Method of suppressing torsional vibration noise of automobile drive-train system based on discrete wavelet

Abstract

In order to solve the problem of low efficiency and low efficiency of traditional methods, a method based on discrete wavelet is proposed to suppress the torsional vibration noise of automobile transmission system. Based on the operation mechanism of automobile transmission system, the transmission system model is built. In this model, the features of torsional vibration of transmission system were analyzed and the vibration signals were measured. The hardware equipments were used to collect the noise caused by torsional vibration, and then the discrete wavelet processing technology was used to quantify the torsional vibration noise. Based on the quantized noise data, the torsional vibration noise of automobile driveline was suppressed by active suppression and passive suppression. The experimental results show that the suppression time of this method for different noise size is less than 0.5 s, far less than the traditional method. Experimental results prove that the designed noise suppression method can greatly reduce the torsional vibration noise, so it has good application effect.

Keywords

Torsional vibration mechanics model noise sampling vibration signal differential equation

1 Introduction

The vehicle noise is one of the main noise pollution sources in urban traffic. With the increasing strictness of vehicle noise laws and regulations, how to solve the internal and external noise of vehicles becomes more and more important the automotive industry. The noise produced by the torsional vibration of automotive drive-train system has become more prominent [4 , 20].

In order to reduce the influence of torsional vibration noise on the life of automobile drive-train system and the drivers, it is necessary to reduce the torsional vibration frequency and suppress the noise. Before the noise suppression, it is necessary to understand the relationship between torsional vibration and noise. Generally, the noise is generated by vibration. The torsional noise is caused by the vibration during the operation. These vibrations are mainly due to the deterioration of contact area between the drive-train system and the change of the contact friction coefficient with the relative sliding. With the change of friction coefficient, the friction between the brake disc and the friction plate also changes, and the brake is affected by this alternating force, resulting in self-excited vibration and continuous noise [8]. Generally, the range of sound frequencies that can be heard by the human is 20 Hz-20000 Hz, and ultrasound is more than 20000 hz. There is a close relationship between vibration and noise. Essentially, the noise intensity and vibration speed amplitude are related. The sound pressure decreases with the decrease of vibration speed. At present, the main suppression principles include: reducing the torque fluctuation rate of engine crankshaft, improving the torsional vibration characteristics of gear-train system, improving the natural vibration characteristics of box body, and taking vibration isolation measures. Through the practical application, it is found that the suppression effect of traditional method is limited by the actual space environment, leading to poor suppression effect [7]. Therefore, a method of suppressing torsional vibration noise of automobile drive-train system based on discrete wavelet is proposed. Compared with the traditional method, the discrete wavelet analysis technology is introduced. The discrete wavelet analysis technology is to discretize the scale and translation of basic wavelet and analyze the relevant torsional signal and noise signal, and thus to get the specific scheme of noise suppression, so the proposed has better application effect.

2 Basic definitions

2.1 Model of automotive drive train

During the operation of the drive-train system, a certain torsional vibration may be produced. The calculation for the influence degree of excitation frequency on the natural frequency reflects the risk degree of resonance in system, which is mainly related to the moment of inertia and torsional stiffness of component. It is related to the structure of equipment. It is not the vibration in actual operation. When the vibration frequency exceeds a certain range, the noise will be generated. The fundamental reason of torsional vibration is the imbalance between the active torque and the reactive torque of the rotating machinery. The torsional vibration has great destructive effect, which can change the torsional stress acting on the shaft, increase the fatigue damage and reduce the service life. The severe torsional vibration will lead to the damage or fracture of haft system. The torsional vibration fault contains may forms. According to the frequency characteristics, the torsional vibration of shaft system is divided into three basic forms: subsynchronous resonance, supersynchronous resonance and oscillating torsional vibration.

