Noise analysis of interior structure under powertrain excitation

To accurately identify the structural noise problem caused by vibration in the cockpit, an experimental study was conducted on a certain type of SUV under uniform acceleration conditions. Based on the planning of the multi-body system dynamics model, a transfer path model with secondary contributions is constructed, and the load is identified using the single degree of freedom model and multi-frequency bandwidth model under the OPAX method based on this path. The results indicate that the second-order vibration of the powertrain is transmitted to the entire suspension system through the X direction of the right suspension. The second-order vibration of the suspension system is then transmitted to the Z direction of the right rear bolt of the subframe, causing the entire subframe vibration and ultimately reaching the target point. This structural path has the greatest impact on the interior noise of the vehicle. This path research method can more accurately determine the main excitation points that cause interior noise problems on a certain path and better understand the overall energy transfer characteristics along the transmission path.


Introduction
With the continuous progress of automobile manufacturing technology, the noise problem in the cockpit has become one of the important indicators for evaluating the performance of automobiles.This article mainly focuses on the issue of interior structural noise in vehicles.The formation of interior structural noise is mainly caused by the vibration of the powertrain transmitted to the entire vehicle body through suspension and bolts.The vibration of the body structure is coupled with the air, resulting in noise problems in the cockpit.
At present, a large number of scholars at home and abroad have conducted research on the issue of structural noise in cars.Luo et al. [1] and Chen et al. [2] used numerical methods such as finite and boundary element methods to simulate and analyze interior noise.However, if the modal density increases or the analysis is conducted under high-frequency sound vibration, the computational complexity of the finite element method will sharply increase.Thus, the finite element method has limitations.Wen et al. [3] used Statistical Energy Analysis (SEA) to study the structural noise inside vehicles.Although many coupling loss factors are established, the workload is enormous, and it may still be difficult to meet all the requirements for structural noise analysis inside the vehicle.Guo et al. [4] used the Transfer Path Analysis (TPA) method to explore the issue of interior structural noise in vehicles.Unlike the above two points, this method can effectively control the overall situation regardless of low, medium, and high-frequency sound vibrations and can choose methods such as classical TPA, OPAX, OTPA, etc. [5] with different workloads based on experimental demands.This article takes a certain type of SUV as the research object and explores the issue of structural noise inside the vehicle.The OPAX method is comprehensively selected as the experimental method, and a multi-level path theory method is introduced for the multi-body system of the suspension and subframe.Based on the mechanical structure of the SUV, a transfer path model is planned and constructed to maximize the analysis of the entire mechanical system's transfer path with a certain workload.This method can showcase the path details of multi-level connected mechanical systems and also provide optimization ideas and directions for addressing the source of problems at all levels in the later stage [6].

OPAX method modeling process
This experiment mainly studies the problem of powertrain vibration caused by engine excitation under uniform acceleration conditions and the transmission of noise inside the vehicle through the secondary structure transmission path.The transmission of powertrain noise through the air transmission path will not be elaborated in detail.The response points of the noise experiment are all generated by the linear superposition of the contributions of each path.If there are n paths, then the total contribution of the response points is  (ω).
(1)  (ω) is the total contribution generated by the superposition of n structural paths at the target point; H ki (ω) is the frequency response function on the i-th path from the passive end to the target point, transmitted by the active end under load excitation; F i (ω) is the structural load acting on the active end of the i-th path; N is the total number of structural transfer paths;  is the frequency.

Load model determination
Establishing a load identification model is the core step of the OPAX method.The structural load is established by collecting working condition data and obtaining transfer functions, and the structural load is represented as: F i (ω)=f(Parameteres,a ai (ω),a pi (ω)) (2) eeres represents the model parameters to be identified.
) ( aai  and ) ( a i p  respectively refer to the vibration acceleration of the active and passive ends of the powertrain suspension system.The commonly used load identification models are the single degree of freedom model (SDOF) and the multi-frequency bandwidth model (MB).(SDOF) is only applicable to the connection of elastic components [7], and load identification is represented as: (3) m i , c i and k i are the mass, damping coefficient, and stiffness coefficient of the elastic element on the i-th path, respectively; j is the imaginary part of the complex number.MB is suitable for various elastic and rigid connections [8].The approximate value of dynamic stiffness within a certain frequency band in MB is: ) Therefore, in the first level transmission path, the suspension supporting the powertrain is made of rubber material, so the model chooses SDOF [9].In the second level transmission path, the subframe is rigidly connected by bolts, and the model chooses MB.The calculation method for the total contribution of additional indicator points is consistent with the target point, which can be expressed as: (5) simultaneously perform order analysis on the additional indicator points and target points obtained from the test, with m order slices selected for the operating data, and select rotational speed sampling points for each order slice [10].Equation ( 5) can be rewritten as a matrix form: X are the parameters solved in the matrix m , C and k .It is the parameter to be identified in Equation (3) or Equation ( 4) by substituting it.The dynamic stiffness curve and corresponding structural loads of the suspension components can be obtained, using the TPA theoretical formula:

Interior noise test on Level 2 path
We verify the feasibility of the secondary path OPAX method by using a domestic SUV as the experimental object.The powertrain suspension system of the car is a three point rubber suspension, and four-point bolts rigidly connect the subframe.We install acceleration sensors on the suspension of the test SUV and the active and passive ends of the subframe.The noise test target point is the driver's right ear, and the indicator point is the passenger's left ear and the center position of the rear seat.The test conditions are all fixed and uniform acceleration conditions.The layout of some sensors is shown in Figure 1 and 2.

