Variance of whole-body vibration of seated person in passenger car

Abstract

The variability in whole-body vibration (WBV) of a seated person measured in the passenger car was evaluated. The vibration variability was evaluated as a function of the International Roughness Index (IRI). Vibration was measured on 58 test vehicles of 6 different categories. A two-parameter regression function relating the overall vibration total value to its 95% confidence interval and IRI was estimated. The identified regression function may help detect the IRI threshold. The IRI threshold could be derived from the boundaries of comfort reactions to vibration environments, as specified in ISO 2631-1: 1997. Calculation of a 95% confidence interval for the measured overall vibration total value at the seat surface showed that a single IRI value can correspond to vibration values that span up to comfort levels according to ISO 2631-1:1997.

Keywords

Ride comfort whole-body vibration (WBV)passenger car road roughness International roughness index (IRI)

Introduction

The International Roughness Index (IRI) is the most popular longitudinal road roughness index^1,2 and is highly correlated with overall ride quality, dynamic wheel loads, overall vehicle operating cost, and overall surface condition.³

Passenger ride comfort has been a subject of interest for many years.^4,5 The number of published results quantifying the variability of whole-body vibration (WBV) across different vehicle types on test sections of varying smoothness is limited. Papers^6–17 reported the WBV measurement on single or a small number^2,3 of test vehicles. Other authors^18–28 reported the WBV for 4 or more different passenger cars. The results of measured WBV for 4 passenger cars were reported in 18–21,24, for 5 cars in 22,23, for 6 cars in 24, for 12 cars in 26, for 25 cars in 27, and for 35 cars in 28. Table 1 provides an overview of in situ vibration measurements for 4 or more passenger cars, in chronological order.

Table 1.

Survey of frequency-weighted acceleration measurements in a passenger car (more than 4).

Reference	Vehicle	Acceleration measuring point on the seat	Direction	Test sections	v (km/h)	Time	Weighted RMS acceleration (m/s²)	STD (m/s²)	RSD (%)	Range
18	Passenger car (4)	Driver (3)	x,y,z (12 translation and rotation signals on the seat, seat back, and feet)	Endurance road (seat surface)	40	180 s	1.72	0.35	20.5	1.39–2.2
18	Passenger car (4)	Driver (3)		Uneven road (seat surface)	40	180 s	2.29	0.58	25.5	1.7–3.0
27	Passenger car (25)	Driver	z	Public roads	N/A		0.39 (median)	0.14	35.9	0.26–0.75
21	Passenger car (4)/Taxi (Toyota, Nissan, Honda, and Ford)	Driver (247)	z	Urban roads	32	∼1800 s	0.31	0.06	16.1	0.17–0.55
26	Passenger car (12) (taxi, Nissan) of different mileage	Driver (12)	x, y, z	Paved roads without excessive bumps	N/A	4 h	0.31 (Z-axis)	0.02	6.8	0.26–0.34
26	Passenger car (12) (taxi, Nissan) of different mileage	Driver (12)	x, y, z	Paved roads without excessive bumps	N/A	4 h	0.38 (total)	0.03	8.2	0.32–0.44
23	Passenger car (5)/Toyota (1), Nissan (2), Ford (1), Mitsubishi (1)	Passenger	z	Rural (5 km)	55	N/A	0.4	0.03	7.5	N/A
				Provincial (5 km)			0.25	0.03	12	N/A
				Urban (10.6 km)			0.27	0.02	7.4	N/A
				All (20.6 km)			0.3	0.02	6.7	0.27–0.32
22	Personal car (5)	Driver	x, y, z	slow urban traffic	5–30	104 h	0.42	0.17	40.5	–
				Ordinary urban traffic	30–50		0.43	0.21	48.8	–
				Carriage roads traffic	50–80		0.36	0.14	38.9	–
				Highways and motorways	80–130		0.48	0.15	31.2	–
				Total			0.43	0.18	41.9	–
24	Passenger car (6)	Passenger (4)	x, y, z (8 signals on the seat, feet, and back)	Highway (4 subjects)	80	N/A	0.57	0.08	13.9	0.41–0.71
24	Passenger car (6)	Passenger (4)	x, y, z (8 signals on the seat, feet, and back)	Uneven road (2 subjects)	40	N/A	1.12	0.2	13.9	0.77–1.4
19	Passenger car (4)/VW, Renault, Ford, Fiat	Driver	x,y,z	Asphalt road	30	60 s	0.42	0.05	12.1	0.37–0.49
				Asphalt road	60		0.58	0.09	15.1	0.50–0.68
				Cobbled pavement	30		0.54	0.02	4.5	0.52–0.57
				Cobbled pavement	60		0.84	0.12	14.2	0.69–0.95
25	Personal car (4)/Mitsubishi ASX, Toyota HIACE, Toyota HIACE modified, Buick GL8	Driver	z	Mountain highways	20–60	N/A	0.208–0.520 (mean)0.149–0.379 (median)	–	–	–
20	Passenger car (4)/VW, Renault, Ford, and Fiat	Driver	x, y, z	Asphalt road	40	N/A	0.48	0.09	18.4	0.38–0.59
20	Passenger car (4)/VW, Renault, Ford, and Fiat	Driver	x, y, z	Cobblestone pavement	40	N/A	0.80	0.16	19.6	0.59–0.90
28	Passenger car (35)/Taxi (Pride, Samand, Peugeot)	Driver (35)	x, y, z	Urban roads	20–50	696–1221 s	0.62	0.07	10.9	0.57–0.70

