A multi-unit tracked vehicle such as a continuous haulage system is widely used in underground mining applications due to its high mobility and payload capacity on rugged and soft terrain. To automate such a system, a high fidelity model of a tracked vehicle is essential in designing a controller for each tracked vehicle in the system, and a system model is required to simulate its response to input commands. This thesis presents the 2-D mathematical models of a tracked vehicle and a multi-unit tracked vehicle. All existing track-terrain interaction models are investigated and modified. By employing the modified track-terrain interaction model and applying Newton's second law of motion, the equations of motion of both single and multi-unit tracked vehicles can be derived. Computer programs for simulating the motions of these tracked vehicles on level ground have been implemented on a digital computer based on the derived system of differential equations. The fourth-order Runge-Kutta and Keun's methods are adopted to numerically integrate these differential equations. The simulation results clearly show that the programs can accurately predict the motion of a tracked vehicle maneuvered on horizontal plane, and closely predict the response of a multi-unit tracked vehicle operated on level ground its command inputs. / Master of Science

Vibrations caused by rough road excitations influence tracked vehicle dynamic performance. Good capabilities of such vehicles like high mobility, manoeuvrability and comfort are guaranteed by optimal suspension systems. The suspension systems of tracked vehicles are exposed to extreme operating conditions. This creates a conflict between ride comfort and handling that is even greater than the conflict between ride comfort and handling for general road vehicles. Tracked vehicles must be able to traverse not only rough roads but also smooth terrains. The challenges in developing an optimized suspension system for tracked vehicles include the high and changeable damping forces required for tracked vehicles crossing rough terrains. The use of active or semi-active suspension systems overcomes the limitations inherent in the conventional passive suspension. However, active suspension systems are expensive, complicated to design and have high power demand. Thus, semi-active suspension systems have emerged as a good compromise between active and passive suspension system. There is considerable current research on the applications of magnetorheological (MR) fluid dampers for semi-active suspensions of executive brand of some cars. However, there is very little research on semi-active devices for tracked vehicle suspension. In fact, currently, there is no commercially available large scale MR dampers in the market that produce the high damping force to suit such applications. In response to these requirements, this research proposes a novel semi-active tracked vehicle suspension system that uses MR dampers to improve the ride comfort and handling characteristics of tracked vehicles. It also assesses the dynamics of the new suspension with various semi-active control methods. This study is conducted in four phases. The first phase provides a numerical investigation on the dynamic performance of a seven-degrees-of-freedom (7-DOF) passive suspension model of the armour personnel carrier (APC) M113 tracked vehicle. The numerical investigation considers the influence of variation of five suspension design parameters on the vehicle dynamic performance. These parameters include number, locations of hydraulic shock absorber, damping coefficient, suspension and wheel stiffnesses. The results indicate that the optimal suspension performance is attained by using two or three dampers. The best locations for these dampers are at the extreme road wheels i.e. the first, second and last road wheel stations. Moreover, the vehicle performance is reduced when the damping coefficient is increased. Additionally, low suspension stiffness offers better vehicle ride while high wheel stiffness degrades the vehicle performance. These results identify the limitations inherent in the conventional passive suspension. For the second phase, the dynamic characteristics of the hydraulic, hydro-gas and MR dampers are experimentally measured and fitted using the Chebyshev orthogonal functions to produce the restoring force surfaces for each damper, which are compared. On one hand, the restoring force surfaces of the hydraulic and hydro-gas dampers show fixed properties at specified frequencies. On the other hand, the restoring force surfaces of the MR dampers show properties that can be controlled at the same specified frequencies by the variation of the applied current levels. Thus, the potential and the effectiveness of the controllable properties of MR dampers for semi-active vibration control is demonstrated. Also, in this phase, the best set of parameters to use in the modified Bouc-Wen model to characterise the MR dampers, has been derived. The third phase of the project is also experimentally based. A new and novel test rig which represents the 7-DOF scaled suspension model of the tracked vehicle is designed and fabricated. The primary purpose of the test rig is to evaluate the performance of the proposed suspension with MR dampers. Furthermore, experiments are conducted on the test rig to evaluate some semi-active control methods and their effectiveness in reducing suspension vibration. The results show that the use of two or three MR dampers at the extreme wheels offers optimal suspension performance. This confirms the numerical results that are derived from the full scale passive suspension system with hydraulic dampers. The experimental results also show that skyhook control and hybrid control (which combines groundhook and skyhook controls) of the semi-active suspension are more effective in reducing the road-induced vibration and improving the suspension dynamic behaviours. Also, validations of the predicted responses of the semi-active scaled MR suspension model with the measured responses have been presented. The fourth and final phase provides a numerical simulation on the development and evaluation of the semi-active control methods for a full scale tracked vehicle suspension with MR dampers using the validated suspension model. Three semi-active control strategies are proposed. The first two controllers are the skyhook and hybrid controls which provide better suspension performance. In addition, the third controller, which is an intelligent fuzzy-hybrid control system, is used to optimize the suspension performance. The results from this intelligent system are compared with the two traditional control methods (skyhook and hybrid controls) under bump, sinusoidal and random excitations. It is shown that the proposed controller can enhance simultaneously the vehicle ride and handling characteristics.

