# Effect of Control Measures on Wheel/Rail Noise When the Vehicle Curves
## 1 Introduction  
Railway squeal noise is difficult to study because of its mechanism, wheel/rail interaction and random acoustic behaviour. Squeal generates as a railway vehicle negotiates a narrow curve, producing a tonal noise of high amplitude. Typically, the noise is radiated from the wheels and has most of its energy between 400 Hz and 10 kHz (in the frequency band where human beings are most sensitive to noise). In the process of curving, a series of railway wheel modes (particularly the wheel's axial modes) are easy to be excited, which may lead to curve squeal [1; 2; 3]. Known practical solutions for railway squeal in a particular curve include friction modification [4; 5] and wheel damping treatments [6; 7; 8; 9]. These solutions can reduce the occurrence of squeal for some special circumstance. Curve squeal noise has received increased attention by means of simulations and tests. Most previous research considered that the mechanism of railway curve squeal is mainly a kind of self-excited vibration due to the nonlinear creep forces [1; 3; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19]. [PERSON] [1] found that the main excitation mechanisms of squeal were related to lateral direction stick-slip phenomena which introduced unstable wheel/rail forces and vibrations. Slope of the creep force-creepage curve becomes negative instead of a constant value when the creepages reach a high level. Many models to simulate curve squeal were developed based on [PERSON]'s squeal theory. Most of the models begin with a characteristic of the creepage-dependent friction coefficient. [PERSON] [10], for example, applied [PERSON]'s model to terms. In a review article, [PERSON] [11] described the state of the art of railway curve squeal up to 1985. He suggested that this model should include finite element models of railway wheel dynamics, numerical models for the dynamics of bogies in curves and details of the friction coefficient versus creepage. Since then, [PERSON] et al. [12] developed a modal model for the wheel and calculated itsself-excited vibrations in the time domain through introducing [PERSON]'s formula for the falling friction coefficient in the sliding region. [PERSON] [13] included a finite element model of the wheelset and a modal model of the rail. The creep force formula is derived from [PERSON]'s theory [20] of rolling contact, extended to include a falling regime based on [PERSON]'s formula to resemble experimental findings more closely at large creepages. [PERSON]'s work has been extended further by [PERSON] [14] who included vehicle dynamics simulations in a time-domain curve squeal calculation. [PERSON] [21] introduced a simplified friction law into SIMPACK using a modified FASTSIM for curve squeal calculations based on [PERSON]'s work and TWINS. [PERSON] [16] developed an annular disc model and analyzed its vibration response in time domain. [PERSON]'s work made a contribution to understanding of the disc vibration and its modal shapes when squeal noise occurs due to lateral creepage. In order to consider railway wheel geometry, [PERSON]'s model needs to be improved. [PERSON] et al. [16] also presented a curve squeal model considering lateral creepages. The difference was that his model was developed in frequency domain. Noise radiation was predicted using the standard components of the TWINS software [22]. The model of [PERSON] was extended by [PERSON] and [PERSON] [17] by including the case of wheel flange contact, which usually occurred at the leading wheel at high rail. [PERSON] et al. [18] presented a curve squeal model including not only tangential dynamics (friction force) but also normal dynamics on the wheel/rail contact zone. The model can predict the unstable wheel modes and the corresponding squeal level and spectrum. [PERSON] [23] reviewed the curve squeal models, and developed a curve squeal model including a self-excited loop and relationship between wheel/rail motions and contact forces.