Frequency-weighted RMS acceleration, specified in ISO 2631-1: 1997,²⁹ was mainly used for WBV and ride comfort evaluation in papers.^{3–17,19–23,25} Several works^18,24 used an approach in accordance with BS 6841: 1987.³⁰

The vibration was primarily measured in the vertical direction^{18,21,23,25,27} and in three perpendicular axes on the seat surface.^{19,20,22,26,28} Some authors measured more acceleration signals: 8 signals²⁴ and 12 acceleration signals¹⁸ at the seat surface, the feet, and the seat back. Vibrations were measured on the driver’s seat^{19–22,25–28} or the passenger’s seat.^18,23,24

Reported values of the overall vibration total value varied substantially under different test conditions. The mean vibration total value on the seat ranged from 0.3 to 0.5 m/s².^{21–23,26,27} The measured vibration levels at the car seat surface were no more than 1.5 m/s².³¹

Most of the measurements were provided at lower speeds up to 80 km/h. Only Moschioni et al.²² measured WBV on highways at speed intervals of 80–130 km/h. The total measurement time ranged from 60¹⁹ to 180 s¹⁸ to several hours.²⁶

The test section road roughness level was described qualitatively as smooth, rough, etc. The IRI^1–3,32 of the travelled test section was reported only in Perera et al.,⁶ Wang et al.,⁷ Zhang et al.,⁸ Žuraulis et al.,¹¹ and Kirbaş and Karaşahin¹². In these works, a small number of test vehicles (up to 3) were used.

Salehi Sahlabadi et al.²⁸ used the highest number, 35, of test vehicles, Chen et al.²¹ used the highest number of test subjects (247), Park et al.¹⁸ used the highest number of measured acceleration signals, 12, namely translation and rotation on the seat, seat back, and feet.

The relative standard deviation (RSD) of the vibration total value ranged from 6.7%²³ to 48.8%.²² The highest RSDs were reported by Moschioni et al.,²² (31.2–48.8)%; Paddan and Griffin²⁷, 35.9%; Park et al.,¹⁸ 20.5–25.5%; and Vella et al., 18.4–19.6%.

Limitations of the provided WBV measurements (Table 1):

• using one or at most several vehicle speeds^{18,19,21,23,24};

• using lower vehicle speeds up to 60–70 km/h,^{18–21,23,25,28} which do not cover typical vehicle speeds on motorways;

• using a single or a limited number of test sections^18–20,23;

• using test sections with a rare occurrence in the road network²⁵ or short test sections^18,19;

• IRI or other pavement smoothness index of the test section was not measured or known;

• using only the vertical direction of acceleration measurement^{18,21,23,25,27};

• a small number of vibration measurements under specific conditions; and

• the acceleration RMS value was calculated only from the total Vibration Dose Value.²⁷

A limited number of in situ measurements were provided for different passenger cars travelling at various vehicle speeds and for test sections of different categories. This study evaluated the variability in measured WBV on the driver and passenger seat surfaces and on the feet in the passenger car as a function of IRI. WBV variability related to the IRI was not previously published. Múčka^33,34 reported the relationships between WBV and IRI.

The study focused on variability among vehicles and road conditions, not among human subjects. The weight of tested people (one passenger, 82 kg (Body mass index (BMI) = 24 kg/m²), and two drivers, 85 kg (BMI 24.7 kg/m²) and 90 kg (BMI = 24.4 kg/m²) was in line with global age-standardised mean BMI that was 24.2 kg/m² (24.0–24.4) in 2014 in men.³⁵

Body mass influences the vibration response. Only a few references addressed the influence of body weight on WBV for in situ measurements in passenger cars. Kirbaş and Karaşahin³⁶ measured the weighted acceleration in vertical direction (a_wZ) at the driver’s seat of a passenger car (lower middle-class C segment) on the test section of 960 m at speeds of 20, 30, 40, and 50 km/h with three drivers weighing 58 kg, 80 kg, and 113 kg. Results showed similar a_wZ values for driver weights of 58 kg and 80 kg at all speeds, and slightly lower values (by 5 %) for a weight of 113 kg.