In view of the noise caused by abnormal vibration of three gear full throttle of MPV, the power train model of the whole vehicle is built by considering the structural characteristics of engine, clutch, gearbox, transmission shaft, main reducing gear, half axis and wheel. Taking the actual cylinder pressure of engine under the condition of three gear full throttle as the input, the dynamic simulation analysis is carried out, so that the angular acceleration curve that flywheel end and the transmission input end change with the engine speed can be obtained. Meanwhile, the correctness of the multi-body dynamic model is verified by comparative analysis. Based on the dynamic response of power transmission system, we focus on the angular acceleration of the parts which are vulnerable to torsional vibration, and thus to analyze the dynamic response characteristics of power transmission system. Due to the actual analysis, we assume that the input of model can be simplified as the pulse signal loading on the flywheel without affecting the simulation accuracy and credibility and considering the complex excitation of various harmonics of engine. In addition, it is not necessary to consider the impact of the dynamic characteristics of the cardan joint on the motion of drive train and the spatial attitude, and the influence of various clearances, such as gear clearance, universal joint clearance should be ignored [13]. According to the simplification principle of power train equivalent system, we can simplify the components in drive train, so as to get the moment of inertia and stiffness parameters, and thus to establish the model of whole power train. As shown in Fig. 1.

Fig.1

Structure of automobile transmission system.

Fig.2

Model of torsional vibration.

Table 1

Mechanical model parameters of torsional vibration of drive train

Drive train unit	J/(kg*m²)	C/(Nms*rad-1)	K/(Nmrad-1)
flywheel	0.288	0.2	–
clutch	–	10	2.864
transmission	0.03	2	–
shaft	1.51*10-7	0	22.031
main difference of assembly	2.70*10-7	1.0	–
drive shaft	7.96*10-7	0	7.538
wheels	2.0	10	4.750

According to the actual principle of automobile transmission system, the transmission sequence is determined as: engine—clutch—speed transmission—transmission shaft—differential mechanism—half shaft—driving wheel.

2.2 Analysis of torsional vibration characteristics of transmission system

2.2.1 Torsional vibration mechanical model

By aggregating the rotational inertia of rotor to many nodes along the axis, we can get the concentrated mass of rotational inertia and elastic deformation and the model rotor composed of elastic shaft segments [6]. The whole shaft system can be simplified to the model shown in Fig. 2 through the dynamics analysis on the torsion process of automobile transmission system.

The whole torsional vibration model can be expressed as follows: ${\begin{matrix} θ_{12} = θ_{1} - θ_{2} \\ \frac{d θ_{12}}{dt} = ω_{12} \\ J_{2} \frac{d ω_{12}}{dt} c ω_{12} + k θ_{12} = T_{c} \end{matrix}$ (1)

Where, c is the torsional vibration damping and k is the stiffness. T_c is the load torque. The whole system of automobile transmission is composed of flywheels, clutches and gearboxes. Under the model of torsional vibration mechanics, the torsional mechanical equations of all parts in transmission system are established. The torsional mechanical equation of flywheel is: $T_{0} - T_{1} = J_{0} \frac{d ω_{0}}{dt} + C_{f} ω_{0}$ (2)

The torsional mechanical equation of clutch can be expressed by Equation 3. $T_{1} = k_{c} \int_{0}^{t} (ω_{0} - ω_{1}) dt + C_{c} (ω_{0} - ω_{1})$ (3)

Similarly, the formula of the torsional mechanical equation of the gearbox in the automobile transmission system is: ${\begin{matrix} T_{1} - T_{2} = J_{g} \frac{d ω_{1}}{dt} + C_{g} ω_{1} \\ n_{g} = \frac{ω_{1}}{ω_{2}} \end{matrix}$ (4)

In the above formula, the parameter T₁ represents the input torque of engine. T₂ is the torque transmitted by the drive-train components. C_g is the equivalent damping coefficient of drive-train component. n_g is the first-grade speed ratio of speed transmission, and its value can be seat as 6.602 [15 –17]. In addition, ω₁ is the angular speed of drive train component. The parameter value of each component of drive train is shown in Table 1.

2.2.2 Torsional vibration measurement and signal processing

Fig.3

Schematic diagram of inherent characteristics of drive-train torsional vibration.

