationship between the vibration of the F/S and the sound power agrees well with the theory, and that the vibration of the F/S is the main cause of radiated noise. Moreover, the radiated noise with various rotary speeds, loaded torques and assembly errors is measured and examined. The influences of rotary speed and torque are explained by the noise-generation mechanism on the basis of the velocity amplitude of the F/S. The noise becomes large with the increase of assembly error, but the amplitude of displacement is not increased. This is confirmed by the resonance between the F/S and experiment apparatus.

Tribological aspects of a strain wave gearing system with specific reference to its space application

Strain wave gearing (SWG), also known as harmonic drive gear, has been used in many space applications. In 2003, a development of grease-lubricated-type SWG for space flight applications was begun. The life tests of the SWG exposed to vibration test and thermal vacuum test were performed in vacuum. The life test results showed that the in-vacuum operating life of the SWG was significantly short compared with the in-atmosphere life, which is normally corresponding to a rolling fatigue life of wave generator bearing. This may be mainly caused by the severe wear at the wave generator—flexspline interface, where the lubricant is not supplied easily into the clearance in vacuum.

A New Device for Converting Rotary Motion into Linear Motion Study of Rotary-to-Linear Harmonic Drive® (Harmonic Linear Drive®)

This paper describes a new concept for linear motion based on the similar theory of strain wave gearing, which has been used for more than forty years by Harmonic Drive Systems Inc. Gear teeth are replaced by screw threads and rotation of the input side generates linear translation at the output. Besides design flexibility and reasonable costs, the new rotary-to-linear harmonic drive® has shown promising potential in positioning accuracy as well as in high load capacity. It is able to compete (and to surpass in some features) with ball screw or lead screw systems.

3127 波動歯車装置における歯面荷重分布および歯元応力分布の導出(S34-2 伝動装置の基礎と応用(2) 歯車の強度,21世紀地球環境革命の機械工学:人・マイクロナノ・エネルギー・環境)

Strength of tooth root in flexible spline (FS) in Strain Wave Gearing (SWG) becomes a problem so that FS has a very thin rim. Because SWG repeat elastic deformation, tooth root in FS is often damaged. Therefore, we want to know the tooth root stress in FS calculated by the finite element method, but contact between each element in SWG is overly complicated. For this reason, this paper describes contact analysis and comparison between calculated and experimental values. Analytical model was made in several stages so that two-dimensional model becomes similar real model. As a result, the calculated values approximate to the experimental values, so this analysis method shows valid.

203 波動歯車装置における高周波振動に関する研究(OS06-1 歯車の振動・騒音I)

The rotational transmission error of the strain wave gearing is the main cause of the tortional vibration. In this study confirmed the high frequency vibration generation in the strain wave gearing. First, the weighing device of the rotational transmission error was produced. This device can measure the rotational transmission error of the strain wave gearing can be measured in the high resolution evaluation. Next, do the Fourier transform of the rotation transmission error , and the error margin element of higher-order was confirmed. Moreover, the vibration of the output axis was measured, and the generation of the high frequency vibration was confirmed in reduction ratio 1/50.