Approval sheet STUDY ON AGRICULTURAL TRACTOR OPERATOR SAFETY IN ROLLOVER ACCIDENTS A Dissertation Presented for the Doctor of Philosophy Degree The University of Tennessee, Knoxville Farzaneh Khorsani Kouhanestani December 2016 ii iii Copyright © 2011 by Farzaneh Khorsani Kouhanestani All rights reserved. DEDICATION I dedicate my work to My Mother Nahid Khailian and My Father. Ali Khorsandi ACKNOWLEDGEMENTS I would like to thank my Major advisor Prof. Paul D. Ayers for all of his supports during my Ph.D. program. I learnt a lot from him. Also, I would like to thank my committee members, Prof. John B. Wilkerson, Prof. Robert B. Freeland, and Dr. Timothy J. Truster who provided me with great support especially for their valuable suggestions and revision to the papers. I would like to express my gratitude for my parents, Nahid Khalilian and Ali Khorsandi, my sister, Zohreh Khorsandi, and my brother, Saeid Khorsandi for all their support in whatever I do in my life. Also, I would like to thank my awesome friends both in Iran, in the U.S. and in other parts of the World who have been part of my journey: Saman Souri, Duncan Mochiki, Casey Sullivan, Isacc Jeldes, and Lilian Wanjiro, for all of their supports. I also want to thank my fellow students and friends: Dillan Jackson. Jake Dixon, Guilherme de Moura for helping me in the experimental tests. I would like to tanks all of the faculty members and staff of BESS, especially whom that support me, Dr. William Hart, Dr. Eric Drumm, Mr. Scott Tucker, Artan Xhaferaj, Lesia Rucker, and Marine Sandra. ABSTRACT Agriculture is one of the most dangerous industries in the US. Tractor accidents are the major cause of death in agriculture, producing about one half of the fatal accidents. Tractor overturn is the most common cause of death in tractor accidents. Three projects related to tractor operator safety in rollover accident were defined. The aim of first project is to develop a Finite Element (FE) model to predict the Roll-Over Protective Structure (ROPS) performance under the standard SAE J2194 static test. The developed model was validated by comparing the model results with experimental test results. The developed model can predict the experimental test results with error less than 25%. The rigid ROPS are not appropriate for working in low overhead clearance zones. The foldable ROPS (FROPS) was designed to solve the rigid ROPS problem, but lowering and raising the conventional FROPS is time consuming and strenuous. The actuation forces to raise and lower the FROPS were not well known. In the second project a measurement system was designed to measure the actuation force and the angle of the foldable ROPS. Two measurement setups were developed to examine the effect of speed and friction on the actuation torque. Results showed that both friction and speed had significant effect on actuation torque. In the third project a model was developed to predict the effect of liquid shift on agricultural machineries CG height calculation. The CG location is one of the determinant factors for finding the stability angle. When the tractor tilting angle is higher than the stability angle the tractor will rollover. The new ISO 16231 uses lift axle method to determine, the CG height and is subject to inaccuracy related to liquid shift (ISO, 2014). The model was validated by comparing the results with experimental results of two small wagons and a full size tractor. The developed model predicted the measured CG height with less than 5% error. The effect of liquid shift on CG height measurement for a vehicle with 16% liquid is 19.5% and for the tractor with 2% of liquid is 0.35%. Table of Contents 1 CHAPTER I INTRODUCTION 8 1.1 DEVELOPING A FINITE ELEMENT MODEL 10 1.1.1 ROLLOVER PROTECTIVE STRUCTURE (ROPS) 10 1.1.2 STANDARD SAE J2194 10 1.1.2.1 CLEARNCE ZONE 11 1.1.2.2 12 1.1.2.3 LONGITUDINAL LOADING TEST 12 1.1.2.4 FIRST AND SECOND VERTICAL LOADING TEST 13 1.1.2.5 OVER LOAD TEST 13 1.1.3 MODELING 13 1.1.4 SUMMARY 14 1.2 MEASURING THE FORCES TO ACTUATE A FOLDABLE ROPS 15 1.2.1 CONVENTIONAL FROPS 15 1.2.2 PASSIVE SYSTEMS 15 1.2.3 ACTIVE SYSTEM 18 1.2.4 AUTOMOTIVE ACTIVE SYSTEM 19 1.2.5 OECD CODE 20 1.2.6 DEVELOPING THE MEASUREMENT SETUP 22 1.2.6.1 ANGULAR DISPLACEMENT SENSOR 22 1.2.6.1.1 RESISTIVE DISPLACEMENT SENSOR 23 1.2.6.1.2 INDUCTIVE TRANSDUCER DISPLACEMENT SENSOR 24 1.2.6.1.3 OPTICAL ENCODER DISPLACEMENT SENSOR 25 1.2.6.1.4 MAGNETIC DISPLACEMENT SENSOR 25 1.2.6.1.5 INDUCTION POTENTIOMETER (SYNCHRO/RESOLVER DISPLACEMENT SENSOR) 26 1.2.6.1.6 ACCELEROMETER 28 1.2.6.1.6.1 TEST THE STATIC CALIBRATION 29 1.2.6.1.6.2 DYNAMIC CALIBRATION TEST WITH FORK 31 1.2.6.1.6.3 DYNAMIC CALIBRATION TEST WITH ROPS 34 1.2.6.1.6.4 TANGENTIAL ACCELERATION (aθ) AND CENTRIFUGAL ACCELERATION (ar) 35 1.1.1.1 ACTUATION FORCE 37 1.2.6.1.7 LOAD CELL SELECTION 37 1.2.6.1.8 TORQUE TRANSDUCER SELECTION 38 1.2.6.1.9 TORQUE TRANSDUCER 38 1.2.6.1.10 MEASUREMENT SETUP 39 1.2.7 SUMMARY 41 1.3 THE EFFECT OF LIQUID SHIFT ON CG HEIGHT MEASUREMENT 43 1.3.1 NOMENCLATURE 43 1.3.2 COORDINATE SYSTEM 43 1.3.3 INTRODUCTION AND LITERATURE REVIEW 44 1.3.4 PENDULUM METHOD 44 1.3.5 LIFTING AXLE METHOD 45 1.3.6 STANDARD ISO /DIS 16231 47 1.3.7 SUMMARY 50 1.4 REFERENCES 51 2 CHAPTER II DEVELOPING AND EVALUATING A FINITE ELEMENT MODEL FOR PREDICTING THE ROLLOVER PROTECTIVE STRUCTURE NONLINEAR BEHAVIOR UNDER SAE J2194 STATIC TEST 54 2.1 ABSTRACT 54 2.2 INTRODUCTION AND LITERATURE REVIEW 55 2.2.1 ROPS PERFORMANCES AND REGULATIONS 55 2.2.2 MODELING 56 2.3 JUSTIFICATION 58 2.4 OBJECTIVE 58 2.5 MATERIAL AND METHODS 59 2.5.1 DESIGN THE ROPS WITH CRDP 59 2.5.2 EXPERIMENTAL TEST 61 LONGITUDINAL (REAR) LOAD TEST 61 2.5.2.1 TRANSVERSE (SIDE) LOADING 62 2.5.2.2 PARAMETERS OF PERFORMANCE 62 2.5.3 FINITE ELEMENT MODEL 63 2.5.3.1 MATERIAL PROPERTIES 64 2.5.3.2 MESH GENERATION 66 2.5.3.3 DETERMINING THE BOUNDARY CONDITION 66 2.6 RESULTS AND DISCUSSION 67 2.7 Conclusion 76 1. ACKNOWLEDGEMENTS 76 2.8 REFERENCES 78 3 CHAPTER III The effect of speed on foldable ROPS actuation forces 80 3.1 Abstract. 82 3.2 Introduction 82 3.3 Material and methods 85 3.3.1 Measurement setup 85 3.3.1.1 POWER SETUP 86 3.3.1.2 SENSING SETUP 86 3.3.2 Experimental test design 87 3.3.3 Developing a theoretical model 88 3.4 Results and Discussion 89 3.5 Conclusions 98 ACKNOWLEDGEMENTS 99 3.6 References 99 3.7 Appendix 100 3.7.1 Material and method 100 3.8 Conclusion 104 4 CHAPTER Ⅳ modeling the effect of liquid movement on the center of gravity location of off-road vehicles 129 5 130 7 VITA 132 CHAPTER I INTRODUCTION Agriculture is one of the most dangerous industries in the US (Bureau of Labor Statistics, 2014). Tractor accidents are the major cause of death in agriculture, producing about one half of the fatal accidents. Tractor overturn is the most common cause of death in tractor accidents. Roughly one third of the fatal tractor accidents are rollover accidents. The rollover accident happens when the vehicle tilting angle is higher than the static overturning angle (SOA) which is a function of center of gravity (CG) height. Finding the CG height more accurately could lead to less overturn accidents. The most effective way to prevent overturn deaths during an overturn accident is use of a rollover protective structure (ROPS) in combination with a seat belt. A ROPS is a structure which absorbs a portion of the impact energy generated by the tractor weight in the rollover accident. The ROPS decreases the possibility of severe human injuries by providing a clearance zone to protect the operator among the ROPS envelope. Three projects related to agricultural tractor operator safety in rollover accidents are defined. The first project involves developing a Finite Element (FE) model to predict the ROPS nonlinear performance for ROPS which are designed with Computer-based ROPS Design Program (CRDP). ROPS must pass a standard ROPS test prior to certificate. The experimental standard tests are expensive, time consuming and laborious. The aim of this project is to develop a FE model to predict the ROPS performance under the standard SAE J2194 static test. The developed model was validated by comparing the model results with experimental test results. In the second project a system was designed to measure the actuation force and the angle of the foldable ROPS. The rigid ROPS are not appropriate for working in low overhead clearance zones such as orchard. The foldable ROPS was designed to solve the rigid ROPS problem, but lowering and raising the conventional foldable ROPS is time consuming and strenuous. The actuation forces must meet the allowable force levels based on OECD Standard. A fold assist mechanism would be helpful for raising and lowering the ROPS but in order to design a fold assist mechanism the actuation force should be measured in advance. Two measurement setups were developed to examine the effect of speed and friction on the actuation torque. In the third project a model was developed to predict the effect of liquid shift on agricultural machineries CG height calculation. The CG location is one of the determinant factors for finding the stability angle. When the tractor tilting angle is higher than the stability angle the tractor will rollover. The new ISO 16231 uses lift axle method to determine, the CG height and is subject to inaccuracy related to liquid shift (ISO, 2014). The model was validated by comparing the results with experimental results of two small wagons and a full size tractor. DEVELOPING A FINITE ELEMENT MODEL Tractor accidents are the major cause of death in agriculture. One half of the fatal agricultural accidents are related to tractor accidents Tractor related fatalities include being run over or be crushed by tractor, engagement in moving parts of the tractor, accidents on road way, and tractor overturn (Reynolds & Groves, 2000). Tractor overturn is the most important cause of death in tractor accidents (Springfeldt, 1996). Tractors overturn caused (Chisholm, 1979c) by slipping on steep slopes, bumping against obstacles, turning sharp curves, and shearing the soil. Tractor rollover account for up to one third of all tractor related fatalities (Murphy & Yoder, 1998). The most effective way to prevent overturn deaths is the use of ROPS in combination with seat belt. ROLLOVER PROTECTIVE STRUCTURE (ROPS) ROPS is a frame or cab which is installed on the tractor to minimize the possibility and severity of operator injury in rollover accidents. ROPS provides a clearance zone among the envelope of the ROPS to protect the operator in rollover accident. ROPS design is a big challenge for tractor manufacturer and increase the ROPS production expenses. Too rigid structure inserts a big shock to the operator body which causes serious operator injuries (Chen, Wang, Zhang, Zhang, & Si, 2012) and inserts a big force and moment to the chassis. Too flexible structure deforms greatly under the load and infringes the clearance zone or leaves the clearance zone unprotected. The ROPS performance criteria must be examined with one of the standard tests. STANDARD SAE J2194 SAE J2194 (1997) is an official procedure which was