The objectives were as follows:

• Evaluate the variability of the WBV on the driver and passenger seat surface and feet for different vehicle types, road categories, road roughness level, and various car speeds; and

• Evaluate the variability in WBV as a function of IRI.

The novelty and the contribution to the knowledge were as follows:

• Evaluation of WBV variability on the same road test section as a function of the IRI and vehicle speed.

• Evaluation of WBV variability as a function of road category – motorway, 1^st class road, and 2^nd class road.

• Processing a broad range of real test sections and a range of vehicle speeds;

• Cover the typical representatives (passenger cars) of the vehicle fleet; and

• Consider the six acceleration signals measured on the seat surface and feet, in three orthogonal axes.

Methods

Road profiles

Longitudinal road profiles were measured by an inertial profilometer³⁷ that meets the requirements of an ASTM E950 Class 1 profiling device.³⁸

The IRI is based on the simulation of the roughness response of a quarter-car model^1–3,32,38 travelling at 80 km/h³² and is also implemented in ASTM E1926-08³⁹ and used in Pavement Management Systems.^1,2,40,41 The mean IRI (m/km) was calculated in two parallel wheel paths located at lateral distances of 0.6 m and 2.1 m from the right edge, and the track was equal to 1.5 m:

IRI = \frac{{IRI}_{LEFT} + {IRI}_{RIGHT}}{2}

Three road categories were processed: motorways with a speed limit of 130 km/h, 1^st and 2^nd class roads with speed limits of 90 and 50 km/h (non-urban roads/urban roads).

Whole-body vibration

The overall vibration total value a_V on the seat surface and feet was calculated by²⁶

a_{v} = \sqrt{{k_{Fx}^{2} a_{wFx}^{2} + k_{Fy}^{2} a_{wFy}^{2} + k_{Fz}^{2} a_{wFz}^{2} + k}_{Sx}^{2} a_{wSx}^{2} + k_{Sy}^{2} a_{wSy}^{2} + k_{Sz}^{2} a_{wSz}^{2}}

(1)

wherea_wSx, a_wSy, a_wSz (m/s²) – frequency-weighted RMS accelerations on the seat surface.a_wFx, a_wFy, a_wFz (m/s²) – frequency-weighted RMS accelerations on the feet.k_Sx, k_Sy, k_Sz, k_Fx, k_Fy, k_Fz – multiplying factors for comfort evaluation.where k_Sx = k_Sy = 1.4, k_Sz = 1, k_Fx = k_Fy = 0.25, and k_Fz = 0.4.Acceleration was measured in three orthogonal directions: x- (longitudinal, i.e., fore-and-aft), y- (lateral), and z- (vertical).

The overall vibration total value on the seat surface, a_vSEAT, was calculated by

a_{vSEAT} = \sqrt{k_{Sx}^{2} a_{wSx}^{2} + k_{Sy}^{2} a_{wSy}^{2} + k_{Sz}^{2} a_{wSz}^{2}}

(2)

Two variables were used to quantify the variability of the a_V and a_VSEAT, relative range (RelRange) and relative standard deviation (RSD), which are defined as follows

RelRange (a_{v}) = 100 \times \frac{\max (a_{v}) - \min (a_{v})}{mean (a_{v})} %

(3)

RSD (a_{v}) = 100 \times \frac{std (a_{v})}{mean (a_{v})} %

(4)

Table 2 presents the scale of the vibration total value acting on a seated human body according to ISO 2631-1: 1997. Comfort levels correspond to likely reactions of passengers in public transport.⁴²

Table 2.

Expected comfort reactions to vibration environments according to the ISO 2631-1: 1997.

Overall vibration total value (m/s²)	Expected comfort reaction
<0.315	Not uncomfortable
0.315–0.63	A little uncomfortable
0.5–1.0	Fairly uncomfortable
0.8–1.6	Uncomfortable
1.25–2.5	Very uncomfortable
>2 m/s²	Extremely uncomfortable

Whole-body vibration measurement system

WBV was measured by a compact measurement system^43,44 equipped with two three-axial accelerometers,⁴⁵ a GPS sensor,⁴⁶ an acquisition unit,⁴⁷ an acquisition software,⁴⁸ and a laptop. Figure 1 shows a scheme for in situ vibration and GPS measurements in a passenger car. The acceleration signal was sampled at 200 Hz in 2017–2018 and at 250 Hz in 2019 and 2020. GPS data were sampled at 5 Hz. Road unevenness and WBV were mutually synchronized in line with recorded geographic coordinates – latitude and longitude data. The change in the acceleration data sampling rate did not affect the computed weighted accelerations, and filtering and weighting were the same for all measurements, in line with ISO 2631-1: 1997. Seat position and posture control were set as standard and comfort for vehicle operation and driving. Sensor alignment was verified in each vehicle.

