Keywords

1 Introduction

With the higher requirement of riding comfort, the full-floating commercial vehicle cab suspension is being widely used. This research of air spring cab suspension contains a series of advantages which including low and stabilized system natural frequency, good vibration isolation effect, light weight, low noise, and that are the reasons for being widely applied in middle- and high-class commercial vehicles [1]. However, this kind of cab suspension can only bear radial force, and guide mechanism is thus required to be attached to strengthen its lateral stability, which may unavoidably make the system much more complicated. As the cab suspension system plays a key role in the vehicle system, researchers from home and abroad are also devoting themselves to exploring its performance of every aspect [2,3,4,5,6,7]. At the beginning of the product design, designers generally adopt simple empirical formulas or simplified simulation models [8,9,10] which are of great advantages for mature products with fixed design process. But it may have problems in complicated new products. In later developing stages of cab suspension, one possible way to solve the design defect is repeatedly revising design according to the result of prototype vehicles’ repeated road test, or doing rectification and modification according to feedback from the market, which greatly increases procedure and cost of design, and reduces market competitiveness [11,12,13,14]. It can be seen that some problems are still there in the research process of cab suspension system.

The method that adopting simulation design and bench scale test in this research process of air spring cab suspension can ensure the accuracy of design, and greatly shorten the design cycle, and cut the cost. To explore the vibration performance, firstly ADAMS/View was adopted to build the dynamic model and the cab suspension’s vibration isolation performance was analyzed. The vibration test of cab suspension in four-channel road simulator was conducted to verify the effectiveness of the built dynamic model. Secondly, a cab suspension finite element model was built by using RADIOSS according to the boundary condition of dynamic model, and experimental verification of full-load working condition was also conducted. Accordingly, the strength of cab suspension in various limiting condition was analyzed. Finally, the system fatigue test on fatigue testing machine was conducted to check the fatigue resistance of both structure and elastic parts of the cab system based on which corresponding design problems could be modified. The method mentioned above is of high value in engineering application and promotion.

2 Cab Suspension Dynamic Performance

Cab suspension dynamic performance is strongly related to the spatial structure arrangement. So it needs to explore and check the rationality of particular spatial structure. Air spring cab suspension system in this paper is consisted of front suspension and rear suspension. The front air springs are arranged vertically, and mainly bear vertical force; the rear air springs are arranged obliquely which can bear both vertical and lateral forces. The cab suspension system consists of considerable number of bushes which greatly increase the system freedom. In this way, the cab suspension can bear the pitching moment, yawing moment and rolling moment from the cab within the limit travel. Also, the large number of Elastic elements may improve the system vibration isolation if they are adjusted.

2.1 Cab Suspension Bench Test

To explore the vibration isolation effect of elastic elements (air springs and bushes) on air spring cab suspension system, the cab suspension was launched between the developed equivalent cab and four-channel road simulation testing bench (as shown in Fig. 1). The equivalent cab is developed according to the mechanical dynamics conversion principle, so the equivalent one has the same mass, center-of-mass coordinate, and moments of inertia as the original one. The four-channel road simulation testing bench is mainly consisted of servo-linear actuators, hydraulic control system, dynamic and static test software, load holders, relevant attachments, and so on. Hydraulic control system controls linear movement of actuators. The movement signals are measured and received by corresponding sensors, and then fed back to the computer after processed to complete a closed-loop control. The four servo-linear actuators can move independently with different input road spectrum (displacement spectrum) which can simulate the real working condition of the running vehicle.

Fig. 1
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Bench test

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Every air spring of the cab suspension system works with one altitude valve which connected to center plenum chamber so it can keep every air spring’s inner pressure as its setting value by inflation and bleeding. And it makes sure that the running vehicle can turn bad working condition into quite good work condition. In another word, the stiffness value of the air spring can always stays in the adjacent area of the inflection point of the inverse S curve (air spring’s stiffness curve).

In order to investigate dynamic characteristics of the cab suspension system, the air spring’s inner pressure was set to a normal working pressure (5 bar) and the acceleration sensors were placed on the input terminal and output terminal of relevant elastic elements (each sensor must be vertical arranged) to measure the vertical acceleration (as shown in Fig. 2). The filtered acceleration signals can be translated into displacement signals by twice integrals so that they are of the same formats as the input signals.

