Multibody Dynamic Stress Simulation of Rigid-Flexible Shovel Crawler Shoes

Transcription

1 minerals Article Multibody Dynamic Stress Simulion Rigid-Flexible Shovel Crawler Shoes Samuel Frimpong * and Magesh Thiruvengadam Department Mining and Nuclear Engineering, Missouri University Science and Technology, Rolla, MO 65409, USA; mtwv8@mst.edu * Correspondence: frimpong@mst.edu; Tel.: Academic Editor: Tuncel M. Yegulalp Received: 31 March 2016; Accepted: 14 June 2016; Published: 25 June 2016 Abstract: Electric shovels are used in surface mining operions to achieve economic production capacities. The capital investments and opering costs associed with shovels deployed in Athabasca oil sands formion are high due to 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 initiion, propagion and premure figue failure. The objective this paper is to develop a model to characterize crawler stresses and deformion for P&H 4100C BOSS during propel and loading using rigid-flexible multi-body dynamic ory. A 3-D virtual prototype model rigid-flexible crawler track assembly and its interactions with oil sand formion is simuled to capture model dynamics within multibody dynamics stware MSC ADAMS. The modal and stress shapes and modal loads due to machine weight for each flexible crawler shoes are genered from finite element analysis (FEA). The modal coordines from simulion are combined with mode and stress shapes using modal superposition method to calcule real-time stresses and deformion flexible crawler shoes. The results show a maximum von Mises stress value 170 MPa occurring in driving crawler shoe during propel motion. This study provides a foundion for subsequent figue life analysis crawler shoes for exting crawler service life. Keywords: surface mining; crawler-terrain interactions; rigid-flexible multi-body dynamic ory; virtual prototype simulion; modal analysis; modal stress recovery 1. Introduction The electric shovel is widely used in surface mining operions. The lower works shovel consist propel and crawler systems, as shown in 1. The crawler dimensions, merial properties and shovel load acting on lower works in 1 are based on P&H 4100C BOSS electric shovel [1,2]. The crawler consists a crawler track assembly, front and rear idlers, lower rollers and guide rails [3]. The crawlers are made up shoes th are connected toger by link pins to form a continuous chain. The shovel reliability deps on crawler track service life. The crawler supports entire machine load and payload during its opering cycle. The dynamic loads from this interaction can cause stress loading crawlers, wear and tear, crack and eventual failure. Frimpong and Li [4] modeled interaction between shovel dipper and oil sands formion and determined dynamic stresses in boom during crowding and digging using rigid-flexible multi-body dynamics ory. The results showed th von Mises stress joint locion between boom and upper structure exceeded merial yield strength. Frimpong and Li [5] exted ir study [4] to analyze stresses in shovel front- components. They found highest stresses around region where hoist rope is tached to dipper. Minerals 2016, 6, 61; doi: /min

2 shovel crawler-terrain interactions during propel P&H 4100C BOSS shovel. They developed a 3-D virtual model crawler-terrain interactions in MSC ADAMS. Their results included shoe kinemics, contact forces on shoes, joint forces in link pin and total terrain deformion. The stress distributions are required to study figue life for exted service. Thus, objective this study is to model stress loading crawler shoes during shovel s opering cycle within Minerals 2016, 6, MSC ADAMS View/Flex/Durability and MSC NASTRAN [9 13] as a basis for future figue failure life studies. 1. Shovel crawler-formion interactions. 2. Rigid-Flexible Frimpong and Multi-Body Thiruvengadam Dynamics [6 8] studied Crawler-Terrain rigid multi-body Interactions dynamic simulion shovel crawler-terrain Frimpong and interactions Thiruvengadam during propel [6 8] developed P&H 4100C crawler-terrain BOSS shovel. assembly They developed ( 1) based a 3-D virtual on P&H model 4100C crawler-terrain Boss shovel crawler interactions dimensions in MSC(Table ADAMS. 1). Theircrawler results included shoes were shoe genered kinemics, contact Solidworks, forcesbased on shoes, on joint actual forces in crawler linkshoe pin and for total same terrainshovel deformion. [1,2]. The oil stress sand distributions terrain are modeled required as a tocontinuous study figue system life with for exted a finite number service. Thus, 2-degree objective freedom this (DOF) study spring is todamper model oil sand stressunits. loading The oil sand crawler terrain shoes had during a total length, shovel s width opering and depth cycle within 70, 32.5 MSCand ADAMS 2 m, View/Flex/Durability respectively. Each oil sand MSC unit size NASTRAN was 7 m [9 13] 7 m as2 am, basis resulting for future in 50 figue oil sand failure units. life studies. 2. Rigid-Flexible Multi-Body Table 1. Crawler Dynamics dimensions Crawler-Terrain P&H 4100C Interactions electric shovel [1]. Frimpong and Thiruvengadam Measurements [6 8] developed Dimensions crawler-terrain assembly ( 1) based on P&H 4100C Boss shovel crawler Width dimensions Crawler Shoes (Table 1) The m crawler shoes were genered in Solidworks, based on actual crawler Width shoe Crawler for same shovel 12.8 [1,2]. m The oil sand terrain is modeled as a continuous system with a finite Length number Crawlers 2-degree 11.6 freedom m (DOF) spring damper oil sand units. The oil sand terrain had a total length, width and depth 70, 32.5 and 2 m, respectively. Each oil sand This unit study size was makes 7 m ˆ two 7 m changes ˆ 2 m, resulting to in oil 50 sand oil sand model, units. (i) terrain size reduction to 19 m 13 m 1 m (from 70 m 32.5 m 2 m) and (ii) unit size reduction to 1 m 1 m 1 m (from Table 1. Crawler dimensions P&H 4100C electric shovel [1]. 7 m 7 m 2 m), resulting in 247 oil sand units. The decrease in oil sand unit size increases total number parts in multi-body system, but can accurely approxime oil sands load Measurements Dimensions deformion model. Any furr decrease in oil sand unit size caused increased computional Width Crawler Shoes m time and, hence, was not tempted. 2 shows geometric track model, comprising 13 shoes, Width Crawler 12.8 m in contact with terrain. The Length terrain Crawlers shows footprint 11.6 a single m crawler track with 4 to 5 m exted space around track. Any additional exted space had a negligible effect on total deformion terrain and crawler-terrain interaction dynamics. Table 2 contains stiffness (k) This study makes two changes to oil sand model, (i) terrain size reduction to 19 m ˆ 13 m ˆ 1 m and damping characteristics and terrain and crawler properties. The shoes and oil sand units are (from 70 m ˆ 32.5 m ˆ 2 m) and (ii) unit size reduction to 1 m ˆ 1 m ˆ 1 m (from 7 m ˆ 7 m ˆ 2 m), identified by numbers to 261, with Part 1 being default ground link in MSC ADAMS, as shown resulting in 247 oil sand units. The decrease in oil sand unit size increases total number parts in in 2. multi-body system, but can accurely approxime oil sands load deformion model. Any The 13 crawler shoes are numbered 1 to 13 in blue ( 2) as alterne names for Parts 2 to 14, furr decrease in oil sand unit size caused increased computional time and, hence, was not with part 7 as shoe #6. The reference global coordine system is loced point O, as shown in tempted. 2 shows geometric track model, comprising 13 shoes, in contact with terrain. 2. A rigid virtual prototype simulor is developed in MSC ADAMS and modified to genere The terrain shows footprint a single crawler track with 4 to 5 m exted space around rigid flexible prototype model. track. Any additional exted space had a negligible effect on total deformion terrain and crawler-terrain interaction dynamics. Table 2 contains stiffness (k) and damping characteristics and terrain and crawler properties. The shoes and oil sand units are identified by numbers 2 to 261, with Part 1 being default ground link in MSC ADAMS, as shown in 2.

