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Advanced research initiatives in the application of automation, robotics and intelligence to solve problems associated with machine-machine, machine-humans, machine-layouts and machine-inanimate objects interactions in surface mining environments to eliminate fatalities.
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Dump truck tire stress simulation for
extended service life
S. Frimpong* and G. Galecki
Robert Quenon Endowed Chair and professor and
associate professor, respectively, Missouri University of Science & Technology, Rolla, MO
*Corresponding author e-mail: frimpong@mst.edu
E-mail: ggalecki@mst.edu
Y. Li
Structural engineer, Bucyrus International, Milwaukee, WI; e-mail: liyinglzh@yahoo.com
R. Suglo
Associate professor, University of Mines and Technology, Ghana
Abstract
Dump truck tires are often used in long-haul roads in rugged terrain, with high rolling and grade re-
sistances. These conditions increase the ton-kilometer-per-hour (tkm/hr) or short-ton-mile-per-hour
(stmph)rating of tires, leading to tread wear, cuts and complete failures. The load-bearing capacities
of these tires are sometimes exceeded, with truck overloading, overstressing, heating and subsequent
failures. In addition, truck tire demand far exceeds the current supply capacity, with long lead ordering
time. This condition has caused severe tire shortage, and the problem is expected to be sustained in the
long-term. Industry has taken extensive practical measures to prolong tire service life with significant
results. However, this problem can be solved through fundamental and applied research initiatives.
This paper pioneers a research effort in tire service life using multibody physics, fatigue failure modes
and soil failure dynamics to develop tire-road contact force dynamics. A virtual prototype simulator of
the tire-road contact, using the CAT 775E (with standard tire 24.00R35) was developed and simulated
within the MSC.ADAMS/NASTRAN environments. The results show the areas of the loaded tires with
maximum Von Mises, principal and shear stresses, which could result in fatigue failure, tire wear and tear
and blowouts. The maximum Von Mises stresses on the six truck tires are between 35 and 58 MPa. The
maximum shear stresses are also between 19 and 33 MPa. These stresses will cause early tire failures given
an average operating schedule of between 20 and 24 hours per day. The isolated areas with maximum
stresses will be subjected to further studies to reduce stress intensity while preserving tire performance.
Introduction
Off-highway dump trucks are widely used in surface mining
operations. Based on industry demand, Caterpillar, Komatsu,
Hitachi and other manufacturers have developed large dump
trucks, with payloads up to 360 t (400 st). These large trucks
face challenges in interacting with haul road environments
during operation. The surge in demand for energy, miner-
als and construction materials has created a corresponding
strong demand for truck tires. Currently, truck tire demand
far exceeds the supply capacity, with long lead ordering time.
This condition has caused severe tire shortages in the industry,
resulting in increased tire costs. Analysis of the demand-supply
imbalance shows that this shortage is expected to be sustained
in the long-term, thus creating the need for tire protection to
extend service life.
Truck tire protection requires an environment that prevents
tire overheating and subsequent reversal of the vulcanization
process, wear and tear, and complete tire failure. The ton-kilo-
meter-per-hour (tkm/hr), or short-ton-mile-per-hour (stmph),
performance of tires must be maintained under the critical rating
(Caterpillar, 2010) to ensure long-term economic performance.
Performance above the critical tire tkm/hr (stmph) rating results
in overheating, carcass separation (Fig. 1a), tread wear (Fig.
1b) and blowouts (Fig. 1c). The industry has taken extensive
practical measures to prolong tire service life with signicant
results. However, the long-term solution of this problem will be
achieved only through advanced research initiatives. Research
must focus on tire fatigue life and the bearing capacity and
wearing surface characteristics of haul roads.
Stresses must be minimized to maximize a tire’s service
life. Previous research has focused on estimating friction
coefcients, pressure-sinkage relationships, tire-road contact
Paper number TP-11-028. Original manuscript submitted May 2011. Revised manuscript accepted for publication February
2012. Discussion of this peer-reviewed and approved paper is invited and must be submitted to SME Publications Dept.
prior to Sept. 30, 2013. Copyright 2013, Society for Mining, Metallurgy, and Exploration, Inc.
Key words: Opencast mining, Modeling and simulation, Slurry, Continuous mining
2012 Transactions of the Society for Mining, Metallurgy, and Exploration, Vol. 332, pp. 422-429.
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forces and on attenuating tire-soil interactions effects. Bekker
(1969) and Wong (1984) modeled a static vehicle sinkage on
a loading surface with uniform normal pressure and without
horizontal load. Soil terrains were subjected to truck loads in
vertical and/or horizontal planes, making it difcult to predict
the exact soil load-deformation relationship. Ferretti et al.
