Driving over raised pavement markers (RPMs) spaced at different spacing, the human body will experience different vibrations. To explore whether RPMs situated at the exit ramp of an expressway induce a good vibration warning effect, this paper determines the spacing of RPMs situated along a deceleration lane and curved ramp. Models of roads, vehicles, and RPMs are first established in the ADAMS software, after which an integrated human-chair model constructed in SolidWorks is imported into ADAMS, and then the complete model is formed so that vibration simulations of different types of vehicle at different spacing and speeds can be carried out. The results show that the vibration warning effects of the spacing proposed by the existing Chinese specifications and this paper are basically between level III and level IV, the driver’s subjective feeling is between less comfortable and uncomfortable, and both induce a good vibration warning effect. For a linear deceleration lane, when considering traffic safety, a spacing of 3 m is recommended; when considering the economy, a spacing of 6 m is recommended. For a curved deceleration lane and curved ramp, according to the actual curve radius, the spacing of RPMs can refer to the spacing recommended in the paper. In addition, the vibration warning effect for cars and semi-trailer trucks initially increases with an increase in the speed; then, after reaching a certain peak speed, the effect decreases with an increase in the speed, and finally, it tends to become gentle at speeds exceeding 100 km/h. The vibration warning effect for a semi-trailer truck is better than that for a car under the same spacing and speed.
Raised pavement markers (RPMs) are often served as centerlines, lane lines, and edge lines on road, and they also play an important role in various pavement markers. Accordingly, RPMs are often used on the exit ramps of expressways. In this condition, RPMs not only function as a visual marker but also have the vibration warning effect when vehicles drive over the RPM.
As an important component of the expressway system, exit ramps constitute the only means to transition from an expressway to local roads. Nevertheless, the traffic environment on an exit ramp is more complex than that of the mainline and the entry ramp. Therefore, the exit ramp has become a traffic bottleneck and an accident-prone point for expressways. Accident statistics in the United States indicate that more than 30% of expressway accidents occur on or near an expressway exit, and more than half of them are related to exit ramps [
Another factor that affects the safety benefits of the RPM is the spacing. The spacing of RPMs is the main factor that influences the effectiveness of RPMs [
In addition to affecting the function of visual guidance for the RPM, the spacing is also one of the main factors affecting the vibration effect of the RPM. The vibration warning function of the RPM can provide a good warning for the driver who deviates from the normal lane to alert them to adjust the driving direction in time and avoid accidents. At present, there are few researches on the vibration warning effect of the RPM. Only Deng [
Accordingly, scholars have proposed some indicators and methods for evaluating the driver’s comfort. Zheng [
Due to the exit ramp being difficult to identify and the road alignment on an exit ramp changing quickly, and the high speed of the vehicle, many vehicles will inevitably drive over RPMs located along the edges of the lanes on exit ramps. In this case, the vibration warning function of the RPM can effectively remind the driver that the vehicle has deviated from the normal lane. However, previous studies on RPMs are mainly based on the suggested spacing by the function of visual guidance, and few studies have considered the effect of vibration warning. And when the spacing of RPMs is different, whether drivers feel the vibration is different or not, there is no quantitative conclusion on the level of the vibration warning effect corresponding to the different vibration. In addition, previous studies on vibration simulation are all based on the evaluation of vehicle vibration, without considering the true bearer of vibration -- the subjective feelings of human, which is obviously unreasonable.
Therefore, this paper first determines the spacing of RPMs in each section of expressway exit ramp, and the evaluation standard was established with reference to the Method of Running Test-Automotive Ride Comfort (GB/T4970-2009). Models of roads, vehicles, and RPMs were established based on ADAMS software, and a 9-DOF human-chair model was established in combination with SolidWorks. The vibration warning effect of RPMs was then analyzed under different combinations of spacing, speeds, and vehicle types.
An expressway exit ramp consists of a deceleration lane, an easement curve, and a curved ramp. Among them, the deceleration lane is divided into direct-type and parallel-type lanes [
The vibration warning effect of RPMs along an exit ramp is closely related to the spacing of RPMs. If the spacing is too sparse, the vibration effect will be insufficiently strong, while if the spacing is too dense, it will not only cause damage to vehicles but also call for a higher cost. Therefore, the spacing of the RPM at the curved ramp and the deceleration lane should be determined before analyzing the vibration warning effect of RPMs. For the deceleration lane, China’s relevant regulations stipulate that the linear shape of the deceleration lane should be consistent with the mainline shape of the expressway. Furthermore, when the mainline is a circular curve, the deceleration lane should adopt a curved shape with a curvature that is either similar or identical to that of the mainline [
Schematic diagram of the study area of the RPM at the exit of the expressway: (a) freeway exit ramp (straight mainline); (b) freeway exit ramp (curved mainline).