3 Minerals 2016, 6, Minerals 2016, 6, Crawler track oil sand terrain interactions. Table Merial properties system Density Mass Elastic Poisson s Stiffness (k) Damping Body Density Elastic Poisson s Stiffness (k) Damping Body (kg/m (kg/m 3 ) 3 (kg) Mass (kg) ) Modulus Modulus Rio Rio MN/m MN/m (kns/m) (kns/m) Crawler Shoe GPa Crawler Shoe GPa Oil-sand Oil-sand MPa 20 MPa The kinemics and applied forces used to genere rigid prototype simulor are discussed The 13 crawler shoes are numbered 1 to 13 in blue ( 2) as alterne names for Parts 2 to in following paragraphs this section. 14, with part 7 as shoe #6. The reference global coordine system is loced point O, as shown in Kinemic Constraints: These include joint, spring-damper element, and motion constraints. 2. A rigid virtual prototype simulor is developed in MSC ADAMS and modified to genere The rigid crawler shoes are connected to each or using spherical and parallel primitive joint rigid flexible prototype model. constraints. Oil sand units are held toger with spherical and in-plane primitive joints. Each unit is The kinemics and applied forces used to genere rigid prototype simulor are discussed in connected to ground link using a spring-damper element with a 1-m length. The cross-sectional following paragraphs this section. area unit is 1 m 2 with a spring length 1 m. The stiffness (k) is equal to elastic modulus Kinemic Constraints: These include joint, spring-damper element, and motion constraints. The oil sand (E) in Table 2. The translion propel motion crawler is obtained by imposing a rigid crawler shoes are connected to each or using spherical and parallel primitive joint constraints. motion constraint (in Equion (1)) on shoe 13 its center mass (COM) in global positive Oil sand units are held toger with spherical and in-plane primitive joints. Each unit is connected to x-direction using cubic STEP function in MSC ADAMS. ground link using a spring-damper element with a 1-m length. The cross-sectional area unit is 1 m 2 with a spring length Propelling 1 m. The stiffness (k) is equal to elastic modulus oil sand (E) in Table 2. The translion propel motion 2 3 crawler is obtained by imposing 0.012t t ; 0 t 5 s a motion constraint (in Equion (1)) on shoe 13 its center mass (COM) in global positive x-direction using 0.1 ; 5 < t 10 s cubic STEP function in MSC ADAMS. v x () t ( ) ( t 10 ) 2 ( t 10 )» = m / fis (1) Propelling ;10 < t 15 s t Loading t 3 ; 0 ď t ď 5 s 0.1 v x ptq " ; 5 ă t ď 10 s Disabled * ;15 < t 40 s 0.1 ` p 0.1q pt 10q pt 10q m{s (1) 5 ; 10 ă t ď 15 s The crawler track moves in remaining five DOFs (two translions Loading fl and three rotions) during propel. This motion constraint is deactived when loading begins to allow six-dof Disabled ; 15 ă t ď 40 s movements. The motion constraint in Equion (1) causes crawler track to (i) accelere from rest; (ii) propel The crawler constant track velocity; moves inand remaining (iii) decelere five DOFs to rest (two translions working face. and Motion three rotions) constraints during are propel. also imposed This motion on oil constraint sand units is deactived ir COMs when to allow loading 2 DOFs. beginsfrimpong to allow six-dof and Thiruvengadam movements. The [6] motion define constraint kinemic equions Equion (1) governing causes crawler joint and track motion to (i) constraints accelerebetween from rest; adjacent (ii) propel crawler constant shoes and velocity; oil sand and units. (iii) decelere to rest working face. Motion constraints are also imposed on oil External sand units Forces ir on Crawler COMs toshoes: allowexternal 2 DOFs. forces Frimpong crawler and Thiruvengadam shoes are (i) contact [6] define forces kinemic between crawler equions shoes governing and terrain; joint (ii) and gravity; motion and constraints (iii) distributed between loads adjacent on crawlertracks. shoes and The oil gravity sand force units. is a user-defined input in MSC ADAMS. The contact force is a time varying force comprising normal and frictional forces and frictional torque. This force is estimed using in-built contact algorithms in MSC ADAMS and parameters in Table 3 [8].

4 4. Load distributions on crawler shoes after digging. Machine weight; Dipper Load. Minerals 2016, 6, External Forces on Crawler Shoes: External forces on crawler shoes are (i) contact forces between crawler shoes and terrain; (ii) gravity; and (iii) distributed loads on crawler tracks. The gravity force is a user-defined input in MSC ADAMS. The contact force is a time varying force comprising normal and frictional forces and frictional torque. This force is estimed using in-built contact algorithms in MSC ADAMS and parameters in Table 3 [8]. Minerals 2016, 6, Table 3. Contact parameters used in study [8,10,14]. Table 3. Contact parameters used in study [8,10,14]. Normal Normal Force Force Friction Force Force Contact Stiffness (k, (k, N/m) ˆ 10 8 Stic Stic Coecient Coecient (µs) (µ s ) 0.4 Max. Contact Damping (c(cmax,, N N s/m) ˆ 10 4 Dynamic Dynamic Coecient (µd) d ) 0.3 Force Exponent (e) Stic Stic transition velocity (Vst, st m/s), m/s) 0.01 Max. Max. Penetrion Depth (d, (d, m) m) ˆ Dynamic Dynamic transition transition velocity velocity (Vd, d m/s), m/s) The total load comprises shovel weight (minus crawler weight) and dipper payload. The shovel weight is constant but dipper payload varies with time and fill factor. The shovel cycle consists (i) propel to working face (0 (0 < t t < < s); s); (ii) (ii) merial excavion (15 (15 < t < 22.5 t < 22.5 s); (iii) s); (iii) hoisting hoisting and and swinging swinging from from face face to haul to haul truck truck (22.5 (22.5 < < t < t < 30 30s); s); (iv) merial dumping into haul truck (30 < t < 33.5 s); and (v) swinging after dumping to digging face (33.5 < t < 40 s). During propel, load on each crawler shoe is isonly due to to empty machine weight. The The total total machine weight weight for for P&H P&H 4100C 4100C BOSS BOSS is 1,410,184 is 1,410,184 kg [1]. kg [1]. The The total total machine machine load load (excluding crawler crawler shoe shoe weight) weight) for for P&H P&H 4100C 4100C BOSS BOSS is is 630,185 kg. kg. This Thisload is isdistributed uniformly on crawler shoes 1 13 in 3. Therefore, machine load/shoe in contact with ground is equal to kn. 3. Machine weight distribution on crawler shoes during propel. During digging, non-uniform machine and and dipper dipper loads loads act on act on crawler crawler shoes. shoes. The total The dipper total weight dipper for weight P&H for 4100 P&H C BOSS 4100 isc 890 BOSS kn. is It890 is assumed kn. It is th assumed (i) dipper th load (i) dipper is uniformly load is distributed uniformly on distributed crawler on tracks, crawler and thus, tracks, dipper and thus, load/track dipper is load/track 445 kn; (ii) is 445 dipper kn; load (ii) dipper acts only load onacts only 7 front crawler 7 front shoes; crawler and (iii) shoes; shoes and 1, (iii) 2, 3, shoes 4, 5 and 1, 2, 6 3, do4, not 5 and support 6 do any not dipper support load any and, dipper refore, load and, highest refore, dipper highest load acts dipper on shoe load 13acts and on shoe lowest 13 on and shoe 7. lowest The total on shoe distributed 7. The total loaddistributed on each crawler load shoe on each is equal crawler to machine shoe is equal plus to dipper machine load, plus as shown dipper in load, as shown 4. During swinging, 4. During maximum swinging, machine maximum and dipper machine loadsand shiftdipper to middle loads shift shoes, to resulting middle in symmetric shoes, resulting load distribution, in symmetric withload highest distribution, load on with shoe 7, highest load on swinging, shoe 7, as shown inswinging, 5. as During shown dumping, 5. During dipper load dumping, reduces todipper zero and load reduces to zero dumping, and only symmetric dumping, machine only load, symmetric in machine 5a, acts on load, crawler in shoes 5a, acts During on crawler return, shoes machine During loadreturn, is redistributed machine and, load is redistributed return, and, uniform load return, in 3uniform acts on shoes load in acts on shoes 1 13.