(1999) modeled and simulated a dynamic model of a wheeled
agricultural vehicle on a soil terrain to overcome the limitations
of static models. Fervers (2004) and Kwasniewski et al. (2006)
have used nite element methods (FEM) to estimate tire-road
interaction. However, the current FEM models neglect the ef-
fects of dynamic contact force on tire stress.
This study addresses tire performance under dynamic impact
loading conditions. The truck is a multi degrees-of–freedom
(DOF), nonlinear multibody dynamic system. Thus, the theory
of multibody dynamics is used to create its kinematics and
dynamic models (Hegazy et al., 1999). Six DOFs, starting
from the basic Newton-Euler rigid body model, account for
vehicle dynamics. Four DOFs govern the revolute joints con-
necting the truck to the tires. Four driving torques are applied
to the tires through four revolute joints based on the propul-
sion control by Rubinstein and Hitron (2004). The road has a
zero percent grade, and is constructed with two materials (a
subgrade and a base) dened by their stiffness and damping
characteristics. The road material was created to be continu-
ous elastic-supported soil units connected with springs and
dashpots with two DOFs (Das, 1983).
The road formation was subjected to a contact force from
the truck tires. This contact force is modeled as a function of
the weight distribution of the loaded truck and the structural
conditions of road bed and surface materials. An integrated
truck tire-road model is established to dene tire stress and
road deection behavior. The FE tire model yields the stress
equations by applying the component mode synthesis to dy-
namic equilibrium equations. The MSC.ADAMS (Wilson and
Sadler, 1991; MSC, 2010a) package is used to virtually design
and analyze this problem. The virtual prototype model is used
to examine the operating system by simulating its deformation,
deection and stress-strain relationships. The principal and
Von Mises stresses are used to examine the tire performance
under dynamic loading conditions. The tire shear stresses are
also used to examine the shearing due to tire-road contact and
the impact on tread wear and failure.
Tire-road interactions under dynamic loading
Figures 2a and 2b show the respective dump truck machinery
and the tire-road contact force. The truck consists of the main
body, two front (single) and two rear (dual) tires (Fig. 2a).
Haul road materials must protect the integrity of the subgrade
and the truck tires (Fig. 2b).
The road materials also provide tire traction and adequate
bearing capacity to sustain the weight of the largest loaded
truck. Depending on the incident load, travel speed, the one-
way haul distance and the total travel resistance, dump truck
tires may deform within its elastic boundary or permanently.
Subgrade protection requires vertical layers of sub-base, base
and wearing surface materials on top of the subgrade, depending
on the intensity and distribution of the incident load (Frimpong,
2011; Kaufman and Ault, 1977).
Mechanics of tire-road interactions
The mathematical model of the truck-road interaction
Figure 1 — Tire fatigue failure: (a) carcass separation, (b) tread wear, (c) tire blowout.
Figure 2 — Dump truck machinery: (a) truck-tire geometry, (b) tire-road interactions.
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consists of three submodels, which include the tire-haul road
contact, tire FE and load-deformation models. The three models
are based on the following two assumptions: (i) the tire contact
surface is a at homogeneous road surface and (ii) the tire is
modeled as a torus-shaped wheel, as dened by Chakraborty
et al. (2005). The front:rear tire load distribution of the loaded
truck is 33%:67%. Assumption (i) implies that this load dis-
tribution is uniformly distributed on the set of front and rear
tires (Caterpillar, 2010).
Tire-road contact model. Figure 3 shows the contact force
components, which include the normal reaction Fn, lateral resis-
tance Ft, longitudinal reaction Fl and the self-aligning moment
MZ (Frimpong and Li, 2007). The normal reaction acts in the
direction normal to the tire-road contact plane. This force is
a function of road deection and its rate of change, which are
based on road stiffness and damping characteristics (Fig. 4).
The lateral resistance is caused by the tire sliding laterally on
the road with noticeable sinkage. This force is related to the
normal force and the coefcient of lateral resistance. The trac-
tion force and motion resistance constitute the tire longitudinal
reaction. The traction force is the product of the coefcient
of friction and the normal reaction. The tire realigning torque
acts around the tire vertical directional vector (Blundell, 2000).
This torque stabilizes the tire in the vertical plane to prevent
sliding. The governing equations are provided in Frimpong
and Li (2007) and Li and Frimpong (2008).
Haul road deformation model. Figure 4 shows the de-
formation of a haul road unit resulting from dynamic impact
loading by a truck. The road is subjected to a contact force from
the truck tire (Fig. 4a). The model is created as a continuous
system with a nite number of units connected by spherical
joints, using a mass-spring-dashpot system with two DOFs (Fig.
4b). The road undergoes translational (bounce) and rotational
(pitch) motions. The mass is equal to the mass of a road unit
and the spring stiffness and dashpot represent the respective
elastic modulus and the damping characteristic of the road
material. The governing equations are provided in Frimpong
and Li (2007) and Li and Frimpong (2008).