Discrete wavelet transform (DWT) is a time-scale analysis method of signal. The window size is fixed, and the time window and frequency window can be changed. DWT is also a time-frequency localization analysis method, which is suitable for monitoring the transient abnormal phenomenon in the normal signal [3]. Therefore, the wavelet transform is used to estimate the transient torsional vibration in main shaft. According to the transient stator torsional vibration, the signal is measured, and the wavelet transform algorithm is used to estimate the transient torsional vibration process of main shaft. Supposing that x (t) is a square integrable function and φ (t) is the basic wavelet function. Thus: $\begin{matrix} {WT}_{x} (α, τ) = \frac{1}{\sqrt{α}} \int x (t) φ^{*} (\frac{t - τ}{α}) dt \\ = 〈 x (t), φ_{α τ} (t) 〉 \end{matrix}$ (5)

α is the scale factor. τ reflects the displacement. The function of scale factor is to make the basic wavelet φ (t) stretch out and draw back. The continuous wavelet transform and analysis are performed on the stator torsional vibration signal. In a series of frequency bands with the same selectivity, the discrete wavelet filter can be used to reflect in the wavelet time-frequency window with good filter characteristics, so as to obtain the special information contained in the signals [10].

2.2.3 Analysis of natural frequency characteristics

Because the automobile driveline is a small damping system, the damping parameters have less influence on the inherent characteristics of driveline. In order to calculate simply, the damping effect can be ignored. In order to analyze the inherent characteristics of driveline, it is necessary to simplify some nonlinear factors in driveline as the linear analysis. For the time-varying moment of rotational inertia J_i of time-varying vibration of piston crank connecting rod mechanism, its time-varying characteristics are mainly caused by its reciprocating motion mass. According to the principle that the average kinetic energy of one cycle around the crankshaft centerline is equal, the average value of piston crank connecting rod mechanisms is obtained [18, 19]. Considering the influence of the free gear and the constant mesh transmission gear on the torsional vibration, the system of undamped torsional vibration differential equations in the form of driveline matrix is established $M \ddot{θ} (t) + K θ (t) = {0}$ (6)

In Equation 6, the variable M is the system inertia matrix. K is the stiffness matrix of system. θ (t) is the angular displacement matrix of drive train. Through the calculation of variable parameters, the characteristic model of natural frequency of torsional vibration of drive train is obtained and shown in Fig. 3.

2.2.4 Incentive analysis of engine

In order to calculate the forced vibration, it is necessary to obtain the excitation moment of system. In the driving condition, there are many kinds of excitation in the whole drive train. In the analysis of torsional vibration of drive train, the engine excitation occupies the most important position. It is necessary to make a comprehensive analysis on the engine excitation torque [9]. The spectrum of the excitation vibration moment of engine in drive train is shown in Fig. 4.

Fig.4

Auto spectrum of excitation moment.

Based on the spectrum in Fig. 4, the single-cylinder engine has two external forces: vertical force and torsional moment. Since the combustion of gas is the internal action of the cylinder, the external vertical force of single cylinder engine is the inertial force caused by the rotation of engine crankshaft. Thus: $F_{z} = - m_{s} r ω^{2} (cos ω t + λ_{p} cos 2 ω t)$ (7)

The external torsional moment is the superposition of gas torque and inertia torque. The total torque four-cycle engine is: $M_{x} = M_{xm} + M_{xg}$ (8)

The effective output of torque of single cylinder engine is from the gas torque. The torque fluctuation of engine is composed of the fluctuation of gas torque and the inertia torque. The half-order component is from the gas torque generated by gas combustion, and the integral-order fluctuation is formed by the superposition of the inertia torque and the gas torque [1].

2.2.5 Solving the differential equation of torsional vibration of drive train

The equivalent system model of torsional vibration of drive train is built. According to the theorem of moment of momentum, the differential equation of torsional vibration of drive train can be established $[J] {\ddot{θ}} + [c] {\dot{θ}} + [K] {θ} = {M}$ (9)

Where, [J] is the matrix of rotational inertia. [c] is the damping matrix. [K] is the stiffness matrix. {θ} is the angular displacement vector. {M} is the excitation moment. By substituting the specific value of each variable into Equation 9, we can get the solution of torsional vibration equation of drive train.

