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Inerter, a new type of mass element, can increase the inertia of motion between two endpoints. In order to study the dynamic inertia effect of inerter–spring–damper suspension for heavy vehicle on ride comfort and road friendliness, the inerter–spring–damper suspension is applied and its mechanism is studied. This paper establishes a half vehicle model of inerter–spring–damper suspension for heavy vehicle. The parameters of inerter–spring–damper suspension for heavy vehicle are optimized by multi-objective genetic algorithm and system simulations are carried out. The parametric influence of different spring stiffness, damping coefficient, inertance, and load on suspension performance is also studied. The simulation results demonstrate that the centroid acceleration and pitch angular acceleration are improved by 24.90% and 23.54%, respectively, and the comprehensive road damage coefficient is reduced by 4.05%. The results illustrate that the inerter–spring–damper suspension can decrease the vertical vibration of vehicle suspension especially in low frequency and reduce the road damage. The analyses of suspension parameters perturbation reveal their different effect laws of the different wheels on vehicle ride comfort and road friendliness, which provide a theoretical basis for setting parameters of inerter–spring–damper suspension. Keywords Heavy vehicle, inerter–spring–damper suspension, parameter matching, ride comfort, road friendliness Introduction In recent decades, with the rapid development of global economy and highway transportation, heavy vehicles as the main equipment for freight transport, their production scale, and quantity are also growing rapidly. Heavy vehicles have become the main factors of road damage due to their heavy load and dynamic tire load during driving. Road friendliness is the performance of reducing road damage caused by tire load as much as possible 2 3 when vehicles are driving on uneven roads. The research shows that the damage of vehicle to road is mainly related to the axle load and the tire ground contact, and the dynamic tire load is the decisive factor to cause road fatigue damage and improve road friendliness. In the case that road conditions cannot be greatly improved, the damage to the road caused by dynamic tire load can be reduced by improving the suspension system for heavy vehicle. In this way, the road friendliness will be improved while improving the ride comfort. School of Automotive and Traffic Engineering, Jiangsu University, Zhenjiang, China Hunan Province Key Laboratory of Intelligent Manufacturing Technology for High-performance Mechanical Equipment, Changsha University of Science and Technology, Changsha, China Corresponding author: Yujie Shen, School of Automotive and Traffic Engineering, Jiangsu University, Zhenjiang 212013, China. Email: shenyujie@ujs.edu.cn Creative Commons CC BY: This article is distributed under the terms of the Creative Commons Attribution 4.0 License (https:// creativecommons.org/licenses/by/4.0/) which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/open-access-at-sage). 2 1336 Journal of Low Frequency Noise, Vibration and Active Control 40(3) Journal of Low Frequency Noise, Vibration and Active Control 0(0) Aiming at the coordination of road friendliness and ride comfort of vehicle suspension, the vehicle–road interaction of heavy vehicle was studied in the 1990s. They concluded that suspension parameters, driving speed and road grade are the main factors affecting dynamic tire load. Kyongsu and Hedrick of the United States found that the dynamic tire load is much larger than the static tire load. The deduction and test verified that the semi-active suspension controlled by bilinear disturbance observer can effectively reduce the dynamic tire load, thereby reducing the damage of heavy vehicle to the road. Sun of the University of Texas took the peak value of dynamic tire load as the optimization objective to design vehicle suspension. By changing the weighting coeffi- cient, the active suspension system designed effectively improves the comprehensive performance of suspension. Xie et al. of the University of Macau proposed a semi-active suspension based on integrated fuzzy-wheelbase preview control, which improves the road friendliness of heavy vehicle while taking into account ride comfort. The traditional passive suspension and semi-active suspension mainly adopt the optimization method of 8–10 11 damping coefficient and spring stiffness to achieve performance coordination. The research shows that the heavy vehicle needs to reduce the spring stiffness and improve the damping coefficient to achieve it. However, a significant reduction in stiffness may lead to deterioration of the suspension working space. Obviously, heavy vehicles are limited by the inherent structure of “spring–damper” in the efficient coordination of road friendliness and ride comfort, so the further improvement of performance meets the theoretical bottle- neck. Active suspension force generator can take both performance into account, but it has high energy con- sumption when used in heavy vehicle, which is not in line with the development direction of low-carbon vehicle. In 2002, Professor Smith invented the two-terminal mass element “inerter,” which effectively introduced mass impedance into the vibration isolation system and laid the foundation theory of vehicle inerter–spring–damper (ISD) suspension. Then, the performance benefits in passive vehicle suspensions employing inerter were studied by 14 15 Smith and Wang. Afterward, Hu et al. used inerter to improve multiple performance requirements especially suspension deflection performance. Shen et al. investigated an improved design of dynamic vibration absorber by using the inerter, and the ISD suspension can effectively improve the damping performance. At present, ISD 17–19 20,21 22,23 suspension has been widely employed in vehicle engineering, civil engineering, and train suspension, which shows that ISD suspension system