developed for testing ROPS performance of wheeled agricultural tractors. The SAE J2194 is modified form of SAE J1194 (1977) which had been used several years for testing ROPS performance (Ayers, Dickson, & Warner, 1994). SAE J1194 was developed mainly based on three studies which conducted about thirty years ago (Chisholm, 1979a, 1979b, 1979c). The SAE J2194 includes three types of standard tests; field upset, dynamic, and static test. In the field upset test a tractor is driven up a ramp. In the impact test the impact forces are inserted by means of a 2000 kg mass that acts as a pendulum. The dynamic test can be used for the static test includes sequences of four static forces which are inserted to the ROPS gradually, two vertical forces and two horizontal forces in which application rate is 5 mm s-1. The field upset is similar to the real rollover accident (B. J. Clark, Thambiratnam, & Perera, 2006). The repeatability of field upset test is low, the expenses is high and needs large amount of man power. The dynamic test is better able to simulate the rollover accident in comparison with the static test but deflection measurement during test is difficult. The repeatability of dynamic test is poor, the test endangers the test staff life and chassis of the tractor might be completely destroyed during the test with a poorly designed ROPS (Rondelli & Guzzomi, 2010). The static test is less demanding than two other tests, collecting the data is easy, the results are reliable and accurate (Ross & DiMartino, 1982). Majority of the manufacturers select the static test (A. Fabbri & Ward, 2002). SAE J2194 requires either the static or dynamic test or both to certify ROPS performance (Harris, Mucino, Etherton, Snyder, & Means, 2000). Based on SAE J2194 the static test is applicable for tractors heavier than 800 kg. The static test usually consists of sequences of four static tests including, longitudinal, first vertical, transverse load test, second vertical loading test, and in some special cases over load test. The static test performance requirements would be met if the structural members absorb a predefined level of energy in longitudinal and transverse tests and tolerate a specific force in vertical test without violating intrusion and exposure criteria. The ROPS should not infringe the clearance zone (intrusion criteria) and ROPS should not leave clearance zone unprotected from the ground plane (exposure criteria). In the next sections the definition of clearance zone and these four static tests based on SAE J2194 standard test for two post ROPS are described. CLEARNCE ZONE The clearance zone is defined as the safe zone that ROPS provides to protect the operator in rollover accidents. SAE J2194 standard defines the clearance zone based on vertical reference plane and seat reference point. The vertical reference plane passes vertically from the seat reference point (SRP) and the center of steering wheel (Fig. 1.1). Figure ‎1.1. Clearance zone from the side (SAE J2194). LONGITUDINAL LOADING TEST The longitudinal load should be applied horizontally and parallel to the longitudinal tractor median plane with rate less than 5 mm/s. The load is applied to the uppermost transverse structural member of the ROPS which is most likely to strike the ground first in an overturn accident (Fig. 1.2). The first longitudinal test must be inserted from rear of the ROPS until the ROPS absorbed energy (E) is equal to: E= 1.4 M (1.1) Where E is absorbed energy (J) and M is tractor reference mass in (kg). The absorbed energy is the area under force- deflection curve. Tractor reference mass is determined as “A mass, not less than the tractor mass, selected for calculation of the force and energy inputs to be used during test.” Commonly, unladen mass of tractor is selected as the reference mass. Unladen mass of tractor is equal to the total mass of vehicle with the ROPS fitted, full liquid tanks (fuel, lubricant, and coolant), and a 75 kg driver (Rondelli & Guzzomi, 2010). Figure ‎1.2. Static tests. (a) Longitudinal load (b) first and second vertical load test (c) Transverse loading test (SAE J2194). FIRST AND SECOND VERTICAL LOADING TEST The first vertical load is inserted vertically to the uppermost structural member which is called cross bar (Fig. 1.2). The inserted load (F) is equal to: F=20 M (1.2) Where F is applied force (N). Exerting load should be stopped at least 5 seconds after cessation of any visually detectable movement. The second vertical test for two post ROPS is exactly the same as the first vertical test (Fig. 1.2). TRANSVERSE LOADING The transverse load which is also called side load must be inserted horizontally at 90 degrees to the longitudinal median plane of the tractor. The side load should be applied to the structural member uppermost on the side (Fig. 1.2). The test stops when the absorbed energy is equal to: E= 1.75 M (1.3) OVER LOAD TEST The over load test is required when the applied force decreases by more than 3% over the last 5% of the deflection attained when the absorbed energy by ROPS under side load test reaches 1.75 times of the mass of tractor. The over load test consists of continuing the horizontal loading from 5% of original required energy to 20 % additional energy. MODELING FE is a numerical approach used to obtain approximate solutions of boundary value problems in engineering. A boundary problem is a mathematical problem in which one or more dependent variables must satisfy a differential equation everywhere within a known domain of independent variables and satisfy specific conditions on the boundary of the field (Hutton & Wu, 2004). Several authors used commercial FE software packages to predict ROPS performance under standard test such as, ANSYS (Alfaro, Arana, Arazuri, & Jarén, 2010) and Abaqus (B. Clark, 2005; Thambiratnam, Clark, & Perera, 2009). SUMMARY The experimental standardized tests are expensive, laborious, time consuming, and destructive. About one third of ROPS fail the standard tests and the test failure postpones ROPS production project and increases the project expenses. Using the experimental test alone can’t improve ROPS design and performance. Modeling has been introduced as a method that can simulate ROPS performance in rollover accidents, speeds up the design process and reduces the ROPS production expenses. Therefore researchers have used combination of experimental test and mathematical model to improve and test ROPS performance. Although computer models are able to predict the force-deflection curve of ROPS but the experiment test cannot be replaced with computer models. The modeling approach is needed to increase the possibility that the designed ROPS is likely to pass the standard prior to the experimental test. There is no nonlinear FE model available to predict the behavior of rear mount two post ROPS which was designed with Computer-based ROPS Design Program (CRDP). In the first project a FE model was developed to examine the performance of the rear mount two-post ROPS, designed by CRDP. MEASURING THE FORCES TO ACTUATE A FOLDABLE ROPS Working with retrofitted tractor in places with low overhead clearance zones such as, as orchard, and animal confinement buildings is hard and in some cases impossible. In order to facilitate tractor operation in low overhead clearance zones, foldable ROPS (FROPS) have been developed. The foldable ROPS can be divided to several groups, conventional, passive, active, and automotive active FROPS. The conventional FROPS are manually folded, re-erected, and locked. The passive FROPS include lift assist mechanisms that help the operator to fold down and raise the ROPS. The active FROPS or powered systems fold and re-erect upper part of the FROPS by electrical, mechanical, or hydraulic power but, operator controls the ROPS position. The automated active FROPS automatically deploy during rollover accident (Robinson et al., 2012). CONVENTIONAL FROPS In conventional FROPS when the tractor reaches a point with low overhead clearance zone, tractor operator turns off the tractor engine, leaves the seat, releases the quick lock, removes the pin, folds down the ROPS, comes back to the seat, turns on the tractor and continues the work. After passing the overhead obstacle the operator repeats all of the previous steps to raise the ROPS. Lowering and raising the ROPS is a time consuming and strenuous process (Panek & Kolli, 1998) therefore, the operator prefers to leave the FROPS in inoperative position (Ayers, 2015). The number of retrofitted tractors with ROPS has increased recently but, the number fatal roll-over accidents of tractors with folded down ROPS has increased. National Institute for Occupational Safety and Health (NIOSH) reports no fatalities related to rollover accident with folded down ROPS before 2003 but, the percentage of fatal rollover accident with folded down ROPS increased sharply to 25% in 2005 and to 50% at 2012 (FACE, 2014). The survey done by European Commission members showed that 40% of fatalities and serious injuries happened when the ROPS was in inoperative position in rollover accident (Hoy, 2009). PASSIVE SYSTEMS Several passive mechanisms were developed to minimize the actuation force and help the operator to raise and lower the ROPS with less effort in comparison with conventional FROPS (Finch, Martinez, & Sandoval, 1998; Ludwig, 1990; Panek & Kolli, 1998; Sheehan, 1992). The passive systems are generally low cost and simple in comparison with powered and automotive systems (Robinson et al., 2012). Ludwig (1990) equipped ROPS with a lever arm and claimed that the operator doesn’t need to leave the vehicle seat to raise or re-erect the ROPS. The lever arm slide down with gravity force when the ROPS was in inoperative position (Fig. 1.5). The ROPS could be locked in raised or lowered position by means of pins which were inserted in holes at the pivot point bracket (Ludwig, 1990). This mechanism needed a clearance zone rearward of the ROPS as big as the height of the upper part of the FROPS to allow the upper part to move pivotally. Turning the upper part was awkward and required the operator to leave the seat (Finch et al., 1998). Figure ‎1.3. FROPS with lever arm, in inoperative position (Ludwig, 1990). Sheehan (1992) designed a telescopic rollover protective structure for orchard tractors. The protective member was attached to a compression spring. The compression spring housed within the lower section and facilitated movement of the protective member to the raised position (Fig. 1.6). A locking mechanism fixed the movable member to restrict the movement in both lowered and raised positions (Sheehan, 1992). The telescopic FROPS mechanism was expensive and difficult to construct (Finch et al., 1998). Figure ‎1.4. The telescopic mechanism in inoperative position (Sheehan, 1992). Panek and Kolli (1998) developed a passive fold assist mechanism which had a handle and a lift assist spring. The ROPS included a support structure and a cross member which was pivotally coupled to the support structure. The handle was mounted on the cross member and the lift assist was pivotally