2.2.6 Calculation of torsional vibration of drive train

The calculation of the torsional vibration is related to the vibration mode. The torsional vibration mode can be divided into the undamped free vibration mode and the damped forced vibration mode. The undamped free vibration mode means that the system will not be subject to external force after the initial disturbance. The undamped vibration means that there is no loss of system energy caused by friction or other resistance during the vibration [2]. According to the features of undamped free torsional vibration, the parameters in Equation 9 are updated. The motion differential equation under the vibration mode is as follows: $[J] {\ddot{θ}} + [K] {θ} = {0}$ (10)

Suppose that the solution of Equation 10 is: ${θ} = {Ae}^{j ω t}$ (11)

Finally, the generalized feature equation can be obtained. $[K] {A} - λ [J] {A} = {0}$ (12)

Where, λ is the feature value, and {A} is the eigenvector corresponding to the feature value. In the same way, the calculation result of vibration under the forced damping mode can also be obtained.

2.3 Noise sampling

The mechanism of torsional vibration noise produced by automobile drive train is the vibration caused by torsional friction. Some moving interfaces have special characteristics. If the static friction is greater than the dynamic friction, this may lead to the friction sliding effect. When the friction sliding effect occurs, the speed of moving parts will generate the single jump or continuous jump, which changes greatly between a small value and a large value, thus forming the relaxation impact vibration of parts [14]. The generation and propagation process of torsional vibration noise of automobile drive train is shown in Fig. 5.

Fig.5

Flow chart of generation and propagation of vibration noise.

Based on the noise generation and propagation process in Fig. 5, some signal acquisition devices are installed on the specify location of drive-train model according to the device connection mode shown in Fig. 6.

Fig.6

Connection of signal acquisition device.

The relevant signal acquisition equipments are used to regard the noise pseudo signal X_A in the drive-train model as the band-pass signal that is limited on (f_l, f_h). Thus, the band-pass sampling rate of noise can be set as: $f_{s} = \frac{2 f_{l}}{n - 1}$ (13)

Where, n is a positive integer, indicating the sampling frequency. f_s is the noise sampling rate. If the power spectral density of noise signal X_A is defined as ρ, and the power spectral density of noise in band is ρ_n. Then, the signal-to-noise ratio after sampling will decrease: ${SNR}_{s} = \frac{ρ}{ρ_{n} + (i - 1) N_{0}}$ (14)

Where, i is the order of noise signal. The noise sampling results are shown in Fig. 7.

Fig.7

Frequency sampling results.

2.4 Noise quantization based on discrete wavelet

Figure 8 shows the flow of acquisition and quantization of noise signal by discrete wavelet transform.

Fig.8

Quantization Flow of discrete wavelet.

Continuous wavelet transform is performed on any continuous noise signal function. In practical application, in order to facilitate computer analysis and processing, it is necessary to discretized the scale factor a and displacement factor b. The scale factors are discretized by power series, and the displacement factors are uniformly discretized within the scale, so that there is a power relation between scales. Respectively, wavelet function and discrete wavelet transform are: ${\begin{matrix} ψ_{j, n} (t) = a_{0}^{- \frac{j}{2}} ψ (a_{0}^{- j} t - {nb}_{0}) \\ Wf (j, n) = \int_{- \infty}^{\infty} f (t) ψ_{j, n} (t) dt \end{matrix}$ (15)

Where, a is scale factor corresponding to frequency information. b is displacement factor, corresponding to space-time information [5]. At this time, a and b are continuous variables. Based on the operation condition of Equation 15, the floating rule of discrete wavelet coefficient is determined as shown in Fig. 9.

Fig.9

Floating rule of wavelet coefficients.

According to the actual conditions of discrete wavelet quantization, the corresponding coefficient values are selected. And then, they are introduced into Equation 15 to output the final noise quantization result of torsional vibration of automobile transmission system.

