This paper deals with the generation mechanisms of the low frequency squeals generated in a rigid type of a car and a bicycle disc brake experimentally. In the case of out-of-plane squeal generated in a car disc brake, the natural frequencies of the out-of-plane vibration of the disc and caliper are close to the squeal frequency, and the out-of-plane squeal was concluded to be caused by the excitation of the coupled out-of-plane vibration of the disc and caliper by Coulomb friction. The vibration modes of the brake units during squealing are also investigated. Additionally, the relationship between the rate of squeal occurrence and both the direction of disc rotation and the effect of pad cut area are investigated. And the effect of the rubber installation to the pads on squeal is also investigated. In the case of in-plane squeal generated in a bicycle disc brake, it has been made clear that the squeal is mainly a torsional vibration of the disc and hub in the in-plane direction of the disc surface caused by dry friction which the frictional characteristics have a negative slope with respect to the relative velocity.

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Preventing brake squeal is a significant task in brake development because brake squeal bothers users, thereby reducing a vehicle's commercial value. Many researchers have tried to find the mechanisms that cause brake squeal, so the number of complaint to brake squeal is declining. However, brake squeal sometimes appears after a vehicle has been in use for years even though it was not generated early in the vehicle's life. In order to enable people to use vehicles for a long time with a high satisfaction level, it is important to find the factor that causes brake squeal to arise gradually because of specific changes; so we focused on the stiffness of brake pads, which are always wearing during braking, because the pads' stiffness correlates with brake squeal. This study presents the influence of pads' surface texture on disk brake squeal. Pads with different surface texture were prepared by changing the braking time and machining. We measured the pads' stiffness, which we evaluated by exciting a pad at the frequency and vibration amplitude that cause brake squeal. The measurement results show that pads' stiffness increases as their surface becomes smoother, which means that the surface stiffness of pad influences the pads' stiffness. Finally, we used a numerical model to analyze the generation of squeal, which is caused by pads' surface texture.

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The pressure between a disk and a pad become un-uniform when the pad inclines due to the moment of frictional force applied when braking. The pad stiffness also becomes un-uniform because the stiffness depends on the pressure. The influence of the un-uniformity of the stiffness between the disk and the pad on squeal generation is examined by using a surface-contact-analysis model. To facilitate the stability analysis, the model consisted of a minimum element that can reproduce the squeal vibration. Specifically, the model was composed of a disk with one degree of freedom (out-of-plane direction) and a pad-caliper with two degrees of freedom (rotational and translational). The disk and the pad-caliper are connected by a distributed spring. The analytical result clarified that the coupled vibration of the disk and the pad-caliper became unstable when the pad stiffness was un-uniform, and the self-excited vibration (squeal) was then generated. Additionally, the influence of the un-uniformity of the pressure between the disk and the pad on squeal generation was examined by executing squeal tests. The moment of the frictional force could be counterbalanced by enlarging the load added to the trailing side edge of the pad, which resulted in uniform pressure between the disk and the pad. The results of the squeal test clarified that squeal was not generated when the pressure between the disk and the pad was adjusted to become uniform.

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This study presents experimental and analytical results of squeal vibration in the disk-pad-caliper system, which is modeled after an actual disk brake. The system consists of a disk clamped along an inner edge and a pad supported by a plate spring (caliper). The frequency of squeal becomes higher as the thickness of the plate spring becomes large, and as the thrust load grows large. The squeal vibration of the disk near the contact area between the disk and the pad has translational motion, and the squeal vibration of this pad-caliper has translational and rotational motion. The disk and the pad-caliper vibrate with the same amplitude and the same phase at a point in the contact area. Therefore we analyzed the disk-pad-caliper system as a pin-disk model, which combined the disk with the pad-caliper by the point.

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This paper deals with a contact optimization problem from some methodologies which have been reported up to now in order to reduce brake squeal noise and fundamentally investigates how to make the contact region or contact shape between pads and a disk rotor. At first, a finite element model is built up for the assembled brake system and a complex eigenvalue analysis is conducted. The contact surfaces between the pads and a rotor are divided into eight regions. Each region is used as a parameter to find out the better contact condition. In the case of parametric studies, however, multiple squeals can not be controlled because of the size or shape of divided region. Therefore, a new approach is proposed by using a simple model simulation. It adopts a distributed spring model as a property of contact stiffness, and calculates the sensitivity of each spring for a squeal. If the sensitivity is positive and at a high level, the corresponding spring is removed. The proposed method is applied to automobile disk brakes. As a result of several simulations, it is confirmed that the proposed method is practical.