attached to the support structure and cross member (Fig. 1.7). The lift assist mechanism decreased the lifting force by means of a spring and eased the re-erecting process by means of a handle. Figure ‎1.5. Passive lifts assist mechanism with a handle (a) In raised position. (b) In folded down position (Panek & Kolli, 1998). Finch et al. (1998) developed a collapsible passive FROPS which the upper section was pivotally connected to the fixed lower section by means of a four-bar linkage. The linkage permitted the upper section to turn pivotally rearward and immediately behind of the lower section in the lowered position (Fig. 1.8). The engagement surfaces of the lower and upper parts were slanted with respect to the axis of the legs in raised position in order to facilitate the movement of the upper section between the lowered and raised positions. A locking pin fixed the structure in both positions (Finch et al., 1998). Figure ‎1.6. Collapsible FROPS in folded down and raised position a) In raised position. (b) In lowered position (Finch et al., 1998). ACTIVE SYSTEM In the active systems a power system folds down and re-erects the ROPS but, the process needs operator command. Operator does not need to leave the seat and the ROPS may be folded down and raised when the vehicle is in motion (Robinson et al., 2012). Since the structure of the ROPS changes, the entire required ROPS test should be done again to validate the ROPS performance in upright position. The active system is more expensive and complex than conventional and passive systems (Robinson et al., 2012). Ayers et al. (2012) developed an active system that ROPS was lowered and raised by an electrical motor which the motor shaft was attached to the upper part of the ROPS by means of a fork. An electrical system was used to command the ROPS to fold down and re-erect by pushing a bottom (Fig. 1.9). The total time for lowering/unpinning and raising /pinning was 20 second. Figure ‎1.7. Active ROPS (Ayes et al., 2012). AUTOMOTIVE ACTIVE SYSTEM In the automotive active system no operator action is required and the operator does not control the ROPS position. This system is very convenient but, more expensive and complex than the other systems. The performance of the control system must be tested and validated before applying. All the performance requirements for ROPS must be tested (Robinson et al., 2012). NIOSH developed a low-profile Auto ROPS (AROPS) which automatically and rapidly deploys during rollover event (Powers et al., 2001). AROPS consists of two telescopic tubes which are extended by a spring during rollover accident (Fig. 1.10). This ROPS is made of three parts, sensor, control system, and deployment system. The automatic sensor measures the tractor tilting angle and the control system commands the deployment system to releases the upper tube. AROPS normally is in lowered position but when the vehicle operating angle increased and overturn condition is detected by sensor the ROPS will be deployed. AROPS can protect the operator in rollover accident even in low clearance zones (Powers et al., 2001). Howard (1998) tested the performance of the second generation of AROPS and results showed that the AROPS deployed in less than 0.3 s and latched securely. The 3rd generation AROPS is the smallest and the most effective AROPS for protecting the operator in rollover accidents (Alkhaledi, Means, McKenzie Jr, & Smith, 2013). Figure ‎1.8. Structure and mechanism of auto ROPS (Powers et al., 2001). OECD CODE The OECD (2014) standard code is under development for official testing of agricultural tractors FROPS performance. The actuation force is defined as the force that inserted tangential to the trajectory of the crossbar to the grasping area (OECD, 2014). The grasping area is the area that operator exerts the actuation force manually to raise and lower the ROPS. The grasping area includes the cross bar of the ROPS, and the additional handles for lifting the ROPS (Fig. 1.11). The actuation force during the folding down process, which starts from +90 degree, must be exerted in downward direction to the crossbar of the ROPS. In some FROPS, at a special angle the actuation force is equal to zero and after this angle the actuation force must be inserted in upward direction to the crossbar to keep the ROPS from falling. This special angle is called breaking point. Figure ‎1.9. Grasping area. The maximum allowable actuation force is defined based on three accessible zones. These zones are accessible for a standing operator while raising and lowering a ROPS manually with no fold assist mechanism (Fig. 1.12). Figure ‎1.10. Side view of accessible zones zone І: Comfort zone. Zone ІІ: accessible zone without forward leaning of the body. Zone ІІІ: Accessible zone with forward leaning of the body (OECD, 2014). The dimension of accessible zones for folding and raising the ROPS are defined with respect to the horizontal plane of the ground, and vertical planes passing through the outer part of the obstacle that limit the position or displacement of the operator. These three zones are defined based on anthropometric data of small man and medium size woman (OECD, 2014). The maximum allowable actuation force depends on the zone that the operator exerts the force (Table 1.1). In order to check the OECD code requirements, the actuation force or torque must be measured every 5 degree during raising and lowering the ROPS. Table ‎1‑1. Maximum allowable forces based on the accessible zones. Zone І ІІ ІІІ Acceptable force (N) 100 75 50 DEVELOPING THE MEASUREMENT SETUP The final goal of this study is to measure the angles and the actuation torques of the conventional FROPS. The procedure includes five steps, developing the sensor, sensor calibration, applying the sensor, develop a theoretical model to predict the actuation torques, and comparing experimental test results with theoretical model results. In the first step a torque-angle measurement sensor and an attachment mechanism were developed. The developed system was calibrated before applying. The developed system was used to measure the actuation torques-angle of 2 sizes of FROPS in five levels of turning speed. The results are presented in chapter 3. Another measurement setup was developed to examine the effect of friction on actuation-angle of FROPS. A theoretical curve was developed to predict the actuation torque- angle curve. The results of the developed model were compared with the experimental test results. An angular displacement sensor and a torque measurement sensor were applied to develop the actuation torque-angle sensor. Two different measurement systems were proposed for developing the sensor and the second one was selected for experimental test. ANGULAR DISPLACEMENT SENSOR The turning angle is the relative angle of the upper part of the FROPS to the horizon. The angle of the raised ROPS is around +90 degree and is equal to zero when the upper part of the ROPS is in horizontal position and the angle is a negative value around -90 when the ROPS is completely folded down. The angle sensor range should be at least 180 degrees to measure the turning angle from -90 to 90 degree. The angular displacement sensor must be able to work in field condition in Knoxville and nearby areas in Tennessee, which based on National weather service (2015) data, the humidity is up to 100% and temperature is between -20 and +105°F. The FROPS upper part angle can be measured with different sensors such as, resistive, optical encoder, magnetic, synchro/resolver displacement sensors, and accelerometer. In the following section the application of displacement sensor for angle measurement will be explained and the sensors are compared to find the best match for the research. The accelerometer sensor model Crossbow CXL04LP3 was selected to measure the turning angle. This type of sensor possesses all of the required properties (Range, Resolution, Environmental properties, and etc…) for this study. Some of the other sensors has the required properties, too, but the problem is that, these sensors should be installed in line with the motor shaft and pivot point, which increases the length of the setup and increases the effect of torsional deflection and consequently the error in torque and angle measurement. The accelerometer was attached to the upper part of FROPS by means of a magnet without disturbing the performance of the torque sensor and motor. RESISTIVE DISPLACEMENT SENSOR The resistive displacement sensors are commonly called potentiometer or Pots. A Pot is an electromechanical device which basically made of an electrical conductive wiper and a fixed resistive element. The wiper is attached to the shaft and moves according to the rotary shaft. The wiper moves against the fixed resistive element and “divided” the fixed resistive element in two parts (Fig. 1.14). Figure ‎1.11. Rotary potentiometer a) Schematic b) The circuit (Mathivanan, 2007). The resistance of the resistive element is a function of the length ratio of these two parts. The output is analogue voltage that can be used directly or digitized (Morris & Langari, 2012). The advantages and disadvantages of Pots are listed in table 1.2. Table ‎1‑2. The advantages and disadvantages of Pots (Mathivanan, 2007), Antonelli et al., 2014). Advantage Disadvantage · Easy to use · Low lost · Non-electronic · High amplitude output · Proven technology · Limited to the resistive element width · The sensor is affected by inertial loading, frictional load and consequently wear · Large force for moving the contacts INDUCTIVE TRANSDUCER DISPLACEMENT SENSOR Inductive transducers work based on the principles of magnetic circuits and can be divided in two groups, self-generating and passive. The self-generating sensors work based on the principal of the electrical generator. The relative motion between the conductor and magnetic field or a varying magnetic field induces a voltage to the conductor. In some instruments the magnetic field changes as the conductor moves, which finally induces a voltage to the generator. In the inductive sensors the relative motion between the conductor and the magnetic field is supplied by a measurand motion which usually is mechanical motion. The passive transducer requires an external source of power and the transducer just modulate the excitation signal (Antonelli et al., 2014). The Rotary Variable Differential Transformer (RVDT) is a passive inductive transducer which has many applications. RVDT has an E-shaped core which the primary winding is wound on the center leg and the two halves of the secondary winding are on the outer leg of the core. The armature is rotated by an externally applied force about the pivot point and above the center legs of the core (Fig. 1.15). Figure ‎1.12.The inductive displacement sensor a) schematic of RVDT. b) Electrical circuit (Antonelli et al., 2014). When the armature rotates from its reference point, the reluctance through one half of the secondary coil is decreased and increased through the other coil. The electromagnetic fields in the secondary windings are different in the magnitude