<p> The movement of diamond drills by tracked vehicles and drill trailers in south Central Keewatin was studied during the summer of 1980. Tests of the physical ground strength showed that the ability of the terrain to resist disturbance from tracked vehicle operations depended on two main physical factors: the type of surficial material and the presence of water. Moisture contents varied throughout the summer so that the response of till and peat to compression and shear was not constant. As the summer proqressed, the increasing depth of thaw and gradual surface drying caused strengthening of both major types of surficial material. As a result, vehicle trafficability gradually increased throughout the summer. While surface rutting increased the depth of thaw compared to an undisturbed site, especially in peat, after the first few weeks of the thaw this had little apparent effect on vehicle trafficability. In many cases the vehicle disturbance was largely aesthetic giving the impression that the terrain disturbance was much more serious than it actually was.</p> <p> Although the load distribution of the vehicle tracks concentrated much of the longitudinal stress directly beneath the bogie wheels, in most cases the performance of the tracked vehicle itself was adequate. However, problems caused by the drill trailer wheels resulted in unnecessary mechanical strain on the vehicles and created marked increases in terrain disturbance.</p> / Thesis / Bachelor of Arts (BA)

The use of robotics in hazardous environments is becoming more common, where autonomy can handle the dull, dirty and dangerous jobs that humans have previously supported. This thesis focuses on the design of a helicopter deployable unmanned ground vehicle for use in hazardous environments, and presents the benefits of heterogeneous unmanned vehicle teams for operation in beyond line-of-site hazardous environments. The design of a ground robot that is capable of being flown on the undercarriage of a Yamaha RMAX unmanned air vehicle is presented. The robot is size, weight, and power limited and must be capable of traversing rough, unstructured terrain. The results of testing show that the design criteria for size, weight, and mobility are met. A path planning algorithm is developed using the A* search algorithm for the planning of optimal paths through rough terrain. The algorithm makes use of a vehicle/terrain interaction model to compute the cost of path traversal. In the CONOPS, the terrain model is generated real-time during a mission through the use of a stereovision system carried on the helicopter, which station-keeps above the ground robot. The algorithm simulates the robot on the terrain and presents the best feasible path to the operator to aid in teleoperated robot navigation. Simulations of the planning algorithm provided feasible paths over a rough terrain environment. A user study was conducted that evaluates the abilities of both mono- and stereo-vision systems in providing the teleoperator with adequate situational awareness with the intent of proving that stereovision data is more effective at aiding the user in making timely navigation decisions. The results of the study showed that the helicopter-mounted stereovision system was more efficient than the monovision system with respect to navigation time, the number of invalid moves, and total moves required for navigation of a simulated rough terrain environment. / Master of Science

Devido as severas condições as quais veículos militares blindados de esteira são submetidos, o desenvolvimento de modelos que representam o comportamento dinâmico destes veículos torna-se imprescindível, para além da possibilidade de avaliação das intensidades das vibrações ocorrendo na cabine, ser possível criar veículos que tenham vantagens na mobilidade, fator esse que engloba tanto a transposição de obstáculos, como a rodagem em condições menos severas, e por fim, no tempo e na exatidão dos disparos, afetada pelas respostas dinâmicas que o veículo fornece. Para ser possível encontrar um veículo que desempenhe tais condições de forma satisfatória, apenas