Figure 1.

Scheme of in situ whole-body vibration measurement in a passenger car.

Test vehicles

Six different vehicle categories were used in the test campaign – small and large family cars, limousines, city cars, sport utility vehicles (SUVs), and cargo vans. Test vehicles (Table 3) were produced between 2005 and 2019, with actual vehicle mileage ranging from 1,600 km to 150,000 km. An average time delay between road roughness and WBV measurement was about 4 months. The passenger (82 kg) and two drivers (85 and 90 kg) were used as the test subjects.

Table 3.

Overview of the used test vehicles for WBV vibration.

Test subject	Test subject weight (kg)	WBV measurement	Years of measurement	Sections length (km)	Number of test vehicles	Test vehicle categories	Year of production range	Millage range (km)
Passenger	82	Seat surface and feet	2017	1471.7	9	4 – small family cars,	2005–2017	1,600-120,000
						2 – large family cars,
						1 – SUV, city car, light commercial vehicle
Passenger	82	Seat surface	2017–2020	4138.5	28	15 – small family cars,	2005–2020	13–252,000
						4 – SUV, light commercial vehicles,
						3 – large family cars,
						1 – city car, supermini
Driver	85&90	Seat surface	2018–2020	2666.8	21	11 – small family cars,	2007–2020	13–252,000
						4 – light commercial vehicles,
						3 – SUV,
						2 – large family car,
						1 – supermini

Whole-body vibration and International Roughness Index

Single test section

The variability of the overall vibration total values a_V and a_VSEAT across different cars was first shown in a randomly selected test section of the 2^nd road class. Table 4 shows the statistics of measurement on the 2^nd road class No. 572 from Most p. B. to Lehnice for 9 test vehicles. The basic statistics of the a_V and a_VSEAT were evaluated, including mean, standard deviation (std), median, and 5^th and 95^th percentiles (P5, P95). The 95^th percentile prediction interval for a new observation was estimated.

Table 4.

Statistics of overall vibration total values a_V and a_VSEAT on the passenger seat on 2^nd class road No. 572 from Most p. B. to Lehnice.

	Vehicle type	Mileage (km)	v (km/h)		a_v (m/s²)					a_vSEAT (m/s²)
	Vehicle type	Mileage (km)	Mean	std	Mean	std	Median	P5	P95	Mean	std	Median	P5	P95
1	Ford Transit	120,000	72.5	14.8	0.79	0.31	0.85	0.32	1.24	0.69	0.26	0.76	0.29	1.06
2	Hyundai	115,000	67.1	12.8	0.64	0.21	0.69	0.30	0.94	0.56	0.18	0.61	0.27	0.82
3	Skoda Citigo	1600	69.1	14.4	0.63	0.19	0.67	0.34	0.92	0.55	0.16	0.59	0.30	0.81
4	Skoda Fabia	120,000	72.1	15.4	0.66	0.23	0.66	0.32	1.03	0.59	0.21	0.60	0.29	0.93
5	Skoda Octavia	12,000	77.3	20.2	0.73	0.24	0.73	0.37	1.10	0.65	0.21	0.66	0.34	0.99
6	Skoda Rapid	21,000	74.6	18.3	0.65	0.22	0.66	0.29	0.99	0.59	0.20	0.61	0.27	0.91
7	Skoda Superb	66,000	78.2	20.1	0.59	0.20	0.58	0.31	0.91	0.53	0.17	0.52	0.29	0.80
8	Skoda Yeti	12,000	73.1	16.5	0.74	0.26	0.77	0.38	1.16	0.67	0.22	0.69	0.36	1.02
9	Volkswagen Golf plus	60,000	80.0	20.5	0.67	0.22	0.68	0.36	1.01	0.60	0.20	0.61	0.32	0.92
	Relative range (%)		17.5		29.6		38.7	29.2	32.1	27.4		39.1	30.9	29.3
	RSD (%)		5.7		9.4		11	10.1	10.9	9.3		11.2	10.6	10.5

The test section length was 18 km, and the IRI = 4.24 ± 1.29 m/km. The IRI data were stored at a 100 m sampling interval. The mean vehicle speed of test vehicles ranged from 67.1 to 80 km/h. Table 4 provides an overview of measured WBV for specific vehicle types. Overall vibration total values a_V and a_VSEAT statistics were calculated from N segments of 100 m length. Relative standard deviation (RSD) and relative range of acceleration, a_V and a_VSEAT (Equations 3 and 4), were added to show the WBV variability among vehicle types.

