Extraction of modal parameters from structures that undergo excitation can be tracked back to the 1960s. Several approaches were formulated for analysing such data. Some of these approaches are; Auto Regressive-Moving Average models (ARMA) (Karakan 2008), Power Spectral Density functions, random decrement processing together with time domain parameter extraction and cross-correlation functions that also does time-domain parameter extraction. Akaike first studied the ARMA and used in the analysis of systems with ambient excitation. Such a system that was tested with the procedure was machine tools. Another closely associated method referred to as Maximum Entropy Method (MEM) was applied in analysing offshore structures that undergo excitation from waves (James, Carne and Lauffer 1995, p. 260).
Random decrement procedure was developed for processing of ambient-excitation data. The method enabled the use of a time-domain parameter extraction for the very first time and in particular the Ibrahim Time domain (ITD) technique. In recent years, the most preferred method of analysis, especially applied to brake system modes is the complex eigenvalue analysis.
Brakes are essential components that ensure the safety of vehicles moving on the ground. Materials that form the structure of the brakes should, therefore, possess the desired set of properties that include; a high friction coefficient, low weight, good compressive strength and thermal capacity (Maleque, Dyuti and Rahman 2010, p. 2).
Stiction is a low-frequency noise, of not more than 200 Hz, caused by stick-slip motion that occurs between the disc and pad interfaces at low speeds. It is not only associated with the disc speed but also the difference between static and dynamic coefficients of friction for both the friction material and the disc (Maleque, Dyuti and Rahman 2010). Specifically, the static friction coefficient should be more than the dynamic friction coefficient for stick-slip to occur. Stick-slip is, therefore, a brake instability that depends on the system inertias as well as stiffness as a result of suspension and calliper mounting (Fieldhouse et al., 2017, p. 326).
The function of the disc brake.
A vehicle's disc brake is made up of the following parts; master cylinder and piston, brake hose, brake fluid, disc and calliper. The master cylinder stores the brake fluid which upon pulling or pressing of a lever exerts pressure on the brake. The brake hose is a conduit for the oil and builds up the pressure to the brakes. The central part of the brake is the disc plate or rotor and the brake callipers containing brake pads and rotor in between. The shape of the disc rotors could be round or wavy and have holes that are sequentially drilled for purposes of heat dissipation. Much heat is generated when the brakes are applied hard and frequently. Because of the holes, there is an increased number of edges on the disc rotor surface hence removal of heat from brake callipers and brake pads. The disc calliper constitutes pots or pistons. The hose for the brake fluid is connected to the disc calliper. The force from the brake fluid pushes the pots against the brake pads bringing the vehicle to a stop.
How the modal properties affect the functioning of a disc brake.
Vibrations exerted during motion of a vehicle negatively impact the driving comfort and safety. The brake disc structure experiences vibrations that are triggered by forces and heat energy. A typical material for such parts is grey cast iron. An oscillatory wave propagation test was conducted on two different samples, varying by material, chemical composition, physical and chemical properties. One of the samples was grey pearlitic cast iron containing uniform flake graphite. The other sample was that of ST3S grade standard quality structural steel. The results of this test indicated the possibility of identifying signal frequency constituents relating to the part’s geometry as well as the structural material type.
Since grey pearlitic cast iron is characterised by high vibration damping, proper casting and self-lubrication ability, it is common in automotive and locomotive industries. Modern technologies have been applied to the manufacture of metallurgical products targeting high material parameters. However, there is still a negative impact as a result of the inclusions arising from processing of scrap or alteration of the properties during manufacturing or repair works.
Titanium alloys together with their composites have the capacity of reducing the brake rotor disc weight, being around 37% less of cast iron material with similar dimensions. They also offer better corrosion resistance and high-temperature strength (Rahman et al., 2010, p. 2).
Aluminium alloy based metal matrix composites reinforced with ceramic particulate also show more significant potential for brake rotor applications. Compared to grey cast iron, they have a lower density, a higher thermal conductivity and can reduce the weight by up to 50 – 60 % (Ashraf, Bryant and Fieldhouse 2017). However, with repeated braking, the friction coefficient is lowered and results to wearing of the brake pad. Hence the friction properties of this type of brake are poorer than the regular brake discs.
An addition of 20 % volume of SiC particulate enhances the wear resistance, improves high-temperature strength and increases stiffness (Ashraf, Bryant and Fieldhouse, 2017). However, three problems arise with this aluminium composite rotor. First, segregation of SiC particles in the process of solidification cannot be avoided due to the difference in density between aluminium and SiC. Secondly, there is low product liability due to a significant reduction of material ductility in formation of the composite. The third challenge is that the composite lacks a solid lubricant like graphite. Missing graphite is associated with low breaking efficiency, galling and adhesive wear.