The relevant regulations in China do not specify the spacing of the RPM on the curved ramp. By establishing a model of the driver’s visual field, Lin calculated the spacing of RPMs on a circular curve and the specific spacing is shown in Table
Spacing for the radius of a circular curve.
Design speed |
20~30 | 30~40 | 40~60 | 60~80 | 80~100 | 100~120 |
---|---|---|---|---|---|---|
General value of minimum radius of circular curve |
30~65 | 65~100 | 100~200 | 200~400 | 400~700 | >700 |
Spacing |
2.25~3 | 3.5~4.5 | 4.5~7 | 7~11 | 11~15 | 15 |
Based on statistical survey data from the first Highway Survey and Design Research Institute of China, the most frequently used radii of curved ramp on the expressway exit ramp in China are 60 m ~ 80 m, 150 m ~ 210 m, and 280 m ~ 1000 m. This article selects three radii, namely, 70 m, 180 m, and a critical radius of 700 m from the most frequently used curved ramp radii as simulation parameters. In combination with Table
When the mainline of the expressway is a straight line, the linear shape of the deceleration lane is also a straight line. At this point, according to the example in relevant Chinese specifications [
In contrast, when the mainline of the expressway is a circular curve, the deceleration lane should have a curvature that is similar or identical to that of the mainline. In China, design speeds of 60 km/h, 80 km/h, 100 km/h, and 120 km/h are considered for the mainline of an expressway. According to Table
When a car drives over an RPM, the process through which the driver experiences vibrations is very complicated. When the car seat is shaken by the body of the vehicle, the car seat will absorb a component of the vibration and transmit the remainder to the driver. Past studies have employed the vibration of the vehicle body instead of the vibration experienced by the driver which is obviously unreasonable. Accordingly, to reflect the actual situation and explore the vibrations on the human body, it is essential to construct a dynamic human-chair-vehicle model. The human model was carried out in SolidWorks according to the dimensions of the various parts of the human body and the ranges of joint angles of the sitting posture [
The vehicle models of cars and semi-trailer trucks are created in ADAMS and the constructed human-chair model is imported through ADAMS/VIEW. Then, the man-chair-vehicle integration model is obtained. The car is selected from Santana 2000. In addition to the seats, other parameters of the car and semi-trailer truck are based on the software default values. The complete model is shown in Figure
The man-chair-vehicle integration model (Take Santana 2000 as an example).
The Road Builder module in ADAMS is easy to operate and contains many parameters with which to define the road. Accordingly, this paper constructs a 3D road model of the deceleration lane and curved ramp by the given node coordinates. When the mainline is a straight line, the deceleration lane is built along a straight line with a length of 200 m. When the mainline is curved, the deceleration lane is established along a circular curve, and the radii of the deceleration lane are 200 m, 400 m, and 700 m, while the radii of the curved ramp are 70 m, 180 m, and 700 m as the simulation road radius. The following three parameters also use the default values: the width of the road is 3.75 m, the slope of the longitudinal slope is 0, and the friction coefficient is 0.9. The length, width, and height of the RPM studied in this paper are set as 10 cm, 10 cm, and 2.5 cm, respectively [
Flowchart of building simulation model.
After running the model, we make a preliminary simulation to determine the experimental factors. Because the changes of various structural parameters of vehicles have complex effects on vibration, we do not consider the influence of the variation of vehicle parameters on the experiment in the preliminary simulation experiment. Only two factors, the vehicle type and the vehicle speed, are selected as variables. The preliminary simulation also shows that, in addition to the spacing of RPMs, the vehicle type and the vehicle speed have a great influence on the vibration warning effect. And when the simulation time is 15 s, the vehicle can drive over RPMs many times, which is sufficient for collecting experimental data. Therefore, the processing parameters, such as the spacing of the RPM, vehicle type, vehicle speed, and simulation time, are selected as the simulation parameters. The simulation speeds on the deceleration lane are 55 km/h, 60 km/h, 65 km/h, and 70 km/h [
Simulation scheme parameters.
Section | Cars and semi-trailer trucks | ||||
---|---|---|---|---|---|
Spacing [m] | Speed |
Radius |
Time | ||
Deceleration lane | Linear | 3 | 55/60/65/70 | / | 15 |
4 | |||||
5 | |||||
6 | |||||
Curved | 7 | 55/60/65/70 | 200 | 15 | |
11 | 400 | ||||
15 | 700 | ||||
|
|||||
Ramp curve section | 4 | 40/50/60 | 70 | 15 | |
6 | 180 | ||||
15 | 700 |
After entering the relevant simulation parameters into the software and running the model, Adams/Car will output the three-axis acceleration curves of the x-axis, y-axis, and z-axis of the seat cushion, seat back, and foot.