has good vibration isolation performance. Thoresson et al. using a gradient-based approximation method optimized a vehicle’s suspension parameters for ride comfort and handling. The undesirable effects associated with noise in the gradient information are effectively reduced. Javanshir et al. optimized geometric parameters of suspension system using integrated anti-roll bar and coiling spring, and effects of optimization of suspension system during various parameters are compared. Silveira et al. compared symmetrical (linear) shock absorbers and asymmetrical (nonlinear) shock absorbers. The comparisons show that the nonlinear system has a smoother and more progressive performance, both for vertical and angular movements. In addition, Seifi et al. presented a new multi-objective optimization method to improve ride comfort, vehicle handling, and workspace using nonlinear asymmetrical dampers. In general, the effect of reducing heavy vehicles on road surface damage can be achieved by adjusting or changing the suspension structure of heavy vehicles to reduce the dynamic tire load. However, traditional passive suspension and semi-active suspension mainly achieve road friendliness and ride comfort performance coordina- tion by optimizing suspension damping coefficient and spring stiffness, which is limited by the inherent structure of traditional spring–damper structure, therefore the lifting effect is limited. In addition, the research of vehicle ISD suspension is a multivariable and multi-objective problem. The design of component parameters should not only meet the requirements of ride comfort but also have better road friendliness. For heavy vehicle suspension system parameters, the current research mainly focuses on the param- eter performance optimization based on vehicle ride comfort or road friendliness, while there are few studies on the combination of ride comfort and road friendliness. Moreover, the parameters of heavy vehicle suspension system are mostly compared and analyzed on the basis of traditional passive suspension, which takes less sus- pension parameters into account. There is also a lack of discussion on inerter component in the research reports of the simulation analysis and the influence of parameters changes on heavy vehicle suspension. Therefore, the study on the main parameters of heavy vehicle ISD suspension needs to be expanded, which requires a lot of model data simulation work in ISD suspension for heavy vehicle, evaluation of simulation results, and analysis of parameter selection. In this paper, the inerter is creatively applied to the field of heavy vehicle, and the principle of ISD suspension with the inerter for heavy vehicle is analyzed on the basis of the dynamic inertia effect of inerter. The action mechanism of ISD suspension for heavy vehicle on road friendliness and ride comfort is also studied, so as to realize the coordinated optimization of road friendliness and ride comfort for heavy vehicles. In order to improve the comprehensive performance of an ISD suspension for heavy vehicle, the multi-objective genetic algorithm is Yang et al. Yang et al. 1337 3 adopted as the optimization method of ISD suspension structural parameters based on establishing a half vehicle model. The perturbation effects of spring stiffness, damping coefficient, inertance and load on road friendliness, and ride comfort for heavy vehicle are studied, which provides a theoretical basis for further research and coor- dinated control of ISD suspension for heavy vehicle. In order to improve the comprehensive performance of heavy vehicle ISD suspension, based on the establish- ment of half car model, multi-objective genetic algorithm is used to optimize the main parameters. The organization of this paper is as follows. The half vehicle model of heavy vehicle ISD suspension is established in Establishment of ISD suspension model for heavy vehicle section. The parameters of ISD suspen- sion for heavy vehicle are optimized in Optimization of ISD suspension parameters for heavy vehicle section. And System simulation analysis section carries out the system simulation and obtains the simulation result of heavy vehicle. Then, the influence of parameters perturbation on ISD suspension performance of heavy vehicle is analyzed in Performance analysis of ISD suspension with parameters perturbation section. Finally, conclusions are drawn in Conclusion section. Establishment of ISD suspension model for heavy vehicle According to Shen et al., in the three-element structure, the inerter is connected in series with the damper first, and then in parallel with the spring. On this basis, considering the body structural characteristics of heavy vehicle, the half vehicle structure model of three-axle heavy vehicle ISD suspension is established, as shown in Figure 1. It should be pointed out that the vehicle is a complex nonlinear mechanical network system in motion. In order to facilitate the study of ISD suspension for heavy vehicle, the following assumptions are made for the established model: The stiffness of the body and frame is much higher than that of the suspension, that is to say, assuming it is rigid body. Vehicles are symmetrical in left and right, and the road surface roughness conditions on both sides are the same. Besides, vertical and pitching motions in the plane are considered only in the analysis. The tire always keeps contact with the road surface without jumping when the vehicle is moving at a constant speed on the road. Assuming that the road surface roughness corresponding to the tire on the same side of the axle is different and there is a response hysteresis caused by the wheelbase. The vibration caused by the engine, transmission system, and so on is neglected. Based on the above assumptions, a six-free-degree vibration differential equation is established according to Newton’s second law. The vertical vibration equation at the centroid of the car body is M z € ¼ F þ F (1) b b c f The pitching motion equation of the car body around the centroid is I h ¼ eF � aF (2) b b c f The vertical vibration equation of the front axle is M z € ¼ k ðz � z Þþ c ðz_ � z_ Þ� F (3) f 1 tf f 1 tf f 1 f b b f r z θ 1 c c M M M f m r c k c tm tf tf k k tm tr tr f z z r Figure 1. Half vehicle model of heavy vehicle ISD suspension. 