Novel power hop model for an agricultural tractor with coupling bouncing, stick-slip, and free-play dynamics

Self-excited pitch and bounce oscillation occasionally occurs when a tractor pulls a high-draft load on dry soil. This dynamic instability is referred to as the power hop phenomenon. Power hop drastically degrades tractor performance and ride quality and can result in damage to the tractor, operator injury, and soil compaction. Power hop dynamics are characterised by three typical nonlinear elements; i.e., vertical jumping or bouncing, longitudinal stick-slip dynamics, and free-play in the joint between the tractor and implement. This paper couples these nonlinear elements and develops a novel power hop model for time-domain simulation. The occurrence process of power hop was demonstrated using the developed model using numerical experiments. Parametric investigations were conducted varying the drawbar pull, soil, and tyre conditions. The original draft load, joint clearance, static friction coefficient, ratio of coefficients of dynamic and static friction, front tyre stiffness, and rear tyre stiffness were taken as control parameters. The developed model predicted appropriately the occurrence of power hop for a higher draft load, drier soil, and “front stiff and rear soft” tyre stiffness conditions. The results agree obtained with conventional knowledge concerning power hops accumulated by previous experimental research. Thus, the developed model provides a strong platform adopting measures to control and suppress power hops.

[1]  K. Sakai,et al.  Impact dynamics model for a nonlinear bouncing tractor during inclined passage , 2019, Biosystems Engineering.

[2]  T. S. Collins,et al.  Loads in tractor linkages when transporting rear-mounted implements: Development of modelling and measurement techniques , 1991 .

[3]  Per-Olof Gutman,et al.  New models for backlash and gear play , 1997 .

[4]  Maxime Hubert,et al.  Bouncing dynamics of a spring , 2014 .

[5]  Ken Nakano,et al.  Two dimensionless parameters controlling the occurrence of stick-slip motion in a 1-DOF system with Coulomb friction , 2006 .

[6]  酒井 憲司,et al.  Experimental Analysis of Nonlinear Dynamics and Chaos in Bouncing Tractor. , 2000 .

[7]  Sakae Shibusawa,et al.  FREE PLAY AS A SOURCE OF NONLINEARITY IN TRACTOR–IMPLEMENT SYSTEMS DURING TRANSPORT , 2002 .

[8]  L. O. Garciano,et al.  Experimentally Obtained bifurcation Phenomenon in Chaotic Tractor Vibrating in Time and Frequency Domain , 2005, Int. J. Bifurc. Chaos.

[9]  Masahisa Watanabe,et al.  Numerical Analysis of Tractor Accidents using Driving Simulator for Autonomous Driving Tractor , 2019, ICMRE'19.

[10]  K. Aihara,et al.  BIFURCATION STRUCTURE OF VIBRATIONS IN AN AGRICULTURAL TRACTOR-VIBRATING SUBSOILER SYSTEM , 1999 .

[11]  Hans B. Pacejka,et al.  Tire and Vehicle Dynamics , 1982 .

[12]  K. Sakai,et al.  Numerical analysis of steering instability in an agricultural tractor induced by bouncing and sliding , 2020 .

[13]  Adam B. Flaugh.  Studies on Power Hop Using a Nonlinear Model of an Agricultural Tractor , 2011 .

[14]  S. Strogatz.  Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering , 1995 .

[15]  酒井 憲司,et al.  Theoretical Analysis of Nonlinear Dynamics and Chaos in Bouncing Tractor. , 1999 .

[16]  Albert C. J. Luo,et al.  The dynamics of a bouncing ball with a sinusoidally vibrating table revisited , 1996 .

[17]  R. Leine,et al.  Stick-Slip Vibrations Induced by Alternate Friction Models , 1998 .

[18]  Mehta,et al.  Bouncing ball with a finite restitution: Chattering, locking, and chaos. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[19]  P. J. Holmes.  The dynamics of repeated impacts with a sinusoidally vibrating table , 1982 .

[20]  T D Gillespie,et al.  Fundamentals of Vehicle Dynamics , 1992 .

[21]  N. Vandewalle,et al.  Completely inelastic ball. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  K. Sakai,et al.  Chaos emerging in soil failure patterns observed during tillage: Normalized deterministic nonlinear prediction (NDNP) and its application. , 2017, Chaos.

[23]  Kazuyuki Aihara,et al.  NONLINEAR VIBRATIONS IN AN AGRICULTURAL IMPLEMENT SYSTEM , 1994 .

[24]  F. Elmer.  Nonlinear dynamics of dry friction , 1997, chao-dyn/9707004.

[25]  Ugo Galvanetto,et al.  Sliding bifurcations in the dynamics of mechanical systems with dry friction—remarks for engineers and applied scientists , 2004 .

[26]  Frank M Zoz.  The Cause of Powerhop , 2007 .