and the phase as a result of the applied displacement. The output voltage is linear for limited rotation of the armature (-45deg<ɵ<+45deg).The advantages and disadvantages of RVDT are listed in table 2.3. Table ‎1‑3. The advantages and disadvantages of inductive transducer sensor (Mathivanan, 2007). Advantages Disadvantages · Inherently frictionless · No physical contact between core and coil · Long or infinite mechanical life · High resolution · Very stable · Relatively insensitive to radial motion · Isolation between input and output · Excellent repeatability · Since the output is proportional to input voltage and frequency, both voltage and frequency excitation should be highly stable · Complicated signal conditioning system is required for phase detection OPTICAL ENCODER DISPLACEMENT SENSOR The angular optical encoders are commonly termed rotary or shaft encoder, since they usually detect the rotation of a shaft. Optical rotary shaft encoders use light to transform the movement in to electrical signals. The devices basically made of two parts, the grating and the detection part. The grating part is made of fixed and moving grating. The moving grating is a disc with radial lines which is attached to the measurand. The fixed grating represents the measurement standard. The measurement is based on the relative position of moving grating respect to the fixe one (Fig.1.16). Figure ‎1.13. Shaft encoder (Antonelli et al., 2014). MAGNETIC DISPLACEMENT SENSOR These sensors rely on the electromagnetic fields and the magnetic properties of the material. Inductive sensors work based on magnetic field properties but they work based on voltage inducement in a conductor and can measure the displacement in very limited range. There are several types of the magnetic sensors such as, magnetostrictive, magnetoresistive, Hall Effect, and magnetic encoders. The magnetic sensor can measure either increment or absolute displacement (Antonelli et al., 2014). A magnetostrictive sensor uses a ferromagnetic element to detect the location of a magnet which is displaced along the sensor length. Ferromagnetic materials such as Iron and nickel have a property which was named megnetostriction. The size and shape of ferromagnetic materials under the effect of magnetic field change due to the change in the crystal structure (Antonelli et al., 2014). The magnetoresistive sensor works based on the change in the electrical resistance of the magnetic material. The electrical resistance of the magnetic material changes when a magnetic field is applied. The electrical resistance of the most magnetic material decrease when a magnetic field applied perpendicular to the current flow (Antonelli et al., 2014). The Hall Effect is a property exhibited in conductors affected by a magnetic field. A voltage potential appears across the conductor when a magnetic field is applied at right angles to the current flow (Antonelli et al., 2014). The angular magnetic encoders use a sensing element, read head, and a mechanical enclosure with an input shaft and a brushing. The read head is a disc of magnetic media onto which digital information is stored. The encoded media records the information as magnetized and non-magnetized area. The basic concept of the magnetic encoder is like the shaft encoder (Antonelli et al., 2014). INDUCTION POTENTIOMETER (SYNCHRO/RESOLVER DISPLACEMENT SENSOR) The Induction potentiometers are electromagnetic transducers which work based on transformer technology. The sensor is basically made of three parts, two wound coils and a core. The change in the magnetic flux between two wound coils of a transformer achieved by varying the amount of coupling from the primary winding (excited) to the secondary (coupled) winding. The coupling can be generated by moving on of the winding with respect to the other one or by moving the core element that provides a flux path between the two windings (Fig. 1.17). Figure ‎1.14. The induction potentiometer has windings on the rotor and the stator (Antonelli et al., 2014). The difference between the induction potentiometer and the RVDT is that the windings are placed on a stator with two slots (Fig. 1.17). The differences between RVDT and inductive potentiometer are shown in table 1.4. Table ‎1‑4. The advantages and disadvantages of the induction potentiometer in comparison with RVDT (Antonelli et al., 2014). Advantage Disadvantage · The output will have greater sensitivity (more volts per degree) · Better signal to noise ratio · Higher accuracy in most cases · Additional windings · More physical space is required · Greater variation over temperature · Greater phase shift due to additional winding The resolver has multi slot on the stator and two sets of the windings are designed in a concentric coil set and distributed in each quadrant of the laminated stack (Fig. 1.18). A close approximation to sine and cosine wave can be generated on each of the secondary windings. The multi slot rotor lamination and distributing the winding in the rotor, with sine and cosine wave form can improved the accuracy and range even further. Figure ‎1.15. The resolver stator has distributed coil windings on a 16- slot lamination to generate sine wave (Antonelli et al., 2014). The term “synchro” defines an electromagnetic position transducer that has a set of three phase output windings that are electrically and mechanically spaced by 120instead of the 90spacing found in a resolver. In the rotor primary mode, the synchro is excited by a single-phase ac signal on the rotor. As the rotor moves 360, the three amplitude modulated sine waves on the three phases of the output have a discrete set of amplitudes for each angular position. By interpreting these amplitudes, a table can be established to decode the exact rotary position (Antonelli et al., 2014). ACCELEROMETER The accelerometer can measure both the static and dynamic acceleration. The tilting angle of an object can be measured with accelerometer since the static objects are subjected to the gravitational force (g) of the earth and therefore the gravity is the acceleration being measured. The accelerometer can be measure the ROPS angle between -90 to +90 degree and the acceleration will change between +1g to -1g. In order to achieve the highest degree of resolution an accelerometer with low g and height sensitivity should be used. The relationship between the tilting angle and out-put voltage is not linear, the sensitivity at 0 degree (the sensing axis is parallel with horizon) is maximum and by increasing the titling angle the sensitivity will decrease (Clifford & Gomez, 2005). The relationship between the angle and the acceleration depends on the installation direction (Fig. 1.16). If the sensing axis (X) and the direction of gravity are parallel when the object which is in horizontal position, equation 1.4 will be used to calculate the tilting angle: Where, VOUT is accelerometer output in Volts, V0 is accelerometer output in Volts in horizontal position, ΔV/Δg is sensitivity, 1g is earth gravity, and θ is tilting angle. Figure ‎1.16 Gravity component of the tilted X-axis accelerometer (Clifford & Gomez, 2005). From the Crossbow CXL04LP3 specification sheet the sensitivity and the Vo for X, Y, and Z directions are presented in table 1.5. Table ‎1‑5. Sensitivity and the Zero-G Voltage (Vo) of Crossbow CXL04LP3 X axis Y axis Z axis Zero-G Voltage (Vo) 2.545 2.544 2.547 Sensitivity (ΔV/Δg) 0.511 0.511 0.520 In this study the X-axis of the accelerometer is perpendicular to the trajectory of the ROPS which means that, the accelerometer measures the radial acceleration in X direction. The Y-axis of the accelerometer measures the acceleration tangential to the ROPS trajectory. The gravitational acceleration can be measured both in X and Y direction. For this study, acceleration in X direction was used for angle calculation and acceleration in Y direction was used for calibration. TEST THE STATIC CALIBRATION The angle was measured by the Fowler Mini-Mag Protractor model 54-422-450-1 and Crossbow CXL04LP3 accelerometer and also an analog protractor. The measured values by Fowler digital sensor are considered as true measurement and compared with the measured values by accelerometer. The angle was measured from +90 to -90 statically. Results are shown in figure 1.17. There is a good agreement between two sensors measurement. The average error is 0.02% and RMSE is 0.15 degree. Figure ‎1.17. The measured angle by Folwer digital sensor and the accelerometer from +90 to -90 in X direction. The out-put of the accelerometer sensor was converted to angle by equation 1.4. In order to examine sensitivity and V0, at least two outputs of the accelerometer are required, the output in +90, or -90, and 0. The maximum output of the sensor in X direction happens when the ROPS angle is +90 and minimum happens when the ROPS angle is -90. The maximum output of accelerometer in Y direction happens when the ROPS angle is 0 (Figure 1.18). Therefore by finding maximum or minimum of accelerometer in X direction and minimum output in Y direction, The sensitivity and V0 can be calculate. The V0 is the accelerometer output in 0 g or 0 angle. The sensitivity was measured by knowing the acceleration in a known point and the sensor output at that point, the acceleration in +90 is +g and in -90 is –g. Figure ‎1.18. The maximum accelerometer output in X direction happens at +90 and minimum value happens at -90. The maximum accelerometer output in Y direction happens at 0 degree. DYNAMIC CALIBRATION TEST WITH FORK The motor and the fork were used to test the dynamic calibration of the accelerometer (Fig. 1.19). The fork was turn by means of a motor and the accelerometer is attached 8 inch far from the pivot point of the motor. Figure ‎1.19. Dynamic Calibration of accelerometer The fork was turn with maximum and minimum possible speeds and the results showed that there is no significant difference between the accelerometer output in the low (1.8 RPM) and high (8.7 RPM) speeds and also in static condition (Fig. 1.20), as the maximum values did not changes. The angle for two levels of speed is calculated and is shown in figure 1.21. It appears that rotational speed has very little influence on the torque angle relationship, especially at the maximum torque values. This will be explored in the future, but may not be implemented in the field testing. The proposed OECD working document describes a maximum rotational speed of 20 deg/sec (3.3 rpm) when testing the automatic locking system. This speed will be my target speed during field testing. The sensor repeatability is shown in figure 1.22. Figure ‎1.20. The accelerometer output in 720 degree turns (two revelations) Figure ‎1.21. Accelerometer output (degree) for low and high turning speed. Figure ‎1.22. Accelerometer Repeatability DYNAMIC CALIBRATION TEST WITH ROPS The ROPS was used to examine the performance of accelerometer, as the lever distance (r) of the FROPS is higher than the fork and the final goal of this study is to measure the angle of the FROPS. The X, Y, and Z direction of the accelerometer relative to