4 1338 Journal of Low Frequency Noise, Vibration and Active Control 40(3) Journal of Low Frequency Noise, Vibration and Active Control 0(0) The vertical vibration equation of balanced suspension is (4) RMz € ¼ k ðz � z Þþ c ðz_ � z_ Þþ k ðz � z Þþ c ðz_ � z_ Þ �ðk � k Þh d �ðc � c Þh d � F c tm m c tm m c tr r c tr r c tr tm c tr tm c c The pitching motion equation of the balanced suspension is € € I h þðM þ M Þd h ¼ðk z � k z Þd þðc z_ � c z_ Þd� c c m r c tr r tm m tr r tm m (5) 2 2 ðk þ k Þh d �ðc � c Þh d �ðk � k Þz d �ðc � c Þz_ d tm tr c tm tr c tr tm c tr tm c The suspension force is F ¼ k ðz � z Þþ u f f 1 2 f (6) F ¼ k ðz � z Þþ u c r c 5 r Among equations (4) and (6) RM ¼ M þ M þ M (7) m c r u ¼ b ðz € � z € Þ¼ c ðz_ � z_ Þ f f 1 11 f 11 2 (8) u ¼ b ðz € � z € Þ¼ c ðz_ � z_ Þ r r c 22 r 22 5 When the pitch angle h is small, the following approximation of equation (8) can be obtained z ¼ z � ah 2 b b (9) z ¼ z þ eh 5 b b In the above formulas, M is the body mass, z is the vertical displacement of the body mass center, F and F b b f c are the force of front suspension and balance suspension. h is the centroid angular acceleration and h is the b c balance suspension pitch angle. M is the unsprung mass of the front suspension, M , M are the unsprung mass f m r of the balanced suspension respectively, M is the mass of the balanced rod, I , I are the rotational inertia c b c coefficients of the body and the balanced suspension respectively, k , k ,k , k , k are the spring stiffness f r tf tm tr coefficients of the front suspension, spring stiffness of balanced suspension, tire stiffness coefficients of front, middle, and rear wheels, respectively, c , c , c , c , c are the damping coefficients of front suspension and f r tf tm tr balanced suspension, tire damping coefficients of front wheel, middle wheel, and rear wheel, respectively, z , z , z , z , z , z , z are the displacement inputs of the front wheel, the middle wheel, and the rear wheel, the m r 1 c 11 22 vertical displacements of the front suspension and the balanced suspension, the inerter displacements of the front suspension and the balance suspension, respectively, b , b are the inertance of the front suspension and the f r balanced suspension, respectively. a, e, d are the distance between the front axle and the centroid, the distance between the center of balance rod and the centroid, and the length of the balance rod, respectively. Optimization of ISD suspension parameters for heavy vehicle In order to determine the parameters of ISD suspension for heavy vehicle, the traditional passive suspension with mature parameters is taken as the contrast object. On the basis of DFL1250A9, a three-axle heavy vehicle, the related parameters of heavy vehicle are shown in Table 1. Considering the multi-parameters and multi-objective of suspension system, the multi-objective genetic algo- rithm is adopted as the optimization method of ISD suspension structural parameters for heavy vehicle, and the system parameters are determined by numerical simulation. There are six key parameters to be optimized k c b k c b X ¼½ � (10) f f r r r f Yang et al. Yang et al. 13395 Table 1. Relevant parameters of inerter–spring–damper (ISD) suspension for three-axle heavy vehicle. Name Value Vehicle mass M /kg 11,523 Unsprung mass of front suspension M /kg 412 Unsprung mass of balanced suspension M , M /kg 676 m r Mass of balanced rod M /kg 177 Rotational inertia of body I /(kg�m ) 55,502 Rotational inertia of balanced rod I /(kg�m ) 351 Tire stiffness of front wheels k /(N/m) 11,00,000 tf Tire stiffness of middle wheels k /(N/m) 22,00,000 tm Tire stiffness of rear wheels k /(N/m) 22,00,000 tr Tire damping coefficient of front wheel c /(N�s/m) 3500 tf Tire damping coefficient of middle wheel c /(N�s/m) 7000 tm Tire damping coefficient of rear wheel c /(N�s/m) 7000 tr Distance between the front axle and the centroid a/m 3.64 Distance between the center of balance rod and the centroid e/m 2.71 Length of the balance rod d/m 1.3 Then, three vehicle ride comfort indexes and one road friendliness index are selected as optimization objectives. As the above four performance indicators have different units and orders of magnitude, it is necessary to establish a unified objective function. The four performance indexes of ISD suspension for heavy vehicle are divided by traditional passive suspension indexes, and their quotient sum is taken as the objective unified function. Therefore, the optimization of evaluation indexes of ride comfort and road friendliness is transformed into the minimum value problem of unified objective function. The expression of the unified objective function is BAðXÞ SWSðXÞ DTLðXÞ JðXÞ minT ¼ w þ w þ w þw (11) 1 2 3 4 BA SWS DTL J pas pas pas pas In the equation, T is the fitness function (unified objective function), BA(X), SWS(X), are the root mean square (RMS) values of body acceleration, suspension working space, and dynamic tire load of ISD suspension for heavy vehicle, respectively. J(X) is the road damage coefficient of ISD suspension for heavy vehicle. BA , SWS , pas pas DTL are the RMS values of body acceleration, suspension working space, and dynamic tire load of traditional pas passive suspension, respectively. J is road damage coefficient of traditional passive suspension. Among them, pas the BA(X) and BA include four specific values respectively: body acceleration, front suspension acceleration, pas balance suspension acceleration, and centroid angular acceleration. The SWS(X) and SWS include two specific pas values respectively: working space of front suspension and working space of balanced suspension. The DTL(X) and DTL include three specific values respectively: dynamic tire load of front wheel, dynamic tire load of middle pas wheel, and dynamic tire load of rear wheel. w , w , w , w are