Fig. 2
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Acceleration sensors’ position

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2.2 Cab Suspension Dynamic Model

Cab suspension bench test is restricted. In some harsh conditions, therefore simulation method is quite suitable. In ADAMS/View, the rigid-flexible coupling method was adopted to build cab suspension dynamic model (as shown in Fig. 3). The horizontal stabilizer bar of the front suspension and portal frame of the rear suspension were modeled as elastic bodies, and the other structures as rigid body. The air springs were simulated with Spring-Damper model, and the bushes with Bushing model. In the cab, one driver and two passengers along with one toolbox were fixed to the specified location which characterized the full-load condition. The sprung mass is up to 1600 kg, much larger than the unsprung mass. The whole degree of freedom of the dynamic model is 102 which is large enough to reflect the dynamic characteristics.

Fig. 3
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Dynamics model of cab suspension

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2.2.1 The Stiffness Characteristic of Air Spring

Diaphragm-type air spring is wildly used in the cab suspension system. The stiffness curve seems like an inverse S curve which means the stiffness value is relatively small near the equilibrium point while much larger when stretched or compressed a large stroke. The stiffness can be fitted by the following formula [14]:

$$ \begin{aligned} K & = \frac{{mD^{2} (p_{r} + p_{a} )}}{V}x^{2} + \frac{{2mDS_{0} (p_{r} + p_{a} )}}{V}x \\ & \quad + \frac{{mS_{0}^{2} (p_{r} + p_{a} )}}{V} + p_{r} D \\ \end{aligned} $$
(1)

where K is the stiffness value, pr is the inner air spring pressure, pa is the atmospheric pressure, m is poly-tropic index, S0 is the effective area of air sac on the equilibrium position, D is the changing rate of air sac’ s effective area, V is the volume of air spring, and x is the displacement of air spring.

As it is difficult to fit the stiffness curve directly from the tension and compression test, formula (1) was integrated, and the relation between the air spring’s load and internal pressure was obtained, which is a cubic equation with one unknown. The air spring’s load is proportional to internal pressure as shown in formula (2), where F0 is a constant.

$$ \begin{aligned} K & = \frac{{mD^{2} (p_{r} + p_{a} )}}{3V}x^{3} + \frac{{mDS_{0} (p_{r} + p_{a} )}}{V}x^{2} \\ & \quad + \frac{{mS_{0}^{2} (p_{r} + p_{a} )}}{V}x + p_{r} Dx + F_{0} \\ \end{aligned} $$
(2)

The diaphragm-type air spring’s load-displacement curve was tested under the normal temperature environment by adopting electro-hydraulic servo-vibration system made by the MTS company from the USA, and it was fitted by formula (3) under the normal working pressure (5 bar). The unit of load is N, while displacement is mm. As discussed above, the air spring cab suspension system can always work on the initial set position (see Fig. 4) which means the displacement x is relevantly small. Owning to the quite small coefficient of the two and three party of x, formula (3) could be substituted with (4). Then, the linear stiffness of air spring could be identified as 12.5 N/mm.

Fig. 4
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Load-displacement curve

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$$ F = 0.0077x^{3} + 0.1311x^{2} + 12.50x + 3486 $$
(3)
$$ F = 12.5x + 3486 $$
(4)

2.2.2 The Damping Characteristic of Air Spring

The damping characteristic of diaphragm-type air spring is equivalent to the viscous damping, so the velocity-load curve of the front and rear air spring suspension was tested by adopting WDTS-IV electric dynamometer under normal temperature condition. Its damping curve can be fitted with formula (5) according to the linear viscous damping model.

$$ {\kern 1pt} F = c \cdot v{\kern 1pt} {\kern 1pt} $$
(5)

where F is the damping force, c is the viscous damping, and v is the testing speed.

