Michael Ketting
Comparing load conditions of plane and false-ellipse running surface contours of track links in running gears for construction equipment
Journal of Terramechanics, Volume 48, Issue 4, August 2011, Pages 241-246, ISSN 0022-4898, 10.1016/j.jterra.2011.06.001.
http://www.sciencedirect.com/science/article/pii/S0022489811000358
Abstract: To improve durability and fatigue strength, it is advisable to give running surfaces of track links in undercarriages for construction equipment a false-ellipse profile. Such a profile resembles the contour of a running surface of a railway rail. Kinematic conditions as they exist for the track run in the undercarriage of construction equipment can however not be compared with those of a railway. Moreover, construction equipment in field operation is in particular faced with problems like lateral inclinations and misalignments between running surfaces of track link and bottom roller. For all this it is necessary to have a look at the load conditions of track links. This article makes clear that, above all with a view to the fact that in the past only plane running surface profiles were used for construction equipment applications, designing track link running surfaces with a false-ellipse profile has considerable advantages compared to plane running surfaces even at a misalignment ratio of just 1/5 of the maximum width of track link running surface.
Keywords: Construction equipment; Running surface; Durability; Fatigue strength; Hertz compression
Bruce Maclaurin
A skid steering model using the Magic Formula
Journal of Terramechanics, Volume 48, Issue 4, August 2011, Pages 247-263, ISSN 0022-4898, 10.1016/j.jterra.2011.04.002.
http://www.sciencedirect.com/science/article/pii/S0022489811000218
Abstract: The paper describes a computer model for predicting the steering performance and power flows of a notional skid steered tracked vehicle. The force/slip characteristics of the rubber track pads are calculated by means of the so-called Magic Formula. Relevant parameters for the Magic Formula are derived from the limited amount of data available from traction tests with a tracked vehicle on a hard surface. The computer model considers the vehicle in steady state motion on curves of various radii and allows for lateral and longitudinal weight transfer, roll and pitch motions and the effects of track tension forces. Vehicle dimensions, Magic Formula parameters and the equations of motion are set up in a Microsoft Excel spreadsheet and solutions obtained using the Solver routine. Model outputs are described in terms of driver control input and various power flows against lateral acceleration. Maximum lateral acceleration is generally limited by the available engine power. In some conditions the outer track sprocket could be transmitting almost twice the maximum net engine power. For vehicles with a single electric motor/inverter driving each sprocket, these units would need to be able to transmit these high intermittent powers.
Keywords: Skid steering; Magic Formula; Tracked vehicle; Double differential; Steering response; Power flows
C. Senatore, C. Sandu
Off-road tire modeling and the multi-pass effect for vehicle dynamics simulation
Journal of Terramechanics, Volume 48, Issue 4, August 2011, Pages 265-276, ISSN 0022-4898, 10.1016/j.jterra.2011.06.006.
http://www.sciencedirect.com/science/article/pii/S0022489811000401
Abstract: Off-road operations are critical in many fields and the complexity of the tire-terrain interaction deeply affects vehicle performance. In this paper, a semi-empirical off-road tire model is discussed. The efforts of several researchers are brought together into a single model able to predict the main features of a tire operating in off-road scenarios by computing drawbar pull, driving torque, lateral force, slip-sinkage phenomenon and the multi-pass behavior. The approach is principally based on works by Wong, Reece, Chan, and Sandu and it is extended in order to catch into a single model the fundamental features of a tire running on soft soil. A thorough discussion of the methodology is conducted in order to highlight strengths and weakness of different implementations. The study considers rigid wheels and flexible tires and analyzes the longitudinal and the lateral dynamics. Being computationally inexpensive a semi-empirical model is attractive for real time vehicle dynamics simulations. To the best knowledge of the authors, current vehicle dynamics codes poorly account for off-road operations where tire-terrain interaction dominates vehicle performance. In this paper two soils are considered: a loose sandy terrain and a firmer loam. Results show that the model realistically predicts longitudinal and lateral forces providing at the same time good estimates of the slip-sinkage behavior and tire parameters sensitivity.
Keywords: Off-road tire dynamics; Slip sinkage; Multi-pass; Lateral force; Traction; Tire parameter influence; Mobility
S.K. Patel, Indra Mani
Effect of multiple passes of tractor with varying normal load on subsoil compaction
Journal of Terramechanics, Volume 48, Issue 4, August 2011, Pages 277-284, ISSN 0022-4898, 10.1016/j.jterra.2011.06.002.
http://www.sciencedirect.com/science/article/pii/S002248981100036X
Abstract: A field experiment was conducted on alluvial soil with sandy loam texture, in a complete randomized design, to determine the compaction of sub-soil layers due to different passes of a test tractor with varying normal loads. The selected normal loads were 4.40, 6.40 and 8.40 kN and the number of passes 1, 6, 11 and 16. The bulk density and cone penetration resistance were measured to determine the compaction at 10 equal intervals of 5 cm down the surface. The observations were used to validate a simulation model on sub-soil compaction due to multiple passes of tractor in controlled conditions. The bulk density and penetration resistance in 0–15 cm depth zone continuously increased up to 16 passes of the test tractor, and more at higher normal loads. The compaction was less in different sub-soil layers at lower levels of loads. The impact of higher loads and larger number of passes on compaction was more effective in the soil depth less than 30 cm; for example the normal load of 8.40 kN caused the maximum bulk density of 1.53 Mg/m3 after 16 passes. In 30–45 cm depth layer also, the penetration resistance increased with the increase in loads and number of passes but to a lesser extent which further decreased in the subsoil layers below 45 cm. Overall, the study variables viz. normal load on tractor and number of passes influenced the bulk density and soil penetration resistance in soil depth in the range of 0–45 cm at 1% level of significance. However, beyond 45 cm soil depth, the influence was not significant. The R2 calculated from observed and predicted values with respect to regression equations for bulk density and penetration resistance were 0.7038 and 0.76, respectively.