the weighted coefficients of different performance 1 2 3 4 indicators and their values are equal. According to Cole and Cebon, the road damage coefficient J is calculated by the 95th percentile aggregate fourth power force, and its formula is 1:65r 4 J¼1 þ (12) m 4 4 4 4 In the formula, A is the power sum of dynamic load and static load, r is the standard deviation of A , and 4 4 m is the mean value of A . The constraints of the unified objective function are UB < X < LB i ¼ 1; 2; 3 � � � ; 6 (13) BAðXÞ < BA > pas SWSðXÞ < SWS pas s:t: (14) DTLðXÞ < DTL > pas JðXÞ < J pas 6 1340 Journal of Low Frequency Noise, Vibration and Active Control 40(3) Journal of Low Frequency Noise, Vibration and Active Control 0(0) Yang et al. 7 Figure 2. Time domain diagram of random road input. Table 2. Parameter optimization results. Name Value Spring stiffness of front suspension k /(N/m) 2,92,000 Spring stiffness of balanced suspension k /(N/m) 15,43,000 Damping coefficient of front suspension c /(N�s/m) 40,420 Damping coefficient of balanced suspension c /(N�s/m) 29,520 Inertance of front suspension b /kg 1500 Inertance of balanced suspension b /kg 2000 Among them, X is the parameters collection to be optimized. UB and LB are the upper and lower limits of parameters to be optimized, respectively. In addition, the mathematical characteristics of the optimization algorithm in this paper are as follows: the optimal individual coefficient is 0.3, the population size is 40, the maximum evolution algebra is 50, the stop algebra is 200, and the fitness function deviation is 0.01. It is assumed that the vehicle runs at a uniform speed of 20 m/s on the B grade road surface with a driving time of 20 s and a sampling time interval of 0.005 s. The Gauss white noise with the intensity of 20 dB and the mean value of zero is taken as the road input. The time domain diagram of random road input is shown in Figure 2. In addition, the time when the front wheel, middle wheel, and rear wheel of heavy vehicle receive the road input is different in the optimization simulation process. Therefore, the value of wheelbase divided by speed is consid- ered as delay in the simulation. The optimization results of ISD suspension parameters are shown in Table 2. System simulation analysis It is assumed that the vehicle runs at a uniform speed of 20 m/s on B grade road. Compared with traditional heavy vehicle suspension, the influence of ISD suspension on ride comfort and road friendliness is analyzed. Under random input conditions, the results of time domain simulation and frequency domain simulation are shown in Figure 3, Tables 3 and 4. As can be seen from Figure 2, when heavy vehicle travel at a uniform speed of 20 m/s on B grade road surface, the centroid acceleration, suspension working space and dynamic tire load of ISD suspension are reduced to Figure 3. Suspension performance comparison. varying degrees than those of traditional passive suspension in time domain. In frequency domain, the centroid acceleration, suspension working space, and dynamic tire load of ISD suspension are significantly lower than those of traditional suspension in the range of 0–5 Hz, while they are almost the same as those of traditional 23.54% respectively in time domain analysis, and the working spaces of front suspension and balanced suspension suspension in the range of 5–15 Hz. are improved by 21.82% and 8.11% respectively, and the RMS values of dynamic tire load of front, middle, and Combining Figure 3 and Table 4, we can see that the RMS values of centroid acceleration and pitch angular rear wheel decrease by 7.80%, 3.50%, and 3.87%, respectively. In frequency domain analysis, the ISD suspension acceleration of ISD suspension, compared with traditional passive suspension, are improved by 24.90% and of heavy vehicle effectively reduces the peak resonance of suspension in 0–5 Hz band compared with traditional Yang et al. Yang et al. 13417 Figure 3. Suspension performance comparison. 23.54% respectively in time domain analysis, and the working spaces of front suspension and balanced suspension are improved by 21.82% and 8.11% respectively, and the RMS values of dynamic tire load of front, middle, and rear wheel decrease by 7.80%, 3.50%, and 3.87%, respectively. In frequency domain analysis, the ISD suspension of heavy vehicle effectively reduces the peak resonance of suspension in 0–5 Hz band compared with traditional 8 1342 Journal of Low Frequency Noise, Vibration and Active Control 40(3) Journal of Low Frequency Noise, Vibration and Active Control 0(0) Yang et al. 9 Table 4. Root mean square (RMS) comparison of suspension performance. RMS of traditional Suspension performance index passive suspension RMS of ISD Suspension Improvement (%) Centroid acceleration/(m/s ) 1.3013 1.0448 24.90 Pitch angular acceleration/(rad/s ) 0.3573 0.2732 23.54 Working space of front suspension/m 0.0055 0.0043 21.82 Working space of balanced suspension/m 0.0037 0.0034 8.11 Dynamic tire load of front wheel/N 3435 3167 7.80 Dynamic tire load of middle wheel/N 8678 8374 3.50 Dynamic tire load of rear wheel/N 9504 9136 3.87 ISD: inerter–spring–damper; RMS: root mean square. Table 5. Range of inerter–spring–damper (ISD) suspension parameters. Parameter Range of values Spring stiffness of front suspension/(N/m) 1,46,000–4,38,000 Spring stiffness of balanced suspension/(N/m) 7,71,500–23,14,500 Damping coefficient of front suspension/(N�s/m) 20,210–60,630 Damping coefficient of balanced suspension/(N�s/m) 14,760–44,280 Inertance of front suspension/(kg) 750–2250 Inertance of balanced suspension/(kg) 1000–3000 Sprung mass No load–full load passive suspension. In addition, the low-frequency resonance frequency decreases and the vibration isolation performance improves significantly, which effectively improves the ride comfort of heavy vehicle. Table 3 shows that the 95th percentile aggregate values of front, middle, and rear wheels of ISD suspension for heavy vehicle decrease by 5.11%, 3.65%, and 4.29% respectively, and the comprehensive road damage coefficient decreases by 