A NEW METHOD FOR GENERATING VIRTUAL MODELS OF NONLINEAR HELICAL SPRINGS BASED ON A RIGOROUS MATHEMATICAL MODEL

This paper presents a new method for generating nonlinear helical spring geometries based on a rigorous mathematical formulation. The model was developed for two scenarios for modifying a spring with a stepped helix angle: for a fixed helix angle of the active coils and for a fixed overall height of the spring. It allows the development of compression spring geometries with non-linear load-deflection curves, while maintaining predetermined values of selected geometrical parameters such as the number of passive and active coils and the total height or helix angle of the linear segment of the active coils. Based on the proposed models, Python scripts were developed that can be implemented in any CAD software offering scripting capabilities or equipped with Application Programming Interfaces. Examples of scripts that use the developed model to generate the geometry of selected springs are presented. FEM analyses of quasi-static compression tests carried out for these spring models have shown that, using the proposed tools, springs with a wide range of variation in static load-deflection curves can be obtained, including progressive springs with a high degree of nonlinearity in the characteristics. The obtained load-deflection curves can be described with a high degree of accuracy by power function. The proposed method can find applications in both machine design and spring manufacturing

Model i badania symulacyjne zderzenia wielopunktowego w płaskim układzie wieloczłonowym z uwzględnieniem tarcia

This article presents a mathematical model of a planar system for the multipoint, oblique, and eccentric impact of rough bodies. The created model served for numerical investigations of the system’s behaviour. To analyse the influence of various parameters, three simplified cases were defined. Each of these cases focused on different aspects of the simulation. The first case was used to determine how many contacting bodies undergo impact at a given time point. This result was then compared with the experimental observations, which gave good agreement. The second case investigated the influence of the body configuration and the coefficient of friction (COF) on the sliding process during impact. Depending on the parameter values, the sliding process was divided into three main areas: slip-reversal slip, stick-slip, and continuous slip with increasing sliding velocity. The third case focused on the energy dissipation expressed by the coefficient of restitution (COR) and the angle of incidence of the initiating impact; this case showed possible improvement areas of the used impact force model.W artykule przedstawiono model matematyczny płaskiego zderzenia wielopunktowego. Konfiguracja zderzających się ciał pozwalała na wystąpienie zarówno zderzenia mimośrodowego jak i ukośnego oraz uwzględniała tarcie. Opracowany model posłużył następnie badaniom symulacyjnym. W celu przeanalizowania wpływu różnych parametrów na zachowanie systemu zdefiniowano trzy uproszczone przypadki. W pierwszym badano, jaka ilość ciał bierze jednocześnie udział w zderzeniu. Przeprowadzone porównanie otrzymanych wyników z obserwacjami eksperymentu pokazało dobrą zgodność. W drugim przypadku badano wpływ konfiguracji zderzających się ciał oraz współczynnika tarcia na przebieg procesu poślizgu w trakcie zderzenia. W zależności od wartości parametrów możliwe są trzy główne scenariusze: poślizg–zmiana kierunku poślizgu, poślizg–zatrzymanie poślizgu, ciągły poślizg ze wzrastającą prędkością poślizgu. Trzeci przypadek skupiał się na dyssypacji energii wyrażonej poprzez współczynnik restytucji oraz kierunku uderzenia inicjującego; przypadek ten pokazał obszary, w których wykorzystany model siły zderzenia wymaga dopracowania

Prediction of the plastic component parts durability with use of a drop test simulation Przewidywanie trwałości produktów z tworzyw sztucznych z użyciem symulacji testu zrzucania /

Tyt. z nagłówka.Bibliogr. s. [40].W poniższej publikacji opisana jest metoda wykonywania symulacji testu zrzucania dla elementów wykonanych z materiałów polimerowych. Przedstawione zostały możliwe do użycia modele materiałowe wraz z modelem użytym w symulacji. Ukazane zostały także testy materiałowe konieczne do uzyskania parametrów modelu wraz z wynikami pomiarów. Jako przykład, zamodelowany został test zrzucania obudowy skrzynki bezpiecznikowej samochodu, wykonanej z Polipropylenu z 20% dodatkiem talku. Wyniki symulacji zostały porównane ze zdjęciami wykonanymi za pomocą systemu wizyjnego, podczas rzeczywistej próby zrzucania obudowy skrzynki bezpiecznikowej.This paper describes the method of performance of a drop test simulation for elements made of polymeric materials. Possibilities to use material models were described and material model choices were shown. Material tests needed to obtain material model parameters were presented and the results of analysis and measurement data were shown. As an example a drop test of the housing of a car electrical box made of Polypropylene with 20% Talc filler (PPTD20), have been simulated in ABAQUS/Explicit and results have been compared with data registered by a video camera system during the real drop test of this housing.Dostępny również w formie drukowanej.SŁOWA KLUCZOWE: test zrzucania, nieliniowy zależny od prędkości sprężysto-plastyczny model materiałowy, MES. KEYWORDS: drop test, nonlinear rate dependent elastic-plastic material model, FEA

