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Strain wave gearing (also known as harmonic gearing) is a type of mechanical gear system that uses a flexible spline with external teeth, which is deformed by a rotating elliptical plug to engage with the internal gear teeth of an outer spline.
The German company Harmonic Drive SE manufactured the first series-produced gears under the product name or registered trademark Harmonic Drive.
Strain wave gearing has some advantages over traditional gearing systems such as helical or planetary gears, including:
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High gear reduction ratios are possible in a small volume (a ratio from 30:1 up to 320:1 is possible in the same space in which planetary gears typically only produce a 10:1 ratio).
Disadvantages include a tendency for 'wind-up' (a torsional spring rate) in the low torque region.
Strain wave gearing is commonly used in robotics[3] and aerospace.[4] It can provide gear reduction but may also be used to increase rotational speed[citation needed], or for differential gearing.
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The basic concept of strain wave gearing (SWG) was introduced by C.W. Musser in a patent[5][6] while he was an advisor at United Shoe Machinery Corp (USM). It was first used successfully in by USM Co. and later by Hasegawa Gear Works under license of USM.[citation needed] Later, Hasegawa Gear Work became Harmonic Drive Systems located in Japan and USM Co. Harmonic Drive division became Harmonic Drive Technologies.[7][8]
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Cross section of a harmonic gear.The strain wave gearing uses the elasticity of metal. The mechanism has three basic components: a wave generator (2 / green), a flex spline (3 / red), and a circular spline (4 / blue). More complex versions have a fourth component normally used to shorten the overall length or to increase the gear reduction within a smaller diameter, but still follow the same basic principles.
The wave generator is made of two separate parts: an elliptical disk called a wave generator plug and an outer ball bearing. The elliptical plug is inserted into the bearing, forcing the bearing to conform to the elliptical shape but still allowing rotation of the plug within the outer bearing.
The flex spline is shaped like a shallow cup. The sides of the spline are very thin, but the bottom is relatively rigid. This results in significant flexibility of the walls at the open end due to the thin wall, and in the closed side being rigid enough to be tightly secured (to a shaft, for example). Teeth are positioned radially around the outside of the flex spline. The flex spline fits tightly over the wave generator, so that when the wave generator plug is rotated, the flex spline deforms to the shape of a rotating ellipse and does not slip over the outer elliptical ring of the ball bearing. The ball bearing lets the flex spline rotate independently to the wave generator's shaft.
The circular spline is a rigid circular ring with teeth on its inside. The flex spline and wave generator are placed inside the circular spline, meshing the teeth of the flex spline and the circular spline. Because the flex spline is deformed into an elliptical shape, its teeth only actually mesh with the teeth of the circular spline in two regions on opposite sides of the flex spline (located on the major axis of the ellipse).
Assume that the wave generator is the input rotation. As the wave generator plug rotates, the flex spline teeth which are meshed with those of the circular spline slowly change position. The major axis of the flex spline's ellipse rotates with wave generator, so the points where the teeth mesh revolve around the center point at the same rate as the wave generator's shaft. The key to the design of the strain wave gear is that there are fewer teeth (often for example two fewer) on the flex spline than there are on the circular spline. This means that for every full rotation of the wave generator, the flex spline would be required to rotate a slight amount (two teeth in this example) backward relative to the circular spline. Thus the rotation action of the wave generator results in a much slower rotation of the flex spline in the opposite direction.
For a strain wave gearing mechanism, the gearing reduction ratio can be calculated from the number of teeth on each gear, in a similar manner to a cycloidal drive:
R = flex spline teeth &#; circular spline teeth flex spline teeth , &#; 1 < R < 0 {\displaystyle R={\frac {{\text{flex spline teeth}}-{\text{circular spline teeth}}}{\text{flex spline teeth}}},\quad -1<R<0}
Note that the reciprocal of the reduction ratio is sometimes referred to with the same phrase and symbol.
For example, if there are 202 teeth on the circular spline and 200 on the flex spline, the reduction ratio is (200 &#; 202)/200 = &#;0.01
Thus the flex spline spins at 1/100 the speed of the wave generator plug and in the opposite direction. Different reduction ratios are set by changing the number of teeth. This can either be achieved by changing the mechanism's diameter or by changing the size of the individual teeth and thereby preserving its size and weight. The range of possible gear ratios is limited by tooth size limits for a given configuration.
This reduction ratio is applicable to the configuration where the circular spline is fixed, the wave generator the input and the flexible spline the output. In case the circular spline also rotates, the following relation holds between the rotational velocities of the three parts:[9]
ω F S = R ω W G + ( 1 &#; R ) ω C S {\displaystyle \omega _{FS}=R\omega _{WG}+(1-R)\omega _{CS}}
Mind that R {\displaystyle R} is negative and small.
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The electrically driven wheels of the Apollo Lunar Rover included strain wave gears.[10] Also, the winches used on Skylab to deploy the solar panels were powered using strain wave gears.[citation needed]
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The Harmonic Drive block represents a compact, high-ratio speed reduction mechanism that contains three key components:
Strain wave generator
Elliptical gear
Circular ring gear
A harmonic drive is backlash-free with a high-ratio of speed reduction by design. This is advantageous for systems that require precise gear positioning. The base shaft turns the strain wave generator, which is elliptical with bearings around the circumference. The bearings allow the strain wave generator to rotate within the elliptical gear. The elliptical gear is flexible, and the motion of the strain wave generator causes the vertices of the elliptical gear to move. This deformation of the ellipse causes the teeth of the elliptical gear to slowly climb the teeth of the circular ring gear. The ring gear has more teeth than the elliptical gear to allow for this motion. The elliptical gear transmits torque to the output shaft while rotating within the ring gear.
Meshing occurs concurrently at both vertices of the elliptical gear. This design doubles the teeth in mesh, thereby increasing the torque capacity of the drive system.
The internal meshing between the two gears causes the elliptical gear axis to spin counter to the elliptical strain wave generator.
Large reduction ratios arise from the near-equal gear tooth numbers. The effective gear reduction ratio is
r=nEnC&#;nE&#;,
where:
r is the gear reduction ratio.
nC is the number of teeth on the circular ring gear.
nE is the number of teeth on the elliptical gear.
The Simple Gear block provides the foundation for this block.
You can enable rotation of the circular ring gear by setting Ring gear
rotation to On. The block exposes port
R, which allows you to control the rotational motion of the
ring gear by using a mechanical rotational input signal.
Note
The Ring gear rotation parameter determines how you parameterize meshing losses.
When you set Ring gear rotation to
Off, the block calculates the efficiencies using the
Simple Gear block implementation. In this case,
you parameterize the meshing losses the same way you would for the
Simple Gear block. However, when you select
On, the block calculates the efficiencies by
implementing the Planetary Gear block. For this case,
you parameterize the meshing losses the same way you would for the
Planetary Gear block.
You can model
the effects of heat flow and temperature change by enabling the optional thermal port. To enable
the port, set Friction model to Temperature-dependent
efficiency.
Use the Variables settings to set the priority and initial target values for the block variables before simulating. For more information, see Set Priority and Initial Target for Block Variables.
Contact us to discuss your requirements of Strain Wave Gear. Our experienced sales team can help you identify the options that best suit your needs.