4.05% compared with traditional passive suspension, which effectively improves the road friendliness of heavy vehicle. Compared with traditional passive suspension, the low-frequency resonance frequency and peak value of resonance peak of ISD suspension of heavy vehicle are reduced, and the vertical motion characteristics of the system are improved. Therefore, ISD suspension of heavy vehicle can effectively improve ride comfort and road friendliness of heavy vehicle. Performance analysis of ISD suspension with parameters perturbation For heavy vehicle, the performance of suspension not only affects the ride comfort but also affects the road friendliness of vehicle. Therefore, the influence of spring stiffness, damping coefficient, inertance, and load on <ontinued. suspension performance is analyzed in this paper. The ranges of spring stiffness, damping coefficient, inertance, and sprung mass of ISD suspension are shown in Table 5. Influence of spring stiffness combination on suspension performance Table 3. The 95th percentile aggregate contrast. According to the spring stiffness values of front suspension and balanced suspension in Table 5, the effect of spring stiffness changes on ride comfort and road friendliness is analyzed in time domain, as shown Road damage coefficient Traditional passive suspension ISD suspension Improvement (%) in Figure 4. 18 18 Front wheel 1.9074 10 1.8099 10 5.11 From Figure 4, it can be seen that the RMS values of centroid acceleration, pitch angular acceleration, dynamic 18 18 Middle wheel 8.2489 10 7.9479 10 3.65 tire load of middle and rear wheels, and road damage coefficient increase with the increase of front suspension 18 18 Rear wheel 9.1089 10 8.7177 10 4.29 spring stiffness, while the increase of balanced suspension spring stiffness has little effect on them. The dynamic 18 18 Vehicle integration J 7.3246 10 7.0282 10 4.05 tire load of front wheel decreases first and then increases with the increase of spring stiffness of balanced sus- pension. The RMS values of working space of front suspension and balanced suspension have a wave-like change ISD: inerter–spring–damper. Yang et al. Yang et al. 13439 Table 4. Root mean square (RMS) comparison of suspension performance. RMS of traditional Suspension performance index passive suspension RMS of ISD Suspension Improvement (%) Centroid acceleration/(m/s ) 1.3013 1.0448 24.90 Pitch angular acceleration/(rad/s ) 0.3573 0.2732 23.54 Working space of front suspension/m 0.0055 0.0043 21.82 Working space of balanced suspension/m 0.0037 0.0034 8.11 Dynamic tire load of front wheel/N 3435 3167 7.80 Dynamic tire load of middle wheel/N 8678 8374 3.50 Dynamic tire load of rear wheel/N 9504 9136 3.87 ISD: inerter–spring–damper; RMS: root mean square. Table 5. Range of inerter–spring–damper (ISD) suspension parameters. Parameter Range of values Spring stiffness of front suspension/(N/m) 1,46,000–4,38,000 Spring stiffness of balanced suspension/(N/m) 7,71,500–23,14,500 Damping coefficient of front suspension/(N�s/m) 20,210–60,630 Damping coefficient of balanced suspension/(N�s/m) 14,760–44,280 Inertance of front suspension/(kg) 750–2250 Inertance of balanced suspension/(kg) 1000–3000 Sprung mass No load–full load passive suspension. In addition, the low-frequency resonance frequency decreases and the vibration isolation performance improves significantly, which effectively improves the ride comfort of heavy vehicle. Table 3 shows that the 95th percentile aggregate values of front, middle, and rear wheels of ISD suspension for heavy vehicle decrease by 5.11%, 3.65%, and 4.29% respectively, and the comprehensive road damage coefficient decreases by 4.05% compared with traditional passive suspension, which effectively improves the road friendliness of heavy vehicle. Compared with traditional passive suspension, the low-frequency resonance frequency and peak value of resonance peak of ISD suspension of heavy vehicle are reduced, and the vertical motion characteristics of the system are improved. Therefore, ISD suspension of heavy vehicle can effectively improve ride comfort and road friendliness of heavy vehicle. Performance analysis of ISD suspension with parameters perturbation For heavy vehicle, the performance of suspension not only affects the ride comfort but also affects the road friendliness of vehicle. Therefore, the influence of spring stiffness, damping coefficient, inertance, and load on suspension performance is analyzed in this paper. The ranges of spring stiffness, damping coefficient, inertance, and sprung mass of ISD suspension are shown in Table 5. Influence of spring stiffness combination on suspension performance According to the spring stiffness values of front suspension and balanced suspension in Table 5, the effect of spring stiffness changes on ride comfort and road friendliness is analyzed in time domain, as shown in Figure 4. From Figure 4, it can be seen that the RMS values of centroid acceleration, pitch angular acceleration, dynamic tire load of middle and rear wheels, and road damage coefficient increase with the increase of front suspension spring stiffness, while the increase of balanced suspension spring stiffness has little effect on them. The dynamic tire load of front wheel decreases first and then increases with the increase of spring stiffness of balanced sus- pension. The RMS values of working space of front suspension and balanced suspension have a wave-like change 10 1344 Journal of Low Frequency Noise, Vibration and Active Control 40(3) Journal of Low Frequency Noise, Vibration and Active Control 0(0) Yang et al. 11 Figure 5. Influence of damping coefficient combination on suspension performance. Figure 4. Influence of spring stiffness combination on suspension performance. Influence of damping coefficient combination on suspension performance According to the values of the damping coefficients of the front suspension and the balanced suspension in Table 4, the effects of the variation of the damping coefficients on the ride comfort and road friendliness of with the increase of