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A squeal test using a pad with a different thickness demonstrated that a squeal with a higher frequency can be generated if a thin pad is used. The factors that changed as a result of pad thickness were termed 'difference of pad rigidity' and 'dimension difference in the thickness direction of the pad', and the influence each factor exerted on the squeal was clarified. First, the dynamic stiffness of the pads used for the squeal tests were measured by adding a vibration that imitated the frequency and amplitude of the squeal. The measurement showed that the pad rigidity becomes hard when the pad thickness becomes thin. In addition, the pad vibrated with the same amplitude and the same phase from the frictional contact surface to the back plate in the thickness direction. The pad rigidity is in inverse proportion to the pad thickness because the pad can be viewed as springs in series in the thickness direction. Next, the influence that pad thickness exerted on squeal was analyzed by using a surface contact analysis model that reproduced the pad rigidity with a distributed spring and the dimension difference in the thickness direction of the pad with distance from the contact surface to the rotational center of the pad. Results showed that the squeal frequency becomes high when the pad rigidity becomes hard. If the dimension in the thickness direction of the pad becomes small, the squeal is not generated easily; however, the dimension does not influence the squeal frequency.

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This paper deals with the occurrence mechanism of the squeal generated in the rigid type disk brakes for car and its countermeasure by cutting a part of the pad surfaces in the circumferential and radial directions experimentally and theoretically. The squeal reduction has been investigated by using a bench test rig separating a brake unit consisting of rotor, caliper and pads only from a brake assembly, when verifying countermeasure against the squeal in the car disk brakes. However, the squeal generated in actual cars cannot he exactly reproduced on a bench test rig. Hence, in this paper, by using two different bench test rigs installed a common brake unit, the common features of the squeal phenomena and the effective countermeasure were made clear. Moreover, a simple analytical model coupled between rotor and caliper through pads regarded as elastic elemet was applied to the analysis of the low frequency squeal of the rigid type disk brake. It was confirmed that the analytical results were in a fine agreement with the experimental ones.

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This paper presents an analytical model coupled between rotor and caliper through pads to analyze the low frequency squeal of floating type disk brake, and describes the analytical results, compared with the experimental ones shown in the previous report. From the analysis, it was made clear that the squeal changes according to the contact distribution in the circumferential and the radial directions between rotor and pads, that is, in the case of cutting a part of pad surfaces in the circumferential direction, it is effective for squeal reduction to cut the pointed end pad surfaces of leading side on the inner side, and in the case of cutting a part of pad surfaces in the radial direction, it is effective for squeal reduction to cut outer pad surfaces of inside in the radial direction. It was confirmed that these analytical results were in a fine agreement with the experimental ones.

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The squeal phenomenon is often generated in bicycle disc brakes. This paper deals analytically with the generation mechanism and the criterion of whether or not the squeal occurs. According to the experimental studies, it has been made clear that the squeal is mainly in-plane vibration in the direction of disc surface with the frequency about 1kHz caused by frictional characteristics with negative slope with respect to the relative velocity. An analytical model of the bicycle disc brake system has been devised to confirm the experimental results, in which a coupled in-plane and out-of-plane vibrating system is composed of the disc, hub, caliper and spokes. The resulting frequency of squeal and the unstable vibration modes of the disc and spokes from the analytical model agreed well with the experimental results.

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鳴きの発生条件とその振動的特徴を把握するための基礎試験を行い、その結果を基にして、ブレーキ系各部品が接触力と摩擦力で結合されたシミュレーションモデルと鳴き発生を予測できる理論計算法を開発した。その計算法を用いて、パラメトリック計算を行い、効果的な鳴き防止対策を検討した。その対策案に対して効果確認試験を実施し、本計算法の妥当性、有効性を確認した。

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Squeal and chatter phenomena are often generated in bicycle disc brakes. The squeal is in-plane unstable vibration along the disc surface caused by dry friction with negative slope with respect to the relative velocity. The squeal is generated in the vibrating system including the brake unit, spokes and hub. According to experiments, the chatter is generated in a certain limited range at high disc temperatures, and is nonlinear frictional vibration in which the out-of-plane unstable vibration of the disc due to Coulomb friction and the squeal are combined through the internal resonance relationship between the out-of-plane and in-plane vibrations caused by the increase in disc temperature during braking. First, we propose a simple nonlinear system with three degrees of freedom which possesses the essential vibration factors included in a bicycle disc brake system to investigate whether or not the coupled nonlinear vibration due to the internal resonance occurs. Then, we numerically confirm the mechanism of the chatter generated in a bicycle disc brake by nonlinear analysis.

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マウンテンバイクに使用されるには1kHzの鳴きと，500Hzのビビリが発生する．この発生メカニズムを実験的に解明した結果，鳴きはロータ面内方向の負の勾配による摩擦自励振動であること，ビビリは鳴き現象にロータ面外方向の振動がロータの温度上昇に伴って重なり合った現象であることが明らかになった．

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