The mean value of a_v varied from 0.59 to 0.79 m/s², the relative range was 29.6%, and the relative standard deviation was 9.4%. The mean value of a_vSEAT varied from 0.53 to 0.69 m/s², the relative range was 27.4%, and the relative standard deviation was 9.3%. The relative range of acceleration a_V median value was up to 40%.

Figure 2 shows the relation a_v = f(IRI) for 2^nd class road No. 572 from Most p. B. to Lehnice for 9 test vehicles. The relation a_VSEAT and a_V on the IRI was fitted by a two-parameter relationship

a_{VSEAT} = {IRI}^{b_{1}} + b_{2}

(5)

where b₁ and b₂ are regression function coefficients. The fitting function (solid line) and the 95% confidence interval (dashed line) for observations were added to Figure 2.

Figure 2.

The relation between the overall vibration total value a_V (a) and a_VSEAT (b) and IRI for 2^nd class road sample.

Figure 2 shows the wide range of 95% confidence interval for acceleration a_VSEAT that ranged approximately from 0.15 to 0.92 m/s², and for a_V from 0.15 to 1.05 m/s² for a particular value of IRI = 3 m/km. This broad range of a_V belongs to several ride comfort reactions according to the ISO 2631-1: 1997²⁹: not uncomfortable (<0.315 m/s²), a little uncomfortable (0.315–0.63 m/s²), fairly uncomfortable (0.5–1 m/s²), and uncomfortable (0.8–1.6 m/s²).

Group of test sections

The difference in WBV between vehicles was calculated for a wide range of real road sections and test vehicles. Table 5 shows the results for a_VSEAT at the passenger seat surface by road category.

Table 5.

Overall vibration total value a_VSEAT on the passenger seat surface.

Road class	Test road	Length (km)	Number of vehicles	IRI (m/km)		v (m/km)		a_VSEAT (m/s²)
Road class	Test road	Length (km)	Number of vehicles	Mean	std	Mean	std	Mean	std	Median	Rel. range	RSD
2^nd	II/572, Most – Lehnice	18	9	4.24	1.29	73.8	4.2	0.61	0.06	0.59	27.4	9.3
	II/572, Lehnice – Most	20	9	4.47	1.31	71.1	3.3	0.65	0.07	0.65	37.2	10.2
	II/502, Púchovská – Modra	15.9	11	3.31	1.57	60.4	2	0.50	0.02	0.50	13.2	3.8
	II/502, Modra – Púchovská	14.8	11	3.33	1.42	58.4	4.1	0.49	0.02	0.49	17.7	4.7
	II/501, Lozorno – Jablonica	46.7	5	3.23	1.1	69.2	1.8	0.56	0.04	0.54	18.5	7.3
	II/590, Malacky – Borský Mikuláš	31.1	5	2.03	0.9	75.9	3.5	0.40	0.02	0.40	13.3	5.5
	II/500, Borský Mikuláš – Kuty	13.3	6	2.36	0.94	66.6	3.2	0.39	0.07	0.36	44.1	17.3
1^st	I/2, Bratislava – Velke Levare	35	8	2.85	1.25	70	2.8	0.50	0.06	0.50	35.7	11.4
	I/2, Velke Levare – Kuty	15.6	8	1.91	0.75	85.9	5.1	0.49	0.04	0.50	29.4	9.2
	I/2, Bratislava – Velke Levare	31.3	9	2.67	1.17	67.7	1.8	0.46	0.03	0.45	22.2	7.3
	I/2, Velke Levare – Kuty	15.3	6	2.04	0.82	81	5.1	0.46	0.04	0.46	23.4	7.7
	I/2, Patronka – Lozorno	16.3	5	2.66	1.24	60.7	2.5	0.41	0.03	0.41	16	6.3
	I/51, Jablonica – Holic	11	5	2.26	1.45	77.1	3.4	0.41	0.03	0.41	15.8	6.5
	I/2, Bratislava – Malacky	30	5	2.56	1.21	62.9	2.1	0.37	0.02	0.36	13.3	5.1
Motorway	D2, Kuty – Zahorska Bystrica	44.3	8	1.25	0.47	121.7	7.2	0.39	0.02	0.39	17.8	5.6
	D2, Kuty – Zahorska Bystrica	33.9	10	1.1	0.36	105.5	10.9	0.32	0.03	0.32	37.3	10.1
	D2, Kuty – Zahorska Bystrica	34.9	4	1.3	0.43	130.5	4.2	0.42	0.02	0.42	8.8	4
	D2, Kuty – Zahorska Bystrica	44.3	5	1.23	0.42	119	6.4	0.38	0.07	0.38	43.6	17.6