spring stiffness of balanced suspension and front suspension, respectively. It is not difficult to heavy vehicle are analyzed in the time domain, as shown in Figure 5. find that the influence of front suspension spring stiffness on ride comfort and road friendliness is higher than that From Figure 5, it can be seen that the RMS values of centroid acceleration, pitch angular acceleration, working of balanced suspension spring stiffness. The reason is that the middle and rear axles of heavy vehicle need to bear space of balanced suspension, dynamic tire load of middle wheel, dynamic tire load of rear wheel, and road most of the body weight. The value of balanced suspension spring stiffness is much larger than that of front suspension, so the influence of RMS and road damage coefficient is different. damage coefficient decrease with the increase of front suspension damping coefficient, while the RMS values of Yang et al. Yang et al. 1345 11 Figure 5. Influence of damping coefficient combination on suspension performance. Influence of damping coefficient combination on suspension performance According to the values of the damping coefficients of the front suspension and the balanced suspension in Table 4, the effects of the variation of the damping coefficients on the ride comfort and road friendliness of heavy vehicle are analyzed in the time domain, as shown in Figure 5. From Figure 5, it can be seen that the RMS values of centroid acceleration, pitch angular acceleration, working space of balanced suspension, dynamic tire load of middle wheel, dynamic tire load of rear wheel, and road damage coefficient decrease with the increase of front suspension damping coefficient, while the RMS values of 12 1346 Journal of Low Frequency Noise, Vibration and Active Control 40(3) Journal of Low Frequency Noise, Vibration and Active Control 0(0) Yang et al. 13 front suspension working space and front wheel dynamic tire load increase with the increase of spring stiffness of Influence of inertance combination on suspension performance balanced suspension. Comparing and analyzing the influence of front suspension damping coefficient and bal- According to the inertance of front suspension and balanced suspension in Table 4, the effects of inertance on ride anced suspension damping coefficient on ride comfort and road friendliness, the influence of front suspension comfort and road friendliness of heavy vehicle are analyzed in time domain, as shown in Figure 6. damping coefficient on ride comfort and road friendliness is greater under the same change rate. In the parameters design, in order to make the vehicle have good ride comfort and road friendliness, the larger front suspension damping coefficient and the smaller balanced suspension damping coefficient should be selected appropriately. Figure 6. Influence of inertance combination on suspension performance. Figure 7. Influence of load change on suspension performance. Yang et al. Yang et al. 1347 13 Influence of inertance combination on suspension performance According to the inertance of front suspension and balanced suspension in Table 4, the effects of inertance on ride comfort and road friendliness of heavy vehicle are analyzed in time domain, as shown in Figure 6. Figure 7. Influence of load change on suspension performance. 14 1348 Journal of Low Frequency Noise, Vibration and Active Control 40(3) Journal of Low Frequency Noise, Vibration and Active Control 0(0) Yang et al. 15 From Figure 6, similar to the effect of damping coefficient, it can be seen that the influence of centroid Funding acceleration, pitch angular acceleration, balanced suspension working space, middle wheel dynamic tire load, The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this rear wheel dynamic tire load, and road damage coefficient decrease with the increase of front suspension iner- article: This research was funded by the National Natural Science Foundation of China under Grant 51705209, 52072157, and tance, and when the front suspension inertance is larger than a certain value, the change of the above indexes 52002156, the China Postdoctoral Science Foundation under Grant 2019M651723 and 2020M671355, the Zhenjiang Key tends to be flat. The RMS values of the front suspension working space and the dynamic tire load of front wheel Research and Development Program under Grant GY2019006, the Jiangsu Postdoctoral Research Foundation under Grant decrease with the increase of the inertance of the balanced suspension. The application of inerter in suspension 2020Z246 and the Hunan Key Laboratory of Intelligent Manufacturing Technology for High-performance Mechanical system, combined with other components, effectively improves vehicle ride comfort and road friendliness. Equipment (Changsha University of Science & Technology) under Grant 2020YB07. Comparatively speaking, the change of the front suspension inertance has a greater impact on ride comfort and road friendliness than the balanced suspension inertance within the allowable range of suspension working ORCID iD space. The larger values of the front suspension inertance and the balanced suspension inertance should be Long Yan https://orcid.org/0000-0002-4355-4412 selected appropriately when designing suspension parameters. References Influence of load change on suspension performance 1. Cole DJ and Cebon D. Truck suspension design to minimize road damage. Proc IMechE Part D J Automobile Eng 1996; The function of multi-axle heavy vehicle is mainly to carry goods. The sprung mass of the vehicle varies greatly 210: 95–107. under the condition of no load and full load. Therefore, when the sprung mass is in the state of no load, half load, 2. Xia RX, Li JH, He J, et al. Linear-quadratic-Gaussian controller for truck active suspension based on cargo integrity. Adv and full load, the regularity of ride comfort and road friendliness for heavy vehicle is analyzed compared with the Mech Eng 2015; 7. https://doi.org/10.1177/1687814015620320 traditional passive suspension, as shown in Figure 7. 