非旋转轮胎的试验模态分析毕业课程设计外文文献翻译、中英文翻译

目 录1英文文献翻译31.1Modal analysis on tire with respect to different parameters31.2中文翻译132专业阅读书目182.1机械设计182.2机械原理182.3材料力学192.4现代工程图学192.5互换性与技术测量202.6机电传动控制202.7机械制造基础212.8机械制造技术212.9数控技术222.10理论力学221英文文献翻译1.1Modal analysis on tire with respect to different parametersThis paper presents experimental modal analysis of non-rotating tires under different boundary conditions. A test rig with four guides in vertical (radial) direction and two guides in axial direction was designed to support the tire-rim assembly with a free support. The setup permits to carry out the experiments on the grounded supported tire-rim assembly while changing the value of the static load acting on the wheel axis. Under static load condition, it is found that, tire deflec-tion depends on the applied static radial force in a hysteresis manner and a third-order polynomial was used to fit the data during loading and unloading conditions. The relationship between static stiffness in radial direction and tire deflection is nonlinear and depends on loading/unloading con-ditions for different tire pressures. The response of the tire is quite similar to the response of vis-cously damped mass system for impulse force which is provided by an impact hammer. The results show that the system modal parameters can be obtained respective of loading or unloading conditions with a maximum difference of 1.992% for frequency values and 3.66% for damping val-ues. This study has a practical value for the description of mechanical properties of tires.2016 Production and hosting by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license1.Introduction The requirements for automobile dynamic characteristics become higher due to increase of automobile speed. The auto-mobile contacts the road surface through tires, which will affect the behavior of the automobile significantly. The requirements for tire are high abrasion resistance, optimumstiffness characteristics and low rolling resistance. Due to the complex structure of tire, modal analysis is a powerful means for the study of dynamic characteristic of tires. The tires are influenced by the complex structure and the working con-ditions, and it is difficult to separate their effects. Using modal parameters identified by experimental modal analysis tech-nique to determine the dynamic behavior of a tire reflects its intrinsic characteristics. Such analysis must be independent of the tire working conditions, and should be identified via modal test in dependant of the ambient conditions. Thus experimental modal analysis on tires will be more reasonable and can be standardized. In this paper the related issues have been studied and discussed carefully. The following aspects must be investigated in the experimental modal analysis of the tires:（1）The type of support of the tire (i.e., fixed support or freely suspended).（2）The means of excitation (i.e., using impact hammer or elec-tric exciter).（3）The selection of the sensors to reduce the additional mass and stiffness of the tested object as much as possible.In order to obtain reliable test results with sufficient accu-racy, it is important to eliminate the error of measurement aris-ing from aliasing and leakage which are inevitable in frequency domain analysis.Modal analysis of passenger vehicle tires started in 1960s. A major contributor to this study was Pacejka who proposed a semi-empirical tire model known as the magic tire formula. His experiments focused on comparing the behavior of bias play with new radial tires. The experiments were carried out using a fixed axle test setup with radial excitation. Consider-able amount of work has been done by Zegelaar and Yam et al. to examine the three dimensional mode shapes of passenger tire. Zegelaar examined the in-plane vibrations of such a tire in free and standing conditions. Experimental modal analysis is performed by placing tri-axial accelerometers around the tire tread and hitting the tire in various places with a modal hammer. The input force from the hammer is recorded along with the outputs of the accelerometers in order to determine the frequency response function between the input and output force. The experimental results were com-pared with analytical results derived from the flexible ring model proposed by Gong. Yam et al.used a similar test setup and analyzed the full three-dimensional motion of the tire to get its in-plane and out of plane vibrations. Their results showed that the first flexible mode occurs around 120 Hz, which agrees with Zegelaars results. In the analysis by Yam et al. only the free tire modes were examined. There are num-ber of methods that have been used for examining the presence of nonlinearities in experimental modal testing. Sine sweep and harmonic input tests can be particularly useful for detecting effects such as nonlinear resonances. Exciting the system at one-half, one third, twice, and three times the linear natural frequency can reveal nonlinear resonances that are common nonlinear systems. It is quite common for sinusoidal inputs at one frequency to excite a resonance at a different frequency in a nonlinear system. This does not happen in a linear system, and a slow sine sweep test of a harmonic excitation is useful to detect such an occurrence. Superposition is only strictly valid for linear systems. The superposition principle can be used to detect nonlinearities in a system by observing deviations from linear superposition. Nyquist plots are also on way to detect nonlinearities. For linear system excited close to resonance, the Nyquist plots are circular. For a nonlinear system, the Nyquist plots can become distorted into ellipses or other shapes. Nonlinear resonances may be a problem in experimental modal analysis. The excitation of one mode at a particular fre-quency can lead to a response at another frequency as well as participation of other