Table 2

Parameters of experimental objects

Vehicle structural parameters		Engine power parameters		Transmission system parameters (transmission ratio)
Quality	910 kg	Minimum speed	900 r/min	1 stop iA	2.5
The center of gravity position	0.5	Maximum speed	5540 r/min	2 stop iA	1.7
Wheel radius	0.3 m	Most powerful	64 kw	3 stop iA	1.25
Windward area	1.9 m²	Corresponding rotational speed	5000 r/min	4 stop iA	1
Coefficient of rolling resistance	0.01	–	–	Half shaft iG	4
C	0.3	–	–	–	–

2.5 Suppression of torsional vibration noise

2.5.1 Active suppression

For the selection of control strategy, the controller is used to control the vibration of drive-train unit module, and then the discrete wavelet joint control strategy is used to control the vibration. In the application of controller, it is necessary to adjust the parameters in controller until a good control effect is achieved. The parameter adjustment method is as follows. Firstly, the integral gain and differential gain are set as 0, then the proportional gain increases gradually from zero to the limit gain. At this time, the output value of controller oscillates with a constant value. The proportional, integral and differential gains are set according to different types of limit gain and oscillation period [12]. After that, the discrete wavelet control is introduced based on the original controller. The brake is used to compensate the inherent disturbance of brake system. Finally, signal and noise show different characteristics after wavelet transform, so that the wavelet transform can be used to reduce noise and improve signal-to-noise ratio.

2.5.2 Passive suppression

The passive way to suppress the noise is to install viscoelastic materials on the corresponding equipment. The viscous effect of viscoelastic materials between the contact surfaces mainly exists in the smooth and clean surfaces, and it is an impediment to the relative movement caused by the force between the molecules on the two surfaces. The hysteretic and internal friction of viscoelastic materials is closely related to the change frequency of stress. It is not difficult to imagine the dependence of contact friction for the speed under the hysteretic effect. Moreover, the hysteresis effect depends on the intrinsic property of viscoelastic material. In conclusions, the function of sticking damping layer on the base plate of brake block is regarded as the dynamic friction between the contact surfaces, which is characterized by the sliding friction coefficient.

Fig.10

Position of vibration measuring point.

3 Experimental analysis of effect test

The purpose of test experiment is to test the effect of the method of torsional vibration noise suppression of automobile transmission system based on discrete wavelet in practical application. In this paper, the finite element method (method 1) and the boundary element method (method 2) are used as comparison methods to compare the noise suppression effect and efficiency of different methods.

3.1 Experimental parameters and process settings

The test object is a newly developed automobile transmission system. The specific parameters of test object are shown in Table 2.

The experimental platform has several functions, such as towing function, deceleration braking and thermal stability recovery. The test method is to fix the brake disc on the rotating shaft, so as to drive the linear inertia of vehicle by the rotating inertia. The brake noise is detected by the pickup. Finally, the value in sound pressure level is obtained through the spectrum analyzer.

Through this experimental equipment, the noise frequency, sound pressure level and other influencing factors of brake can be measured under different working conditions. The experimental results reproduce the noise of brake in the actual working condition. In order to reveal the mechanism of friction noise, the vibration acceleration of brake block along the tangential motion and radial motion can also be measured in the experiment, and then the main frequency components can be obtained through spectrum analysis. According to the above effect test principle, we can determine the noise test point on the object, which is shown in Fig. 10. Finally, we can install the pickup on the test point.

The experimental standard of noise is the experimental method which is internationally recognized. This method can detect the brake noise. In this experiment, the noise level and the time of duration should be measured and recorded. During measurement, the pick-up head of sound meter is put in the rotating plane of brake, and the pick-up head is installed in the wind cap. It is necessary to measure the ambient noise value and record it before braking action, so as to correct the measured noise value. This experiment is to compare the brake assembly before and after modification, so only one fixed point is selected. In order to reduce the influence of sound wave and reflected sound wave, the microphone should be close to the noise radiation surface of experimental object, so that the direct sound of the measured noise source becomes the main part of the measured noise. Thus, the near-field measurement method is adopted. If the microphone is too close to the sound source, the sound field is unstable. During the whole experiment, a tripod is used to fix the sound meter at thus measuring point, and a w wind cap is used to cover the microphone and thus to avoid the influence of air flow.