ROPS is shown in figure 1.23.The angle based on sensor output in X direction was calculated and shown in figure 1.24. Figure ‎1.23. The accelerometer attachment to the upper part of the ROPS Figure ‎1.24. The accelerometer output (Degree) in X direction. TANGENTIAL ACCELERATION (aθ) AND CENTRIFUGAL ACCELERATION (ar) The circular movement of the upper part of the ROPS is non uniform which means that the speed is not constant. The effect of these acceleration on accelerometer output were calculated in this section. The upper part movement includes two parts: a) The non-uniform circular motion from 0-0.5 second. The non-uniform circular motion includes the Tangential acceleration (aθ) and Centrifugal acceleration (ar), figure 1.25. b) The uniform circular motion 0.5 sec after the start point to 0.5 sec before the stop point (assume that the time for motor to reach the selected speed is 0.5 second and the velocity change rate is constant), figure 1.25. Figure ‎1.25. Tangential acceleration (aθ) and Centrifugal acceleration (ar) Two accelerations affect the accelerometer measurement, which are: The gravitational acceleration (g) which is constant and equal to 9.81 m/s2 and changes from (+g to –g) The acceleration due to circular motion of the upper part of the ROPS which evolves: Tangential acceleration (aθ): Due to change in magnitude of velocity, Centrifugal acceleration (ar): Due to change in in direction of velocity, In this study the X-axis of the accelerometer is perpendicular to the trajectory of the ROPS which means that, the accelerometer measure the radial acceleration in X direction. The Y-axis of the accelerometer measures the acceleration tangential to the ROPS trajectory. Therefore the tangential acceleration due to uniform circular motion just affects the acceleration in X direction. The acceleration due to non-uniform motion affects the acceleration measurement both in X and Y direction. The gravitational acceleration can be measured both in X and Y direction. A. THE FORK ) min (1.7) ) max (1.8) The linear velocity is calculated by: V=rw= (m/s) (1.9) The acceleration is calculated: ) min (1.11) ) max (1.12) When the fork turns for 360 deg, the accelerometer out-put changes from 2047 to 3017 (985 mv) and the acceleration changes 19.62 m/S2. The FSO error is %2. B. THE ROPS ) (1.13) ) (1.14) ) (1.15) ) (1.16) When the ROPS turns for 180 deg, the accelerometer out-put changes from 2047 to 3017 (985 mv) and the acceleration changes 19.62 m/S2. The error is %2.5 1.1.1.1 ACTUATION FORCE The actuation force can be measured directly as force or can be measured indirectly as torque. In the direct measurement the exerted actuation force can be measured with a force transducer, and the torque can be measured by a torque transducer. The transducers that measure the force and torque are made of elastic members that convert the mechanical quantity to deflection or strain. A deflection sensor such as strain gauge can be used to give electrical signals proportional to the quantity of the measured force or torque. The characteristics of the transducer depend on the size, shape, and material properties of the elastic member and the deflection sensor properties (Dally, Riley, & McConnell, 1993). LOAD CELL SELECTION The elastic members that commonly used in the load cells are links, beams, rings, and shear webs. The link type load cell can measure both the tensile and compression. The four strain gages are attached to the elastic member and wired to each other by Wheatstone bridge circuit (Dally et al., 1993). The beam type is usually used for measuring low level loads where the link type load cell is too stiff to measure the force (Dally et al., 1993). This type of load cell seems to be inappropriate for this this research, since the load cell requires measuring the high level of tension and compression loads. The ring type load cell is made of a ring as the elastic member. The deflection usually measure with linear variable differential transformer (LVDT). This type of sensor can measure the wide range of loads (Dally et al., 1993). This type of sensor is big and not appropriate for this research. The shear web load cell known as low profile or flat load cell is useful for application where the space is limited along the line of action of load. This load cells is compact and stiff and appropriate for measuring the dynamic loads with high frequencies (Dally et al., 1993). TORQUE TRANSDUCER SELECTION An electromechanical torque transducer basically is made of a circular shaft as the strain member which the deflection is measured by means of strain gages. The strain gages are mounted on two perpendicular 45 degree helices that are diametrically opposite one another. The strain gages are attached together in a Wheatstone bridge configuration. The applied torque to the sensor causes bending or shearing in the gage area and the torque transducer generates an output voltage signal proportional to the torque. Transducers can be divided in to two categories, rotary (dynamic) and reaction (static). The reaction transducer can measure torque without rotation but, the rotary torque transducer rotates multiple times as a part of the system. Normally, the reaction torque transduce has a cable to supply the excitation voltage to the Wheatstone bridge and for the output signal. Since using a cable for rotary is not practical, several methods such as slip ring, rotary transformers, rotating electronics, rotating digital electronics and radio telemetry are used to transfer power and signal (Dally et al., 1993). The static transducers are appropriate for this research, since the upper part rotates about 180 degree. A static reaction torque cell (OMEGADYN Inc. model TQ420-2K) was used to measure the torque. TORQUE TRANSDUCER The torque was measured by a Reaction Torque Cell model TQ420-2K. The torque transducer range is 0 to 225 Nm. The torque transducer is attached between the motor and the fork to measure the actuation torques to fold down and raise the fork. The torque transducer performance was tested by adding known weight to a known distance from the axis of the torque transduces. The sensor measured torque with the given calibration had a good agreement with the applied values. The expected torque for experiments is up to 135 Nm (1200 lb.in) therefore, the sensor performance was tested between 0 to 135 Nm (Fig. 1.24). The average error is 0.38% and RMSE is 0.57 Nm. Figure ‎1.26. Torque transducer calibration. MEASUREMENT SETUP Two methods were proposed to measure the actuation force by means of a load cell and one setup was proposed to measure the actuation torque by means of a torque cell. One of the measurement setup was used to measure the actuation force in pre-tests. In this method, the actuation force and angle were measured by means of a load cell, and accelerometer, respectively. A lever arm was attached to the ROPS and a load cell was attached to the lever arm by means of hook. The operator exerts the force to the load cell. The problem of this method is that the operator cannot keep the load cell all the time easily perpendicular to the lever arm and the force direction must be changed at breaking point (Fig. 1.25). Changing the direction of force at breaking angle for makes the measurement inaccurate. Figure ‎1.27. Actuation force measurement by adding a lever arm. The second proposed system includes a load cell, a motor, and a mechanism as shown in figure 2.26. In order to exert the actuation force with special speed the motor will be used to fold down and raised the ROPS. The load cell will be placed between the lever arm and the ROPS. The load cell must be the only attachment point of the fork to the ROPS. The actuation force (F) is equal to: Where F is actuation force (N), l is the distance between the pivot point and the cross bar (m) F1 is the force which is measured by the load cell (N), and l1 is the length of fork (m). Figure ‎1.28. Applying a load cell to measure force. The last proposed measurement setup, measures the actuation torque-angle. This setup was selected for this study. Based on OECD code, the actuation force can be measured in form of torque. A motor was attached to the lower part of the FROPS by means of a platform and the motor turned the upper part by means of a fork. The torque transducer was attached between the motor and the fork (Fig. 1.27). The force can be calculated by equation 1.6. Where T is torque (Nm), F is actuation force (N), l is the distance between the pivot point and the cross bar (m). The developed measurement setup to measure the actuation torque-angle is shown in figure 1.30 and the schematic figure is presented in figure 3.2. Figure ‎1.29. The proposed actuation torque-angle measurement setup. Figure ‎1.30. The final developed measurement setup to measure actuation torque-angle of FROPS SUMMARY The rigid ROPS are not appropriate for working in low overhead clearance zones. The FROPS was designed to solve the rigid ROPS problem but, folding and raising the conventional FROPS are time consuming and strenuous processes. The passive, active, and automotive active FROPS have been developed to solve the conventional ROPS problem. The powered and automatic FROPS systems are expensive, complex, and in some cases the ROPS must be completely replaced with a new one. Manufacturers have retrofitted tractors with ROPS since 1985 and just 59% of the tractors have been equipped ROPS until 2014 (CDC, 2014). Prediction suggests that only 75% of the tractor in service will be equipped with ROPS at 2024 if no other action is taken (Hoy, 2009). By considering the slow rate of applying ROPS, replacing the available ROPS with automotive systems or adding expensive powered systems seems to be impractical. The passive systems are simple and low cost but the actuation force is high. The FROPS actuation forces are not well known and an OECD standard code is developing to regulate actuation forces. Based on OECD standard code the maximum actuation force should not be more than 100 N. Some passive systems employ a lever arm to decrease the actuation force but the strong and the heavy ROPS are required a lift assist mechanism to help the operator (Panek & Kolli, 1998). The actuation force is one of the most important factors that needs to be measured prior to fold assist mechanism design. There was no instrumentation available to measure the actuation force as a function of angle of the FROPS. The developed sensing setup was applied to measure the actuation torque of the FROPS to see whether the FROPS meet the standard requirements. Also the effect of turning speed and friction on actuation torque were evaluated. The measured force and angle values can be used to design a fold assist mechanism. THE EFFECT OF LIQUID SHIFT ON CG HEIGHT MEASUREMENT NOMENCLATURE Symbol Description Unit a Depth of liquid in liquid container m a' Depth of liquid in tilted liquid container, close to the pivot point m a'' Height of liquid triangle in tilted liquid container and close to the pivot point m b length of liquid container m b' Width of liquid triangle in tilted liquid