Establishment of a secondary transfer path model
The experimental object is a certain type of SUV.Under uniform acceleration conditions, the powertrain vibrates and is connected through a rubber suspension, causing the entire suspension system to vibrate through rigid connecting bolts, ultimately causing the subframe to vibrate.The entire vibration transmission is a set of multi-body system dynamics models based on the mechanical structure.
According to the multi-level theory, the powertrain excitation is transmitted from the three-point rubber suspension to the entire suspension system under uniform acceleration conditions, resulting in noise problems in the cockpit as the primary transmission path.In contrast, the vibration of the suspension system is transmitted to the H-shaped subframe through the four-point rigid connection bolts, resulting in noise problems in the cockpit as the secondary transmission path.The secondary transmission path of the cab noise problem is shown in Figure 3.

Secondary transfer path experiment 3.2.1 Order analysis of noise conditions.
Because the data collected by the engine during acceleration conditions are all non-stationary signals, it is necessary to process the data through order analysis.In this article, order analysis uses speed to record the signal and obtain the fast Fourier transform spectrum, also known as order spectrum.The relationship between order, frequency, and speed is: N= 60f n (8) N represents the order, n represents speed, and f represents frequency.Figures 4 and 5 show the Colormap of the target points in the noise experiment.In the first level path, the second-order vibration of the powertrain contributes significantly to the noise in the driver's right ear through the structural transmission path, especially around 3400 rpm.In the secondary path, the second-order vibration of the suspension system is also the main contributor to the cab noise problem.Due to the jerking of the transmission during gear shifting, the structural noise in the cockpit increases significantly near 1600 rpm, 2400 rpm, and 3400 rpm.Therefore, the following text will mainly focus on the contribution analysis of the powertrain and suspension system to determine which transmission path is the main cause of the interior noise problem.  the coherence coefficient approaches 1 during the experimental process is, the higher the quality of the frequency response function is [11].

Analysis of the contribution of the secondary transmission path
After obtaining the order slice and frequency response function data of the target point and additional indicator points, the load identification under the primary and secondary paths was carried out using the SDOF and MB models in the OPAX modules [12].The obtained workload and frequency response function were substituted into Equation ( 1) to obtain the contribution under different paths.Through the order analysis of the second-order path noise in the previous section, the next focus will be on the spectrum of the vibration noise contribution of each path to the target point under the second-order order.
As shown in Figures 6 and 7, the first-order transmission path at 2nd order contributes the most to the interior noise of the vehicle in the X-direction of the right suspension near 847 rpm, 1300 rpm~1649 rpm, and 3900 rpm.In the secondary transmission path, the contribution of the left rear subframe bolt Z direction near 863 rpm, 1300 rpm~1500 rpm, and 3942 rpm to the interior noise problem reaches its peak.From a comprehensive perspective, the vibration energy generated by the acceleration work of the powertrain is first transmitted from the rubber suspension to the entire suspension system, with the largest contribution being in the X direction of the right suspension.The vibration of the suspension system is transmitted to the subframe through bolts, and the greater impact is transmitted in the Z direction of the left rear subframe bolts, ultimately leading to noise issues in the cockpit.According to the speed range that produces a significant contribution, it can also be seen that the clutch jerk caused by shifting during acceleration conditions also affects the internal noise problem of the vehicle.

Conclusion
The main source of structural noise in the cockpit is the 0-200 Hz low-frequency second-order vibration of the powertrain, which is transmitted to the suspension system.As a result, the second-order vibration of the suspension system is ultimately transmitted to the cockpit through the subframe.The structural noise increases significantly around 1500 rpm when shifting from first to second, 2400 rpm when shifting from second to third, and 3400 rpm when shifting from third to fourth due to the jerking of the transmission.Finally, through the analysis of the contribution of the secondary path, the main path that causes structural noise in the vehicle is restored as follows: The powertrain's second-order vibration is transmitted through the right rubber suspension in the X-direction, affecting the entire suspension system.This causes the second-order vibration to pass through the right rear bolt, which is rigidly connected to the subframe, and ultimately results in the entire subframe vibrating.This vibration is then transmitted to the target point of structural noise in the cockpit.
The secondary transmission path model created for the mechanical structure of the SUV, combined with the OPAX method, can more accurately locate the excitation source causing interior noise problems.It replicates the entire transmission path from the excitation to the target point.At the same time, the OPAX method ensures accuracy while greatly reducing workload compared to classic TPA.

Figure 4 .
Figure 4. First level path to driver's right ear Colormap.

Figure 5 .
Figure 5. Secondary path to driver's right Colormap.3.2.2 Acquisition of secondary path frequency response function.We apply the Impact Testing module under the LMS Test Lab for hammer method frequency response function testing.We use a hammer to strike the suspension and the passive end of the subframe in three directions: X, Y, and Z.The closer

Figure 6 .
Figure 6.The contribution spectrogram of the first set of data is used under order 2.

Figure 7 .
Figure 7.The contribution spectrogram of the second set of data is used under order 2.