5 on each crawler shoe is equal to machine plus dipper load, as shown in 4. During swinging, maximum machine and dipper loads shift to middle shoes, resulting in symmetric load distribution, with highest load on shoe 7, swinging, as shown in 5. During dumping, dipper load reduces to zero and dumping, only symmetric machine Minerals load, in 2016, 6, 61 5a, acts on crawler shoes During return, machine load is redistributed 5and, 21 return, uniform load in 3 acts on shoes Minerals 2016, 6, Load Load distributions distributions on on crawler crawler shoes shoes after after digging. digging. Machine Machine weight; weight; Dipper Dipper Load. Load Load distributions on crawler shoes after swinging. Machine weight; Dipper Load. 5. Load distributions on crawler shoes after swinging. Machine weight; Dipper Load. The cubic STEP function defines total load as a function load and time. For example, crawler The shoe cubic 7 STEP has a function total load defines (i) total kn load for as propel a function (M); (ii) load 384 and kn time. For example, digging crawler (D); shoe (iii) has kn a total load (i) swinging kn (S); for (iv) propel 541 kn (M); (ii) 384 kn dumping (G); digging and (v) (D); (iii) kn 732 kn return swinging (M). Equion (S); (iv) (2) 541 defines kn step function dumping for (G); crawler and (v) shoe kn return (M). Equion (2) defines step function for crawler shoe 7. M t 15 s» fi M 2 t 15 t t ď 15 s M + ( D M ) ı 15 < t < 22.5s M ` pd Mq t t ă t ă 22.5 s D t s = t 22.5 s 2 D ` t t D ps ( S Dq ` t ` D) < t < s 2 t ă t ă s Load t 30 s Load = S t = 30 s N S ` pg Sq ` N (2) t 30 2 ` (2) t ă t ă 33.5 s 2 G t 30 t t 33.5 s S + ( G S) < t < 33.5 s G ` pm Gq ` t ` t ă t ă 40 s fl M t = 30 40s s 2 t 33.5 t 33.5 Similar load distributiong + ( M G) < t < s equions can be obtained 3 2 for or crawler 33.5 shoes, as shown in shows th load digging and swinging operions on each crawler shoe is M t = 40 s equal to sum machine weight and dipper payload (in s 4 and 5). These loads are applied Similar as point load loads distribution centroid equions each can crawler be obtained shoe. for or 7 shows crawler shoes, virtual as rigid shown body in crawler-terrain 6. simulor. 6 shows th The rigid load crawler shoes are digging replaced and with swinging flexibleoperions crawler on each to simule crawler shoe rigid flexible is equal to crawler-terrain sum machine interactions. weight and dipper payload (in s 4 and 5). These loads are applied as point loads centroid each crawler shoe. 7 shows virtual rigid body crawler-terrain simulor. The rigid crawler shoes are replaced with flexible crawler shoes to simule rigid flexible crawler-terrain interactions.

6 Similar load distribution equions can be obtained for or crawler shoes, as shown in 6. 6 shows th load digging and swinging operions on each crawler shoe is equal to sum machine weight and dipper payload (in s 4 and 5). These loads are applied as point loads centroid each crawler shoe. 7 shows virtual rigid body Minerals crawler-terrain 2016, 6, 61 simulor. The rigid crawler shoes are replaced with flexible crawler shoes 6 to 21 simule rigid flexible crawler-terrain interactions. 6. Load distributions on crawler shoes. 6. Load distributions on crawler shoes. Minerals 2016, 6, Three-dimensional virtual rigid track-terrain interaction. 3. Rigid Flexible Multi-Body Model The front and middle sets crawler shoes are subjected to maximum loads from both machine and dipper payloads. These These maximum loads loads can can cause cause a large a large stress stress buildup buildup in in crawler crawler shoes shoes th can th cause can cause figue figue failure. failure. This study This study captures captures stresses stresses on on front and front middle and middle crawler crawler shoes using shoes rigid flexible using rigid flexible multibody multibody dynamics dynamics ory. ory. The three front crawlershoes shoes (11, (11, and and 13) 13) and and middle middle ones ones (6, 7 and (6, 78) and are made 8) areflexible made flexible using modal usingneutral modal file neutral (MNF) file [11, (MNF) 12 and [11,12,15]. 15]. An MNF An MNF file is file genered is genered for each for each shoe shoe using using MSC MSC NASTRAN NASTRAN [13]. [13]. The The front front shoes shoes capture capture digging digging loads loads and and middle shoes capture swinging loads. Generion Modal Neutral File File (MNF): The The geometric models models shoes shoes 6, 7, 6, 8, 7, 11, 8, 11, 12 and 12 and 13 are 13 imported are imported into MSC into MSC PATRAN PATRAN to genere to genere a finitea element finite element (FE) mesh (FE) using mesh 10-node using tetrahedral 10-node tetrahedral elements. The elements. shoe merial The shoe is assumed merial is to assumed be linear and to be isotropic. linear and Table isotropic. 2 contains Table 2 merial contains properties merial for genering properties for flexible genering body. The flexible machine body. load The onmachine each crawler load shoe on each is scaled crawler to genere shoe is scaled time to varying genere loads time during varying shovelloads operion. during Four shovel tachment operion. nodes Four with tachment 6 DOFs are nodes genered with 6 DOFs joint are locions genered in crawler joint locions track assembly. in Rigid crawler body track spider assembly. web elements Rigid body (RBE2) spider are used web toelements connect (RBE2) tachment are used nodes to connect joint tachment center to nodes surface nodes joint around center to hole surface nodes joint [15]. around hole The component joint [15]. mode synsis (CMS) from Frimpong and Li [4], and Craig [16], is carried out on The meshed component crawler mode shoes synsis using (CMS) modal from analysis Frimpong solver and inli MSC [4], NASTRAN. and Craig [16], CMS is carried consistsout constraint meshed and fixed crawler boundary shoes using normal modes. modal Seventy analysis sixsolver fixedin boundary MSC NASTRAN. mode shapes CMS areconsists exported from constraint MSC NASTRAN and fixed boundary into MNF. normal CMS generes modes. Seventy 100 component six fixed modes boundary thmode include shapes 24 constraint are exported and 76 from fixed MSC boundary NASTRAN modes. into These MNF. modes CMS are generes ortho-normalized 100 component with associed modes th nural include frequencies. 24 constraint The first and six 76 orthogonalized fixed boundary Craig-Bampton modes. These modal modes basisare areortho-normalized rigid-body modes with nural associed frequencies. nural frequencies. The first six orthogonalized Craig-Bampton modal basis are rigid-body modes with nural frequencies. These are deactived during multi-body dynamic simulion in MSC ADAMS. A sample mesh for shoe 7 and different mode shapes with frequencies (f) up to 1200 Hz are shown in s 8 and 9. The reduced modal results are exported into an MNF file, which contains generalized stiffness and mass mrices, Eigenvalues, mode shapes, stress modes, modal loads,

