It was determined
that the screeching noise was only generated when the motor was running
at less than 600 rpm, which is essentially during the Turn On and Turn
Off stages of the hair dryer.
Figure 1 shows that the frequencies of these high pitches ranged from 4-24
KHz, and the intensity of the first pitch is always the highest. As the frequency
increases, the amplitude of the pitch decreases. It was then surmised that
the second and third peaks were the harmonics of the first pitch.
Figure 1. FFT plot
of screeching noise in #300 motor. The revolution of the motor is less
than 600 rpm.
After further investigation,
the engineers determined that this "unwanted" noise originated from the
vibration of the electric motor's brush leaf. There are several parameters
that contribute to this kind of noise, which are usually related to normal
load, asperity, hardness, cleanliness, and lubrication on the contact
region of the surfaces. In this case, the spring load of the leaf and
the copper content of the brush were playing important roles in generating
the noise. This was associated with friction and adhesion between the
carbon brush and the commutator.
As the carbon brush
slides across the surface of the commutator, friction and adhesion drag
the brush. As the leaf is attached to the brush, the dragging force will
pull the leaf in a tangential direction of rotation. This action causes
constant deflection of the leaf that results in stress build-up inside
the leaf. In order to release this internal stress energy, the leaf will
try to restore itself to its original position and will eventually bounce
back to its equilibrium position.
The brush leaf can
be considered as a cantilever, and the following "Rubber-Ruler" model
demonstrates this mechanism in a much simpler way. A block of rubber
sticker is mounted on the tip of a rubber ruler, as shown in Figure 2.
This assembly is pressed against the surface of the table and is being
pulled in the direction as indicated.
A brush leaf model explains the mechanism of friction-induced vibration,
in which the maximum amplitude occurs near the middle section of
the leaf system. It is normally a high order mode shape.
As this happens, the
encircled portion of the ruler will start to move up and down periodically.
This is known as the "tapping action." Eventually, this vibration or
tapping action will give rise to noise. As the frequency of vibration
approaches the natural frequency of the ruler, resonance will occur.
The frequency of vibration is mainly determined by friction and the geometry
of the assembly.
In the case of a rectangular
block with an even frictional coefficient over the contact surface, the
tapping action of the cantilever concerns bending mode shapes only. Generally,
the tip of the cantilever will not have a large amplitude movement, and
most of the maximum amplitude will happen near the bending region of
the body. At this moment, this part of the cantilever is acting like
the diaphragm of a speaker that produces noise.
Individual parts have
their own natural frequencies. For example, a violin string at a certain
tension will vibrate only at a set number of frequencies, which is why
you can produce specific musical tones. The entire string is going back
and forth in a simple bow shape on a base frequency. Harmonics and overtones
occur because individual sections of the string can vibrate independently
within the larger vibration. These various shapes are called "modes." The
base frequency is said to vibrate in the first mode, and so on up the
ladder, as can be seen in Figure 3. Each mode shape will have an associated
frequency. Higher mode shapes have higher frequencies.
In order to investigate
the mode shapes and frequencies of the brush leaf, a model was built
with the aid of a popular 3D solid modeling software called Solidworks.
This model was then imported directly into the Finite Element Analysis
software Algor. The details of the model were as follows:
Material Description: Thermal
Expansion Coefficient (21.1Á-204.4ÁC)
Mass Density: 8.3593
x 10-9 Ns2/mm/mm3
Elasticity Modulus: 1.31
x 105 N/mm2
Poisson's Ratio: 0.33
of Expansion: 1.746e-5 1/ÁC
Shear Modulus of
Elasticity: 49248 N/mm2
Figure 3. Mode shapes for typical
Results show that the natural
frequency of the high-order twist mode matches the experimental result,
i.e. the natural frequency of this mode shape is around 7,720 Hz, with
a percent of error equal to approximately +/-3.5 percent.
As can be seen in Figure 4,
the maximum amplitude of the vibration occurs mainly on the ends of the
flanges of the brush leaf. In fact, the leading end of the brush leaf
generates minimum vibration. It is identical to how the leaf looks as
it is pressed against the commutator.
As a result, the vibration is
concentrated near the edges of the central area of the brush leaf. It
is very similar to the "Rubber-Ruler" model and, hence, the vibration
will be reduced if the deflection of the leaf can be minimized.
4. Mode shape of #300 brush leaf is shown when the mode frequency
is 7,720 Hz. The calculated result is close to the experimental
one, which is approximately 8,000 Hz.
of Brush Leaf
As previously stated,
the vibration of the brush leaf generates the noise. Simply, the amplitude
of vibration will be reduced if the deflection of the leaf is restricted.
From the "Rubber-Ruler" model for the tapping mechanism, it was found
that a pre-stressed beam provided more vibration than an unloaded or
less loaded cantilever.
The following criteria
should then be considered when developing a new brush leaf design:
- Reduce deflection
on the load beam.
- Retain or improve
the orientation of commutation.
- Retain or optimize
the spring load.
- Retain or optimize
the rate of spring load versus deflection
The new design developed
by the engineers involved reinforcing certain parts of the brush leaf,
and changing bend angles and the stiffness of the material.
of Acoustic Measurement
new brush leaf was installed into the original motor and similar
acoustic tests were conducted for comparison. The test sample
is shown in Table 1.
As shown in Figures
5 and 6, the peaks that appeared in the original motor disappeared on
the noise spectrum of the new motor. Some tiny ripples can be observed,
but those are the resonance peaks.
The screeching noise
was completely eliminated. Installing the new motor into the hair dryer
proved that the new brush leaf design successfully suppressed the friction-induced
vibration noise. The new brush leaf also cuts down running noise by about
4 dB and 3 dB at Low and High speed, respectively.
Figure 5. Acoustic noise spectrum of original motor. Input = 1.5 V d.c.
Figure 6. Acoustic noise spectrum of new motor. Input = 1.5 V d.c.
Longer Life Advantage
In conclusion, the
engineers determined that the new brush leaf can suppress both the running
and the stopping noise for the hair dryer. Since the total deflection
of the new leaf is reduced, the maximum internal stress is kept below
the yield strength of the material. It also will help to reduce the phenomenon
known as "stress relaxation" and, hence, the life of the motor will be
extended. In addition, the smaller leaf maintains a more stable performance
throughout the life of the motor.
is provided by Johnson
Electric, Hong Kong.