modes. Chanpong et al. carried out experiments to measure the frequency response function for four different settings which were aluminum alloy rim assem-bled with a tire and mounted on a stand, aluminum alloy rim assembled with tire and placed on a soft cushion, a steel rim assembled with the tire and mounted on a stand and finally a steel rim assembled with the tire and placed in a soft cushion. The soft cushion support was equivalent to free support. The roving impact test was applied to the rim in order to identify the natural frequencies of both aluminum alloy and steel rims. The frequency response data of roving impact hammer tests on a wheel tire assembly were processed using MES cope software for identifying its mode shape. Their results have shown that the significant vibration response amplitude peak is between 200 and 250 Hz which is related to the tire cavity resonance noise. A detailed investigation on the available tire models with a description of their capabilities and application areas has been provided by Ammon, Lugner and Plchl, and Lugner et al. Most tire models typically consist of two separate parts. The first part is represented by the struc-tural modal analysis which describes the structural stiffness, damping and inertia properties of the tire. The second one is the tread/road contact model which is able to furnish an esti-mation of the contact pressure distribution and the distributed friction force. Many authors suggest direct methods for esti-mating the tire parameters. They are based on embedded sen-sors, such as strain gauges, surface acoustic wave or MEMS sensors, which allow direct measurement of the tire deformations or tiring surface vibrations.The main objective of this study was to determine the nat-ural frequencies and the modal damping ratios of a passenger vehicle tire. The experiments are carried out for both a free tire setup suspended from above and a free tire support using a soft cushion. Then, a new design of a test rig is introduced to sup-port the tire with a free support in both radial and axial direc-tions. Also, the tire can be treated as a fixed support in radial and axial directions. The results of the freely suspended meth-ods and the new experimental test setup are to be compared. The setup permits to carry out the experiments on the freely supported tires while changing the load on the tire.2.The types of support of the tire-rim assemblyThe tire-rim assembly may be tested in a free condition or grounded. Free condition means that the test object is not attached to ground at any of its coordinates and is, in effect, freely suspended in space. In this condition, the struc-ture will exhibit rigid body modes which are determined solely by its mass and inertia properties. In practice, it is not possible to provide a truly free support but it is generally feasible to provide a suspension system which closely approximates this condition. This can be achieved by supporting the structure on very soft springs such as a light elastic band. Also, the steel-rim may be assembled with a tire placed on a soft cushion. The soft cushion support is equivalent to a free sup-port. The type of support is referred to as grounded because it attempts to fix a selected point on the tire to the ground. A new modal analysis test facility is designed and installed. Fig. 1a shows how the tire is suspended by a light elastic band, while Fig. 1b shows the suspension of the tire using very soft springs provided in the test rig. The rig has four vertical guides with linear bearings to provide the movement of the tire assem-bly in vertical direction while neglecting the friction effect of the guides. This is equivalent to the free support using the elas-tic band. Fig. 2a illustrates the free support of the tire assembly using a soft cushion, and Fig. 2b shows that the test rig may be used as a free support in axial direction. The tire assembly may be rigidly supported in vertical direction and guided in axial direction by two linear bearings to reduce the effect of the fric-tion between the axle of the assembly and the blocks which support the tire assembly. Fig. 3 shows the grounded support of rim-tire assembly. The rim-tire assembly is guided to move in the vertical directions as a result of load acting on the tire through the axle of the rim-tire assembly. A power screw arrangement is used to apply the load on the tire 18. A strain gauge based load cell is used to measure the value of the apply-ing load. The load acting on the tire causes radial deflection which is measured using a precise dial gauge, as shown in the figure. By plotting the relation between the acting load on the tire and the tire deflection, the static stiffness of the tire may be obtained. This experiment is repeated for different val-ues of the tire inflation pressure to determine its effect on the static stiffness of the tire-rim assembly.3. Analysis of frequency band (range)Some pre-tests were carried out to select the frequency band (range). The experimental set-up was composed of a piezoelec-tric tri-axial accelerometer type 3560-c (BK), an impacthammer type 8202 (BK) with an aluminum tip, and a multi-analyzer pulse system type 350-c (BK). The analyzer was used to record tire-rim assembly response and hammer excitation, and to produce the fast Fourier transform (FFT) spectra of vibration signals. Finally, a trigger was used to synchronize the acquisition of the force and acceleration/displacement sig-nals. Output signals of the accelerometer and force transducer of the impact hammer were connected to the frontal channels of the FFT analyzer and then connected to a computer through a data cable. The exponentially decaying window is used to force the data to better satisfy the periodicity require-ments of the Fourier transform process, thereby minimizing the distortion effects of leakage. Fig. 4 shows the impulse force and the