The air spring damping can be divided into compression damping and restoring damping (as shown in Fig. 5), and most of the energy is consumed on restoring stroke, so the restoring damping is much larger than the compression one. As the centroid of the cab is more closer to the front suspension whose air spring has much lager vertical stroke, the air spring’s damping from the front suspension is much larger than the rear one. With comprehensive consideration of the vibration effect, the restoring damping was chosen as the simulation input value. Thus, the front air spring’s damping value is 8051 N s/m, and the rear one is 4959 N s/m, respectively.

Fig. 5
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Velocity-load curve

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2.2.3 The Stiffness Characteristic of Bush

The main role of bushes in the cab suspension is increasing the elastic degree of freedom and supporting the cab, and due to the small volume, the damping value of bush is so small that can even be ignored. Figure 6 shows the location of bear bushes, some of the bushes have holes in the direction without extra load, so the stiffness may be much smaller.

Fig. 6
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Location of bear bushes

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The stiffness of cab suspension’s various bushes was tested by using DJW dynamic and static stiffness of rubber fatigue testing machine under normal temperature. The result of bush stiffness test is shown in Table 1. The bush from the front suspension has much larger stiffness than the rear one with consideration of emergency braking or other exceptional case.

Table 1 Stiffness of bushes
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2.3 Comparison Between the Results of Simulation and Experiment

The same road spectrum of rub garment board (as shown in Fig. 7) was put into the corresponding channel of the test bench and the dynamic simulation model at the same time, and the displacement of the corresponding position (Fig. 2) was exported. Table 2 shows the contrast results of experiment and simulation.

Fig. 7
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Road spectrum of rub garment boards

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Table 2 Experimental and simulation data
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From the table, it can be seen that the max error of the simulation result is no more than 13%, and the min error is less than 4%, which meets the engineering requirement. So, the dynamic model has certain reliability.

2.4 Optimization of Cab Suspension Vibration Isolation Performance

In the cab suspension dynamic model, the cabin seat vertical acceleration power spectrum density function was set as the optimization goal, and the air spring’s linear term stiffness value and the damping values were set as optimization variables, and the pitch angle and rolling angle of the cab were set as the constraints, and adopted the generalized reduced gradient method to optimize the system parameters. Results show that the stiffness value contributes much less to goal compared to the damping value, and the rear damping has the highest sensitivity. With comprehensive consideration, the linear term stiffness value of the optimized air spring is set as 18.8 N/mm, the damping values of the front and rear suspension are 8214 and 3879 N s/m, respectively.

3 Cab Suspension Static Performance

Once the spatial structure and elastic element’s dynamic performance parameters are set, the dynamic behavior of the cab suspension system is then determined. However, that is only the beginning of the R&D process, as the static performance (such as static strengthen and static stiffness) also plays a very important role in the design of cab suspension.

3.1 Static Strength Test with Full-Loaded Cab

The equivalent cab was installed on the cab suspension, and several bags of sand (a total of 300 kg) were put to the specified location to simulated the working condition when the cab is full-loaded. The equivalent cab was slowly lifted along the vertical direction, until there were no external forces affecting on the cab suspension. According to the engineering experience, the strain gauges were attached to the smooth surface where there may have more possibility to generate stress concentration (as shown in Fig. 8). The lateral stabilizer bar (Point O) was attached with a unidirectional strain gauge, which was 45° to the axis. The turnover supports of the cab (Point AL and AR) suffer forces from all directions, so the three-direction strain rosette was attached to the bottom plan. The other positions were attached with unidirectional strain gauges, and they were all laid out along the vertical direction. All the strain gauges remained stationary for 24 h before the strain gauge was demarcated and reset. Then the equivalent cab was landed as slowly as possible to make sure that the cab suspension suffered steady force, at the same time the strain values were recorded until the cab landed completely. The test was repeated three times, and the average values were taken as the final test results.

Fig. 8
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Location of the strain gauges

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3.2 Static Strength Simulation with Full-Loaded Cab

HYPERMESH was used to mesh the cab suspension. Sheet metal parts were meshed as shell elements, and complex casts parts were replaced with tetrahedron solid element. The bushes were simulated with CBUSH element and the air spring with CELASI element to characterize the linear stiffness and damping. Bolted connection and welding were substituted with RBE2 element. All the parts in the cab suspension were set with proper element sizes. The cab suspension finite element model is shown as Fig. 9.