Calculation of maximal collision force in kinematic chains based on collision force impulse

This paper presents a new method for calculating maximal collision forces in kinematic chains based on their impulses. Its main advantage is its simplicity as it is based on algebraic equations. Collisions between the feed, hammer and rotor in a hammer crusher are used as a case study to show the implementation of the proposed method. The obtained results are then compared with a reference time-domain model. The proposed method can be used by mechanical engineers in early design phases to estimate loads acting on parts during collisions as well as to search for more optimal geometrical parameters

Experimental analysis of transverse stiffness distribution of helical compression springs

This paper presents the results of an experimental analysis of the distribution of transverse stiffness of cylindrical compression helical springs with selected values of geometric parameters. The influence of the number of active coils and the design of the end coils on the transverse stiffness distribution was investigated. Experimental tests were carried out for 18 sets of spring samples that differed in the number of active coils, end-coil design and spring index, and three measurements were taken per sample, at two values of static axial deflection. The transverse stiffnesses in the radial directions were tested at every 30 angle. A total of 1,296 measurements were taken, from which the transverse stiffness distributions were determined. It was shown that depending on the direction of deflection, the differences between the highest and lowest value of transverse stiffness of a given spring can exceed 25%. The experimental results were compared with the results of the formulas for transverse stiffness available in the literature. It was shown that in the case of springs with a small number of active coils, discrepancies between the average transverse stiffness of a given spring and the transverse stiffness calculated based on literature relations can reach several tens of percent. Analysis of the results of the tests carried out allowed conclusions to be drawn, making it possible to estimate the suitability of a given computational model for determining the transverse stiffness of a spring with given geometrical parameters

Determination of the Preload of Bolts for Structural Health Monitoring of a Multi-Bolted Joint: FEM Approach

The reliability and safety of bolted joints is one of the crucial engineering problems during design of mechanical structures. In this paper, finite element method was used to investigate an asymmetrical, seven-bolted joint. The modelling takes into account the phenomenon of friction and the mechanics of contact between the joined elements. The bolts were preloaded using two different approaches: single and multi-pass. The damage of a bolt was simulated by its removal from the model. The conducted research showed influence of the number of preloading passes and its order on the forces acting in bolts both before and after damage. The obtained results were validated by experimental tests and presented as force diagrams for all investigated cases

Determination of the Preload of Bolts for Structural Health Monitoring of a Multi-Bolted Joint: FEM Approach

The reliability and safety of bolted joints is one of the crucial engineering problems during design of mechanical structures. In this paper, finite element method was used to investigate an asymmetrical, seven-bolted joint. The modelling takes into account the phenomenon of friction and the mechanics of contact between the joined elements. The bolts were preloaded using two different approaches: single and multi-pass. The damage of a bolt was simulated by its removal from the model. The conducted research showed influence of the number of preloading passes and its order on the forces acting in bolts both before and after damage. The obtained results were validated by experimental tests and presented as force diagrams for all investigated cases

PREDICTION OF THE PLASTIC COMPONENT PARTS DURABILITY WITH USE OF A DROP TEST SIMULATION

This paper describes the method of performance of a drop test simulation for elements made of polymeric materials. Possible to use material models were described and material model choices were shown. Material tests needed to obtain material model parameters were presented and the results of analysis and measurement data were shown. As an example a drop test of the housing of a car electrical box made of Polypropylene with 20% Talc filler (PPTD20), have been simulated in ABAQUS/Explicit and results have been compared with data registered by a video camera system during the real drop test of this housing

A NEW METHOD FOR GENERATING VIRTUAL MODELS OF NONLINEAR HELICAL SPRINGS BASED ON A RIGOROUS MATHEMATICAL MODEL

This paper presents a new method for generating nonlinear helical spring geometries based on a rigorous mathematical formulation. The model was developed for two scenarios for modifying a spring with a stepped helix angle: for a fixed helix angle of the active coils and for a fixed overall height of the spring. It allows the development of compression spring geometries with non-linear load-deflection curves, while maintaining predetermined values of selected geometrical parameters, such as the number of passive and active coils and the total height or helix angle of the linear segment of the active coils. Based on the proposed models, Python scripts were developed that can be implemented in any CAD software offering scripting capabilities or equipped with Application Programming Interfaces. Examples of scripts that use the developed model to generate the geometry of selected springs are presented. FEM analyses of quasi-static compression tests carried out for these spring models showed that springs with a wide range of variation in static load-deflection curves, including progressive springs with a high degree of nonlinearity in characteristics, can be obtained using the proposed tools. The obtained load-deflection curves can be described with a high degree of accuracy by power function. The proposed method can find applications in both machine design and spring manufacturing