Tire stress prole modeling. FEM is used to model the tire
stress as a function of the generalized accelerations, velocities,
displacements, mass, damping and stiffness, and the load vec-
tor under dynamic equilibrium. The rigid-exible multibody
components result in large matrices, which grow by orders of
magnitudes with increasing exible components.
To reduce the coordinates and matrix sizes, all the exible
bodies are partitioned into rigid-rigid, exible-exible and
rigid-exible components for the mass, stiffness, damping
and kinematic matrices. The solution is further simplied by
applying the component mode synthesis using the eigenvec-
tor and modal coordinate matrices. The resulting tire stress
model is a function of full orthonormalized modal stress and
displacement matrices (Frimpong and Li, 2007). The FE mesh
is generated using parabolic tetrahedral elements with element
size of 200 mm, minimum size of 40 mm, minimum angle of
10 degrees, span angle of 20 degrees, growth rate of 2 and a
modal number of 6 (Frimpong and Li, 2007).
The tire power train control model
In order to understand the tire-road contact force dynam-
ics and the associated stresses, a power train control model is
developed to drive the loaded truck (Fig. 5). The engine torque
is applied directly to the two front tires and two sets of dual rear
tires. The required tire torque vectors τid (i =1-4) are obtained
for a given tire speed ωi (i = 1-4). Four independent single-
input-single-output closed loop control systems are designed
for controlling the tires (Rubinstein and Hitron, 2004). Figure
5 shows the control loop for each tire, which denes the truck
velocity. The control system uses a feedback loop to compute
Figure 3 — Tire-road contact force.
Figure 4 — a) Mass-spring-dashpot road model; b) road response to contact force; x – linear displacement of the center
gravity of the unit; l1 – the distance between contact force and lift side of the unit; l2the distance between contact force
and right side of the unit; and θ – angular displacement of the unit.
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system error vie by nding the difference between the desired
velocity vid and the actual velocity via.
The control system then computes the required torque τid for
controlling the tires as a function of system error. The required
torque signal goes through the characteristic limitation box C to
check the signal. If it is above the characteristic curve, its value
is changed to the maximum available. The output characteristic
limitation is the actual torque τia applied on the tire. The actual
truck velocity via and tire rotational speed ωi are the outputs
from the ADAMS processor. The rotational speed is used for
proper gear selection and denition of the actual torque limit.
The velocity returns to the beginning of the control loop. The
truck model accepts a vector of the tire torque for tire control
and output results (MSC, 2010a).
Rigid-flexible tire simulator environment
The CAT 775E truck, with a GMW of 172 t and a standard
tire of 24.00R35 (E-4), and an oil sands road were used to simu-
late the dynamic tire-road interactions. The loaded maximum
truck speed is 65.8 km/h. The load distributions are 33.3%
and 66.7% on respective front and rear axles. The tire ination
pressure is 655 KPa (Caterpillar, 2010). A homogeneous, soft
and leveled oil sands road is laid on a base of natural soil. The
road formation is visco-elastic with high viscosity (Frimpong
and Li, 2007; Li and Frimpong, 2008). The physical properties
of oil sands and tire-road coefcients are presented in Table
1 (Dusseault, 1977; Frimpong and Li, 2005; Wong, 1984).
The case study focuses on road deformation and dynamic
stress distribution of the tires. The rigid multi-body dynamic
analysis code of MSC.ADAMS is used to solve the contact
forces, the FE tire stress and the power train torque problems
(MSC, 2010a). The tire-road contact is dened as the solid-solid
contact in ADAMS interface. ADAMS uses the effective tire
penetration in the spring-dashpot model to calculate the tire
force on the road. External forces acting between the two bod-
ies serve to maintain continuous contact. The spring stiffness
and damping models are used to model
the respective elasticity of the contact
surfaces and the energy dissipation. The
time histories of the loads and modal
coordinates are accurately predicted
by simulating the dump truck system,
using flexible multibody dynamic
analysis code of ADAMS. The exible
component stresses are calculated at
each time step using the FEM code in
NASTRAN (MSC, 2010b).
CAT 775E rigid-exible prototype
simulator. Figure 6 shows the CAT
775E Simulator in the ADAMS envi-
ronment for simulating the dynamic
behavior or the tire-road contact.
Figures 6a and 6b show simulated
animation outputs of the dump truck
motions through 35 m displacement
within a simulation time of 2 sec corre-
sponding to 50 time steps. The vertical
distance between the truck and oil sands
Figure 5 — Truck tire power train control loop.
Table 1 — Oil sands formation and tire properties at 25° C.