modelos que representem adequadamente as suas propriedades, apresentando respostas das acelerações e deslocamentos, não são suficientes. O objetivo deste trabalho é o desenvolvimento de um modelo numérico que tenha a capacidade de simular as condições dinâmicas extremas as quais um veículo de esteira é induzido, e também, otimizar o modelo, com a finalidade de encontrar molas e amortecedores capazes de proporcionar respostas adequadas às funções custo desenvolvidas. Estas funções objetivo são definidas como a combinação linear da aceleração e deslocamento, verticais e rotacionais, em conjunto de restrições impostas, objetivando encontrar uma combinação ideal para mobilidade, tempo e exatidão nos disparos e por fim, molas e amortecedores adequados as condições de logística Para proposta deste estudo, um modelo matemático 2D e um 3D, de um veículo de esteira, foi desenvolvido. O modelo possibilita a avaliação dos graus de liberdade de deslocamento vertical das massas não suspensas e do deslocamento vertical, arfagem e rolagem da massa suspensa. Os efeitos da esteira são modelados como molas verticais lineares exercendo uma força de restauração para alinhar as rodas de rodagem, proporcional ao deslocamento relativo entre essas rodas. A otimização é feita através de ferramentas numéricas presentes no software comercial Simulink, sendo necessário o desenvolvimento das funções custo que caracterizem os objetivos ideais para cada tipo de análise. Os resultados de simulações numéricas sob a forma de cursos de deslocamento de pontos característicos do casco e deslocamentos dos eixos de rodas em um sistema de coordenadas de referência assumido, também estão incluídos, bem como as quantidades de valor RMS de cada uma das respostas, comparando um veículo padrão, com o veículo com a suspensão otimizada. / Due to the severe conditions in which armored military vehicles are submitted, the development of models that represent the dynamic behavior of these vehicles becomes essential, besides the possibility of evaluating the vibration intensities occurring in the cabin, to be possible to create vehicles that have mobility a factor that encompasses both the transposition of obstacles, and the shooting in less severe conditions, and finally, in the time and accuracy of the shots, affected by the dynamic responses that the vehicle provides. In order to be able to find a vehicle that fulfills these conditions satisfactorily, only models that adequately represent its properties, presenting responses of the accelerations and displacements, are not enough. The objective of this work is the development of a numerical model that has the ability to simulate extreme dynamic conditions such as a tracked vehicle is induced, and also to optimize the model with the purpose of finding springs and shock absorbers capable of adequate alternative answers cost functions developed. These are the goals defined as a linear combination of acceleration and displacement, vertical and rotational, together imposed constraints, aiming to find an ideal combination for mobility, time and precision in the shots and, finally, springs and dampers suitable as logistics conditions To propose this study, a 2D and 3D mathematical model of a tracked vehicle were developed. The model allows the evaluation of the degrees of freedom of vertical displacement of the non-suspended masses and the vertical displacement, pitch and roll of the suspended mass. The effects of the track are modeled as linear vertical springs exerting a restoring force to align the road wheels, proportional to the relative displacement between these wheels. The optimization is done through numerical tools present in Simulink software, and it is necessary to develop cost functions that characterize the ideal objectives for each type of analysis. The results of numerical simulations in the form of displacement courses of characteristic hull points and wheel axle displacements in an assumed reference coordinate system are also included, as well as the RMS value quantities of each of the responses, comparing a standard vehicle with the optimized suspension.