container it may be imaginary m CGl CG of liquid in raised position CGs CG location of solid parts in horizontal position - CG's CG of solid parts in raised position - Ffar Load on fixed axle in raised position (swiveling axle supported in stand) N Ffl Load on left wheel fixed axle in horizontal position N Ffr Load in right wheel fixed in horizontal position N Fsw Load on swiveling axle in horizontal position m h Lifting Height m H The vertical distance between the CG and the rear axle m m Longitudinal movement of CG of liquid in raised position m n Lateral movement of CG of liquid in raised position m o Distance between outer edges of tires on fixed axle deg O Origin - ɵ Lifting angle deg P Width of tires on the fixed axle m r Static load radius wheel swiveling axle (swiveling axle) m R Static load radius wheel fixed axle m Rf Static load on front axle in horizontal position N R'f Static load on front axle in lifted vehicle N Rr Static load on rear axle in horizontal position N W Wheel base of vehicle in horizontal position m W' Vertical projection of wheel base of vehicle in lifted position m Wl The weight of liquid kg Ws The weight of solid kg Wt Vehicle weight N X longitudinal dimension of CG m X'' longitudinal dimension of CG of vehicle in lifted position m X"s longitudinal dimension of CG of vehicle in lifted position m X0 The horizontal distance of the corner of liquid container to the origin m Xl longitudinal dimension of CG of liquids m Xs longitudinal dimension of CG of solid parts m X's longitudinal dimension of CG of solid parts in lifted position m Z CG Height m Z0 The vertical distance of the corner of liquid container to the origin m Zl CG height of liquid m Zs CG height of solid parts m Z's CG height of solid parts in raised position m COORDINATE SYSTEM The coordinate system of the center of gravity (CG) point includes lateral, longitudinal, and vertical distance from origin (Fig. 1.31). The longitudinal dimension of the CG (X) is defined as the horizontal distance from transverse reference plane. The transverse reference plane is defined as the vertical plane respect to the ground plane, which passes the center line of the rear axle of the agricultural tractor. The lateral dimension of the CG (Y) is defined as the horizontal distance from the median longitudinal plane. Median longitudinal plane is the vertical plane respect to the ground plane, which passes through the major front and rear axis midway points. The height of CG (Z) is defined as the vertical distance from the horizontal reference plane which is ground surface (Fig. 1.31). The intersection of the three planes (transverse reference plane, median longitudinal plane, and horizontal plane) is called origin point (O). Figure ‎1.31. Coordinates system and origin point a) Front view. b) Side view. INTRODUCTION AND LITERATURE REVIEW The center of gravity (CG) is the location of a theoretical point representing the total mass of a body. Since off-road vehicles often possess many irregular shapes, it is practically impossible to find the CG location using analytical methods. Various techniques can physically determine the CG of vehicles. These methods are vertical hang, pendulum, lifting axle, and tilt table. The lifting axle method (LAM) is a popular method for determining the CG height of a vehicle. The lateral and longitudinal dimension of CG can be measured when vehicle is in horizontal position, but for measuring the CG height, the vehicle should be tilted. By tilting the vehicle, liquid inside the vehicle moves and changes the load on rear and front axle. The weight distribution on rear and front axle is one of the important factors for determining the CG height based on ISO 16231. But the ISO 16231 does not consider the effect of liquid shift on CG height measurement. PENDULUM METHOD The dynamic pendulum method is the most frequently used method in the testing stations in Europe (A Fabbri & Molari, 2004). The CG calculation in pendulum method is based on simple harmonic oscillation equation. The tractor is placed on an oscillating platform. The combination of tractor and platform is called oscillating mass. The oscillation period is a function of suspension length which is the distance between CG height of oscillating mass and the oscillating platform pivot point. The CG height of the platform is known and the CG height of the tractor can be calculated by measuring the oscillation period of the platform and the combination of the tractor and the platform in two different suspension lengths (A Fabbri & Molari, 2004). Thy dynamic pendulum method introduces some uncertainties due to the friction losses in bearings, and air resistance, liquid motion, tire deflection, loose solid part movement, and platform deflection (A Fabbri & Molari, 2004). A Fabbri and Molari (2004) measured CG height of narrow track agricultural machinery using static pendulum method. An inclined platform was used for the CG height measurement. A cable was attached to the platform and the CG height was calculated based on lateral inclination angle, lateral pulling force with tractor, lateral pulling force without tractor, and the distance from the force application point and the median vertical plane of the tractor. Results showed that static pendulum method is more precise than the dynamic pendulum method. They stated that the static method eliminated the problems underlined with respect to the dynamic method such as, fluid motion, air resistance, the approximation in the simple model of harmonic oscillations and the uncertainties related to the oscillation period measurement (A Fabbri & Molari, 2004). LIFTING AXLE METHOD Measured parameters in lifting axle method are load on front and rear axle of the vehicle in horizontal position, load on lifted axle, and the some structural geometries of the vehicle (Fig. 1.32 and 1.33). The lateral and longitudinal CG measurements are straightforward. The CG height measurement is considerably difficult, since it needs to lift one axle of the vehicle, either the front or rear. The weight of the tractor is equal to the summation of load on the front and rear axle. The CG lateral dimension can be calculated by equation 1.19. Figure ‎1.32. Determination of the longitudinal location of the center of gravity using lifting axle method (Liljedahl, Turnquist, Smith, & Hoki, 1996) (1.19) By lifting the vehicle axle the summation of moments about the rear axle; (1.20) From the geometry of figure 3.3: (1.21) (1.22) (1.23) Subtituting equation 3.5 in to equation 3.4, dividing by cos λ and solving for H: (1.24) the angle λ is the only quantity that cannot be directly measured. However, (1.25) (1.26) (1.27) Figure ‎1.33. Determination of the vehicle location of CG (Liljedahl et al., 1996). Wang, Gao, Ayers, Su, and Yuan (In press) used a test method which was developed based on ISO 16231. They used this test method to minimize the effect of springs, fuels, hydraulic oil, lubrication oil, and elastic cells on the CG height measurement of the zero turning radius (ZTR) mower. They lifted the front axle of the vehicle and measured the force on the front axle five times, and repeated the measurements every one degree. They added and subtracted 0.1 kg (deviation of the accuracy of the scale) from the measured weight on the front axle and calculated the CG height for each angle. If the calculated CG heights based on weight on front axle ± 0.1 kg did not exceed ±4% of the CG height, they reported that CG height as the actual CG height of the ZTR mower. STANDARD ISO /DIS 16231 ISO 16231 is under development for stability assessment of self-propelled agricultural machinery. The CG height affects the vehicle stability (Demšar, Bernik, & Duhovnik, 2012), therefore the first section of ISO 16231 is assigned to measuring CG location of un-laden self-propelled agricultural machinery. The static stability angle (SOA) measurement method is explained in the second section. The CG is measured based on lifting axle method and by means of scales and support stands. The CG height is calculated based on figure 1.34, and 1.35 and table 1.6. Figure ‎1.34. Rear, top, and side view of the machine (ISO, 2014). Figure ‎1.35. Machine in raised position - side view (ISO, 2014). Table ‎1‑6. CG Calculation (ISO, 2014) Data description Symbol Unit Calculation Wheel track of fixed axle T m o-p Total weight of the machine Ft N Ffr+Ffl+Fsw Lateral position of CG (versus center of fixed axle) (positive number means right from center of fixed axle in Figure 3.4) Y [(Ffr*T)+(T/2+a)*Fsw]/Ft-T/2 Longitudinal position of CG (versus center of swiveling axle) x' m W(Ffr+Ffi)/Ft Longitudinal position of CG (Versus center line of the fixed axle) x m W-x' Longitudinal distance between wheel centers w m Vertical projection of wheel base in raised position W' m Angle formed by the line between wheel centers and horizontal through the center of the fixed axle wheels α deg Angle formed by the line between wheel centers and horizontal through the center of the fixed axle wheels in raised position β deg Lifting angle ω deg α+β Vertical projection of longitudinal distance between CG and the swiveling axle in raised position c m Auxiliary line for calculation b m Height of CG z m Standards usually provide some remarks to decrease the error caused by unexpected factor such as, liquid shift and tire deflection. ISO 16231 provides several remarks in order to improve the test procedure (ISO, 2014): 1. Steel wheels should be used in order to avoid error caused by the tire deflection under different loads in different tilting angles. 2. Suspension systems shall be locked. 3. If the steel wheels are not used, the tire should be inflated to the maximum permissible pressure specified by the tire manufacturer. 4. The change in the tire radius in horizontal and tilted position should not be greater than 1.5% of the wheel radius. 5. The plane of the scale should be horizontal and parallel to the ground plane. 6. The wheels on the scale must be free to rotate and be in the position for towing the vehicle. Therefore the parking brakes shall not be applied and the transmission system must be in the position for towing the vehicle. 7. It is recommended to lift the axle with the smaller wheel diameter. 8. Reading the weight on scale shall be done after complete rest of the lifted axle on the scale. 9. It is recommended to lock the swivelling axle with wedges, when lifting the vehicle. 10. The values of weighing during 5 consecutive measurements must fall within a range of 1.0% of the maximum measured load from the fixed axle in raised position. 