When the vehicle drive over RPMs, vibration is generated, and then the driver gets a warning through the touch. The vibration warning effect is related to the vibration acceleration generated by different vehicles driving over the RPM. Therefore, the vibration warning effect can be evaluated by the vibration acceleration. International standard entitled
In order to obtain the weighted acceleration RMS of the human body accurately and quickly, this paper analyzes the spectrum of the three-axis acceleration curves of the x-axis, y-axis, and z-axis of the seat cushion, backrest, and foot generated by Adams/Car. Then, the obtained acceleration self-power spectral density function curve is, respectively, imported into Glyphworks in Ncode software, and then the total weighted acceleration RMS of each point (
The relationship between the human subjective feeling and the combined total weighted acceleration RMS.
The combined total weighted acceleration RMS |
Human subjective feeling | The level of the vibration warning effect |
---|---|---|
<0.315 | No discomfort | I |
0.315-0.63 | A little uncomfortable | II |
0.5-1.0 | Less comfortable | III |
0.8-1.6 | Uncomfortable | IV |
1.25-2.5 | Very uncomfortable | V |
>2.0 | Extremely uncomfortable | VI |
(1) Calculate the total weighted acceleration RMS of each measurement point position:
In the above formula:
(2) The combined total weighted acceleration RMS of the three measuring points is calculated as follows [
In the above formula:
There are three control variables in this paper: the type of vehicle, spacing, and speed, and the observed variable is the combined total weighted acceleration RMS (
ANOVA can be divided into one-way analysis of variance and multivariate analysis of variance according to the type of data design. Because there are three factors in this paper, such as the type of vehicle, spacing, and speed, the multivariate analysis of variance is used in this paper and the 95% confidence interval is taken. Multivariate analysis of variance can not only analyze the independent influence of multiple factors on observed variables, but also analyze whether the interaction of multiple control factors can have a significant influence on the distribution of observed variables and finally find the optimal combination for the observed variables.
Now the type of vehicle, spacing, and speed are converted into classified variables. The classification of each variable is shown in Table
The classification of each variable.
Variable name | Variable value | |
---|---|---|
Type of vehicle | Car | 0 |
Semi-trailer truck | 1 | |
|
||
Spacing | 3 m | 0 |
4 m | 1 | |
5 m | 2 | |
6 m | 3 | |
7 m | 4 | |
11 m | 5 | |
15 m | 6 | |
|
||
Speed | 40 km/h | 0 |
50 km/h | 1 | |
55 km/h | 2 | |
60 km/h | 3 | |
65 km/h | 4 | |
70 km/h | 5 |
The converted variable data was imported into SPSS for Multivariate Analysis of Variance. The results are shown in Tables
Interaction test. The dependent variable: the combined total weighted acceleration RMS.
Source | Type III Sum of |
df | Mean |
F | Sig. (P) |
---|---|---|---|---|---|
Corrected model | 2.633 |
67 | 0.039 | 3.409 | 0.062 |
Intercept | 56.520 | 1 | 56.520 | 4903.704 | 0.000 |
Type of vehicle | 0.415 | 1 | 0.415 | 36.043 | 0.001 |
Speed | 0.278 | 5 | 0.056 | 4.819 | 0.041 |
Spacing | 1.227 | 6 | 0.204 | 17.740 | 0.001 |
Type of vehicle |
0.031 | 5 | 0.006 | 0.540 | 0.742 |
Type of vehicle |
0.205 | 6 | 0.034 | 2.958 | 0.106 |
Speed |
0.199 | 22 | 0.009 | 0.785 | 0.691 |
Type of vehicle |
0.027 | 22 | 0.001 | 0.105 | 1.000 |
Error | 0.069 | 6 | 0.012 | -- | -- |
|
71.209 | 74 | -- | -- | -- |
Corrected total | 2.702 | 73 | -- | -- | -- |
a. R2=0.974 (Corrected R2=0.689).
Main effect test. The dependent variable: the combined total weighted acceleration RMS.