7 hole joint [15]. The component mode synsis (CMS) from Frimpong and Li [4], and Craig [16], is carried out on meshed crawler shoes using modal analysis solver in MSC NASTRAN. CMS consists constraint and fixed boundary normal modes. Seventy six fixed boundary mode shapes are exported Minerals from 2016, MSC 6, 61 NASTRAN into MNF. CMS generes 100 component modes th include 24 constraint 7 21 and 76 fixed boundary modes. These modes are ortho-normalized with associed nural frequencies. The first six orthogonalized Craig-Bampton modal basis are rigid-body modes with These nural are deactived frequencies. during These are multi-body deactived dynamic during simulion multi-body in dynamic MSC ADAMS. simulion A sample in MSC mesh ADAMS. for shoe A sample 7 and mesh different for shoe mode 7 shapes and with different frequencies mode (f shapes ) up to with 1200 Hz frequencies are shown (f) in up s to and Hz 9. are The shown reduced in s modal results 8 and 9. are The exported reduced into modal an MNF results file, are which exported contains into an generalized MNF file, which stiffness contains and mass generalized mrices, stiffness Eigenvalues, and mode mass shapes, mrices, stress Eigenvalues, modes, modal mode loads, shapes, nodal stress coordines, modes, tachment modal loads, nodes nodal and coordines, inertia invariants tachment [11]. nodes and inertia invariants [11]. 8. Meshed 8. Meshed crawler crawler shoe shoe 7 in7 in MSC MSC PATRAN. PATRAN. The MNFs are imported into MSC ADAMS rigid virtual prototype model, in 7, to cree flexible shoes. After creing flexible shoes, changes are made to ir joint connections, contact forces, distributed loads and modal damping to develop rigid flexible virtual prototype simulor for crawler-terrain interactions. Joint constraints: The spherical and parallel primitive joints are replaced with two revolute joints between rigid flexible and flexible flexible crawler shoes. Contact Force: The rigid flexible multi-body system uses a flexible rigid solid contact model to capture contact between each flexible crawler shoe and rigid oil sand mass unit. Table 3 contains parameters for contact forces. Modal loads: The MNF file contains modal loads for uniformly distributed machine weight for flexible FEA crawler shoes 6, 7, 8 11, 12 and 13, as shown in 8. These loads are applied using MFORCE element in MSC ADAMS. The modal loads are scaled as a function time using cubic STEP Function in MSC ADAMS, in 6, for shovel propel and loading. Modal Damping: From modal analysis, 100 ortho-normalized component modes, including 6 rigid-body modes with associed frequencies, are genered for MNF file. Modal damping rios are specified for all flexible crawler shoes in MNF file [11]. The critical damping rios (ζ i ) for mode i = 7, 8... N, as a function modal frequency (f i ), for flexible crawler shoes 6, 7, 8 11, 12, and 13, shown in Equion (3), are applied using FXFREQ function in MSC ADAMS [11,15]. N (=100) is number modes. The completed 3-D virtual model for simuling rigid flexible crawler-terrain interaction is shown in 10. ζ i» ; f i ď 1000 Hz ` p q fi ; f i ą Hz ı fi ; 1000 ă f i ă Hz fi fl i 7, 8,... N (3)

8 Minerals 2016, 6, The MNFs are imported into MSC ADAMS rigid virtual prototype model, in 8, to cree flexible shoes. After creing flexible shoes, changes are made to ir joint connections, contact Minerals forces, 2016, distributed 6, 61 loads and modal damping to develop rigid flexible virtual prototype 8 21 simulor for crawler-terrain interactions. 9. Cont.

9 Minerals 2016, 6, Minerals 2016, 6, Sample modal shapes with von Mises stress priles for crawler shoe 7. f = Hz; 8 20 f = Hz; f = Hz; (d) f = Hz. Joint constraints: The spherical and parallel primitive joints are replaced with two revolute joints between rigid flexible and flexible flexible crawler shoes. Contact Force: The rigid flexible multi-body system uses a flexible rigid solid contact model to capture contact between each flexible crawler shoe and rigid oil sand mass unit. Table 3 contains parameters for contact forces. Modal loads: The MNF file contains modal loads for uniformly distributed machine weight for flexible FEA crawler shoes 7, 8, 9 11, 12 and 13, as shown in 9. These loads are applied using MFORCE element in MSC ADAMS. The modal loads are scaled as a function time using cubic STEP Function in MSC ADAMS, in 6, for shovel propel and loading. Modal Damping: From modal analysis, 100 ortho-normalized component modes, including 6 rigid-body modes with associed frequencies, are genered for MNF file. Modal damping rios are specified for all flexible crawler shoes (d) in MNF file [11]. The critical damping rios (ζi) for mode i = 7, 8 N, as a function modal frequency (fi), for flexible crawler shoes 7, 8, 9 11, 12, and 13, shown 9. in 9. Sample Sample Equion modal modal (3), shapes shapes are applied with with von von using Mises Mises FXFREQ stress stress priles priles function for forin crawler crawler MSC shoe ADAMS shoe [11,15]. f = N Hz; (=100) Hz; is number f = Hz; Hz; modes. f f = = The Hz; completed Hz; (d) (d) f f = = D Hz. Hz. virtual model for simuling rigid flexible crawler-terrain interaction is shown in 10. Joint constraints: The spherical and parallel primitive joints are replaced with two revolute joints between rigid flexible and flexible flexible crawler shoes. Contact Force: The rigid flexible multi-body system uses a flexible rigid solid contact model to capture contact between each flexible crawler shoe and rigid oil sand mass unit. Table 3 contains parameters for contact forces. Modal loads: The MNF file contains modal loads for uniformly distributed machine weight for flexible FEA crawler shoes 7, 8, 9 11, 12 and 13, as shown in 9. These loads are applied using MFORCE element in MSC ADAMS. The modal loads are scaled as a function time using cubic STEP Function in MSC ADAMS, in 6, for shovel propel and loading. Modal Damping: From modal analysis, 100 ortho-normalized component modes, including 6 rigid-body modes with associed frequencies, are genered for MNF file. Modal damping rios are specified for all flexible crawler shoes in MNF file [11]. The critical damping rios (ζi) for mode i = 7, 8 N, as a function modal frequency (fi), for flexible crawler shoes 7, 8, 9 11, 12, and 13, shown in Equion 10. Three-dimensional (3), are applied virtual using rigid flexible FXFREQ function track-terrain in MSC interaction ADAMS prototype. [11,15]. N (=100) is number modes. The completed 3-D virtual model for simuling rigid flexible crawler-terrain The differential-algebraic interaction is shown equions in (DAE) 10. ; governing fi 1000 Hz simulion rigid flexible crawler-formion interaction is derived 2from Lagrange s equion [11] as Equion (4). fi 1000 fi 1000 ζ i = ( ) 3 2 ; 1000 < fi < Hz i = 7,8, N (3) 1 M ξ.. ` M.. ξ 12. ı T.ξ BM Bξ ξ ` Kξ ; fi > ` fg ` Hz D. ı T ξ ` BΨ Bξ λ Q (4) Ψ 0 x rx y z s T is global position vector for rigid/flexible body coordine system origin; γ rψ θ ϕ s T is fixed body Euler angles ; f th 1000rele Hz oriention rigid/flexible i 2 body to global coordinesystem; fi 1000and q rq fi q 8... q N s T is flexible body ζ i = ( ) 3 2 ; 1000 < fi < Hz modal coordines i = 7,8, N ; fi > Hz (d) M is generalized mass mrix, ξ is generalized coordines vector, K is generalized stiffness mrix, f g is generalized gravitional force, D is modal damping mrix, Ψ is vector algebraic constraint equions, λ is Lagrange multipliers, and Q is generalized applied forces. The generalized coordines rigid flexible body, ξ, are given by Equion (5).» ξ q 10. Three-dimensional virtual rigid flexible track-terrain interaction prototype. x γ fi fl (5) (3)