Methods for estimating vehicle-terrain interaction parameters for small scale robotic vehicles have been formulated and evaluated using both simulation and experimental studies. A model basis was developed, guided by experimental studies with an iRobot PackBot. The intention was to demonstrate whether a nominally instrumented robotic vehicle could be used as a test platform for generating data for vehicle-terrain parameter estimation. A comprehensive skid-steered model was found to be sensitive enough to distinguish between various forms of unknown terrains. This simulation study also verified that the Bekker model for large scale vehicles adopted for this research was applicable to the small scale robotic vehicle used in this work. This fact was also confirmed by estimating coefficients of friction and establishing their dependence on forward velocity and turning radius as the vehicle traverses different terrains. On establishing that mobility measurements for this robotic were sufficiently sensitive, it was found that estimates could be made of key dynamic variables and vehicle-terrain interaction parameters. Four main contributions are described for reliably and robustly using PackBot data for vehicle-terrain property estimation. These estimation methods should contribute to efforts in improving mobility of small scale tracked vehicles on uncertain terrains. The approach is embodied in a multi-tiered algorithm based on the dynamic and kinematic models for skid-steering as well as tractive force models parameterized by key vehicle-terrain parameters. In order to estimate and characterize the key parameters, nonlinear estimation techniques such as the Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and a General Newton Raphson (GNR) method are integrated into this multi-tiered algorithm. A unique idea in using an EKF with an added State Noise Compensation algorithm is presented which shows its robustness and consistency in estimating slip variables and other parameters for deformable terrains. In the multi-tiered algorithm, a kinematic model of the robotic vehicle is used to estimate slip variables and turning radius. These estimated variables are stored in a truth table and used in a skid-steered dynamic model to estimate the coefficients of friction. The total estimated slip on the left and right track, along with the total tractive force computed using a motor model, are then used in the GNR algorithm to estimate the key vehicle-terrain parameters. These estimated parameters are cross-checked and confirmed with EKF estimation results. Further, these simulation results verify that the tracked vehicle tractive force is not dependent on cohesion for frictional soils. This sequential algorithm is shown to be effective in estimating vehicle-terrain interaction properties with relatively good accuracy. The estimated results obtained from UKF and EKF are verified and compared with available experimental data, and tested on a PackBot traversing specified terrains at the Southwest Research Institute (SwRI), Small Robotics Testbed in San Antonio, Texas. In the end, based on the development and evaluation of small scale vehicle testing, the effectiveness of on-board sensing methods and estimation techniques are also discussed for potential use in real time estimation of vehicle-terrain parameters. / text

Fossila bränslen är ändliga resurser och FMV menar i sin Tekniska Prognos 2013 att Försvarsmakten redan nu bör planera för en omställning till alternativa tekniker till dagens förbränningsmotor. Den teknik som verkar mest lämplig som interimslösning mellan framtidens vision om ren eldrift och förbränningsmotorn är elhybridteknik. Uppsatsen undersöker hur Försvarsmaktens logistikfunktion påverkas om bandvagnssystemet skulle övergå till seriehybridteknik. Uppsatsens ansats är kvalitativ med en kombination av textstudier, intervjuer samt ett frågeformulär som besvaras av totalt tre personer fördelat på Amf1, FMTS och I19 där samtliga innehar mångårig erfarenhet av bandvagnssystemet. Formulären kompletteras med intervjuer med dessa personer samt personer på BAE Systems som bidrar med teknisk expertis. Slutsatsen är att seriehybridtekniken har potential att både direkt och indirekt påverka logistikfunktionen positivt, men att konkreta vinster är svåra att bedöma med hänsyn till osäkerheter kopplat både mot tekniska faktorer och att tekniken inte är prövad i strid. / Fossil fuels are finite resources and in a report from 2013, the Swedish Defence Material Administration encourages the Swedish Armed Forces to start planning for the transition to alternative propulsion systems to reduce its dependency of fossil fuels. The most promising technology to bridge the gap between pure electric propulsion and today’s internal combustion engine is hybrid electric technology. This essay examines the implications a series hybrid solution would have on military logistics. The method used includes analysis of both scientific reports and of survey answers from personnel in the SAF with several years of experience working with the tracked vehicle Bandvagn 309. The analysis of the survey answers is completed with interviews with these people and others working at BAE Systems who contributes with technical expertise. The essay will conclude that a series hybrid solution would have a positive impact on military logistics even though it is hard to specify how great the effect would be due to technical uncertainties and the fact that the technology is yet to be tested in combat.