11. “Calculate the CG, using the deviation of the accuracy of the scale (+ and -) and determine the percentage of deviation of the height of the CG (+/-). This number shall not exceed +/- 4%. In case it exceeds +/- 4%, the height of the wheel stands shall be increased in order to decrease the deviation.” The lateral and longitudinal dimension of CG can be measured when vehicle is in horizontal position, but for measuring the CG height, the vehicle should be tilted. By tilting the vehicle, liquid inside the vehicle moves and changes the load on rear and front axle. The weight distribution on rear and front axle is one of the important factors for determining the CG height based on ISO 16231. But the ISO 16231 does not consider the effect of liquid shift on CG height measurement. SUMMARY Agricultural machineries are prone to rollover because of off road application, and variable and high location of CG. In order to minimize the risk of rollover accidents, the stability of agricultural machinery should be assessed. The CG height should be measured before stability assessment. The vehicle CG can be measured by several methods such as, vertical hang, tilt table, static and dynamic pendulum method, and lifting axle method. The pendulum method and lifting axle method are the most common methods. The lifting axle method is less demanding, less expensive and easier method than the pendulum method but the accuracy of the lifting axle method is less than the stable pendulum method. In all of these CG measurement methods the vehicle is tilted for measuring the CG height. By tilting the vehicle the liquids inside the vehicle moves. The newly developed ISO 16231 does not consider the effect of liquid shift on CG height measurement in lifting axle method. Although many authors admit fluid affects measurement of CG, no studies have investigated that effect. The significant effect of liquid shift needs to be considered in the CG calculation. REFERENCES Bureau of Labor Statistics. (2014). Census of Fatal Occupational Injuries Summary, 2013. Washington D.C.: Bureau of Labor Statistics. Available at: www.bls.gov/news.release/cfoi.nr0.htm. Accessed 5 October 2015. Alfaro, J. R., Arana, I., Arazuri, S., & Jarén, C. (2010). Assessing the safety provided by SAE J2194 Standard and Code 4 Standard code for testing ROPS, using finite element analysis. Biosystems engineering, 105(2), 189-197. doi:http://dx.doi.org/10.1016/j.biosystemseng.2009.10.007 Alkhaledi, K., Means, K., McKenzie Jr, E., & Smith, J. (2013). 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CHAPTER II DEVELOPING AND EVALUATING A FINITE ELEMENT MODEL FOR PREDICTING THE ROLLOVER PROTECTIVE STRUCTURE NONLINEAR BEHAVIOR UNDER SAE J2194 STATIC TEST This chapter is a reformatted version of a paper, by the same name, submitted to the journal of Biosystems Engineering by Farzaneh Khorsandi, Paul. D. Ayers, Timothy. J. Truster. (Under review) ABSTRACT This research focuses on applying Non-linear Finite Element (FE) techniques to predict ROPS force-deflection curves under the simulated standardized static tests. The Society of Automotive Engineers (SAE) J2194 ROPS static standard test was selected for this study. According to the SAE J2194 standard, ROPS must be capable of absorbing predefined levels of energy under longitudinal (rear) and transverse (side) load tests before collapsing as well as avoiding large deformations that infringe upon the driver’s clearance zone or leave the clearance zone unprotected. A nonlinear finite element approach was developed in Abaqus and applied to predict the response of two rear-mount two-post ROPS under simulated side and rear test conditions: Allis Chalmers 5040 and Long 460. The ROPS were designed with Computer-based ROPS Design Program using a bolted corner bracket assembly to simplify the ROPS design process. The FE model was found to predict the ROPS performance deflection (RPD) with less than 25% error compared to experimental test measurements. The FE model predicted the ROPS behavior under rear loads more accurately than under side loads. Also, the developed FE model based on measured stress-strain curves from test specimens was found to predict the ROPS behavior more accurately than the FE models developed based on the Ramberg-Osgood material model. Keywords: Finite element analysis, ROPS, Standard, Virtual test. Nomenclature Symbol Parameter Unit M Tractor reference mass kg En Absorbed energy J E Modulus of elasticity Pa υ Poison ratio - σy Yield stress Pa σu Ultimate stress Pa Abbreviations ROPS, Roll-Over Protective Structure, FE, Finite element, CRDP, Computer based ROPS Design Program, RAD, ROPS Allowable Deflection, RPD, ROPS Performance Deflection, RO, Ramberg-Osgood. INTRODUCTION AND LITERATURE REVIEW The agriculture industry has been ranked among the most dangerous industries in the United States. The Bureau of Labor reported that approximately 123 farmers and farm workers died from work-related injuries in the US in 2013 (Bureau of Labor Statistics, 2014). Tractor accidents are the leading cause of mortality in agriculture, accounting for one-half of all fatal agricultural accidents (Hoy, 2009). Tractor overturning is the main cause of mortality in tractor accidents (Springfeldt, 1996), which includes tipping the tractor sideways or backward (Ayers, Dickson, & Warner, 1994). Tractor rollover accounts for up to one-third of all tractor-related fatalities (Murphy & Yoder, 1998). The use of a Rollover Protective Structure (ROPS) in a combination with a seat belt has proven to be the most effective method to prevent fatalities from tractor overturning. A ROPS is a frame or cab which is installed on the tractor to protect the operator by absorbing a portion of the impact energy generated by the tractor weight in a rollover accident. The ROPS provides a safe zone, called the clearance zone, between the envelope of the ROPS and tractor seat. Of the several types of ROPS such as two-post ROPS, four-post ROPS, and cab, the most common is the two-post ROPS (Murphy and Buckmaster, 2014), which consists of a reversed U-shaped crossbar located above the head of the operator on posts which are bolted to the vehicle frame or axle housing. ROPS PERFORMANCES AND REGULATIONS The first standard for evaluating ROPS performance was developed in Sweden the 1950s (OEEC, 1959). The use of standard ROPS on tractors in Sweden was a significant factor in decreasing the number of fatal rollover accidents from 15 in 1957 to only one fatality in 1990 (Thelin, 1998). In the United States (US), the Occupational Safety and Health Administration (OSHA) required almost all tractors produced after 1976 and operated by nonfamily employees on US farms to be equipped with ROPS. Only 10% of the farm tractors in the US fall under the OSHA jurisdiction (Reynolds & Groves, 2000). Increasingly since 1985, about 59% of the tractors produced by manufacturers in the US are equipped with ROPS (Ayers et al., 1994); CDC, 2014). However, tractor rollover is still a common type of fatal accident in the US, and a significant amount of tractors are still not equipped with standardized ROPS. The ROPS performance must be determined through applicable standard tests. The SAE J2194 (2009) static test is a low demanding test in which the data collection is straightforward and the results are reliable and accurate (Ross & DiMartino, 1982). Most manufacturers select the static test for ROPS evaluation (Fabbri & Ward, 2002). The static test for rigid two-post ROPS includes a sequence of four static loads: (1) horizontal rear (longitudinal), (2) first vertical, (3) horizontal side (transverse), and (4) second vertical loadings. The displacement rate in the horizontal static test must be less than 5 mm s-1. The ROPS passes the static test if it absorbs a predefined level of energy in longitudinal and transverse tests and tolerates a particular force in the vertical test without structural member rupture. Also, the ROPS should not infringe the clearance zone (intrusion criteria), and the ROPS should not leave clearance zone unprotected from the ground plane (exposure criteria). The ROPS rupture is indicated by incapability to tolerate additional loading. Designing ROPS to pass the appropriate standard is a challenge for manufacturers, which increases the ROPS production expenses. ROPS design requires a balance of 1) ROPS material strength and allowable deflection to meet energy criteria, 2) elastoplastic material properties to decrease peak moments at the mounting brackets, and 3) ROPS positioning and alignment to provide a safe zone for the operator. Excessively rigidity transmits a significant shock to the mounting and exerts a considerable force and moment to the chassis. Overly flexible structures deform substantially under the load and infringe on the safe zone or leave the clearance zone unprotected. MODELING While the static test is less demanding than the alternative dynamic or field-upset test, it is still costly and time-consuming. Fabbri and Ward (2002) reported that about one-third of ROPS standard tests failed at the Bologna test stations in Italy. The test failure prolongs the ROPS production and increases the project expenses. Using the experimental performance test alone does not provide an efficient ROPS design process. Therefore, researchers have used a combination of experimental tests and mathematical models to improve and evaluate ROPS performance (Chen, Wang, Zhang, Zhang, & Si, 2012; Karliński, Rusiński, & Smolnicki, 2008). The ROPS experimental tests have not been replaced with mathematical models, since SAE J2194 does not allow theoretical model results to satisfy the ROPS performance test. Nonetheless, modeling increases the understanding of the ROPS behavior under the standardized test and can be used as a tool to evaluate minor structural modifications and also decrease the possibility of test failure. Several authors developed analytical models for predicting the behavior of ROPS in simulated standardized tests (Clark, 2005; Kim & Reid, 2001; Swan, 1988; Thambiratnam, Clark, & Perera, 2009; Yeh, Huang, & Johnson, 1976). Subsequently, numerical approaches such as the finite element (FE) method have been applied to simulate ROPS deflection under the standard tests. Fabbri and Ward (2002) developed an FE-based program to predict common ROPS behavior under the Organization for the Economic Co-operation and Development (OECD, 2008) and the Economic European Community (EEC, 1987) standardized tests. The developed FE model employed several different material models such as elastic-perfectly plastic, bi-linear, tri-linear or the Ramberg-Osgood model. The FE model results were compared with the results of the experimental test, analytical and numerical models developed with commercial software packages. The developed FE model was accurate for predicting force-deflection to within 30% percent of the actual test values of a two-post ROPS with stiff fixing points to the tractor. In the case of weak fixing points, the FE model results were within 50% of the actual test values. The developed program was able to predict the behavior of cabs and four-post ROPS with errors less than 20%. The accuracy of the program was directly related to the accuracy of the geometry creation, the description of the material properties, and the boundary conditions. Alfaro, Arana, Arazuri, and Jarén (2010) simulated the standardized static test based on the OECD code 4 and SAE J2194 using Abaqus. The FE model predictions for a four-post ROPS and a cab indicated close agreement with experimental test data. They estimate the maximum allowable tractor mass based