10 Minerals 2016, 6, vector. Equion (4) is integred over time using GSTIFF integror with SI2 formulion in MSC ADAMS [10]. The integrion error, E = 0.01 m, is used for each time step during simulion. From start shovel operion, virtual simulor (in 10) is allowed to reach its quasi-stic equilibrium. Virtual simulion propel and loading is carried out for 40 s to capture flexible crawler-terrain interactions. Modal Deformion and Stress Recovery: From ADAMS/FLEX user document, physical displacement or translional nodal deformion (u) FEA nodes on each flexible crawler can be obtained from principle modal superposition in Equion (6). u Xq (6) X is modal mrix with columns populed by ortho-normalized mode shape or eigenvector mode number i (i = 7, 8,... N) and q is obtained from solution Equion (4). The generalized modal mass and stiffness mrices and modal load vector stored in MNF file along with modal damping mrix genered from Equion (3) are used in Equion (4) to obtain q for each flexible body. Similarly, from modal superposition ory, modal stress recovery can be performed using MSC ADAMS/DURABILITY plugin with embedded NASTRAN to recover nodal stresses on each flexible crawler shoes following Equion (7). σ X σ q (7) X σ is ortho-normalized modal stress mrix with columns occupied by stress shape vector mode number i (i = 7, 8,... N). The mode and stress shapes in Equions (6) and (7) are available in MNF file for each flexible crawler shoes. 4. Results and Discussions Kinemics and dynamic results are obtained from simulion experiments virtual flexible crawler system, in shows time variion x, y and z displacements front and middle flexible crawler shoes equilibrium. Table 4 shows x, y, z coordines nearest nodal locions time t = 0 (equilibrium). Both non-linear and linear crawler displacements are shown in global x-direction ( 11a). The x-displacement does not change during loading. 11b shows th crawler slides lerally in negive y-direction during propel and slides in opposite direction for loading. The leral slide is due to oil sand deformion. The maximum leral slide 1.5 cm occurs for shoe 13 during propel. The z-displacement ( 11c) shows fluctuions with bouncing during propel. During loading, displacement changes non-linearly due to non-linear semi-stic loading conditions on crawler shoes. The sharp spikes in z-displacement curve could be due to friction between crawler shoe and edges connected oil sand units. 12 shows a time variion x, y and z velocities for front and middle flexible shoes COM nodes. The x-velocity shoe 13 ( 12a) follows Equion (1) and or shoes are controlled by driver shoes via joints. 12b,c show th y- and z-velocities vary during propel (0 < t < 15 s). The varying leral sliding (y) velocity oscilles between 0.01 m/s. The bouncing crawler z-velocity reaches a maximum during accelerion and decelerion with a maximum range between 0.05 and m/s. During constant velocity propel, z-velocity fluctues between 0.03 and m/s. The x, y and z-velocities are negligible during loading between 15 < t < 40 s, as shown in shows angular velocities crawler shoes about global x, y and z directions. The crawler rolls with fluctuing x-angular velocity 0.5 deg/s, as in 13a, during propel. 13b shows th a large fluctuing angular velocity 15 deg/s develops around y-axis due to revolute joint between adjacent shoes. The crawler also rotes about vertical z-axis with fluctuing velocity 0.5 deg/s in 13c. The x, y and z angular velocities are negligible during loading (15 < t < 40 s), as in 13.

11 Minerals 2016, 6, Minerals 2016, 6, Displacement Displacement crawler crawler shoes shoes in in global global x, x, y y and and z z directions. directions. x-displacement; x-displacement; y-displacement; y-displacement; z-displacement. z-displacement. The x-displacement Table does 4. not Nodal change locions during moved loading. COM flexible 11b parts. shows th crawler slides lerally in negive y-direction during propel and slides in opposite direction for loading. The leral Locion slide (m) is due Part7_Flex to oil sand Part8_Flex deformion. Part9_Flex The maximum Part12_Flex leral slide Part13_Flex 1.5 cm Part14_Flex occurs for shoe 13 during propel. The z-displacement ( 11c) shows fluctuions with bouncing during propel. X During loading, Y displacement changes non-linearly due to non-linear semi-stic loading conditions Zon crawler shoes. The sharp spikes in z-displacement curve could be due to friction between crawler shoe and edges connected oil sand units. 14 shows total contact forces along x, y and z directions for each flexible shoe. The Table 4. Nodal locions moved COM flexible parts. contact force in x-direction ( 14a) is due to longitudinal propelling crawler. In y-direction Locion ( (m) Part7_Flex 14b), y arepart8_flex mainly due to Part9_Flex leral sliding Part12_Flex crawler. Part13_Flex The contact Part14_Flex forces in z-direction X ( 14c) are due to normal crawler forces. The longitudinal (x) and leral (y) forces are modeled Y using Coulomb friction force, and normal (z) forces using impact function in MSC ADAMS. Z Due to large fluctuions in slip velocity during accelerion and decelerion, corresponding x-force fluctuions are also large. These fluctuions decrease during constant velocity phase 12 ( shows 14a). a time variion 14a shows x, y th and z velocities x-force fluctues for front between and middle 0 and flexible shoes ˆ 10 5 N during COM nodes. propel. Thex-velocity x-force during shoe loading 13 ( is negligible 12a) follows in comparison Equion with (1) and propel or and fluctues shoes are between controlled 6000 by driver N. shoes via joints. 12b,c show th y- and z-velocities vary during propel (0 < t < 15 s). The varying leral sliding (y) velocity oscilles between ±0.01 m/s. The bouncing crawler z-velocity reaches a maximum during accelerion and decelerion with a maximum range between 0.05 and m/s. During constant velocity propel, z-velocity fluctues between 0.03 and m/s. The x, y and z-velocities are negligible during loading between 15 < t < 40 s, as shown in 12.

12 Minerals 2016, 6, Minerals 2016, 6, Velocity crawler shoes in global x, y and z directions. x-velocity; y-velocity; z-velocity. 13 shows angular velocities crawler shoes about global x, y and z directions. The crawler rolls with fluctuing x-angular velocity ±0.5 deg/s, as in 13a, during propel. fluctuing angular velocity ±15 deg/s develops 13b shows th a large around y-axis due to revolute joint between adjacent shoes. The crawler also rotes about vertical z-axis with fluctuing velocity ±0.5 deg/s in 13c. The x, y and z angular velocities are negligible during loading (15 < t < 40 s), as in shows total contact forces along x, y and z directions for each flexible shoe. The contact force in x-direction ( 14a) is due to longitudinal propelling crawler. In y-direction ( 14b), y are mainly due to leral sliding crawler. The contact forces in z-direction ( 14c) are due to normal crawler forces. The longitudinal (x) and leral (y) forces are modeled using Coulomb friction force, and normal (z) forces using impact function in MSC ADAMS. Due to large fluctuions in slip velocity during accelerion and decelerion, corresponding x-force fluctuions are also large. These fluctuions decrease during constant 12. Velocity crawler in global x, y and z directions. x-force x-velocity; y-velocity; z-velocity. velocity phase ( 14a).shoes 14aglobal shows between 0 and 12. Velocity crawler shoes in x, y th and z directions. fluctues x-velocity; y-velocity; N during propel. The x-force during loading is negligible in comparison with propel z-velocity. 13 shows angular velocities crawler shoes about global x, y and z directions. and fluctues between ±6000 N. The crawler rolls with fluctuing x-angular velocity ±0.5 deg/s, as in 13a, during propel. 13b shows th a large fluctuing angular velocity ±15 deg/s develops around y-axis due to revolute joint between adjacent shoes. The crawler also rotes about vertical z-axis with fluctuing velocity ±0.5 deg/s in 13c. The x, y and z angular velocities are negligible during loading (15 < t < 40 s), as in shows total contact forces along x, y and z directions for each flexible shoe. The contact force in x-direction ( 14a) is due to longitudinal propelling crawler. In y-direction ( 14b), y are mainly due to leral sliding crawler. The contact forces in z-direction ( 14c) are due to normal crawler forces. The longitudinal (x) and leral (y) forces are modeled using Coulomb friction force, and normal (z) forces using impact function in MSC ADAMS. Due to large fluctuions in slip velocity during accelerion and decelerion, corresponding x-force fluctuions are also large. These fluctuions decrease during constant velocity phase ( 14a). 14a shows th x-force fluctues between 0 and N during propel. The x-force during loading is negligible in comparison with propel Minerals 2016, 6, N. and fluctues between ± Angular Angular velocity crawler shoes shoes about about global global x, x, yy and and zz axes. axes. x-angular x-angular velocity; velocity; velocity crawler y-angular y-angular velocity; velocity; z-angular z-angular velocity. velocity.

