509 by ides editor

Full Paper Proc. of Int. Conf. on Advances in Robotic, Mechanical Engineering and Design 2011

Development of Rotavator in Soil Trenching Applications Chitralekha Dey 1 Amit Jain2 S.G. Hajare3 Research & Development Establishment (Engrs.) Defence Research & Development Organization Dighi, Pune 411 015, India (Email: chitralekha.dey@gmail.com , amitjain.nith@gmail.com , suhas.hajare43@hotmail.com ) Abstract:- Automated soil cutting and digging operations are a frequent requirement in defence applications. The design of various parameters of earth cutting tool becomes extremely challenging with the various constraints associated with the functional requirements of the equipment and the unknown terrain encountered by the cutting tool. The paper outlines in brief the analytical study conducted to determine the various tool parameters such as rotating velocity, number of teeth, cutting depth of teeth. The different forces acting on the tool are enumerated from 3D soil tool interaction model. The forces are calculated for different digging depths and entry angles. Finally the least resistive force is chosen as the design input for the power requirement of the equipment.

III. ROTOR KINEMATICS The rotor trencher executes combined rotational and forward motion during trenching operations. The path of motion of each point on the trencher depends on the circumferential and forward travel velocities, as well as direction of rotation. An understanding of the rotor trencher kinematics is necessary for analysis. In rotor trenchers, the forced rotation of the rotor shaft with working tools fixed to it participates in two motions, namely, the rotary motion around its axis with velocity Vcir and forward travel velocity of vehicle Vf.

I. INTRODUCTION The principle aim of this section is to calculate the force and torque required to be exerted by the trencher to cut through different classes of soil.

Fig.2 Motion of Rotavator

A. Determination of equation of motion Let the rotor trencher of radius R turn through angle α from the original position in time t. For the case of forward or down cut rotation, the point A1 corresponding to the tip of the teeth take a position A1I for a stationary system. In practice, the system is not stationary and a point on the rotor travels along a path that is a combination of forward travel speed and rotor rotational speed. Here, in time t the rotor moves forward a distance equal to Vf x t, and the tip of the teeth finally takes a position A1II.The coordinate of the point A1II is expressed as

Fig.1 Rotavator

II. DESIGN PHILOSOPHY The rotavator or rotary tillage tool primarily comprises of blades mounted on flanges which are attached to the shaft that is driven by vehicle power take off. It is an active tillage tool that processes the soil at a speed that is different from the forward travel speed of the vehicle. The changing location of the tip of the rotor as it processes the soil is one of the key parameters that must be considered when developing a mathematical model for its torque requirements. For a rotor fitted with cutting blades of a given configuration, the instantaneous location of the tip is determined by the kinematics of the rotor. This change in depth, as the blade processes the soil, results in continuous change of the torque requirements from the initiation to the end of the soil cutting process.

Where α = angle of rotation of the teeth with respect to its initial position (rad) t = time of rotation of rotor through angle α The above equation determines the absolute trajectory of motion of rotor trencher teeth. Geometrically this trajectory is a trochoid. 22

Full Paper Proc. of Int. Conf. on Advances in Robotic, Mechanical Engineering and Design 2011 IV. DESIGN INPUT PARAMETERS

by the trencher. Furrow bottom produced by rotary trencher:- During trenching operations, rotating trenchers produce furrow bottoms with peaks of undisturbed soil. The height of these undisturbed peaks is dependent on the direction of rotation, ratio of the peripheral speed to the forward travel speed and the number of teeth. In our problem, the forward travel speed of the vehicle is fixed at 2.1kmph. Hence the only two variables upon which the depth of the furrow bottom is dependent is peripheral speed of the rotor and the number of teeth on the rotor. The mathematical relationship between the height of the undisturbed furrow bottom and the above parameters is:

A. Initial soil conditions In the present study, the initial soil conditions have been taken care of, by taking soil properties of three samples of soil .These soil samples have been collected physically from the site and the properties determined experimentally in the laboratory. The force and the torque requirements are calculated theoretically for the three soil samples, and the worst/maximum value is taken for the design. B. Direction of rotation With the motion of the vehicle fixed in one direction, there can be two directions of motion of the rotor - down-cut direction and up-cut direction. As per literature review, the down-cut direction of rotation is preferred because of the following reasons: (a) The forward thrust generated by down-cut rotors aids in traction (b) The instantaneous behavior of the blade is similar to that of an inclined passive blade, therefore the existing force prediction models can be modified in the development of their torque models. Further more, from the functional requirement point of view, the soil is needed to be deposited along the sides of the trench, to aid in camouflaging. It has been verified experimentally, that in up-cut motion, the soil is carried to the back of the trench along with the rotor and deposited over there. This poses problem with the camouflaging action, which is expected to carry on simultaneously with the trenching operation. Hence from this point of view too, the down-cut direction of motion of the rotor is selected.