Keywords: Soil compaction; Sub-surface soil properties; Penetration resistance; Number of passes; Multiple regression
A. Abo Al-kheer, M. Eid, Y. Aoues, A. El-Hami, M.G. Kharmanda, A.M. Mouazen
Theoretical analysis of the spatial variability in tillage forces for fatigue analysis of tillage machines
Journal of Terramechanics, Volume 48, Issue 4, August 2011, Pages 285-295, ISSN 0022-4898, 10.1016/j.jterra.2011.05.002.
http://www.sciencedirect.com/science/article/pii/S0022489811000346
Abstract: This paper presents a new theoretical model to describe the spatial variability in tillage forces for the purpose of fatigue analysis of tillage machines. The proposed model took into account both the variability in tillage system parameters (soil engineering properties, tool design parameters and operational conditions) and the cyclic effects of mechanical behavior of the soil during failure ahead of tillage tools on the spatial variability in tillage forces. The stress-based fatigue life approach was used to determine the life time of tillage machines, based on the fact that the applied stress on tillage machines is primarily within the elastic range of the material. Stress cycles with their mean values and amplitudes were determined by the rainflow algorithm. The damage friction caused by each cycle of stress was computed according to the Soderberg criterion and the total damage was calculated by the Miner’s law. The proposed model was applied to determine the spatial variability in tillage forces on the shank of a chisel plough. The equivalent stress history resulted from these forces were calculated by means of a finite element model and the Von misses criterion. The histograms of mean stress and stress amplitude obtained by the rainflow algorithm showed significant dispersions. Although the equivalent stress is smaller than the yield stress of the material, the failure by fatigue will occur after a certain travel distance. The expected distance to failure was found to be df = 0.825 × 106 km. It is concluded that the spatial variability in tillage forces has significant effect on the life time of tillage machines and should be considered in the design analysis of tillage machines to predict the life time. Further investigations are required to correlate the results achieved by the proposed model with field tests and to validate the proposed assumptions to model the spatial variability in tillage forces.
Keywords: Spatial variability; Tillage forces; Tillage machines; Fatigue analysis; Life time
Yong Huang, Xin Lu, Rong Zhao, Wen Li
Three dimensional simulation of lunar dust levitation under the effect of simulated sphere body
Journal of Terramechanics, Volume 48, Issue 4, August 2011, Pages 297-306, ISSN 0022-4898, 10.1016/j.jterra.2011.06.005.
http://www.sciencedirect.com/science/article/pii/S0022489811000395
Abstract: Four typical models of irregular lunar dust are built based on the particle shape. Parameters of the simulated sample are determined by dimensional analysis and simulated triaxial test. The simulation was performed by a simulated sphere body acting as the lunar explorer experiencing free fall landing on moon surface from a certain height. Tracking the movement of lunar dust, the motion characteristics and levitation distribution were statistically analyzed. The influences of the landing speed of the simulated sphere body, friction coefficient and stiffness of the particles on the levitation of the dust were also discussed. Results show that the landing speed and the friction coefficient have greater influence on the number and height of levitating particles than other factors. The number and height of levitating particles increase with landing speed. While the friction coefficient increases, the number of levitating particles increases but the levitation height decreases. The stiffness of particle also has some influence on levitation height. The larger the stiffness of particles is, the smaller the levitation height. But it has little effect on the number of levitating particles.
Keywords: Lunar dust; Levitation; Three dimensions
R.A. Irani, R.J. Bauer, A. Warkentin
A dynamic terramechanic model for small lightweight vehicles with rigid wheels and grousers operating in sandy soil
Journal of Terramechanics, Volume 48, Issue 4, August 2011, Pages 307-318, ISSN 0022-4898, 10.1016/j.jterra.2011.05.001.
http://www.sciencedirect.com/science/article/pii/S0022489811000334
Abstract: This paper presents a validated dynamic terramechanic model for rigid wheels with grousers that may be used for planetary and terrestrial mobile robots operating in loose sandy soil. The proposed model is based on established analytical terramechanic theories and incorporates two new dimensionless empirical coefficients. The additional terms in the model are based on existing soil mechanic theories that vary as a function of soil properties, slip conditions, and vehicle loading. The proposed model was able to capture and predict the dynamic oscillations observed in experimental data from a single-wheel testbed for the sinkage, drawbar pull and normal load. For the operating conditions tested in this research the simulation results using the proposed model show an improvement over traditional terramechanic models for capturing the dynamic effects of grousers.
Keywords: Terramechanics; Sandy soil modelling; Pressure sinkage relationship; Rigid wheel; Grousers; Dynamic modelling
I. Gravalos, T. Gialamas, S. Loutridis, D. Moshou, D. Kateris, P. Xyradakis, Z. Tsiropoulos
An experimental study on the impact of the rear track width on the stability of agricultural tractors using a test bench
Journal of Terramechanics, Volume 48, Issue 4, August 2011, Pages 319-323, ISSN 0022-4898, 10.1016/j.jterra.2011.04.003.
http://www.sciencedirect.com/science/article/pii/S0022489811000322
Abstract: The aim of this paper is to study the effect that the rear track width and additional weight placed on the wheels has on the stability of a tractor when driving on side slopes. With the help of a specially constructed test bench the reactions on the wheels under static load were measured for rear track width of 1500, 1650 and 1800 mm. The roll angle of the test bench was gradually increased. The analysis of the experimental results showed that the static limit of overturn was considerably improved, when the width of the rear track was 1650 mm and an additional weight had been used for the uphill wheel.
Keywords: Agricultural tractor; Rear width; Vehicle; Stability; Overturning