Devido as severas condições as quais veículos militares blindados de esteira são submetidos, o desenvolvimento de modelos que representam o comportamento dinâmico destes veículos torna-se imprescindível, para além da possibilidade de avaliação das intensidades das vibrações ocorrendo na cabine, ser possível criar veículos que tenham vantagens na mobilidade, fator esse que engloba tanto a transposição de obstáculos, como a rodagem em condições menos severas, e por fim, no tempo e na exatidão dos disparos, afetada pelas respostas dinâmicas que o veículo fornece. Para ser possível encontrar um veículo que desempenhe tais condições de forma satisfatória, apenas modelos que representem adequadamente as suas propriedades, apresentando respostas das acelerações e deslocamentos, não são suficientes. O objetivo deste trabalho é o desenvolvimento de um modelo numérico que tenha a capacidade de simular as condições dinâmicas extremas as quais um veículo de esteira é induzido, e também, otimizar o modelo, com a finalidade de encontrar molas e amortecedores capazes de proporcionar respostas adequadas às funções custo desenvolvidas. Estas funções objetivo são definidas como a combinação linear da aceleração e deslocamento, verticais e rotacionais, em conjunto de restrições impostas, objetivando encontrar uma combinação ideal para mobilidade, tempo e exatidão nos disparos e por fim, molas e amortecedores adequados as condições de logística Para proposta deste estudo, um modelo matemático 2D e um 3D, de um veículo de esteira, foi desenvolvido. O modelo possibilita a avaliação dos graus de liberdade de deslocamento vertical das massas não suspensas e do deslocamento vertical, arfagem e rolagem da massa suspensa. Os efeitos da esteira são modelados como molas verticais lineares exercendo uma força de restauração para alinhar as rodas de rodagem, proporcional ao deslocamento relativo entre essas rodas. A otimização é feita através de ferramentas numéricas presentes no software comercial Simulink, sendo necessário o desenvolvimento das funções custo que caracterizem os objetivos ideais para cada tipo de análise. Os resultados de simulações numéricas sob a forma de cursos de deslocamento de pontos característicos do casco e deslocamentos dos eixos de rodas em um sistema de coordenadas de referência assumido, também estão incluídos, bem como as quantidades de valor RMS de cada uma das respostas, comparando um veículo padrão, com o veículo com a suspensão otimizada. / Due to the severe conditions in which armored military vehicles are submitted, the development of models that represent the dynamic behavior of these vehicles becomes essential, besides the possibility of evaluating the vibration intensities occurring in the cabin, to be possible to create vehicles that have mobility a factor that encompasses both the transposition of obstacles, and the shooting in less severe conditions, and finally, in the time and accuracy of the shots, affected by the dynamic responses that the vehicle provides. In order to be able to find a vehicle that fulfills these conditions satisfactorily, only models that adequately represent its properties, presenting responses of the accelerations and displacements, are not enough. The objective of this work is the development of a numerical model that has the ability to simulate extreme dynamic conditions such as a tracked vehicle is induced, and also to optimize the model with the purpose of finding springs and shock absorbers capable of adequate alternative answers cost functions developed. These are the goals defined as a linear combination of acceleration and displacement, vertical and rotational, together imposed constraints, aiming to find an ideal combination for mobility, time and precision in the shots and, finally, springs and dampers suitable as logistics conditions To propose this study, a 2D and 3D mathematical model of a tracked vehicle were developed. The model allows the evaluation of the degrees of freedom of vertical displacement of the non-suspended masses and the vertical displacement, pitch and roll of the suspended mass. The effects of the track are modeled as linear vertical springs exerting a restoring force to align the road wheels, proportional to the relative displacement between these wheels. The optimization is done through numerical tools present in Simulink software, and it is necessary to develop cost functions that characterize the ideal objectives for each type of analysis. The results of numerical simulations in the form of displacement courses of characteristic hull points and wheel axle displacements in an assumed reference coordinate system are also included, as well as the RMS value quantities of each of the responses, comparing a standard vehicle with the optimized suspension.