Where, hc = peak height Z= number of teeth in one plane of the rotor

C) Bite length/number of teeth Fig.4. Combination of rotor RPM and number of teeth

The first two combinations of rotor RPM and number of teeth has also been validated and illustrated geometrically. The trochoids of adjacent teeth are drawn at 10 degree accuracy, and the height of the undisturbed furrow is measured geometrically V. SOIL TOOL INTERACTION FORCES i) Length of teeth in contact with soil The first parameter calculated in order to derive an expression for the torque requirement due to soil –tool interaction is the length of the teeth in contact with soil at different instantaneous trenching depth for a single blade. For calculating the same, the trochoid of the blade is drawn by determining the coordinates of the tip of the cutting edge at different instantaneous time moments. Xi = Vf ti +Rcosαi = Vf ti +Rcos (ωti) Yi = R(1-sinαi) = R(1-sin(ωti)) Where i = position of the teeth along the cutting path αi = the angle the blade turns through in time t (rad) ti = time of rotation of teeth through angle α from horizontal Then length of blade in contact with soil is obtained as

Fig. 3

The bite length is determined by considering the process of soil cutting by two adjacent teeth in the same vertical plane. With reference to the above figure, the trajectory of teeth 1 is displaced with respect to the adjacent teeth 2 along the horizontal line, through a certain length Lb called the bite length, where Lb = Vf tb , where

Vf = forward velocity of vehicle tb = time during which the teeth rotates through an angle equal to the angle between two adjacent teeth. Hence bite length is indirectly dependent on the number of teeth attached to the rotor. This parameter is hereby determined from the consideration of furrow bottom height of the trench, produced © 2011 AMAE DOI: 02.ARMED.2011.01.509

Full Paper Proc. of Int. Conf. on Advances in Robotic, Mechanical Engineering and Design 2011 literature – “Recce, A.R., the fundamental equation of earth moving mechanics, in Proceedings of the institution of mechanical engineers, 1964” or the McKyes model failure shape. Geometric boundaries for an idealized separation failure wedge cut by the blade at an instantaneous depth. Based on the above shown soil failure wedge, all the forces acting on the different surfaces are identified as shown in figure. All these forces contribute to the total cutting force designated as Ps, which act at an angle δ, to the normal to the surface of the blade. The description of all the identified force components is as follows: Rectangular surface abed: a) Adhesion force FAD due to adhesion between the teeth and the soil b) Soil - metal friction force on the soil teeth interface c) Force exerted on the teeth by the trencher in the instantaneous direction of movement Ps

Fig.5 Theoretical shear planes in soil at different teeth positions.

The path of the teeth inside the soil is divided into 5 parts and the length of the teeth and angle of entry β at each time moment is calculated ii.) Identification of torque requirement Torque is required by the teeth for the following actions: (i) Overcoming the soil-soil friction on the shear plane (ii) Overcoming the soil-metal friction and adhesion on the span of the teeth (iii) Accelerating the cut soil by the teeth (iv) The continuous penetration resistance by the tip of the teeth in the form of tip reaction. The first step in the development of the mathematical model for torque requirements is to make the following assumptions: A) Width of the pit which has to be dug is assumed. Subsequently the width of soil dug by single teeth is assumed. Three set of teeth with two in each set is staggered and arranged in such a manner that total width of pit is achieved. The following figure illustrates.

Fig.6

Fig.8 Breakdown of soil tool interaction forces

Triangular surface abc a) Equal and opposite reaction normal forces R b) Cohesion force CF2 due to soil cohesion between soil particles c) Soil-soil friction force SF2 Rectangular rupture surface bcfe a) Normal acting force Q b) Cohesion force CF1 due to cohesion between soil particles c) Soil-soil friction force SF1 Triangular surface def a) Equal and opposite reaction normal forces R b) Cohesion force CF2 due to soil cohesion between soil particles Other additional forces identified due to failed soil wedge are: a) Acceleration force Fac: body force resisting the acceleration of the wedge b) Gravitational force W due to the weight of the wedge The angles used in the above figure are: β: Angle that the tool makes with the horizontal during an instantaneous time .this is also known as rake angle ρ: Angle that the rupture surface makes with the horizontal δ: Angle of friction between soil and tool Φ: Angle of soil friction

Soil slices cut by consecutive teeth of Rotavator

B) During an instantaneous time movement, the teeth behave like an inclined passive blade. The second step is the identification of the soil-tool interaction forces model that would enable the prediction of torque requirements. In this regard, 3-D resistance model (Perumpral-Desai-Grisso model give reference) is used, which is better suited to explain soil resistance induced by separation mechanism of inclined cutting blades.

iii) Calculation of each force component The calculation of the identified force components on the teeth is as follows. The calculations are based on the 2-D drawing of the idealized soil failure wedge. Fig. 7 The idealized separation failure wedge is shown in the following figure. The shape of the failure surface is also documented in other