In the process of experiment, there is not necessarily an obvious scream even under the same experimental conditions. It is a smooth friction sound in most of the time. Sometimes, the strong vibration sound may occur, and even a scream. This kind of scream is harmful to people. It is necessary to collect the vibration and noise signals in case of violent vibration or scream. In order to avoid the influence of external noise as much as possible, the baffle and shell which are easy to produce vibration should be removed or fixed, so as to cover the motor to isolate the motor noise. After a period of friction between the brake disc and the brake block, a large number of dust particles are produced due to the wear and tear. When there are many dust particles between the friction surface of brake block and the brake disc, severe vibration will occur, without obvious noise. At this time, we must stop the machine, remove the brake block to keep the dust out of the friction surface and the brake disc surface, and then we can continue the experiment.

3.2 Analysis of experimental results

The noise results collected in experiment are input into the audio processing software and then they are output in the way of sound wave. In addition to the setting of the method of torsional vibration noise suppression of automobile transmission system based on discrete wavelet, the traditional noise suppression method also needs to be set as the comparison method. The two methods are the same for the experimental object and the experimental operation. Through the processing and analysis of third-party software, the noise fluctuation on these two measuring points is shown in Fig. 11.

Fig.11

Experimental results of effect tests.

The acoustic processing results in Fig. 11 show that the decibel of the traditional noise suppression method is higher, and the sound distribution is more scattered, while the acoustic wave corresponding to the method of torsional vibration noise suppression of automobile transmission system based on discrete wavelet is relatively smooth, and the sound distribution is relatively centralized, so the noise suppression effect of the proposed method is better. This is because the method in this paper is based on the quantitative noise data, from the two aspects of active and passive suppression, respectively, to achieve the suppression of the torsional vibration noise of the automotive transmission system.

In order to further verify the effectiveness of this method, taking the efficiency of noise suppression as the experimental index, this paper compares the finite element method (method 1), the boundary element method (method 2) and the noise suppression effect of this method. Figure 12 shows the comparison results of different methods.

Fig.12

Comparison of the time required for noise suppression by different methods.

It can be seen from the analysis of Fig. 12 that the suppression time required by this method for different noise sizes is less than 0.5 s, but the noise suppression time of traditional method 1 and traditional method 2 is significantly higher than that of this method, and the traditional method 1 is still unstable, so it can be explained that the noise suppression efficiency of this method is the highest, and the noise suppression can be completed in the shortest time. This is because the method in this paper uses discrete wavelet processing technology to realize the quantization of torsional vibration noise, thus reducing the complexity of noise suppression and improving the efficiency of noise suppression.

4 Conclusions

Because the automobile power train is a complex dynamic system involving many design parameters, its torsional vibration noise is closely related to the variable conditions and use environment. Although the research on torsional vibration noise of drive train is time-honored, a consistent conclusion from the occurrence mechanism to the analysis method has not arrived yet. In addition, the measures to suppress the noise adopted in the engineering generation are basically empirical. In order to solve the problem that the traditional method has poor noise suppression effect and low suppression efficiency, a method based on discrete wavelet is proposed to suppress the torsional vibration noise of automobile transmission system. From both theoretical and experimental aspects, the discrete wavelet technology provides new research ideas for noise suppression. The designed noise suppression method has researched the torsional vibration and noise of automobile drive train and achieved certain results, the experimental results show that the suppression time of this method for different noise size is less than 0.5 s, far less than the traditional method. but there are still many immature and imperfect research work. Meanwhile, there are some theoretical and application problems to be further studied.

Footnotes

Acknowledgments

The research is supported by National Natural Science Foundation of China (51875201) and Science and technology project of Jiangxi Department of Education (20181BBE50011).

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