Source | Type III Sum of |
df | Mean |
F | Sig. (P) |
---|---|---|---|---|---|
Corrected model | 2.179 |
12 | 0.182 | 21.185 | 0.000 |
Intercept | 49.724 | 1 | 49.724 | 5801.422 | 0.000 |
Type of vehicle | 0.650 | 1 | 0.650 | 75.874 | 0.000 |
Speed | 0.275 | 5 | 0.055 | 6.406 | 0.000 |
Spacing | 1.284 | 6 | 0.214 | 24.965 | 0.000 |
Error | 0.523 | 61 | 0.009 | -- | -- |
|
71.209 | 74 | -- | -- | -- |
Corrected total | 2.702 | 73 | -- | -- | -- |
a. R2=0.806 (Corrected R2=0.768).
It can be seen from Table
As can be seen from Table
Tables
When a vehicle is on the road, it sometimes departs to the left of the lane or to the right of the lane. When the above model is running, the vehicle will also randomly deviate to the left or to the right, which will result in two different directions of vibration acceleration. In each case, there will be the combined total weighted acceleration RMS in both directions, namely, the left combined total weighted acceleration RMS and the right combined total weighted acceleration RMS. In this paper, the deviation to the right of the lane is defined as the deviation to the inside of the lane, and the deviation to the left of the lane is defined as the deviation to the outside of the lane. The specific experimental results are shown in Figures
The combined total weighted acceleration RMS for the deceleration lane: (a) the linear deceleration lane (car); (b) the linear deceleration lane (semi-trailer truck); (c) the curved deceleration lane (car); (d) the curved deceleration lane (semi-trailer truck).
The combined total weighted acceleration RMS for the curved ramp section: (a) the curved ramp section (car); (b) the curved ramp section (semi-trailer truck).
In the speed range of 55 km/h ~ 70 km/h, whether it is the linear deceleration lane or the curved deceleration lane, the combined total weighted acceleration RMS of the car and the semi-trailer truck deviating toward the inside and outside of the lane decrease with an increase in the spacing under the same simulation speed conditions. That is, the denser the spacing of the RPM, the more uncomfortable the driver’s subjective feeling, which means the better the vibration warning effect.
For the linear deceleration lane, when the spacing is either 3 m or 4 m, drivers of the car feel less comfortable or uncomfortable, and the vibration warning effect for the car is between level III and level IV, while drivers of the semi-trailer feel uncomfortable, and the vibration warning effect is mostly level IV. When the spacing is either 5 m or 6 m, most drivers of the car feel less comfortable, and the vibration warning effect is mostly level III, while drivers of semi-trailer still feel uncomfortable, and the vibration warning effect is level IV (Figures
For the curved deceleration lane, the subjective feelings of the driver of the semi-trailer and the car are between the less comfortable and uncomfortable, and also at a medium level. Therefore, regardless of the spacing, mainly corresponding to the radius of the curve, the vibration warning effect of the RPM is better. When the spacing of the RPM is 15 m, the combined total weighted acceleration RMS of the car and semi-trailer truck deviating toward the inside and outside of the lane increase with an increase in the speed at first; however, after reaching a peak at the speed of approximately 65 km/h, it shows a downward trend with an increase in the speed (Figures
Under the same simulation speed and spacing, the combined total weighted acceleration RMS of the semi-trailer truck deviating toward the inside and outside of the lane are larger than those of the car. That is, drivers of the semi-trailer truck feel more uncomfortable than drivers of the car, meaning that the vibration warning effect for the semi-trailer truck is stronger than that for the car.
For the curved ramp section, it is shown in Figures
In the speed range of 40 km/h ~ 60 km/h, with the increase of the spacing, the subjective feeling of the driver is weaker; that is, the vibration warning effect of cars and semi-trailer trucks also decreases as the spacing increases. When the spacing is either 4 m or 6 m, the vibration warning effect for the car is mostly level IV, and most drivers of the car feel uncomfortable; whereas the vibration warning effect for the semi-trailer truck is between level IV and level V, most drivers of the semi-trailer truck feel uncomfortable and a few feel very uncomfortable. Therefore, it also has good vibration warning effect. When the spacing of the RPM is 15 m, the vibration warning effect is the same as the trend for the curved deceleration lane.
Previous research has shown that the change trend of the combined total weighted acceleration RMS for the linear deceleration lane at speeds of 55 km/h, 60 km/h, 65 km/h, and 70 km/h is approximately constant under different spacing; that is, they decrease with an increase in the speed. Meanwhile, the trends of the curved deceleration lane and the curved ramp are similar to that of the linear deceleration lane. When the spacing is 15 m, the combined total weighted acceleration RMS shows a rising trend first and then decreases. However, the variation in the vehicle speed during the actual driving process is more complicated, and these trends are limited to the speed range discussed in the Results part of this paper. However, it is not clear whether the change trends of speeds below and above the speed range discussed herein will be the same. Therefore, this paper analyzes the vibration warning effect for vehicles driving over RPMs in other speed ranges.