Full Paper Proc. of Int. Conf. on Advances in Robotic, Mechanical Engineering and Design 2011

The expression of the acceleration force is

Where γ = unit weight of soil (kN/m3) w = tool width (m)  Cohesion force CF1 The cohesion force acting on the failure surface CF1=CC A3 where CC = soil cohesion (Kn/m3) A3 = area of the rectangular rupture surface (m2)

Fig. 9 Dimensions of soil failure wedge for calculation of forces

Adhesion force: The force of adhesion on the surface, Fad resisting the movement of the wedge on the teeth is Fad = Ca x A1 = Ca x w x L Where Ca = soil metal adhesion factor (kN/m2) = α cu where α = adhesion factor α = 0.45 (Tomlinson recommends average value of α for bored piles in medium stiff to stiff clays) cu= shear strength as given by Coulomb equation in terms of the soil parameters c & φ = c + σ tan φ A1 = area of the teeth in contact with the soil, ‘abed’ (m2) L = length of the teeth in contact with the soil.(m)  Weight of soil wedge The expression for the weight of the failed soil wedge is Obtained as W = γ xw x A2

 Cohesion force CF2 The cohesion force acting on the failure surface CF1=CC A2where CC = soil cohesion (Kn/m3) A2 = area of the triangular surface (m2)

Where, γ = unit weight of soil (kN/m3) = area of triangular rupture surface, abc or def (m2) Forces acting on soil wedge  Soil – soil frictional force on triangular surface abc This is calculated by determining the reaction force R on the surface. The reaction force R is given by R = γ K0 z A2 Where K0 = coefficient of lateral earth pressure at rest = (1-sinφ) Z = depth of the centroid of the wedge from surface of failed soil wedge Hence,

Fig.10 Derivation of the instantaneous total soil resistance force P s

The total soil resisting force is calculated by solving the equilibrium. This is done by resolving the forces in the x and z directions. By combining the above equations and replacing Q from the equations the final expression for total resistance Ps is obtained as

In the above equation, both the resistance force Ps and the soil failure angle ρ are unknown. This implies, that Ps, which is the primary unknown in the equation cannot be determined directly. The soil failure angle and the resistance force however can be determined indirectly by using the passive earth pressure theory that states that, passive soil failure occurs when the resistance is minimum. Consequently through trial error method, the soil resistance force Ps or soil

Acceleration force The instantaneous peripheral speed of any point in a cycloid trajectory is a function of the rotor speed, the forward travel speed and the distance from the rotational axis to the point of interest.

Full Paper Proc. of Int. Conf. on Advances in Robotic, Mechanical Engineering and Design 2011 failure angle can be determined finding the minimum resistance value.

CONCLUSION The challenging tasks of analyzing the soil tool interaction forces have been accomplished successfully.

iv) Resistance force Ps The soil cutting force is finally calculated, at five different instantaneous time moments. The following graph shows the variation of cutting force with depth.

ACKNOWLEDGEMENT Authors gratefully acknowledge the guidance and the encour agement given by Dr. S Guruprasad, Director, R&DE (Engrs) and Shri N.B.Vijayakumar, Joint Director, Combat Engineering in carrying out this work. REFERENCES [1]. “Recce, A.R., the fundamental equation of earth moving mechanics, in Proceedings of the institution of mechanical engineers, 1964” [2]. ASAE 1994 ASAE monograph No.12 Pamela De Vore Hansen Ed. American Society of Agricultural Engineers, 2950 Niles road, St. Joseph Michigan USA. [3]. ASAE Standards. 2000 ASAE Standards 47th Ed. ASAE EP 291.2 DEC 98: Terminology and definitions of soil tillage and soil tool relationships. American Society of Agricultural Engineers, St. Joseph Michigan USA. [4]. 3-D resistance model -Perumpral-Desai-Grisso model. [5]. Chi, L and R.L Kushwaha 1989. Finite element analysis of forces on a plane soil blade. Canadian Agricultural Engineering 31(2):135-140. [6].Chi, L and R.L Kushwaha 1990. A non linear 3-D finite element analysis of soil failure for tillage tools, journal of Terramechanics 27(4):343-366.

Fig. 11 The soil parameters and the interaction forces between the excavator and the environment are very large. Reaction forces can vary considerably depending on terrain geometry, which is assumed to be horizontal in the present case, soil compaction and even climate. Soil varies from hard and frozen in winter, wet in the rainy seasons to dry and powdery in the summers. Moreover the soil is assumed to be homogeneous whereas in practical cases the burying tool may experience non-homogeneous material effects such as boulders etc.Again the failure is assumed to be a general shear failure which may not be the case always as the soil can fail in sudden jerks. Accounting for all these factors a standard factor of safety is taken.