Table 5 shows that the mean vibration total value a_VSEAT at the passenger’s seat surface ranged from 0.39 to 0.65 m/s² for 2^nd class roads, from 0.35 to 0.50 m/s² for 1^st class roads, and from 0.32 to 0.42 m/s² for motorways. Relative range of a_VSEAT ranged from 13.2 to 44.1% for 2^nd class roads, from 13.3% to 35.7% for 1^st class roads, and from 8.8% to 43.6% for motorways. RSD (a_VSEAT) ranged from 3.8 to 17.3% for 2^nd class roads, from 5.1 to 11.4% for 1^st class roads, and from 4 to 17.6% for motorways.

Table 6 shows a_VSEAT at the driver seat surface. Mean vibration total value a_VSEAT at the driver’s seat surface ranged from 0.37 to 0.54 m/s² for 2^nd class roads, from 0.37 to 0.48 m/s² for 1^st class roads, and from 0.35 to 0.43 m/s² for motorways. Relative range of a_VSEAT ranged from 11.5 to 37.1% for 2^nd class roads, from 16.8 to 26.3% for 1^st class roads, and from 9 to 39.6% for motorways. RSD (a_VSEAT) ranged from 4.2 to 14% for 2^nd class roads, from 5.6 to 9.8% for 1^st class roads, and from 4.5 to 14.7% for motorways. The variability of vibration response was similar for driver and passenger seat measurements.

Table 6.

Overall vibration total value a_VSEAT on the driver seat surface.

Road class	Test road	Length (km)	Number of vehicles	IRI (m/km)		v (km/h)		a_VSEAT (m/s²)
Road class	Test road	Length (km)	Number of vehicles	Mean	std	Mean	std	Mean	std	Median	Rel. range	RSD
2^nd	II/502, Púchovská – Modra	15.9	11	3.31	1.57	60.4	2	0.52	0.03	0.51	16.7	5.1
	II/502, Modra – Púchovská	14.8	11	3.33	1.42	58.4	4.1	0.50	0.03	0.50	24.8	6.8
	II/501, Lozorno – Jablonica	46.7	5	3.23	1.1	69.2	1.8	0.54	0.05	0.53	26.7	9.8
	II/590, Malacky – Borský Mikuláš	31.1	5	2.03	0.9	75.9	3.5	0.38	0.02	0.39	11.5	4.2
	II/500, Borský Mikuláš – Kuty	13.3	6	2.36	0.94	66.6	3.2	0.37	0.05	0.36	37.1	14
1^st	I/2, Bratislava – Velke Levare	31.3	9	2.67	1.17	67.7	1.8	0.48	0.03	0.48	16.8	5.6
	I/2, Velke Levare – Kuty	15.3	6	2.04	0.82	81	5.1	0.46	0.04	0.45	22.8	8.7
	I/2, Patronka - Lozorno	16.3	5	2.66	1.24	60.7	2.5	0.42	0.04	0.42	26.3	9.8
	I/51, Jablonica – Holic	11	5	2.26	1.45	77.1	3.4	0.42	0.04	0.42	20.8	9
	I/2, Bratislava – Malacky	30	5	2.56	1.21	62.9	2.1	0.37	0.02	0.35	11.7	5.5
Motorway	D2, Kuty – Zahorska Bystrica	33.9	10	1.1	0.36	105.5	10.9	0.35	0.03	0.35	30.8	8.6
	D2, Kuty – Zahorska Bystrica	34.9	4	1.3	0.43	130.5	4.2	0.43	0.02	0.43	9	4.5
	D2, Kuty – Zahorska Bystrica	44.3	5	1.23	0.42	119	6.4	0.40	0.06	0.40	39.6	14.7

The relation of a_VSEAT [Equation (5)] on the IRI was evaluated for three categories of roads: motorways, 1^st class roads, and 2^nd class roads. Figure 3 shows the relation a_VSEAT = f(IRI) for the passenger seat surface and Figure 4 for the driver seat surface. Vertical lines in Figs. 4 and 5 at 0.8 m/s², and 1.25 m/s² present the lower value of uncomfortable comfort reaction (0.8 – 1.6 m/s²) and lower value of very uncomfortable comfort reaction according to the ISO 2631-1: 1997.²⁹

Figure 3.

Overall vibration total value a_VSEAT on the passenger seat surface: (a) 2^nd class roads, (b) 1^st class roads, (c) motorways, and (d) total sections.

Figure 4.

Overall vibration total value a_VSEAT on the driver seat surface: (a) 2nd class roads, (b) 1st class roads, (c) motorways, (d) total sections.

