APPLIANCE Engineer
A Technology Solution for a Quieter Hair Dryer Motor

Design engineers from Johnson Electric investigated why many hair dryers tend to emit a thin, high-pitched noise when turned on and off.

Unwanted Noise

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.

Figure 2. 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.

Modal Analysis

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: Beryllium Copper

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

Thermal coefficient of Expansion: 1.746e-5 1/ÁC

Shear Modulus of Elasticity: 49248 N/mm²

Figure 3. Mode shapes for typical cantilever-type structure.

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.

Figure 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.

Geometry 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.

Results of Acoustic Measurement

The 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.

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.

This information is provided by Johnson Electric, Hong Kong.