The expected causes of excitation
The brake squeal noise is as a result of the coupling of the rotor disc’s bending modes of vibration and the pad. During vibration, the system resonance gets reduced because of the decrease in joint damping between the pad and disc (Balvedi, Gerges and Tousi 2002, p. 1820). Consequently, the friction forces results to more energy in the system than it can dissipate. This noise can be minimised through sufficient component design, making sure the resonances are apart. Modification of the pad's geometry, like the inclusion of chamfers and slots or modifying the structural properties, can avoid potential modal couplings.
Braking pressure and temperature are system boundary conditions that also influence the modal coupling mechanism. In the case of higher energy generation than dissipation, an increase in system damping can aid in the control of the radiated noise. Brake noise insulators formed from a sandwich of two steel plates with a rubber core are among efficient solutions of mitigating brake noise. The thin insulation is mechanically attached or bonded to the pad backplate. During vibration of the pad in bending modes, the insulator is subjected to mechanical deformation and converts some of the energy into heat through shear damping, leading to the reduction of the component's vibration amplitude.
Fig. 1: Shear damping in the laminated material
A three dimensional model of a vented disc brake component (part file) was modelled in Solidworks software to achieve an accurate representation of a real disc brake. Grey cast iron was selected as the material for the disc brake. The CAD model was then exported to Ansys software for Finite Element Analysis (FEA). Simulation at varying frequencies of vibration was conducted on the brake disk, and deformation noted as shown in the following figures.
Fig. 2: Simulation at 1080.9 Hz
Fig. 3: Simulation at 1081.1 Hz
Fig. 4: Simulation at 1826.8 Hz
Fig. 5: Simulation at 1923.5 Hz
Fig. 6: Simulation at 2507.6 Hz
From the figures above, it can be seen that the deformation happens more at the edge of the brake disc and it increases with the increase in vibration frequency.
Experimental Modal Analysis (EMA) was the second validation in the determination of the dynamic characteristics of the brake disc under boundary conditions. The brake disc was freely suspended on a brake test rig and with application of pressure on it. The Frequency Response Function measurements for the disc brake were recorded and plotted as shown in figure 7. This is done in a similar condition as the Finite Element disc brake model. Analysing the results, it is found that there exists a fair agreement between the results that were and those that were measured.
Fig. 7: FRF measured for the disc brake.
Stiction effect of the brake pad on the disc surface
Stiction is a brake instability characterised as a low-frequency noise occurring between the disc and pad interface at low speeds (James, Carne and Lauffer 1995). Much work has been done towards understanding the primary cause of stiction in brake assemblies, but it remains a challenge that demands further detailed examination. Going by what is known, stiction involves the rigid body oscillation of the brake assembly at the axle. Being a low-frequency noise, it is difficult to replicate in a laboratory set up.
Preliminary tests indicate that whenever stiction occurs, the inboard pad got marked with a trailing series of imprints on the disc surface. However, the outboard surface remains clean showing no evidence of pad imprints. Hence the inboard pad is what causes instability within the brake assembly (Ashraf, Bryant and Fieldhouse 2017). The other observation is that the part-worn pads tend to generate more stiction than freshly-bedded parts.
Experimental modal analysis conducted under constrained conditions was used to measure the natural frequencies in the determination of whether the excitation was by the stick-slip vibration. The frequency response results were obtained from the data acquisition system that was connected to the accelerometer that was mounted on the axle. Low-frequency noise associated with stiction depends highly on the motion of the calliper and twisting around its centre leading to the digging in by the pads to the brake disc. It is therefore vital to examine dynamic deformation of both brake pads and calliper.
Ashraf, N., Bryant, D. and Fieldhouse, J.D., 2017. Investigation of Stick-Slip Vibration in a Commercial Vehicle Brake Assembly. International Journal of Acoustics & Vibration, 22(3).
Balvedi, A.M., Gerges, S.N. and Tousi, S., 2002, August. Identification of brake squeal noise via sound intensity and acoustical measurement. In INTER-NOISE and NOISE-CON Congress and Conference Proceedings (Vol. 2002, No. 4, pp. 1818-1823). Institute of Noise Control Engineering.
James, G.H., Carne, T.G. and Lauffer, J.P., 1995. The natural excitation technique (NExT) for modal parameter extraction from operating structures. Modal Analysis-the International Journal of Analytical and Experimental Modal Analysis, 10(4), p.260.
Karakan, E., 2008. Estimation of frequency response fuction for experimental modal analysis (Master's thesis, ?zmir Institute of Technology).
Maleque, M., Dyuti, S. and Rahman, M., 2010. Material selection method in design of automotive brake disc.