on the ROPS force-deflection curves under the simulated standardized test. Harris et al. (2011) developed an FE model utilizing a bi-linear stress-strain relationship in ANSYS to predict cost-effective ROPS performance under the SAE J2194 and OSHA 29 CFR 1928.52 standard tests. After calibration, the FE model could predict the force for rear load and side load with an accuracy of 10% and 5%, respectively, at the point when the ROPS met the energy criterion. The authors conclude that the SAE J2194 static test provides a more conservative design test than the OSHA static test. JUSTIFICATION The experimental standardized ROPS tests are expensive, laborious, time-consuming, and destructive. About one-third of ROPS fail the standard tests, and the test failure postpones ROPS production project and increases the project expenses. Using the experimental test alone is inefficient in improving the ROPS design and performance. Modeling has been introduced as a method that can simulate the ROPS performance in standard tests, speeds up the design process, evaluates ROPS modifications, and reduces the ROPS production expenses. Although computer models can predict the force-deflection curve of ROPS, the experiment test cannot be replaced with computer models. The modeling approach is needed to increase the possibility that the designed ROPS is likely to pass the standard before the experimental test. Therefore researchers have used a combination of experimental tests and mathematical models to improve and test ROPS performance. There is no FE model available to predict the behavior of rear-mount two-post ROPS designed by newly developed computer-based ROPS design program (CRDP). The designed ROPS using the CRDP are assembled mainly using bolts. The bolted corner bracket attachment at the corners may rotate and absorb some of the energy during the loading test, especially side load test. There is also some adjustment at bolts holes which affects the ROPS deflection. In some of the previous FE models, the model needed to be calibrated to predict the ROPS behavior (Alfaro et al., 2010; Thambiratnam et al., 2009). The material properties and stress-strain behavior are critical inputs of the FE model. None of the online founded FE models have reported using experimentally measured constitutive relations in the plastic region for ROPS. In the previous studies constitutive laws such as Ramberg-Osgood, elastic-perfectly plastic, bi-linear, and tri-linear were used (Fabbri & Ward, 2002; Harris, Winn, Ayers, & McKenzie Jr, 2011; Thambiratnam et al., 2009). OBJECTIVE In this work, an FE model with no calibration, was developed to predict the performance of agricultural tractors ROPS designed by CRDP, under static SAE J2194 standard. The specific objectives comprise of 1) simulating the SAE J2194 static side and rear loading tests for ROPS, 2) predicting the force-deflection results of the ROPS under simulated standard tests, 3) comparing the ROPS performance deflection (RPD) for the simulated and experimental tests, and 4) evaluating the influence of elastic plastic material properties of the ROPS on simulation results. MATERIAL AND METHODS The FE model was developed in three steps: 1) design and manufacture the ROPS, 2) examine the ROPS performance under the experimental test, and 3) develop and validate the FE model. Two ROPS for Allis Chalmers 5040 and Long 460 tractors were designed using CRDP. The behavior of the designed ROPS were evaluated experimentally based on SAE J2194 standard test. The FE model was developed using the commercial FE commercial package Abaqus and validated by comparing the predicted and experimental test results. DESIGN THE ROPS WITH CRDP CRDP was developed to generate quickly ROPS designs based on 46 tractor dimensions and the tractor weight (Ayers, Khorsandi, John, and Whitaker, 2016). The program output is the 2-post, rear-mount ROPS drawings which can be used to construct the ROPS (Figure 1). The drawing includes the posts, crossbeam, baseplate, corner brackets, and strappings. All of the ROPS dimensions were presented in the CAD drawing within a Microsoft Excel file. The parts were assembled using bolts to secure the corner brackets and welding for the strapping and baseplate attachment. The final drawing is presented in figure 1. The constructed ROPS using the CRPD needs to be tested based on standardized experimental tests (Ayers et al., 2016). Figure ‎2.1. Drawing of the designed ROPS using CRDP (a) Front view. (b) Side view. (c) Exploded view (Ayers et al., 2016). The summaries of Allis Chalmers and Long 460 ROPS dimensions are presented in Table 1 and 2. These two models of tractors were selected since they were among the most frequently requested ROPS from New York Center for Agricultural Medicine and Health ROPS retrofit program, and there is no ROPS commercially available for them (Ayers et al., 2016). Table ‎2‑1 The output of CRDP, Summery of material and dimensions for Allis Chalmers 5040 ROPS all dimensions in In. (Ayers et al., 2016). Part Quantity Dimensions Posts Tubing 2 Thickness = 0.1875 Width = 2 Depth = 3 Length = 69.8 Crossbeam Tubing 1 Thickness = 0.1875 Width = 3 Depth = 2 Length = 38.8 Top Baseplate 2 Thickness = 0.75 Length = 8.875 Width = 6.28125 Bottom Baseplate 2 Thickness = 0.75 Length = 8.875 Width = 5.8125 Corner Braces 2 Thickness = 0.375 Length = 12 Width = 12 Baseplate Strapping 1 Thickness = 0.25 Length = 20 Width = 1 Baseplate Strapping 3 Thickness = 0.25 Length = 4 Width = 1 Baseplate Bolts 8 Diameter = 0.5 Grade = 8 Length = 10 Table ‎2‑2. The output of CRDP, Summery of material and dimensions for Long 460 ROPS all dimension in In. (Ayers et al., 2016). Part Quantity Dimensions Posts Tubing 2 Thickness = 0.1875 Width = 2 Depth = 4 Length = 63.4 Crossbeam Tubing 1 Thickness = 0.1875 Width = 4 Depth = 2 Length = 25.3 Top Baseplate 2 Thickness = 1 Length = 9.75 Width = 7.8125 Bottom Baseplate 2 Thickness = 1 Length = 9.75 Width = 5.8125 Corner Braces 2 Thickness = 0.375 Length = 12 Width = 12 Baseplate Strapping 3 Thickness = 0.25 Length = 4 Width = 1 Baseplate Strapping 1 Thickness = 0.25 Length = 5 Width = 2 Baseplate Bolts 8 Diameter = 0.625 Grade = 8 Length = 10 EXPERIMENTAL TEST The constructed ROPS were sent to FEMCO Inc. in McPherson, KS, for experimental static standard tests. The applied loads were regulated based on SAE J2194 standard tests. The test included sequences of rear and side tests. The test was conducted using a ROPS test stand, hydraulic cylinders, a data acquisition system, a force transducer, and a displacement potentiometer. The static tests were stopped when the energy criteria were met, and the ROPS deflections were recorded (Ayers et al., 2016). LONGITUDINAL (REAR) LOAD TEST The rear load was applied horizontally and parallel to the longitudinal tractor median plane. Since more than half of the tractors weight was on the rear wheels, the longitudinal loads were applied from the rear. The load was applied to the cross beam that is typically the first component that contacts the ground in a rear rollover accident (Figure 2). The load was exerted to the cross beam and to the point which is located one-sixth of the cross bar width from one end of the cross beam. The rear load was applied until the ROPS absorbed energy (En) reaches the required energy based on equation (1): En= 1.4 M (1) Where En is the absorbed energy (J), and M is the tractor reference mass in (kg). The absorbed energy is the area under the force-deflection curve. Figure ‎2.2. Rear load test Long 460 ROPS. TRANSVERSE (SIDE) LOADING The side load was inserted horizontally and perpendicular to the median longitudinal plane of the tractor. The side load pushed the one side of the cross beam at which the rear load had not been applied. The test stops when the absorbed energy is equal to: En= 1.75 M (2) PARAMETERS OF PERFORMANCE The reference mass and the required absorbed energies and loads for the Allis Chalmers 5040 and Long 460 tractors are presented in Table 3. The ROPS Allowable Deflection (RAD) is defined as the maximum allowable deflection of the ROPS without violating the intrusion or exposure criteria. The ROPS Performance Deflection (RPD) is defined as the ROPS deflection during the four static tests. The RPD is the ROPS deflection to the point that the ROPS absorbs the predefined levels of energy in horizontal tests and the ROPS deflection under the vertical tests. During all of the tests, the RPD must be smaller or equal to the RAD to satisfy SAE J2194 requirements. A mathematical model was developed, validated, and implemented to evaluate the ROPS exposure criteria of ROPS under the standard SAE J2194 static test (Ayers et al., 1994). The model calculated RAD utilizing tractor dimensions, ROPS mounting points, and ROPS dimensions. The RAD for Allis Chalmers 5040 and Long 460 ROPS were computed using a Matlab code which was based on Ayers et al. (1994) research (Table 3). The intrusion criteria were defined based on the ROPS dimensions and the location of ROPS mounting and clearance zone. Table ‎2‑3. Calculated applied force and required energy as a function of tractor mass based on SAE J2194 standard. Allis Chalmers 5040 Long 460 Tractor mass (kg) 2032 1842 Rear load test, required absorbed energy (J) 2844.8 2578.8 Rear load test, RPD (mm) 229 176 Rear load test, RAD (mm) 420 400 Rear load test, permanent deflection (mm) 96 70 Side load test, required absorbed energy (J) 3556.0 3224.0 Side load test, RPD (mm) 221 168 Side load test, RAD (mm) 295 30 Side load test, permanent deflection (mm) 108 87 FINITE ELEMENT MODEL The ROPS behavior under standard tests were simulated by developing 24 FE models in Abaqus. Abaqus (2011) was selected for this study which is one of the most robust commercial software packages for nonlinear analysis (Yu & Li, 2012). The overall modeling procedure in FE software packages includes six steps to investigate engineering problems such as predicting the nonlinear behavior of ROPS: geometry creation, defining material properties, mesh generation, determining boundary conditions, simulation execution, and post-processing. The developed models include two types of ROPS (Long 460 and Allis Chalmers 5040), two finite element mesh resolutions and element types (C3D4 with global size 0.08, and C3D10M with global size 0.01), two tests (side and rear load test), and three material models (1: Experimental test based on ASTM test, 2: Ramberg-Osgood model based on ASTM test, and 3: Ramberg-Osgood model based on available online data). The designed ROPS for this study were made of tubular elements with a rectangular cross section which are reinforced with two bolted corner plates and welded strappings at the baseplates. The 3D CAD geometry model was drawn in 3D SolidWorks and was imported into Abaqus (Figure 3). Figure ‎2.3. Creation of the ROPS geometry in SolidWorks. MATERIAL PROPERTIES The material properties can have a significant influence on the FE results, and need to be evaluated. Typically, static ROPS testing produces a significant elastic-plastic deflection under SAE J2194 standard test; therefore m