Figure 3(a) shows the wide range of 95% confidence interval for the passenger seat acceleration a_VSEAT that ranged approximately from 0.2 to 0.84 m/s² for IRI = 3 m/km for 2^nd class roads, from 0.2 to 0.82 m/s² for 1^st class roads (Figure 4(b)), and from 0.33 to 0.78 m/s² for motorways (Figure 3(c)).

Figure 4(a) shows the wide range of 95% confidence interval for the driver seat acceleration a_VSEAT that ranged for IRI = 3 m/km approximately from 0.22 to 0.78 m/s² for 2^nd class roads, from 0.2 to 0.83 m/s² for 1^st class roads (Figure 5(a)), and from 0.36 to 0.83 m/s² for motorways (Figure 4(c)).

Figure 5.

Comparison of vibration total value a_VSEAT (mean ± std) from published data with measurement on driver and passenger seat surface.

Table 7 shows the coefficients of the two-parameter regression function a_VSEAT = f(IRI) [Equation (5)] for measurements provided at the driver and passenger seats. Identified coefficients are similar, even if slightly different test sections were travelled, and test subjects (driver/passenger) were different.

Table 7.

Parameters of the Regression Function a_VSEAT = f(IRI).

Measuring point	Road category	N	b ₁	b ₂	RMSE	R	R ²
Passenger seat surface	2nd class	15,648	0.224	−0.764	0.1602	0.635	0.403
	1st class	13,768	0.201	−0.722	0.1542	0.585	0.343
	Motorways	11,977	0.179	−0.667	0.1136	0.500	0.250
	Total	39,659	0.187	−0.696	0.1482	0.653	0.427
Driver seat surface	2nd class	9692	0.202	−0.747	0.1387	0.636	0.405
	1st class	8817	0.198	−0.722	0.1606	0.567	0.322
	Motorways	8167	0.195	−0.652	0.1215	0.503	0.253
	Total	26,676	0.167	−0.682	0.1448	0.590	0.349

Table 8 shows the coefficients of the two-parameter regression function of the upper and lower 95% confidence intervals of the relationship a_VSEAT = f(IRI) [Equation (5)] for measurements provided at the driver and passenger seats. Identified coefficients were similar for both measuring points (driver/passenger).

Table 8.

Parameters of the regression function between the upper and lower bounds of the 95% confidence interval a_VSEAT = f(IRI).

Measuring point	Road category	N	Lower bound of 95% confidence interval		Upper bound of 95% confidence interval
Measuring point	Road category	N	b ₁	b ₂	b ₁	b ₂
Passenger seat surface	2^nd class	15,648	0.224	−1.078	0.224	−0.450
	1^st class	13,768	0.201	−1.024	0.201	−0.420
	Motorways	11,977	0.179	−0.890	0.179	−0.444
	Total	39,659	0.187	−0.896	0.187	−0.406
Driver seat surface	2^nd class	9692	0.202	−1.019	0.202	−0.475
	1^st class	8817	0.198	−1.037	0.198	−0.407
	Motorways	8167	0.195	−0.890	0.195	−0.413
	Total	26,676	0.167	−0.965	0.167	−0.398

The width of the 95% confidence interval of a_VSEAT was for passenger seat surface 0.63 m/s² (2^nd class roads), 0.60 m/s² (1^st class roads), 0.45 m/s² (motorways), and 0.49 m/s² for total sections. For the driver seat surface, it was 0.54 m/s² (2^nd class roads), 0.63 m/s² (1^st class roads), 0.48 m/s² (motorways), and 0.57 m/s² for total sections.

Discussion

The number of published results quantifying the a_VSEAT variability of different cars on the same test section with varying smoothness is limited. The vehicles differ in structural and mechanical properties, in total weight, and they are not able to follow the same wheel tracks due to real traffic conditions; vehicle speed may fluctuate when passing the same test section. Drivers and passengers also differ slightly in weight, which can significantly affect the frequency transmission of vibrations.

The observed variability in WBV at a fixed IRI level can have several reasons:

• different frequency response function (due to vehicle structural and mechanical properties, geometry, total weight, suspension, etc.) between the road-wheel contact and the measuring point at the seat surface;

• used wheel tracks may be different between test vehicles due to real traffic conditions;

• limitation of the IRI index; the substantially different road profiles in wavelength content may yield the same IRI,⁴⁹ etc.

The fitted regression relationship (equation (5)) represents an average trend across many vehicles and operating conditions and is not a predictor for a specific car or passenger.

The ISO 2631-1: 1997²⁹ comfort reaction bands (Table 2) present likely reactions to various magnitudes of overall vibration total values in public transport. The reactions at different magnitudes depend on passenger expectations regarding trip duration, the types of activities they expect to accomplish, and many other factors (acoustic noise, temperature, etc.). The comfort reaction bands serve as a reference framework for interpreting vibration magnitude and illustrating how variability spans multiple comfort categories.