13 13. Angular velocity crawler shoes about global x, y and z axes. x-angular velocity; Minerals 2016, 6, y-angular velocity; z-angular velocity. 14. Contact forces on different crawler shoes. x-contact force; y-contact force; z-contact force. 14. Contact forces on different crawler shoes. x-contact force; y-contact force; z-contact force. Similarly, total y-force or leral force ( 14b) fluctues between 37,370 and 32,178 N during propel and during loading, re are negligible fluctuions between 1000 and 4000 N. The Similarly, total y-force or leral force ( 14b) fluctues between 37,370 and 32,178 N z-force variion ( 14c) shows large fluctuions between and N during during propel and during loading, re are negligible fluctuions between 1000 and 4000 N. The propel, due to bouncing motion crawler track in z-direction ( 11c). Since z-force variion ( 14c) shows large fluctuions between 7.7 ˆ 10 z-position crawler shoes changes due to applied machine and 5 and 1.5 ˆ 10 dipper loads, 5 N during propel, z-forces also due to bouncing motion crawler track in z-direction ( 11c). Since z-position vary non-linearly with time between and as in 14c. The total torque applied crawler shoes changes due to applied machine and dipper loads, z-forces also vary non-linearly on each crawler shoe due to contact forces and frictional torque about global x, y and z with time between 7.6 ˆ 10 directions (not shown in 5 and 3.0 ˆ due to 5 as in 14c. The total torque applied on each crawler space limitions) dep on x, y and z-contact forces. The shoe due to contact forces and frictional torque about global x, y and z directions (not shown in total torque about x and y-axes dep on z-force and, hence, ir distribution is similar to 14 due to space limitions) dep on x, y and z-contact forces. The total torque about x and z-force variion in 14c. The z-torque deps on both x and y contact forces. y-axes dep on z-force and, hence, ir distribution is similar to z-force variion in 14c. Since y-force is an order magnitude smaller than x-force, z-torque variion is The z-torque deps on both x and y contact forces. similar to x-force ( 14a). The maximum magnitude x, y and z torques are , Since y-force is an order magnitude smaller than x-force, z-torque variion is similar , and N m, respectively, and are applied as external forces in Equion (4). 15 to x-force ( 14a). The maximum magnitude x, y and z torques are 7 ˆ 10 6, 1.3 ˆ 10 7, and 3.7 ˆ 10 6 N m, respectively, and are applied as external forces in Equion (4). 15 shows joint reaction forces one two revolute joint constraints between rigid flexible and flexible flexible shoes, with similar forces or revolute joint. The reaction force in x-direction ( 15a) is larger than th in y and z-directions ( 15b,c). This is due to applied motion constraint on flexible shoe 13, which pulls crawler in longitudinal direction to simule shovel propel. The maximum x-reaction force is 1.5 ˆ 10 6 N in shoe 13 during accelerion and decelerion ( 15a). This motion constraint also causes a large reaction force in y-direction in joint connecting flexible parts 13 and 14, with a maximum value 5 ˆ 10 5 N ( 15b). The y-reaction forces in or joints are smaller, with a maximum value five times smaller than th between parts 13 and 14. The z-reaction force in joints between parts in 15c is larger than y-reaction force, with a maximum value 2.5 ˆ 10 5 N. 15c shows th, during loading, a large z-reaction force occurs joints, with negligible reaction forces in or directions.

14 y-direction in joint connecting flexible parts 13 and 14, with a maximum value 5 10 N ( 15b). The y-reaction forces in or joints are smaller, with a maximum value five times smaller than th between parts 13 and 14. The z-reaction force in joints between parts in 15c is larger than y-reaction force, with a maximum value N. 15c shows th, during loading, a large z-reaction force occurs joints, with negligible reaction forces in Minerals 2016, 6, or directions. 15. Reaction forces revolute joint between adjacent crawler shoes. x-reaction force; 15. Reaction forces a revolute joint between adjacent crawler shoes. x-reaction force; y-reaction y-reaction force; force; z-reaction z-reaction force. force. Large fluctuing reaction moments also occur joints about global x and z directions Large fluctuing reaction moments also occur joints about global x and z directions during propel motion. The maximum reaction torque about x and z directions are during propel motion. The maximum reaction torque about x and z directions are 4 ˆ N m. The reaction torque about y-direction is negligible since crawler shoe is 4 N m. free to The rote Minerals reaction in 2016, th 6, torque direction. 61 about y-direction 16 shows is negligible oil sand deformion since crawler during shoe propel is free and to loading, rote in which 14 th 20 direction. is sum 16 deformions shows oil in sand all deformion spring-damper during oil propel sand units and loading, [17]. Large which variions is sum occur during negligible. deformions propel These with in modal negligible all coordines spring-damper variions are for combined oil loading. sand units with modal [17]. Large stresses variions in MNF occur to obtain during real propel time with stress The negligible histories propel in variions and loading flexible for deformions loading. crawler shoe. range between 2.42 and 2.6 cm, and 2.25 and cm, respectively. The largest deformion 2.6 cm occurs during constant velocity propel time t = 5.76 s. The largest loading deformion 2.25 cm occurs during swinging between 22.5 < t < 30 s. 17 shows time varying scale factors (q) in Equion (5) for mode shapes with frequencies within 0 < f < 1200 Hz for one flexible crawler shoes in front set (shoe 13) and in middle set (shoe 7) ( 10). The modal coordine variion for or flexible shoes follows similar distribution. The contribution from mode shapes with frequencies greer than 1200 Hz is 16. Deformion oil sand terrain. 16. Deformion oil sand terrain.

15 stress histories in flexible crawler shoe. Minerals 2016, 6, The propel and loading deformions range between 2.42 and 2.6 cm, and 2.25 and cm, respectively. The largest deformion 2.6 cm occurs during constant velocity propel time t = 5.76 s. The largest loading deformion 2.25 cm occurs during swinging between 22.5 < t < 30 s. 17 shows time varying scale factors (q) in Equion (5) for mode shapes with frequencies within 0 < f < 1200 Hz for one flexible crawler shoes in front set (shoe 13) and in middle set (shoe 7) ( 10). The modal coordine variion for or flexible shoes follows similar distribution. The contribution from mode shapes with frequencies greer than 1200 Hz is negligible. These modal coordines are combined with modal stresses in MNF to obtain real time stress histories in flexible crawler shoe. 16. Deformion oil sand terrain. 17. Time variion modal coordines for crawler shoes 7 and 13. During propel, modal coordines all crawler shoes fluctue but during loading y During propel, modal coordines all crawler shoes fluctue but during loading y have have a smooth non-linear semi-stic variion. 17 also shows th modal coordines for a smooth non-linear semi-stic variion. 17 also shows th modal coordines for mode mode shape 7 is dominant with a maximum scale factor The discontinuity in modal shape 7 is dominant with a maximum scale factor The discontinuity in modal coordines coordines during loading in solution could be due to a large integrion error (E = 1 cm) in during loading in solution could be due to a large integrion error (E = 1 cm) in ADAMS Solver. ADAMS Solver. 5. Dynamic Stress Time Histories for Flexible Crawler Shoes 5. Dynamic Stress Time Histories for Flexible Crawler Shoes s 18 and 19 show von Mises stresses during propel and loading, beginning and s 18 and 19 show von Mises stresses during propel and loading, beginning and shovel operion. The red arrows are contact forces on each crawler shoe, and colored shoes shovel operion. The red arrows are contact forces on each crawler shoe, and colored show von Mises stresses in N/m 2. 18a shows von-mises stresses in six flexible shoes shoes show von Mises stresses in N/m 2. 18a shows von-mises stresses in six rest or quasi-stic equilibrium (t = 0). Even though machine load is uniformly distributed, flexible shoes rest or quasi-stic equilibrium (t = 0). Even though machine load is uniformly middle crawler shoes are still subjected to a large amount stress loading compared to front distributed, middle crawler shoes are still subjected to a large amount stress loading compared crawler shoes. This is due to uneven distribution contact forces on each crawler shoe, as shown to front crawler shoes. This is due to uneven distribution contact forces on each crawler in 18a. During accelerion (between 0 < t < 5 s), front shoe stresses increase more rapidly shoe, as shown in 18a. During accelerion (between 0 < t < 5 s), front shoe stresses than middle shoes, as shown in 18b. increase more rapidly than middle shoes, as shown in 18b. During constant velocity propel (5 < t < 10 s), high stress areas (ě1.5 ˆ 107 N/m 2 ) slightly During constant velocity propel (5 < t < 10 s), high stress areas ( N/m 2 ) slightly increase in middle and front crawler shoes, as shown in 18c. These high stress areas furr increase in middle and front crawler shoes, as shown in 18c. These high stress areas increase during part decelerion phase. About half a second before decelerion furr increase during part decelerion phase. About half a second before phase (t «14.5 s), high stress shoes start to decrease, and t = 15 s, crawler comes to rest, but decelerion phase (t 14.5 s), high stress shoes start to decrease, and t = 15 s, crawler can have free 6-DOF motion due to its interaction with oil sands (Equion (1)). The stress crawler comes to rest, but can have free 6-DOF motion due to its interaction with oil sands (Equion (1)). distribution ( 18d) returns approximely to stress loading condition rest ( 18a). The stress crawler distribution ( 18d) returns approximely to stress loading condition 18 shows th stressed areas in driver crawler shoe 13 is much higher than those induced in rest ( 18a). 18 shows th stressed areas in driver crawler shoe 13 is much higher driven shoes during propel. than those induced in driven shoes during propel.