Oil sands elastic modulus ~140 MPa Tire cornering stiffness constant ~30 KN/deg
Oil sands damping constant ~20 KNs/m Tire-road static friction coefficient ~0.74
Oil sands density 1,600 kg/m3Tire-road dynamic friction coefficient ~0.54
Poisson’s ratio 0.3 Tire-road motion resistant coefficient 0.1
Tire normal stiffness coefficient ~1,000 KN/m Tire-road slip angle
Tire damping constant ~0.47 KNs/m GMW distribution (front:rear) 33%:67%
Figure 6 — a) Simulated animation of truck motion; b) truck tire positional stress
profiles; c) haul road deformation contour; d) tire deflection effect on contact force.
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surface continuously changes during the simulation run based
on the actual response of the road to dynamic impact loading.
This dynamic deformation causes simultaneous displacements
of the road surface in the bounce, roll and pitch directions. The
deformation contours in Fig. 6c show
uneven terrain displacements. The
contact force and the corresponding
tire stress depend on the tire deec-
tion, as shown in Fig. 6d.
CAT 775E simulator verication
and validation. The model is veried
by comparing the road deformation re-
sults from a simplied FEM technique
to the ADAMS Solver (C++) simula-
tion results. The results showed that
the maximum road deformations from
the two techniques are similar, with
between 2% and 6% error variations.
This small error could be attributed
to the static FEM versus the dynamic
ADAMS simulation results. The tire
FE models are validated by examining
Von Mises stress distribution within
the tire fabric and the contact forces
applied to the six tires at time steps 1
(Fig. 7a), 25 (Fig. 7b) and 50 (Fig. 7c).
The contour continuity from steps
1 to 50 reveals homogeneous stress
distributions from the contact force application. The stresses
vary for each time step, with the high stress elds occurring at
the tire-road contact area. The results show that the tire stress
distributions in the FE models are in agreement with the results
of Liukkula (2006) in Fig. 7d.
Figure 7 — Tire Von Mises stress and contact force distributions: (a) time step 1; (b)
time step 25; (c) time step 50; (d) high-stress zones (Liukkula, 2006).
Figure 8 Tire contact force: (a) front normal force; (b) rear normal force, (c) front longitudinal force and (d) rear
longitudinal force.
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Tire stress simulator experimentation and results
analysis
Thorough experimentation, analysis and discussions of
the simulation results have been carried out to investigate the
behavior of the road deections and tire stress deformation.
Tire-road contact forces. Figure 6a illustrates the super-
imposed animation of tire contact forces (red arrow) during
a simulation time of 2 sec. The tire force changes with time
during operation. The forces applied to the two front tires (or
two rear dual tires) are assumed to be equal, because the two
front tires or two rear dual tires are symmetric with respect to
the x-axis (Fig. 2a). The lateral force and aligning torque are
equal to zero in this case study, because the slip angle is 0°.
Figures 8a-d show the respective front normal, rear normal,
front longitudinal and rear longitudinal forces on the truck tires.
The results show that the forces applied to the front and
rear tires uctuate within the simulation period. The uctua-
tion ranges are: (i) front normal tire force = 3 x 105 and 3.4
x 105 N; (ii) rear normal tire force (3 x 105 and 3.8 x 105 N);
(iii) front longitudinal force (0 to 1.8 x 105 N); and (iv) rear
longitudinal tire force (0 to 1.9 x 105 N). The force on the
rear tire is greater than on the front tire, which agrees with the
observation by Siegrist and McAree (2006).
Haul road dynamic deformation. From the truck displace-
ment prole (Fig. 6a), the road surface deforms, in the bounce,
roll and pitch directions. Figure 9a shows the road deformations
corresponding to positions 1-4 (Fig. 6b) over the duration. The
maximum deformations at these positions are given as 0.039 m
(time = 0.45 sec), 0.030 m (time = 0.74 sec), 0.042 m (time =
1.22 sec) and 0.043 m (time = 1.50 sec), respectively. Figure
8b shows the load-maximum deformation relationship with
varying elastic modulus E (60, 120, 180 and 240 MPa), and
tire load from 0 to 57.6 t. For a given modulus, the maximum
deformation value increases nonlinearly with increasing load
from 0 to 57.6 t. For a given load, the deformation decreases
with increasing modulus. The maximum deformation values
of 0.27 m (E = 60 MPa), 0.23 m (E = 120 MPa), 0.18 m (E =
180 MPa) and 0.15 m (E = 240 MPa) have been obtained at the
load of 57.6 t and a minimum value of 0 m at the load of 0 t.
Tire stress simulation and deformation modeling. Tire
stress changes because of variations in the tire-road contact
force during operation. The elastic tire body, subjected to 3D
loading, develops stresses with different magnitudes and in
different directions. The tire will fail if the stress on the system
exceeds the yield stress. There are three “principal stresses”
that can be calculated at any point, in the x, y and z directions
within the tire body. The Von Mises criterion combines these
three stresses into an equivalent stress, which is then compared
to the yield stress of the tire. Thus, the Von Mises stress may
Figure 9 — a) Maximum deformations in positions 1-4; b) elasticity-load-deformation profiles.