The human body’s weight variability was intentionally limited, long-term health outcomes were not assessed, and the findings apply only to short-term vibration exposure in passenger cars under the tested conditions.

IRI is suitable for road screening and infrastructure assessment, but the vibration-based comfort evaluation requires direct WBV measurement or conservative use of upper-bound estimates. If IRI thresholds are discussed, they should be framed as probabilistic and uncertainty aware rather than as single fixed values.

The non-independence of data segments is a limitation. Many 100 m segments come from the same vehicle and trip. This may affect the interpretation of confidence bounds and variability. The dataset cannot be understood as fully independent observations. Each year, the group of test vehicles travelled the same set of test sections of different categories.

The average time gap between road roughness and vibration measurements was about 4 months, which may be considered a limitation. This can add noise to the IRI–WBV relationship and may partly explain variability. Changes in road roughness are most influenced by the winter months, but that was not the case with these measurements.

Vehicle related factors are further sources of variability. Tire pressure, suspension condition, seat stiffness, and vehicle mileage were not standardized. They may be substantial contributors to the observed spread.

Identified width (Table 8) of 95% confidence interval of a_VSEAT ranged from 0.45 to 0.65 m/s². These values are relatively high compared to the comfort level widths according to ISO 2631-1. The first four comfort level classes (Table 2) from “not uncomfortable” to “uncomfortable” in the ISO 2631-1 correspond to a range of 0 to 1.6 m/s².

Figure 5 compares published results of the overall vibration total value measured on the seat surface, a_VSEAT,^{19,20,22,24,26,28} with measurements from this study on the passenger seat surface (Table 5) and the driver seat surface (Table 6). Figure 5 shows that the measured vibration data are in approximate agreement with published measurements.^{19,20,22,24,26,28} Only a week correlation between a_VSEAT and vehicle speed was observed.

The range (mean ± standard deviation) of reported a_VSEAT data was similar to that presented in this study. Moschioni et al.²² measured a substantially higher value of a_VSEAT for vehicle speeds in the range 80–130 km/h on highways and motorways, a_VSEAT = 0.48 ± 0.15 m/s², in comparison with this study, a_VSEAT = 0.35 ± 0.03 m/s² (driver seat surface) and a_VSEAT = 0.32 ± 0.03 m/s² (passenger seat surface).

Conclusions

This paper evaluated the variability of whole-body vibration in public transport at the driver and passenger seat surfaces in a passenger car on roads of various categories. The novelty was in consideration of the road roughness index, IRI, and in the broad measurement range of vehicle speed and road roughness.

• The variability of whole-body vibration across the same test sections when travelling in different types of passenger vehicles was evaluated. Whole-body vibration varied substantially for the same IRI value.

• Overall vibration total value a_vSEAT 95% confidence intervals covers several ride comfort classes, from not uncomfortable to very uncomfortable, at the specific IRI value. This variability is caused by vehicle mechanical and structural properties, vehicle speed, used wheel tracks, human subject dynamic response, and limitations of the IRI approach.

• Measured vibration total values and calculated 95% confidence intervals showed that a single IRI value can correspond to vibration values spanning several comfort levels.

• The identified width of the 95% confidence interval of a_VSEAT ranged from 0.45 to 0.65 m/s². A wider confidence interval was observed for 2^nd and 1^st class roads than for motorways.

• Coefficients of the two-parameter regression function between the overall vibration total value and IRI were estimated as a function of road category and IRI. The relation between a_V and IRI followed the power function with an exponent of ∼0.2.

• The regression function a_vSEAT = f(IRI) may be helpful in detecting the IRI threshold from a ride comfort perspective.

• The vibration measured at higher vehicle speeds above 100 km/h on motorways showed lower or similar values of a_VSEAT in comparison with the vibration measured for vehicle speeds <100 km/h on 1^st and 2^nd class roads; and

• The marked variability in the WBV for the specific IRI indicates the need for an alternative assessment of road roughness that better reflects ride comfort.

Footnotes

Author contributions

Conceptualization, PM; methodology, PM; software, PM; validation, PM; formal analysis, PM; investigation, PM; resources, PM; data curation, PM; writing—original draft preparation, PM; writing—review and editing, PM; visualization, PM; supervision, PM; project administration, PM; funding acquisition, PM. Author has read and agreed to the published version of the manuscript.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was supported by VEGA Scientific Grant Agency of the Ministry of Education, Science, Research and Sport of the Slovak Republic and the Slovak Academy of Sciences (Grant No 2/0151/25).

ORCID iD

Peter Múčka

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