16 Minerals 2016, 6, Minerals 2016, 6, (d) 18. Von-Mises stress distribution in crawler shoes during propel. Stress 18. Von-Mises stress distribution in crawler shoes during propel. Stress equilibrium equilibrium position (t = 0 s); Stress accelerion (t = 5.0 s); Stress position (t = 0 s); Stress accelerion (t = 5.0 s); Stress const. velocity const. velocity (t = 10.0 s); (d) Stress decelerion (t = 15.0 s). (t = 10.0 s); (d) Stress decelerion (t = 15.0 s). 19 shows crawler stress distribution during loading. During digging (15 < t < 22.5 s), stresses increase in front shoes and decrease in middle shoes, as shown in 19a. During swinging (22.5 < t < 30 s), stresses steadily increase in middle and decrease in front, as shown in 19b. 19c shows th, during dumping (30 < t < 33.5 s), a small drop in stress is observed in middle shoes, while a negligible change occurs in front shoes. In return phase (33.5 < t < 40 s), a slight decrease in stresses occurs in middle shoes and increases in

17 propel. This is due to semi-stic nure external applied load ( 6). The shovel is mostly stionary during loading, with a negligible shear motion or slip between crawler and ground. These conditions genere high normal forces ( 14c) with negligible tangential forces on crawler shoes ( 14a,b), resulting in low von-mises stresses. The modal coordine Minerals distribution 2016, 6, in also shows th, during loading, only mode 7 (bing mode caused 17 by 21 normal force in 9) contributes to stresses. (d) Von-Mises Von-Mises stress stress distribution distribution in in crawler crawler shoes shoes during during loading. loading. Stress Stress digging digging (t (t = 22.5 = 22.5 s); s); Stress Stress swinging swinging (t (t = s); s); Stress Stress dumping dumping (t (t = s); s); (d) (d) Stress Stress return return (t (t = s). s). 19 shows crawler stress distribution during loading. During digging (15 < t < 22.5 s), stresses increase in front shoes and decrease in middle shoes, as shown in 19a. During swinging (22.5 < t < 30 s), stresses steadily increase in middle and decrease in front, as shown in 19b. 19c shows th, during dumping (30 < t < 33.5 s), a small drop in stress is observed in middle shoes, while a negligible change occurs in front shoes. In return phase

18 Minerals 2016, 6, (33.5 < t < 40 s), a slight decrease in stresses occurs in middle shoes and increases in front shoes t = 40 s ( 19d). The stress loading returns to equilibrium t = 0 s ( 18a). s 18 and 19 show th crawler stresses during loading are smaller than those during propel. This is due to semi-stic nure external applied load ( 6). The shovel is mostly stionary during loading, with a negligible shear motion or slip between crawler and ground. These conditions genere high normal forces ( 14c) with negligible tangential forces on crawler shoes ( 14a,b), resulting in low von-mises stresses. The modal coordine distribution in 17 also Minerals shows 2016, 6, th, 61 during loading, only mode 7 (bing mode caused by normal force in 17 9) 20 contributes to stresses. 6. Hot Spots in Flexible Crawler Shoes 6. Hot Spots in Flexible Crawler Shoes s 18 and 19 show general stress histories during shovel operion. The maximum nodal s stresses 18 and ir 19 show respective general locions stress in histories flexible during shoes are shovel extracted operion. from MSC The maximum ADAMS/DURABILITY. nodal stresses and ir 20 respective shows locions top five in hot spots flexible (highest shoesnodal are extracted stress) for fromflexible MSC ADAMS/DURABILITY. shoes 7 and 13 (using marker x ). 20 shows The numbers top five after hot spots marker (highest x show nodal stress) ranks for flexible stresses. shoes 7The andmaximum 13 (usingcontour marker x ). value The is 2 numbers 10 5 N/mafter 2 for all marker flexible x show bodies, as ranks shown in stresses. 20. The maximum figure shows contour th value all hotspots is 2 ˆ 10 5 are N/mloced 2 for allaround flexible bodies, link pin as shown joints, in and not 20. on The figure main shows crawler th body. all hotspots are loced around link pin joints, and not on main crawler body. 20. Hot-spots locion in crawler shoes. Part8_flex (Crawler Shoe 7); Part14_flex 20. Hot-spots locion in crawler shoes. Part8_flex (Crawler Shoe # 7); Part14_flex (Crawler Shoe 13). (Crawler Shoe # 13). However, crawler shoe failure in field mainly occurred in roller ph area, and not near link pin regions from this study. The motion constraint (Equion (1)) on shoe 13 COM node pulls track through joint connection between adjacent shoes. This causes a large amount tension or joint reaction force in x-direction ( 15a). This x-joint reaction force is responsible for high stresses in nodes around link pin joint region ( 20). The hot spots informion (von-mises stress, node id, node locion and time) for flexible shoes 7 and 13 are in Tables 5 and 6. The top five hot spots for or flexible shoes (6, 8, 11 and 12) are also loced around link pin joints. The time variion von-mises stresses for highest nodal stresses (hot spot #1) for each part

19 Minerals 2016, 6, However, crawler shoe failure in field mainly occurred in roller ph area, and not near link pin regions from this study. The motion constraint (Equion (1)) on shoe 13 COM node pulls track through joint connection between adjacent shoes. This causes a large amount tension or joint reaction force in x-direction ( 15a). This x-joint reaction force is responsible for high stresses in nodes around link pin joint region ( 20). The hot spots informion (von-mises stress, node id, node locion and time) for flexible shoes 7 and 13 are in Tables 5 and 6. The top five hot spots for or flexible shoes (6, 8, 11 and 12) are also loced around link pin joints. Table 5. Hot spot informion for Part8_flex. Hot Spots Stress (MPa) Node ID Time (s) Locion x (m) y (m) z (m) Table 6. Hot spot informion for Part14_flex. Hot Spots Stress (MPa) Node ID Time (s) Locion x (m) y (m) z (m) The time variion von-mises stresses for highest nodal stresses (hot spot #1) for each part are shown in 21. The maximum nodal stress on flexible Parts 7, 8, 9, 12, 13 and 14 are 53.6, 33.3, 37.07, 49.55, and MPa, respectively. 21 shows th maximum nodal stresses during propel follow x-reaction force distribution in 15a. Since x-reaction forces are larger on parts 14, 13 and 12 in comparison to parts 7, 8 and 9 ( 15a), maximum nodal stresses are also larger on flexible parts 12, 13 and 14 ( 21d f). The yield strength A36 steel crawler merial is 250 MPa [18]. Although maximum nodal stresses in shoes are smaller than yield strength, large fluctuing stresses during propel ( 21) can cause a shoe failure by figue due to crack initiion in link pins. Although crawler shoes do experience tension or pulling forces when it passes over rear idler or tumbler, field observion study undertaken Athabasca oil sand regions indice th P&H 4100C BOSS crawler shoes develop cracks and break mainly roller ph area, while link pin joint lugs remained intact. The crushing force lower rollers, which distribute shovel weight along crawler track [3], is responsible for this behavior and needs to be accounted for in virtual prototype model to accurely predict crawler shoe failure.