Figure 10 — Tire Von Mises stress distributions (display range: 0-2.5 Mpa): (a) shaded Von Mises stress profiles;
(b) wireframe view of Von Mises stresses.
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cause failure even if each of the principal stresses is below
the yield stress of the tire. Shearing also occurs within the tire
body and between the tire surface and the road surface. Shear
stresses also contribute to wear and tear and mechanical failure
of the tire body. Thus, the tire performance is monitored by
measuring the principal stresses, the Von Mises stress and the
shear stress distribution during operation.
Figures 10a-b display their corresponding Von Mises stress
distributions with the shaded and wireframe views at time 1s,
respectively. The maximum Von Mises stresses of 49, 35, 38,
38, 58 and 34 MPa occur at the contact area of tires 1-6, while
the minimum value at 0 MPa at top outside of all tires (appears
in blue). Figures 11a-b indicate the tire maximum principal
stress distributions with the shaded and wireframe views at
time 1 sec, respectively.
The maximum principal stresses of 24, 21, 16, 19, 23 and
16 MPa occur at the contact areas of the tires 1-6 (appears in
red) while the minimum value at -0.6 MPa at all tires (appears
in green). Figures 12a-b display the tire maximum shear stress
distributions with the shaded and wireframe views at time 2
sec. The maximum shear stresses of 28, 19, 21, 22, 33 and
19 MPa occur at the tire contact areas 1-6 (in red), while the
minimum value of 0 MPa occirs at the top outside of all tires
(in blue). It is important to nd these stresses for investigating
the tire fatigue life.
Conclusions
A tire-road contact force dynamic model is developed
using the theories of multibody physics, fatigue failure and
soil failure dynamics to examine truck tire performance in a
mining environment. A virtual simulator of the tire-road con-
tact, using the CAT 775E (with standard tire 24.00R35) was
developed and simulated within MSC.ADAMS/NASTRAN.
The results show that:
1. The forces applied to the front and rear tires uctuate
within the simulation period. The uctuation ranges
are: (i) front normal tire force = 3 x 105 and 3.4 x 105
N; (ii) rear normal tire force (3 x 105 and 3.8 x 105 N);
(iii) front longitudinal force (0 to 1.8 x 105 N); and (iv)
rear longitudinal tire force (0 to 1.9 x 105 N).
2. The maximum deformations are 0.039 m (time = 0.45
sec), 0.030 m (time = 0.74 sec), 0.042 m (time = 1.22
sec) and 0.043 m (time = 1.50 sec), respectively.
3. The maximum Von Mises stresses range between 34 and
58 MPa and the minimum value at 0 MPa. (iv) The
maximum principal stresses range between 16 and 24
MPa and the minimum value is 0.6MPa.
4. The maximum shear stresses range between 19 and 33
MPa and the minimum value is 0 MPa.
These stresses will cause early tire failures given an aver-
age operating schedule of between 20 and 24 hours per day.
The isolated areas with maximum stresses will be subjected
to further studies to reduce stress intensity while preserving
tire performance.
Figure 11 — Tire max principle stress distributions (display range: 0-2.5 MPa): a) shaded maximum principle
stress profiles; b) wireframe view of maximum principal stresses.
Figure 12 — Tire max shear stress distributions (display range: 0-2.5 MPa) (a) shaded maximum shear stress profiles; b)
wireframe view of maximum shear stresses.
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... The work did not evaluate the impact of truck over-loading on truck dynamic forces imposed on haul roads. MBD in MSC.ADAMS and finite element modelling (FEM) in NASTRAN, an FEM software, have also been used to study truck-road interaction dynamics, tire stress profiling and road dynamic deformation [19,20]. The work focused on the truck-road interaction forces and road response of the CAT 775E rear dump truck. ...
... These coefficients are the maximum and steady-state DFC at rated payload. For varying payload, Equations (19) and (20) can be used for estimating the truck tire dynamic forces. Equations (19) and (20) are general forms of Equations (17) and (18), and allow for the evaluation of payload variations. ...
... For varying payload, Equations (19) and (20) can be used for estimating the truck tire dynamic forces. Equations (19) and (20) are general forms of Equations (17) and (18), and allow for the evaluation of payload variations. The dynamic forces from Equations (17)(18)(19)(20) can then be used to estimate the dynamic tire loads in metric tons using Equation (21). ...
Article
Haul roads are designed to bear dynamic truckloads generated during haulage. Current road design methods consider static truckloads, which are lower than dynamic loads. They are also unreliable for designing roads for ultra-large trucks. This paper introduces a methodology for designing roads using dynamic loads for any haul truck. A 3D rigid multi-body dynamic virtual model of CAT 797F was built, verified and validated in MSC.ADAMS to model truck tire dynamic forces generated during haulage. Maximum dynamic forces were 2.86 times static force at rated payload. Industrial useable models that capture truck dynamics are proposed to improve road structural design.