3. Zhao J, Wong PK, Xie ZC, et al. Design of a road friendly SAS system for heavy-duty vehicle based on a fuzzy-hybrid- As shown in Figure 7, the RMS values of centroid acceleration, pitch angular acceleration, balanced suspen- ADD and GH-control strategy. Shock Vibrat 2016; 3: 1–7. sion working space, front, middle, and rear dynamic tire load decrease with the increase of load, while the RMS of 4. Kulakowski BT. Vehicle-road interaction. Philadelphia, PA: ASTM International, 1994, pp. 2–64. 5. Kyongsu Y and Hedrick JK. Active and Semi-Active Heavy Truck Suspensions to Reduce Pavement Damage. University front suspension working space and road damage coefficient increase with the increase of load. Compared with of California Transportation Center Working Papers 1989; 39(4): 620–622. the traditional passive suspension, the evaluation indexes of ISD suspension have improved its ride comfort and 6. Sun L. Optimum design of ‘road-friendly’ vehicle suspension systems subjected to rough pavement surfaces. Appl Math road friendliness under no load, half load, and full load conditions. When the load of heavy vehicle is large, the Model 2002; 26: 635–652. ride comfort is better than that of no load vehicle, but the road damage is aggravated. Thus it can be seen that 7. Xie ZC, Wong PK,Zhao J, et al. A noise-insensitive semi-active air suspension for heavy-duty vehicles with an integrated overloading of heavy vehicle will cause serious damage to the road and reduce the service life of the road, so fuzzy-wheelbase preview control. Mathematical Problems in Engineering 2013; 8: 14–26. overloading behavior should be resolutely eliminated. 8. Wang XL. Semi-active adaptive optimal control of vehicle suspension with a magnetorheological damper based on policy iteration. J Intellig Mater Syst Struct 2018; 29: 255–264. 9. Gad S, Metered H, Bassuiny A, et al. Multi-objective genetic algorithm fractional-order PID controller for semi-active Conclusion magnetorheologically damped seat suspension. J Vibrat Contr 2017; 23: 1248–1266. This paper applies ISD suspension with inerter to heavy vehicle suspension and establishes a half vehicle model of 10. Pang H, Liu F, Xu Z, et al. Variable universe fuzzy control for vehicle semi-active suspension system with MR damper heavy vehicle ISD suspension. Taking both ride comfort and road friendliness as optimization objectives, multi- combining fuzzy neural network and particle swarm optimization. Neurocomput J 2018; 306: 130–140. 11. Ding ZS, Zhao F, Qin YC, et al. Adaptive neural network control for semi-active vehicle suspensions. J Vibroeng 2017; 19: objective genetic algorithm is used to optimize the components parameters of ISD suspension for heavy vehicle. 2654–2669. By analyzing the dynamic inertia mechanism and vehicle performance coordination of the optimized ISD sus- 12. Xie ZC, Wong PK, Zhao J, et al. Design of a denoising hybrid fuzzy-pid controller for active suspension systems of heavy pension, the dynamic inertia mechanism on road friendliness and ride comfort is summarized. Compared with the vehicles based on model adaptive wheelbase preview strategy. J Vibroeng 2015; 17: 883–904. traditional passive suspension, the ride comfort and road friendliness of ISD suspension for heavy vehicle have 13. Smith MC. Synthesis of networks: the inerter. IEEE Trans Automat Contr 2002; 47: 1648–1662. been significantly improved under the condition of 20 m/s driving speed on B grade road. The results show that, 14. Smith MC and Wang FC. Performance benefits in passive vehicle suspensions employing inerters. Vehicle Syst Dyn 2004; compared with traditional passive suspension, the RMS values of centroid acceleration and pitch angular accel- 42: 235–257. eration of ISD suspension are improved by 24.90% and 23.54%, respectively, the working spaces of front sus- 15. Hu YL, Chen MZQ and Sun Z. Passive vehicle suspensions employing inerters with multiple performance requirements. pension and balanced suspension are improved by 21.82% and 8.11% respectively, the comprehensive road J Sound Vibrat 2014; 333: 2212–2225. 16. Shen YJ, Chen L, Yang XF, et al. Improved design of dynamic vibration absorber by using the inerter and its application damage coefficient is reduced by 4.05%, and the ride comfort and road friendliness of heavy vehicle are improved in vehicle suspension. J Sound Vibrat 2016; 361: 148–158. significantly. The influence of parameters perturbation on ISD suspension for heavy vehicle is analyzed. 17. Wang FC, Liao MK and Liao BH. The performance improvements of train suspension systems with mechanical networks. The different effects of spring stiffness, damping coefficient, inertance, and load on ride comfort and road friend- Vehicle System Dyn 2009; 47: 805–830. liness of the front, middle, and rear wheels of ISD suspension for heavy vehicle are summarized. The above results 18. Wang FC, Hong MF and Chen CW. Building suspensions with inerters. Proc IMechE, Part C: J Mechanical Engineering provide a theoretical basis for further research and improvement of parameters setting of ISD suspension for Science 2010; 224: 1605–1616. heavy vehicle. 19. Watanabe M, Hayashi T and Yamakitao M. Wobbling mass effects for a walking robot with inerters. Proc SICE Annual Conference. Hokkaido Univ, Sapporo, JPN, pp. 1073–1078, 2014. Acknowledgements 20. Lazar IF, Neild SA and Wagg DJ. Using an inerter-based device for structural vibration suppression. Earthquake Eng Struct Dyn 2014; 43: 1129–1147. The authors would like to thank the associate editor and the anonymous reviewers for their careful reading and helpful 21. Buelga AG, Lazar IF, Jiang JZ, et al. Assessing the effect of nonlinearities on the performance of a tuned inerter damper. comments. Struct Control Health Monit 2017; 24. https://doi.org/10.1002/stc.1879 22. Wang FC and Liao MK. The lateral stability of train suspension systems employing inerters. Vehicle Syst Dyn 2010; 48: Declaration of conflicting interests 619–643. The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of 23. Jiang JZ, Matamoros S, Alejandra Z, et al. Passive suspensions for ride quality improvement of two-axle railway vehicles. this article. Proc Inst Mech Eng 2015; 229: 315–329. Yang et al. Yang et al. 1349 15 Funding The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was funded by the National Natural Science Foundation of China under Grant 51705209, 52072157, and 52002156, the China Postdoctoral Science Foundation under Grant 2019M651723 and 2020M671355, the Zhenjiang Key Research and Development Program under Grant GY2019006, the Jiangsu Postdoctoral Research Foundation under Grant 2020Z246 and the Hunan Key Laboratory of Intelligent Manufacturing Technology for High-performance Mechanical Equipment (Changsha University of Science & Technology) under Grant 2020YB07. ORCID iD Long Yan https://orcid.org/0000-0002-4355-4412 References 1. Cole DJ and Cebon D. Truck suspension design to minimize road damage. Proc IMechE Part D J Automobile Eng 1996; 210: 95–107. 