20 Although crawler shoes do experience tension or pulling forces when it passes over rear idler or tumbler, field observion study undertaken Athabasca oil sand regions indice th P&H 4100C BOSS crawler shoes develop cracks and break mainly roller ph area, while link pin joint lugs remained intact. The crushing force lower rollers, which distribute shovel weight along Minerals 2016, crawler 6, 61 track [3], is responsible for this behavior and needs to be accounted for in virtual prototype model to accurely predict crawler shoe failure. Minerals 2016, 6, (d) (e) (f) Time Time variion variion highest highest nodal nodal stress. stress. Part7_flex; Part7_flex; Part8_flex; Part8_flex; Part9_flex; Part9_flex; (d) Part12_flex; (d) Part12_flex; (e) Part13_flex; (e) Part13_flex; (f) Part14_flex. (f) Part14_flex. 7. Conclusions 7. Conclusions 3D virtual prototype model an open crawler track on oil sands terrain is developed in MSC A 3D virtual prototype model an open crawler track on oil sands terrain is developed in MSC ADAMS/FLEX/DURABILITY to capture crawler shoe stresses during propel and loading, using ADAMS/FLEX/DURABILITY to capture crawler shoe stresses during propel and loading, using a rigid flexible multi-body dynamics ory. The flexible shoes are genered from MNF using rigid flexible multi-body dynamics ory. The flexible shoes are genered from MNF using Craig-Bampton ory on component mode synsis and dynamic solver in MSC NASTRAN. Craig-Bampton ory on component mode synsis and dynamic solver in MSC NASTRAN. The The load distribution on crawler from machine weight and dipper payload is developed for load distribution on crawler from machine weight and dipper payload is developed for propel and propel and loading. The virtual model is simuled from quasi-stic equilibrium for a period 40 s. loading. The virtual model is simuled from quasi-stic equilibrium for a period 40 s. The propel The propel motion consists accelerion, constant velocity and decelerion phases for first motion consists accelerion, constant velocity and decelerion phases for first 15 s, and loading 15 s, and loading consists digging, swinging, dumping and return for remaining 25 s. consists digging, swinging, dumping and return for remaining 25 s. The kinemics simulion results show th crawler track slides during shovel operion The kinemics simulion results show th crawler track slides during shovel operion with maximum displacement 1.5 cm. During propel, crawler velocities along x, y and z with a maximum displacement 1.5 cm. During propel, crawler velocities along x, y and directions fluctue with a maximum 0.15, 0.01 and 0.04 m/s, respectively. In addition, crawler z directions fluctue with a maximum 0.15, 0.01 and 0.04 m/s, respectively. In addition, can also rote about x-axis (roll) and z-axis (yaw) with a maximum value ±0.5 deg/s. The dynamics simulion results show th, during propel, highly varying contact forces acts along x, y and z directions with maximum values , and N, respectively. Large varying joint reaction forces develop along x-direction with a maximum value N in shoe 13. The distribution shows large stresses link pin region during propel. The maximum von Mises shoe stresses range between 33 and MPa. The maximum nodal stress MPa

21 Minerals 2016, 6, crawler can also rote about x-axis (roll) and z-axis (yaw) with a maximum value 0.5 deg/s. The dynamics simulion results show th, during propel, highly varying contact forces acts along x, y and z directions with maximum values ˆ 10 5, 3.7 ˆ 10 4 and 7.7 ˆ 10 5 N, respectively. Large varying joint reaction forces develop along x-direction with a maximum value 1.5 ˆ 10 6 N in shoe 13. The distribution shows large stresses link pin region during propel. The maximum von Mises shoe stresses range between 33 and MPa. The maximum nodal stress MPa occurs for crawler shoe 13 node 26,178, loced link pin region. The results also show th stress time histories during loading are semi-stic, with a maximum stress 27 MPa, which is far smaller than corresponding maximum stress during propel. Author Contributions: This paper is written by both Samuel Frimpong and Magesh Thiruvengadam. Conflicts Interest: The authors declare no conflict interest. References 1. Joy Global. 4100C BOSS Electric Mining Shovel AC Drive Product Overview Available online: _4100c_boss_ac_bro.pdf?sfvrsn=10 (accessed on 16 June 2016). 2. JOY Global Inc. Electric Rope Shovels. Available online: electric-rope-shovels (accessed on 18 June 2016). 3. P&H MinePro Services. Peak Performance Practices: Lower Works; P&H MinePro Services: Milwaukee, WI, USA, Frimpong, S.; Li, Y. Stress loading cable shovel boom under in-situ digging conditions. Eng. Fail. Anal. 2007, 14, [CrossRef] 5. Frimpong, S.; Li, Y. Hybrid virtual prototype for analyzing cable shovel component stress. Int. J. Manuf. Technol. 2008, 37, Frimpong, S.; Thiruvengadam, M. Rigid multi-body kinemics shovel crawler-formion interactions. Int. J. Mining Reclam. Environ [CrossRef] 7. Frimpong, S.; Thiruvengadam, M. Multi-body dynamic modeling and simulion crawler-formion interactions in surface mining operions. Glob. J. Res. Eng. 2015, 15, Frimpong, S.; Thiruvengadam, M. Contact and joint forces modeling and simulion crawler-formion interactions. J. Powder Metall. Min. 2015, 4, 135. [CrossRef] 9. MSC. MSC ADAMS/View Help Document; MSC: San Diego, CA, USA, Available online: (accessed on 16 June 2016). 10. MSC. MSC ADAMS/Solver Help Document; MSC: San Diego, CA, USA, Available online: (accessed on 16 June 2016). 11. MSC. MSC ADAMS/Flex Help Document; MSC: San Diego, CA, USA, Available online: (accessed on 16 June 2016). 12. MSC. MSC ADAMS/Durability Help Document; MSC: San Diego, CA, USA, Available online: (accessed on 16 June 2016). 13. MSC. MSC NASTRAN Dynamic Analysis User s Guide; MSC: San Diego, CA, USA, Available online: (accessed on 16 June 2016). 14. Frimpong, S.; Galecki, G.; Li, Y. Dump truck tire stress simulion for exted service life. Trans. SME 2012, 332, MSC Stware Learning Center. Available online: (accessed on 16 June 2016). 16. Craig, R.R.; Kurdila, A.J. Fund Structural Dynamics, 2nd ed.; John Wiley & Sons: New York, NY, USA, Frimpong, S.; Li, Y.; Suglo, R. Dynamic torque and soil deformion mechanics and simulion GAP machinery. Special edition on surface mining. J. Powder Metall. Min. 2013, 2. [CrossRef] 18. Harvey, P. Engineering Properties Steel; American Society for Metals: Merials Park, OH, USA, by authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under terms and conditions Creive Commons Attribution (CC-BY) license (