acceleration response in time domain of the tire-rim assembly, which is suspended by an elastic-light band. Fig. 5 shows the force spectrum, acceleration spectrum, and the coherence for a frequency range of 800 Hz. It is found that the force spectrum does not excite all of the frequency ranges shown as evidenced by the roll off of the force spectrum at fre-quency range greater than 200 Hz. The coherence is also seen to deteriorate as well as the frequency is greater than 200 Hz. It is found that the frequency response function is measured much better over the analysis of frequency band (range) of 200 Hz.4. Roving impact testThe purpose of making modal analysis on a tire is to find its natural resonant frequencies. In order to prepare the test, a tire-rim assembly was marked with white dots at profile points and mounted on the test rig. Impact was applied on tire struc-ture at white dot points, these dot points were marked to divide the tire circumference into 15 segments evenly dis-tributed and there are two loops of dot points on the sidewall and 3 loops of dot points on the tread surface. The ideal posi-tion for mounting the response accelerometer is on the tires center line. Four clean impacts were applied at each marked point; the frequency response functions were measured and averaged to identify the modal peak frequencies.5. Analysis of resultsModes or resonances are inherent properties of a structure. Resonances were determined by the material properties (mass, stiffness and damping properties), and boundary conditions of the structure. Free and grounded mountings are the boundary conditions of the tire-rim assembly. Each mode is defined by a natural (modal or resonant) frequency and modal damping. Four different conditions of mounting were investigated for the tire-rim assembly in free condition: (1) suspension by an elastic light band, Fig. 1a; (2) suspension on soft springs in the test rig, Fig. 1b; (3) using a soft cushion; and (4) free sup-port in axial direction on the test rig. By applying the roving impact test, all the FRFs are considered and all of the modes will be seen in the majority of the measurements. For a single reference (input), the original mode indicator function (MIF) is formulated to provide a better tool for identifying closely spaced modes. Basically the mathematical formulation of the MIF is that the real part of the FRF is divided by the magni-tude of the FRF. At resonance frequency, the real part of FRF rapidly passes through zero and the MIF will drop to a minimum in the region of a mode. When the FRF measure-ments are completed, the data reduction process can begin to extract the modal parameters. According to the theory of experimental modal analysis, the modal parameters of the sys-tem can be identified through the curve fitting of the FRF mea-surements. Curve fitting is the analytical process to determine the mathematical parameters which give the closest possible fit to the measured data. This is done by minimizing the squared error (or squared difference) between the analytical function and the measured data. Curve fitters can be classified as local or global. This classification depends on how estimation of the modal parameters is made from the data set of FRF measure-ments. Local methods are applied to one FRF at a time. Glo-bal methods are applied to an entire set of FRFs at once. The operator has to decide which FRF measurement is the best for the application, which modes are of interest, which curve-fitter to use and over what frequency range. During this phase, the global parameters (the modal frequencies and damping) are determined. FRF data can be plotted in a Nyquist format and the circle fitting method is applied in the frequency domain to extract the modal parameters. Here, each resonance region is expected to trace out at least part of a circular arc, the extent depending largely on the interaction between adjacent modes. For a system with well-separated modes, it is to be expected that each resonance will generate the major part of a circle but as the modal interference increases, with closer modes or greater damping levels, it is to be expected that only small seg-ments will be identifiable. However, the Nyquist plot should ideally exhibit a smooth curve and failure to do so may indi-cate a poor measurement technique. The measured FRFs data are imported into ICATS software to calculate the modal parameters.6. ConclusionsThe study introduced a modal analysis of a non-rotating tire under different boundary conditions. The test rig consists of four guides in vertical (radial) direction and two guides in axial direction which was designed to support the tire-rim assembly with a free support. This setup permits us to carry out the experiments with five different set-ups, elastic light band, soft springs carrying the assembly, on soft cushion, free support on axial direction and grounded support of rim-tire assembly. From the experimental work and analysis of the presented results the following conclusions are drawn:To obtain the modal parameters of the tire-rim assembly with free boundary conditions in radial and axial direc-tions, a test rig having four guides in radial (vertical) directions and two guides in axial direction is designed and constructed.The introduced test rig is very efficient and results of the resonance frequencies and damping loss factors agree well with experimental results obtained by free support-ing of the tire-rim assembly in radial (vertical) direction using an elastic light band and free supporting of the assembly in axial direction by using a soft cushion.Frequency response functions are measured by applying a roving impact test to the tire structure at 15 points and response accelerations were measured using accelerome-ters mounted on the tire center line.Stiffness characteristics in radial direction were deter-mined in static way for different val