... They studied 2-D dynamic contact between track and sprocket during the propel motion and presented crawler shoe -sprocket contact forces and reaction forces acting on the pin that connect adjacent crawler shoes. Frimpong et al. [10] developed tire-road contact force model to calculate normal reaction, lateral resistance, longitudinal reaction and self-aligning torque acting on dump truck tire. They calculated normal force based on road stiffness and damping characteristics, lateral resistance using normal force and coefficient of lateral resistance, and longitudinal reaction based on normal force and coefficient of friction. ...
... Frimpong et al. [11] developed virtual prototype simulators in MSC ADAMS to examine the GAP (ground articulating pipeline) torque requirements and GAP carriage-oil sand terrain interactions. They used a contact force model similar to that in [10] to account for GAP track-oil sands interactions. They also used flexible oil sand model to illustrate the dynamic deformation of oil sand terrain under GAP carriage motion. ...
... The crawler shoe model is generated in Solidworks based on the actual crawler shoe model for P&H 4100C Boss shovel [14]. Similarly, the oil sand terrain is made up of spring-damper-oil sand units connected to four adjacent oil sands units by spherical joints [10]. The stiffness (k) and damping (c) values of oil sand terrain are listed in Table 2. ...
Article
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Cable shovels are used in surface mining operations to achieve economic bulk production capacities. The service life of the rawlers and their shoes define shovel reliability, maintainability, availability and efficiency. The crawler track-terrain nteraction generates high time-fluctuating contact forces that result in stress buildup, crack and fatigue failure of wler shoes. In addition, the link pins that connect two crawler shoes can exert large fluctuating pin loads on shoe lugding to shoe breakage. This paper addresses fundamental research into contact forces acting on crawler shoes, joint forces generated in the link pin and total deformation of the formation during shovel propel. During propel, the crawler track is controlled by two drive constraints that cause the crawler to follow straight or turning motions. A virtual prototype simulator of the crawler-terrain interaction dynamics is developed and simulated within the MSC ADAMS environment. The simulation results show that the average penetration depth for different crawler shoes is within the range of 5.9 and 6.7 cm for both types of driving constraints. During translation, the maximum magnitude of contact forces along vertical, longitudinal and lateral directions have respective values of 5.9 × 105 N, 5.5 × 105 N and 1.7 × 105 N. During turning, the crawler track experiences varying bouncing and rolling motions causing maximum magnitude of vertical and lateral contact forces on the crawler shoes to increase 1.15 and 1.42 times the maximum translation values. The total deformation of oil sand terrain for the two motions fluctuates between -0.24 and 0.26 cm and between -1.03 and 1.33 cm, respectively. This study provides solid foundation for further studies on dynamic stress and fatigue failure analysis of crawler shoes during shovel propel and loading operations.
... This simplification of haul roads as smooth flat terrains eliminates an important source of truck-haul road dynamics. Frimpong et al [20] and Li and Frimpong [21] [20,21] presented mathematical and virtual prototype models for mine haul road response to truck dynamic loads, but assumed the road surface to be smooth. ...
... This simplification of haul roads as smooth flat terrains eliminates an important source of truck-haul road dynamics. Frimpong et al [20] and Li and Frimpong [21] [20,21] presented mathematical and virtual prototype models for mine haul road response to truck dynamic loads, but assumed the road surface to be smooth. ...
Article
Trucks experience excitations during haulage due to road roughness, generating dynamic loads. Current mine haul road design techniques assume static tire loads, ignoring dynamic forces. This paper presents mathematical models for estimating tire dynamic forces on haul roads. Models were solved in Simulink® and RStudio® to generate random road profile (class D) according to ISO 8608, and compute dynamic forces for 59/80R63 tire. Results show that road roughness significantly affects impact forces on roads, with tire dynamic forces (1638.67 kN) ~ 1.6 times static forces (~1025 kN) at rated tire payloads. The method presented gives realistic estimates of tire impact forces, which serves as useful input for haul road design.
... This force is estimated using in-built contact algorithms in MSC ADAMS and the parameters in Table 3 [8]. Table 3. Contact parameters used in the study [8,10,14]. ...
... Contact parameters used in the study[8,10,14]. ...
