An experimental comparison of mathematical heavy-duty city bus models to evaluate passenger ride comfort induced by road roughness

Figures & data

Figure 1. Quarter-bus model (3-DOF)

Figure 2. Half-bus model (6-DOF)

Figure 3. Full-bus model (9-DOF)

Table 1. Bus model parameters human & seat

Parameter	Acronym	Value [Unit]	Parameter	Acronym	Value [Unit]
Human mass	mH1/mH2	70 [kg]	Equivalent seat stiffness	kH1/kH2	10,000 [N/m]
			Equivalent seat damping	dH1/dH2	330 [Ns/m]
Distance COM (sprung mass) to seat 1 (x-direction)	aHx1	3.71 [m]	Distance COM (sprung mass) to seat 2 (x-direction)	aHx2	2.09 [m]
Distance COM (sprung mass) to seat 1 (y-direction)	bHy1	0.64 [m]	Distance COM (sprung mass) to seat 2 (y-direction)	bHy2	0.60 [m]

Table 2. Bus model parameters: sprung mass

Parameter	Acronym	Value [Unit]	Parameter	Acronym	Value [Unit]
Permitted gross weight	mPGW	19,000 [kg]	Kerb weight	mKW	10,770 [kg]
Moment of Inertia (y-axis)	IBSy	150,000 [kg m^2]	Moment of Inertia (x-axis)	IBSx	13,000 [kg m^2]
Vehicle width	bveh	2.5 [m]	Wheelbase	lWB	5.8 [m]
Spring coefficient front suspension (max./min. load)	kS1	332,409 [N/m] 189,418 [N/m]	Equivalent spring coefficient rear suspension (max./min. load)	kS2	664,818 [N/m] 378,836 [N/m]
Damping coefficients front suspension (max./min. load)	dS1	50,220 [Ns/m] 29,674 [Ns/m]	Equivalent damping coefficient rear suspension (max./min. load)	dS2	71,023 [Ns/m] 41,965 [Ns/m]
Distance front axle to COM (sprung mass) (x-direction)	aSx1	3.71 [m]	Distance rear axle to COM (sprung mass) (x-direction)	aSx2	2.09 [m]
Distance front suspension to COM (sprung mass)	bSy1	0.64 [m]	Distance rear suspension to COM (sprung mass)	bSy2	0.60 [m]

Table 3. Bus model parameters suspension & unsprung mass

Parameter	Acronym	Value [Unit]	Parameter	Acronym	Value [Unit]
Unsprung mass front	mU1	662 [kg]	Unsprung mass rear	mU2	1333 [kg]
Tyre stiffness front axle	kU1	1,000,000 [N/m]	Equivalent tyre stiffness rear axle	kU2	2,000,000 [N/m]
Tyre damping front axle	dU1	150 [Ns/m]	Equivalent tyre damping rear axle	dU2	300 [Ns/m]
Distance front tyre to COM (unsprung mass)	bU1	1.39 [m]	Distance rear tyre to COM (unsprung mass)	bU2	1.02 [m]
Moment of Inertia front axle (x-axis)	IBUx1	350 [kg m^2]	Moment of Inertia rear axle (x-axis)	IBUx2	620 [kg m^2]
Tyre contact length	lcontact	0.3045 [m]

Figure 4. The flowchart of the experimental set-up

Figure 5. Field measurement set-up a) selected road segment; b) portable accelerometer

Figure 6. IRI value of the Bus lane 45 for every 100 m with four sections (I, II, III, IV) for further investigation (a) left-wheel track; (b) right-wheel track

Table 4. Levels of comfort corresponding to root-mean-square acceleration in ISO 2631–1

Root-mean-square frequency-weighted vertical acceleration awz (m/s^2)	Levels of comfort
less than 0.315	not uncomfortable
0.315 to 0.63	a little uncomfortable
0.5 to 1.0	fairly uncomfortable
0.8 to 1.6	uncomfortable
1.25 to 2.5	very uncomfortable
greater than 2.0	extremely uncomfortable

Figure 7. The frequency-weighted a_{wz_simulation}(t) and a_{wz_measurement}(t) at different sections for the right-wheel-track only

Figure 8. A_{wz_simulation}/a_{wz_measurement} ratios at different sections and the average ratios (standard deviation) (a) using both wheel tracks; (b) using only the right-wheel track where the field measurement was taken

Figure 9. The difference in response from transfer functions of IRI-QCS and QBM as temporal frequency (Hz) and spatial frequency (cycle/m)

Table 5. Comparison of output between different vehicle type modelling, in which simulated results from full-vehicle model is equivalent to the field-measured data

Source	Half- vs. full-vehicle model	Quarter- vs. full-vehicle model	Quarter- vs. half-vehicle model	Wheel-track for quarter- and half-vehicle models	Vehicle type
Ride comfort: awz values [25]	52% error, or FCS = 66% HCS	105% error, or FCS = 49% QCS		one track, Belgian paving road	Car
Roughness index: IRI and HRI [32]			HRI ≈ 80% IRImean (or r = 25%)	both tracks, HRI derived from IRI	Car
Roughness index: IRI, HRI, FRI [37]	FRI ≈ 76% HRI	FRI ≈ 69% IRImean		both tracks, generated road profiles, HRI, FRI derived from IRI	Car
Ride comfort (recent study)	FBM ≈ 95% HBM	FBM ≈ 85% QBM	HBM ≈ 92% QBM	one track, field-measured profiles	Bus
	FBM ≈ 83% HBM	FBM ≈ 75% QBM	HBM ≈ 89% QBM	both track, field-measured profiles

Note: QCS, HCS, FCS: quarter-car, half-car and full-car simulation; IRI, HRI, FRI: International roughness index, half- and full roughness index. QBM, HBM, FBM: quarter-bus, half-bus and full-bus model.

H.A. Hamersma, A comparison of quarter, half and full vehicle model with experimental ride comfort data. In: Proceedings of the ASME 2015 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference. ASME, Boston, Massachusetts, USA, 1–7, 2017.

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