Fig. 9
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Finite element model of cab suspension

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The lower ends of cab suspension were fixed and the upper ends which connected to the cab suffered vertical forces and corresponding moments derived from the dynamic model. The finite element model was submitted to the solver after all were set up.

3.3 Comparison Between the Results of Simulation and Test

The stress values in the static strength test of the relevant parts could be calculated by the strain values and corresponding modulus of elasticity. Table 3 shows the results of simulation and experiment.

Table 3 Stress value
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From the table, it can be seen that the error of simulation value and testing value is below 10%, and it has conformity with the error direction which shows that finite element model is effective and meets the need of engineering analysis.

3.4 Modal Analysis of Cab Suspension

The inherent characteristics of the cab suspension system can be obtained by modal analysis. On the basis of finite element model, the cab suspension system’s free mode was calculated (as shown in Table 4). As the first-order bending frequency of car body is about 5–6 Hz, and the resonance frequency of unsprung weight is about 8–15 Hz, each order’s frequency of the cab suspension is far away from the above scope. Therefore, the vibration of the cab suspension system could be reduced to a proper level which satisfies the driver.

Table 4 Mode of cab suspension
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3.5 Analysis of the Cab Suspension’s Limiting Working Condition

It may always be confronted with all kinds of limiting conditions such as severe traffic fluctuation turbulence, emergency braking, and rapid turn in the course of vehicle running. And that is usually quite difficult to repeat with a physical prototype. However, the finite element simulation analysis is a perfect alternative at this time. In the finite element model, the 3.5 g vertical impact working condition (3.5 times of vertical gravity applied at the cab center-of-mass) was adopted to simulate passing the rough roads with large pit holes, 1 g rolling working condition (1 time of gravity applied at cab center-of-mass toward the lateral side) to simulate sharp turn, and 1 g pitching working condition (1 time of gravity applied at the cab center-off-mass toward the driving direction) to simulate the emergency brake (the system stiffness was not under consideration because cab suspension system has a large amount of elastic parts such as air spring, which has strong nonlinearity). On 3.5 g vertical impact working condition, the local stress of the cab’s turnover support was larger than expected (as shown in Fig. 10a), and this can be solved by local-thickening, adding some stiffeners and so on. On 1 g braking working condition, excessive braking force results in local stress concentration of the connecting plate of the rear suspension (as shown in Fig. 10b), which can be dealt with adding stiffeners, changing material, adjusting bolts’ pretension, and so on. On 1 g rolling working condition, cab suspension system’s stabilizing bearing has local stress concentration (as shown in Fig. 10c) because of large rolling moment, which can be handled with enlarging the fillets, thickening the sheet metal, and so on.

Fig. 10
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Stress concentration parts under different working conditions

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Though some parts of the cab suspension exist yield under limiting working condition, the stress concentration can be solved by local minor adjustment, and these small changes have little influence on dynamic characteristic of the cab suspension system.

4 Fatigue Performance of Cab Suspension

According to the statistics, the fatigue failure accounts for more than 80% among the failure of most mechanical parts. That means, the cab suspension system satisfying the requirement of static limiting strength design does not guarantee its reliability due to its large amounts of mechanical parts, and it usually needs to be tested about the fatigue resistance performance.

The cab suspension in this research contains a large number of elastic elements, which makes it difficult to conduct the fatigue simulation because of the strong nonlinearity in this system. Therefore, a cab suspension fatigue testing machine was developed to study its fatigue characteristics.

4.1 Cab Fatigue Testing Machine

To explore the vertical, longitudinal, and lateral fatigue resistance properties of cab suspension, the fatigue testing machine for cab suspension system was developed, as shown in Fig. 11.