Article
Full-text available
Electric shovels are used in surface mining operations to achieve economic production capacities. The capital investments and operating costs associated with the shovels deployed in the Athabasca oil sands formation are high due to the abrasive conditions. The shovel crawler shoes interact with sharp and abrasive sand particles, and, thus, are subjected to high transient dynamic stresses. These high stresses cause wear and tear leading to crack initiation, propagation and premature fatigue failure. The objective of this paper is to develop a model to characterize the crawler stresses and deformation for the P&H 4100C BOSS during propel and loading using rigid-flexible multi-body dynamic theory. A 3-D virtual prototype model of the rigid-flexible crawler track assembly and its interactions with oil sand formation is simulated to capture the model dynamics within multibody dynamics software MSC ADAMS. The modal and stress shapes and modal loads due to machine weight for each flexible crawler shoes are generated from finite element analysis (FEA). The modal coordinates from the simulation are combined with mode and stress shapes using modal superposition method to calculate real-time stresses and deformation of flexible crawler shoes. The results show a maximum von Mises stress value of 170 MPa occurring in the driving crawler shoe during the propel motion. This study provides a foundation for the subsequent fatigue life analysis of crawler shoes for extending crawler service life.
... The dominating mining method in Ukraine is open-pit one, which involves 92 % of the total iron ore mining, and the major industrial transport, which used for 90-95 % of mined rock hauling, are BelAZ open pit trucks with electrical transmission and payload capacity of 120-136 tones [1][2][3][4][5][6][7][8]. ...
Article
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The study is dedicated to increasing open pit trucks with electrical transmission maneuverability indices. The possibility of forced controllability usage of rear traction wheels of open pit truck with the electrical transmission, which enables them to carry out maneuvers with the usage of a forced additional turn is presented. For the first time, there has been worked out a mathematical model of the forced additional turn. It enables to determine a correlation of rotational speed ratio of rear traction wheels of starboard and port sides of the wheeled vehicle relative to a tire-to-surface friction coefficient. Firstly, the analytical dependences, which allow predicting the indices of open pit trucks maneuverability while using the forced additional turn are determined. The mathematical model adopted to appropriate truck's electric drive control algorithm can lead to trucks performance increasing by means of maneuvering time reducing.
Article
Large capacity shovels are deployed in surface mining operations for achieving economic bulk production targets. These shovels use crawler tracks for effective terrain engagement in these environments. Shovel reliability, maintainability, availability and efficiency depend on the service life of the crawler tracks. In rugged and challenging terrains, crawler wear, tear, cracks and failure are extensive resulting in prolonged downtimes with severe economic implications. In particular, crawler shoe wear, tear, cracks and fatigue failures can be expensive in terms of maintenance costs and production losses. No fundamental research has been undertaken to understand the crawler-formation interactions in challenging and rugged terrains in surface mining operations. This study forms the foundations for providing long-term solutions to crawler failure problems. The kinematic equations governing the crawler-formation interactions have been formulated to characterise the crawler motions during shovel production. These equations capture the motions governing the link pin joint, oil sand terrain joint and driving constraints based on the multi-body rigid theory. Crawler propel is achieved by using prescribed velocities along a translational degree of freedom (DOF) and a translational and rotational DOF. The crawler kinematic solutions show that the 3-D crawler–terrain model results in 132 DOFs and requires dynamic modelling to obtain the unknown degrees of freedom. A 3-D virtual prototype model is built to capture the crawler-formation interaction in MSC ADAMS based on the rigid body crawler kinematics. The virtual prototype simulator is supplied with mass properties of crawler shoe, mass, stiffness and damping characteristics of oil sand and external loads due to machine weight and contact forces to obtain the time variation of position, velocity and acceleration for the crawler–terrain engagement for given driving constraints. The results from the driving constraints yield a non-linear longitudinal motion of the crawler track assembly. The crawler track lateral and vertical displacements during translation-only motion fluctuates with maximum magnitudes of 0.7 and 3.6 cm. Similarly the fluctuating longitudinal, lateral and vertical velocities and accelerations have maximum magnitudes of 0.22, 0.046 and 0.56 m/s and 7.41, 1.73, and 34.9 m/s², respectively. This research provides a strong foundation for further study on developing flexible crawler track model for predicting crawler shoes dynamic stress distributions, cracks development and propagation and fatigue analysis during shovel operations.
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It is known in literature that a wheeled mobile robot (WMR), with fixed length axle, will undergo slip when it negotiates an uneven terrain. However, motion without slip is desired in WMR's since slip at the wheel-ground contact may result in significant wastage of energy and may lead to a larger burden on sensor based navigation algo-rithms. To avoid slip, the use of a variable length axle (VLA) has been proposed in the literature and the kinematics of the vehicle has been solved depicting no-slip motion. However, the dynamic issues have not been addressed adequately and it is not clear if the the VLA concept will work when gravity and inertial loads are taken into account. To achieve slip-free motion on uneven terrain, we have proposed a three-wheeled WMR architecture with torus shaped wheels, and the two rear wheels having lateral tilt capa-bility. The direct and inverse kinematics problem of this WMR has been solved earlier and it was shown by simulation that such a WMR can travel on uneven terrain with-out slip. In this paper, we derive a set of 27 ordinary differential equations (ODE's) which form the dynamic model of the three-wheeled WMR. The dynamic equations of motion have been derived symbolically using a Lagrangian approach and computer algebra. The holonomic and non-holonomic constraints of constant length and no-slip, respectively, are taken into account in the model. Simulation results clearly show that the three-wheeled WMR can achieve no-slip motion achieved even when dynamic effects are taken into consideration.