2. Xia RX, Li JH, He J, et al. Linear-quadratic-Gaussian controller for truck active suspension based on cargo integrity. Adv Mech Eng 2015; 7. https://doi.org/10.1177/1687814015620320 3. Zhao J, Wong PK, Xie ZC, et al. Design of a road friendly SAS system for heavy-duty vehicle based on a fuzzy-hybrid- ADD and GH-control strategy. Shock Vibrat 2016; 3: 1–7. 4. Kulakowski BT. Vehicle-road interaction. Philadelphia, PA: ASTM International, 1994, pp. 2–64. 5. Kyongsu Y and Hedrick JK. Active and Semi-Active Heavy Truck Suspensions to Reduce Pavement Damage. University of California Transportation Center Working Papers 1989; 39(4): 620–622. 6. Sun L. Optimum design of ‘road-friendly’ vehicle suspension systems subjected to rough pavement surfaces. Appl Math Model 2002; 26: 635–652. 7. Xie ZC, Wong PK,Zhao J, et al. A noise-insensitive semi-active air suspension for heavy-duty vehicles with an integrated fuzzy-wheelbase preview control. Mathematical Problems in Engineering 2013; 8: 14–26. 8. Wang XL. Semi-active adaptive optimal control of vehicle suspension with a magnetorheological damper based on policy iteration. J Intellig Mater Syst Struct 2018; 29: 255–264. 9. Gad S, Metered H, Bassuiny A, et al. Multi-objective genetic algorithm fractional-order PID controller for semi-active magnetorheologically damped seat suspension. J Vibrat Contr 2017; 23: 1248–1266. 10. Pang H, Liu F, Xu Z, et al. Variable universe fuzzy control for vehicle semi-active suspension system with MR damper combining fuzzy neural network and particle swarm optimization. Neurocomput J 2018; 306: 130–140. 11. Ding ZS, Zhao F, Qin YC, et al. Adaptive neural network control for semi-active vehicle suspensions. J Vibroeng 2017; 19: 2654–2669. 12. Xie ZC, Wong PK, Zhao J, et al. Design of a denoising hybrid fuzzy-pid controller for active suspension systems of heavy vehicles based on model adaptive wheelbase preview strategy. J Vibroeng 2015; 17: 883–904. 13. Smith MC. Synthesis of networks: the inerter. IEEE Trans Automat Contr 2002; 47: 1648–1662. 14. Smith MC and Wang FC. Performance benefits in passive vehicle suspensions employing inerters. Vehicle Syst Dyn 2004; 42: 235–257. 15. Hu YL, Chen MZQ and Sun Z. Passive vehicle suspensions employing inerters with multiple performance requirements. J Sound Vibrat 2014; 333: 2212–2225. 16. Shen YJ, Chen L, Yang XF, et al. Improved design of dynamic vibration absorber by using the inerter and its application in vehicle suspension. J Sound Vibrat 2016; 361: 148–158. 17. Wang FC, Liao MK and Liao BH. The performance improvements of train suspension systems with mechanical networks. Vehicle System Dyn 2009; 47: 805–830. 18. Wang FC, Hong MF and Chen CW. Building suspensions with inerters. Proc IMechE, Part C: J Mechanical Engineering Science 2010; 224: 1605–1616. 19. Watanabe M, Hayashi T and Yamakitao M. Wobbling mass effects for a walking robot with inerters. Proc SICE Annual Conference. Hokkaido Univ, Sapporo, JPN, pp. 1073–1078, 2014. 20. Lazar IF, Neild SA and Wagg DJ. Using an inerter-based device for structural vibration suppression. Earthquake Eng Struct Dyn 2014; 43: 1129–1147. 21. Buelga AG, Lazar IF, Jiang JZ, et al. Assessing the effect of nonlinearities on the performance of a tuned inerter damper. Struct Control Health Monit 2017; 24. https://doi.org/10.1002/stc.1879 22. Wang FC and Liao MK. The lateral stability of train suspension systems employing inerters. Vehicle Syst Dyn 2010; 48: 619–643. 23. Jiang JZ, Matamoros S, Alejandra Z, et al. Passive suspensions for ride quality improvement of two-axle railway vehicles. Proc Inst Mech Eng 2015; 229: 315–329. 16 1350 Journal of Low Frequency Noise, Vibration and Active Control 40(3) Journal of Low Frequency Noise, Vibration and Active Control 0(0) 24. Thoresson MJ, Uys PE, Els PS, et al. Efficient optimisation of a vehicle suspension system, using a gradient-based approximation method, Part 2: Optimisation results. Math Comput Model 2009; 50: 1437–1447. 25. Javanshir I, Maseleno A, Tasoujian S, et al. Optimization of suspension system of heavy off-road vehicle for stability enhancement using integrated anti-roll bar and coiling spring mechanism. J Cent South Univ 2018; 25: 2289–2298. 26. Silveira M, Pontes BR and Balthazar JM. Use of nonlinear asymmetrical shock absorber to improve comfort on passenger vehicles. J Sound Vibrat 2014; 333: 2114–2129. 27. Seifi A, Hassannejad R and Hamed MA. Use of nonlinear asymmetrical shock absorbers in multi-objective optimization of the suspension system in a variety of road excitations. Proc Imeche 2016; 231: 372–387. 28. Shen YJ, Chen L, Liu YL, et al. Improvement of the lateral stability of vehicle suspension incorporating inerter. Sci China Technol Sci 2018; 61: 1244–1252. 29. Shen YJ, Liu YL, Chen L, et al. Optimal design and experimental research of vehicle suspension based on a hydraulic electric inerter. Mechatronics 2019; 61: 12–19.
"Journal of Low Frequency Noise, Vibration and Active Control" – SAGE
Published: Oct 4, 2020
Keywords: Heavy vehicle; inerter–spring–damper suspension; parameter matching; ride comfort; road friendliness
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