Fig. 11
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Cab suspension fatigue testing equipment

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It mainly consists of hydraulic vibration head, gantry, equivalent cab, base, etc. The equivalent cab has the same mass, center-of-mass coordinates, and the moment of inertia as the original one. It is welded by square tubes and steel plates, with high stiffness, which makes sure that the deformation is small enough. The equivalent cab has three card slots along the vertical, longitudinal, and lateral direction respectively at its centroid position. The hydraulic vibration head can connect to one of the three card slots to test the cab suspension fatigue properties of the relevant direction. With a closed-loop force control system, the hydraulic vibration head can apply stable vibration forces. The hydraulic vibration head is connected to the gantry with joint bearings, which can release the rotational degrees of freedom, avoiding over-constraints of the vibration head. The gantry linked to the vibration head is composed of I-beams and square tubes with high stiffness, and the maximum deformation of working vibration head is no more than 0.1 mm when the exciting force is more than 20,000 N.

4.2 The Cab Suspension Fatigue Test

The vibration head was connected to the vertical card slot (as shown in Fig. 12a), the longitudinal card slot (as shown in Fig. 12b), and the lateral card slot (as shown in Fig. 12c) of the cab respectively to investigate the fatigue properties in the relevant direction.

Fig. 12
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Fatigue test

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In the vertical test, the input force was a sine wave with an amplitude twice as the weight of cab. The balance value of force wave was 0, and the vibration frequency was 1 Hz. The vibration lasted for 50,000 cycles (about 14 h without pause). In the longitudinal and lateral tests, all the input conditions were the same as in the vertical test, except that the amplitude was 0.5 times as the cab weight. As the stress level is relatively low, the mechanical parts in the cab suspension system may encounter high-cycle fatigue problems. The fatigue assessment criteria of the cab suspension are as follows: (1) There are no cracks on the mechanical parts of the system even under the microscope; (2) there are no excessive wear or cracks on the elastic parts; (3) there are no functional damages on the cab turnover structures and locking devices, etc. If there are any cracks on the mechanical parts, the structure could be modified or reinforced on the positions where are likely to appear stress concentration; if there is excessive wear or crack on the elastic parts, they could be dealt with changing the formulation of compound without obviously changing the stiffness characteristics to enhance the wear performance; if the cab turn over structures or locking devices are functionally damaged, they can be solved by either improving the wear resistance or adjusting the stress state of the system.

5 Analysis and Discussion

Aiming at developing the cab suspension, a method that combines simulation design and workbench test has been proposed, which can find the defects of design and correct them in the early stage. The dynamic model of air spring cab suspension has been built and validated by corresponding workbench test. Since there are plenty of elastic components in the cab suspension system, the matching optimization of which can be conducted by a dynamic model, to determine the optimal vibration characteristics of the system. If the corresponding channels of the cab suspension were inputted with complex spectrum obtained from the actual measurement, the status under different working conditions can be simulated, which may be helpful to the dynamic optimization. Although the dynamic model with simplified parameters has high credibility on some working conditions, the nonlinear characteristic still needs to be considered if focusing on the nonlinearity of the system, and that is the focus of future work. The finite element model of the cab suspension with the optimized dynamic boundary conditions has been built and validated by full-load static strength test, and with the help of FE model, the modes of the cab suspension were analyzed, and possibility of resonance between sprung and unsprung components was eliminated. Meanwhile, the FE model was also used to predict the stress distribution of cab suspension under limiting conditions, with which help the structures could be strengthened in time. While the cab suspension has met the requirement of static strength (without considering the static stiffness), it is still necessary to verify the fatigue resistance properties of the system. To this end, the triaxial fatigue testing machine was developed, and the vertical, longitudinal, and lateral fatigue properties of the cab suspension were tested. Then corresponding solutions could be found to solve the problems appeared in the test. And this procedure may be repeated if necessary to make sure that the system works well. Similarly, the method can be applied to other design of systems or vehicles; it is of certain engineering application value.

6 Conclusions

  1. (1)

    In this paper, dynamic model and finite element model were built and validated by corresponding workbench test. The results of simulation and test are consistent with each other. The simulation results can meet the requirement of engineering analysis.

  2. (2)

    Based on the dynamics model, the dynamic properties of cab suspension system could be optimized. With the FE model, the stress state of cab suspension under limiting conditions could be predicted. And the three-dimensional fatigue characteristics of cab suspension were tested using the fatigue testing machine. The results show that this method can greatly shorten the design cycle and reduce the design cost.

  3. (3)

    The proposed design method can also be applied to other vehicle systems or other full vehicles.