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This paper presents a complex vehicle dynamics model which is implemented using the object oriented modeling language Modelica TM . The main focus is on the multi body system (MBS) implementation of the dynamics of the chassis and wheels. The chassis contains models of an independent front suspension with anti-roll bar, as well as of a twist-beam rear axle. Furthermore, a model of the complete powertrain with automatic transmission is included. The resulting model is described in detail and validated against measured data from test drives with a notchback sedan.
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The interaction of dump truck and haul road has been simulated with the dynamic virtual prototype established in this work by combining the multi‐body and soil dynamics with the Automatic Dynamic Analysis Mechanical Systems (ADAMS) software. The tyre forces, road deformation and tyre stresses are simulated. The results indicate that the max deformation value increases non‐linearly with load varying from 0 to 57.6 t and decrease with elastic modulus from 60 to 240 MPa. The result also shows that high stress field applied to each tyre is around contact point between tyre and road.
Article
This is the third in a series of four papers (Parts 1 to 4) looking at the application of computer-based analysis methods to model vehicles and simulate vehicle handling. The material contained in these papers is based on a study carried out in order to investigate the influence of suspension and tyre modelling on the outputs predicted by vehicle handling simulations. The papers deal with analysis methods, vehicle modelling (both in the previous Issue), tyre modelling and handling simulation. In this paper an overview of the use of tyre models in vehicle dynamics is provided. This is followed by a more detailed description of three tyre modelling approaches that can be used for handling simulations. A description is also provided of a computer-based modelling system where FORTRAN routines represent the various models and a computer model of a tyre test rig is used to interrogate the models and data before integrating these into a full vehicle handling simulation. The use of this system to compare the accuracy of the tyre models under consideration is also presented. The examples used to illustrate the concepts explained throughout this series of papers have been generated using the ADAMS (Automatic Dynamic Analysis of Mechanical Systems) program.
Article
Cable shovels are capital-intensive equipment, whose operations are characterized by high stress loading and fatigue failure resulting in high maintenance costs. The operating environment and the stress fields on the boom must continually be monitored to avoid random fatigue failure to achieve reliability, longevity and economic usage. In this paper, the authors develop dynamic models for real-time stress monitoring using a combination of flexible and rigid body approach. A virtual prototype simulator is developed to simulate the cable shovel excavation in oil sands and to examine the motion, stress and local deformation of the boom. The P&H 4100A cable shovel, deployed in the Athabasca oil sands formation, is used to examine the cable shovel boom durability using stress fields simulation. The results show that high stresses occur at regions around the joint between the upper body and the boom, resulting in large deformations. In hard formations, the results show that the stress fields in this region exceed the Von Mises yield strength of steel used in making the shovel boom components. The results also show that the FE nodes of 178, 168, 120, 63, 127 and 84 for 10MPa modulus of elasticity and 127, 61, 126, 45, 60 and 39 nodes for 20MPa modulus of elasticity are the highly stressed nodes with high degree of boom deformation and fatigue failure. The study provides a solid foundation for further study of failure life analysis of the cable shovel components.
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Systems analysis is applied to off-the-road locomotion. Existing knowledge and literature on terrain-vehicle systems are reviewed and integrated from the practical engineering viewpoint. Facilities and equipment required for systems evaluation are described and its management discussed. Mathematical models allow speculation on future developments including terrain measurements, soil-vehicle interface definition, design and performance parameters optimization, and cost effectiveness. Related problems and possible developments in agriculture, earth moving, and industrial and military operations are considered.
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A new approach to the dynamic modelling of tracked vehicles is proposed in this paper, resulting in a 3D, 8 degrees of freedom dynamic model of an agricultural tracked vehicle, having the two independently applied sprocket torques as input variables. The main features of the approach are a new dynamic model of the shear displacement and the adoption of an innovative modelling and simulation environment: MOSES, based on Object-Oriented tools and techniques. Simulation results are reported for a qualitative validation of the model.
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With the use of the numerical method presented in this article, the dynamic analysis of the bus body frame can be carried out even in the designing phase. According to the results, the weak points of the body from the point of view of extreme loads and fatigue can be found and the correction of the construction can be done. As a new method, FEM models with different complexity are used in the different analysis steps. The applicability of the method as a design procedure and the reliability of the proposed models are verified by calculations and measurements concerning a concrete bus type.