Devido as severas condições as quais veículos militares blindados de esteira são submetidos, o desenvolvimento de modelos que representam o comportamento dinâmico destes veículos torna-se imprescindível, para além da possibilidade de avaliação das intensidades das vibrações ocorrendo na cabine, ser possível criar veículos que tenham vantagens na mobilidade, fator esse que engloba tanto a transposição de obstáculos, como a rodagem em condições menos severas, e por fim, no tempo e na exatidão dos disparos, afetada pelas respostas dinâmicas que o veículo fornece. Para ser possível encontrar um veículo que desempenhe tais condições de forma satisfatória, apenas modelos que representem adequadamente as suas propriedades, apresentando respostas das acelerações e deslocamentos, não são suficientes. O objetivo deste trabalho é o desenvolvimento de um modelo numérico que tenha a capacidade de simular as condições dinâmicas extremas as quais um veículo de esteira é induzido, e também, otimizar o modelo, com a finalidade de encontrar molas e amortecedores capazes de proporcionar respostas adequadas às funções custo desenvolvidas. Estas funções objetivo são definidas como a combinação linear da aceleração e deslocamento, verticais e rotacionais, em conjunto de restrições impostas, objetivando encontrar uma combinação ideal para mobilidade, tempo e exatidão nos disparos e por fim, molas e amortecedores adequados as condições de logística Para proposta deste estudo, um modelo matemático 2D e um 3D, de um veículo de esteira, foi desenvolvido. O modelo possibilita a avaliação dos graus de liberdade de deslocamento vertical das massas não suspensas e do deslocamento vertical, arfagem e rolagem da massa suspensa. Os efeitos da esteira são modelados como molas verticais lineares exercendo uma força de restauração para alinhar as rodas de rodagem, proporcional ao deslocamento relativo entre essas rodas. A otimização é feita através de ferramentas numéricas presentes no software comercial Simulink, sendo necessário o desenvolvimento das funções custo que caracterizem os objetivos ideais para cada tipo de análise. Os resultados de simulações numéricas sob a forma de cursos de deslocamento de pontos característicos do casco e deslocamentos dos eixos de rodas em um sistema de coordenadas de referência assumido, também estão incluídos, bem como as quantidades de valor RMS de cada uma das respostas, comparando um veículo padrão, com o veículo com a suspensão otimizada. / Due to the severe conditions in which armored military vehicles are submitted, the development of models that represent the dynamic behavior of these vehicles becomes essential, besides the possibility of evaluating the vibration intensities occurring in the cabin, to be possible to create vehicles that have mobility a factor that encompasses both the transposition of obstacles, and the shooting in less severe conditions, and finally, in the time and accuracy of the shots, affected by the dynamic responses that the vehicle provides. In order to be able to find a vehicle that fulfills these conditions satisfactorily, only models that adequately represent its properties, presenting responses of the accelerations and displacements, are not enough. The objective of this work is the development of a numerical model that has the ability to simulate extreme dynamic conditions such as a tracked vehicle is induced, and also to optimize the model with the purpose of finding springs and shock absorbers capable of adequate alternative answers cost functions developed. These are the goals defined as a linear combination of acceleration and displacement, vertical and rotational, together imposed constraints, aiming to find an ideal combination for mobility, time and precision in the shots and, finally, springs and dampers suitable as logistics conditions To propose this study, a 2D and 3D mathematical model of a tracked vehicle were developed. The model allows the evaluation of the degrees of freedom of vertical displacement of the non-suspended masses and the vertical displacement, pitch and roll of the suspended mass. The effects of the track are modeled as linear vertical springs exerting a restoring force to align the road wheels, proportional to the relative displacement between these wheels. The optimization is done through numerical tools present in Simulink software, and it is necessary to develop cost functions that characterize the ideal objectives for each type of analysis. The results of numerical simulations in the form of displacement courses of characteristic hull points and wheel axle displacements in an assumed reference coordinate system are also included, as well as the RMS value quantities of each of the responses, comparing a standard vehicle with the optimized suspension.

This master thesis describes a study of the main battle tank dynamics in order to investigate the fire precision when a tank is driving in terrain. A model has been developed to simulate the dynamic interaction between the tank's hull and the ground irregularity in MATLAB and SIMULINK through the modelling of the tank's dynamics. Two different models of suspension system have been analysed. One linear model and one hydro-pneumatic model. Further the contribution from the cannon's recoil has been modelled to investigate its contribution to the dynamics of the vehicle. The models developed are on system level and is to be implemented in a larger model. Therefore are the models simplified and the thesis investigates to what degree of simplification the models will accurately predict the movement of the tank. / Denna examensarbete beskriver en studie på stridsvagnsdynamik för att undersöka precision av målträff när stridsvagnen framförs i terräng. En modell har utvecklats för att simulera hur stridsvagnar påverkas av underlagets variation i MATLAB och SIMULINK genom att modellera stridsvagnens dynamik. Två olika former av stötdämpare har undersökts, en linjär modell samt en hydro-pneumatisk modell. Även bidraget från kanonen's avfyrning har modellerats för att se hur rekylens bidrag påverkar rörelsen av stridsvagnen. Målet med studien var att ta fram en så förenklad modell som möjligt. Flera modeller har därför utvecklats för att jämföra förenklingsgraden.