Generally, the starting speed of a vehicle in first gear is approximately 10 km/h; thus, this speed is selected as the minimum simulation speed, and the maximum speed limit on a Chinese expressway of 120 km/h is selected as the maximum simulation speed with 10 km/h as the spacing step. For the deceleration lane, the simulation speeds were selected from the low speed range (10 km/h, 20 km/h, 30 km/h, 40 km/h, and 50 km/h) and the high speed range (80 km/h, 90 km/h, 100 km/h, 110 km/h, and 120 km/h). Similarly, for the curved ramp, the simulation speeds were selected from the low speed range (10 km/h, 20 km/h, and 30 km/h) and the high speed range (70 km/h, 80 km/h, 90 km/h, 100 km/h, 11 0 km/h, and 120 km/h). ADAMS was used to carry out the simulation experiment under the same simulation parameters as described above and summarize the conclusion of this simulation and the conclusion of Results section. The results are shown in Figures
The combined total weighted acceleration RMS for the deceleration lane between 10 km/h and 120 km/h: (a) the linear deceleration lane (car); (b) the linear deceleration lane (semi-trailer truck); (c) the curved deceleration lane (car); (d) the curved deceleration lane (semi-trailer truck).
The combined total weighted acceleration RMS for the curved ramp section between 10 km/h and 120 km/h: (a) the curved ramp section (car); (b) the curved ramp section (semi-trailer truck).
For a linear deceleration lane, the spacing of an RPM of 3 m is recommended when considering safety, whereas a spacing of 6 m is recommended when considering the economy. Therefore, these two representative spacings of 3 m and 6 m are selected for further discussion.
From Figures
The combined total weighted acceleration RMS of the car and semi-trailer truck deviating toward the inside and outside of the lane both increases with the increase of the speed at first and then reaches a peak speed. Next, the combined total weighted acceleration RMS decrease with an increase in the speed and finally become flat. In other words, the vibration warning effect of the RPM first increases with an increase in the speed and then decreases with an increase in the speed after reaching a peak speed value; finally, the vibration warning effect tends to become flat when the speed exceeds 100 km/h. The red curves shown in Figures
The velocity of the vibration warning effect reaching peak values at different spacings.
Section | Spacing |
Car speed peak |
Semi-trailers speed peak | |
---|---|---|---|---|
Deceleration lane | Linear | 3 | 30 | 30 |
6 | 50 | 40 | ||
Curved | 7 | 50 | 50 | |
11 | 55 | 55 | ||
15 | 65 | 65 | ||
|
||||
Ramp curve section | 4 | 30 | 30 | |
6 | 40 | 40 | ||
15 | 70 | 60 |
Therefore, to achieve a better vibration warning effect, it is necessary to select different spacing according to different road alignments and reasonably adjust the spacing of the RPM according to the speed limits.
This study chose the total weighted acceleration RMS as an indicator to analyze the vibration warning effect of RPMs along an expressway exit ramp based on ADAMS in reference to the ride comfort evaluation method. During the experiment, the vibration warning effect changed with the spacing of the RPM, vehicle speed, and vehicle type, among other parameters, and the change laws are as follows:
(1) When the vehicle speed and vehicle type are both fixed, the vibration warning effect weakens as the spacing increases.
(2) When the spacing is fixed, the vibration warning effects for a car and a semi-trailer truck increase with an increase in the speed initially, after which the effects decrease with an increase in the speed after a certain peak is reached; finally, the effect gradually becomes gentle after the speed reaches 100 km/h.
(3) When the spacing and speed are both fixed, the vibration warning effect for the semi-trailer truck is stronger than that for the car.
This study provides suggestions for the spacing of RPMs situated along the exit ramp of an expressway. These suggested spacings are conducive to improving road traffic safety and therefore contribute to reducing traffic accidents. Highlighting the vibration warning effect, the proposed spacing for a linear deceleration lane is 3 m when considering traffic safety, whereas the recommended spacing is 6 m when considering the economy. Furthermore, for the curved deceleration lane and the curved ramp, according to the actual curve radius, the spacing of RPMs can refer to the spacing recommended in Table
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This work was supported by Fundamental Research Funds for the Central Universities of China (no. 310821172007, no. 300102218410, and no. 300102218521) and the Shaanxi Provincial Science and Technological Project (no. 2017JM5104). The authors thank Pingping Liu for her contributions to this paper.