Design and Experimental Study of Progressive Spring for Formula Student Race Car

The purpose of carrying out the present work is to design, manufacture & test the progressive springs on an FS vehicle. This is one type of helical spring with a variable spring rate. The main purpose of designing progressive springs is to avail all the advantages of the variable spring rate over the linear spring rate and better ride quality along with roll control, compared to linear rate springs. We took several factors of vehicle dynamics under consideration before settling on progressive springs. Before starting with the design procedure, we had set objectives and followed the standard methodology of spring design to get the required output. Along with that, we took design philosophy under consideration. We reviewed all the parameters before finalizing the spring material as it is one of the major factors. We carried out all the necessary design calculations to complete the dimensions and stiffness of the spring. The conclusion helped us to achieve better ride quality and roll control accompanying the optimized spring design satisfying all the necessities such as load, stiffness, and deflection of progressive springs.

Analysis and Synthesis of Conical Coil Springs

Springs are mechanical devices that are employed to resist forces, store energy, absorb shocks, mitigate vibrations, or maintain parts contacting each other. Spring wires are commonly coiled in the forms of helixes for either extension or compression. Helical springs usually have cylindrical shapes that have constant coil diameter, constant pitch and constant spring rate. Unlike conventional cylindrical coil springs, the coil diameter of conically coiled springs is variable. They have conical or tapered shapes that have a large coil diameter at the base and a small coil diameter at the top. The variable coil diameter enables conical coil springs generate desired load deflection relationships, have high lateral stability and low buckling liability. In addition, conical compression springs can have significantly larger compression or shorter compressed height than conventional helical compression springs. The compressed height of a conical compression spring can reach its limit that is the diameter of the spring wire if it is properly synthesized. The height of an undeformed conical coil spring can have its height of its spring wire if the spring pitch is chosen to be zero. The variable coil diameter of conical coil springs provides them with unique feature, but also raises their synthesis difficulties. Synthesizing conical coil springs that require large spring compression or small deformed spring height or constant spring rate is challenging. This research is motivated by surmounting the current challenges facing conical coil springs. In this research, independent parameters are introduced to control the diameter and pitch of a conical coil spring. Different conical coil springs are modeled. Their performances are simulated using the created models. The deflection-force relationships of conical coil springs are analyzed. The results from this research provide useful guidelines for developing conical coil springs.

Practical Approach to Functional Testing and Analytical Modeling of Axial Oscillation-Supported Drillstrings

Drillstrings that include one or more axial oscillation tools (AOTs) are referred to as axial oscillation-supported drillstrings. Downhole vibrations induced by these tools in the drillstring are the most efficient method for friction reduction and improving axial force transfer in high-angle and extended-reach wells. Functional testing of axial oscillation tools prior to downhole operations and modeling the dynamic response of axial oscillation-supported drillstring systems are required to predict the performance and functionality of AOTs. This study presents a practical approach for functional testing of axial oscillation tools and a new analytical model for predicting the dynamic response of axial oscillation-supported drillstrings operating at surface conditions. The axial oscillation-supported drillstring is modeled as an elastic continuous system subjected to viscous damping, frictional contact, and displacement (support excitation). The functional test is a unique experimental test procedure designed to measure the pressure drop, pressure fluctuations, and axial displacement of an axial oscillation tool while varying the flow rate and the spring rate of the tool. The introduction of the spring rate as a variable in the new model and functional testing is unique to this study and not considered in the existing literature. Axial displacement and acceleration predicted from the new model closely agrees with the results obtained from the functional tests. The accuracy of the model is also validated with the results of two previously published functional tests. The comparisons demonstrate an average deviation of approximately 14.5% between predictions and measurements. The axial displacement and pressure drop of AOT increased with flow rate or oscillation frequency. The amplitude of axial displacement increased with frequency because of increased pressure drop.

Optimization and Standardization of Flanged and Flued Expansion Joint Design

Flanged and flued type expansion joint (thick wall expansion bellow) used as an integral part of many shell and tube heat exchanger where process conditions produce differential expansion between shell and tubes. It provides flexibility for thermal expansion and also functions as a pressure retaining part. Design of expansion joints is usually based on trial and error method in which initial geometry must be assumed, and accordingly maximum stresses and spring rate are be calculated. Inadequate selection of geometry leads to higher tubesheet and bellow thickness, which increases cost of equipment. This paper presents standardization and optimum design approach of flange and flued expansion bellow fulfilling ASME VIII-1 and TEMA standard requirement. Methodology to define expansion bellow geometry is developed, and geometry dimensions are tabulated for expansion bellow diameter from 300 to 2000 mm and thickness from 6 to 30 mm. Each defined geometry is analyzed using finite element method, and maximum von Mises stresses are calculated for bellow axial displacement from 0.5 to 1.5 mm and internal pressure from 0.1 to 6.5 MPa. Spring rate is also calculated for each defined geometry for consideration in tubesheet calculation. Accordingly, optimum design methodology is developed, tested, and compared with existing design. Results depicted that proposed standardization approach and design methodology will optimize expansion bellow and tubesheet thickness and will also save considerable time in finalization of heat exchanger design.

An Approach for the Systematic Development of Progressive Light Weight Spring Element Concepts in Vehicle Constructions

Commercial vehicles are mostly equipped with pneumatic spring elements which lead to a perfect height levelling and spring rate adjustment under different loading conditions. However, pneumatic springs are not common in light commercial vehicles where passive spring elements, e.g. single- and multi-leaf springs, are still be used. Since those vehicles are covering a wide range of different loads the spring elements frequently exhibit a progressive spring characteristic, i.e. the spring rate is adjusted under deflection as soon as the load is increased. The need for light weight design also relates to light commercial vehicle so that glass fibre reinforced plastic (GFRP) has become a suitable substitute for high strength steel. Furthermore GFRP allows for innovative as well as functionally and technologically improved constructional solutions of progressive spring elements, e.g. the single-leaf spring approach by Schürmann et al [1].However, the above mentioned solution is sometimes rather solitaire and no systematic approach for its genesis exits. Hence, this contribution shows an approach for a more systematic development of progressive light weight spring element concepts in vehicle construction. Different approaches of implementing a progressive spring rate characteristic are presented in the introduction. A simple analytical model of a bending beam considering a variety of boundary conditions has been set up to discuss the effect of bearing stiffness on the spring rate.The model serves as a basis for a kind of toolbox for a more systematic approach for the development of the desired progressive spring elements. It allows to identify and to select a balanced concept for a progressive light weight spring element which also considers the application of the appropriate spring material at any specific part of the construction.

Influence of Bellows Setting on Its Spring Rate and on Temperature Adjustment of Electromechanical Thermostats

The precision and stability of adjusted temperatures are critical requirements for electromechanical thermostats. The key element in meeting the requirement is a thermostat bellows. It is a convertor of pressure into force that actuates the mechanical system of the thermostat. Convolutions enabling the axial movement of the bellows cause that the bellows is partly behaving as a spring. Therefore, the bellows has its own spring rate. The setting of the bellows spring rate influences the critical parameters of the thermostat. The aim of the article is to find the difference between the setting done by bellows producer and setting done by thermostat producer and its influence on the thermostat adjustment.

Enhanced Formulae for Determining Both Free Length and Rate of Cylindrical Compression Springs

Cylindrical compression springs have been commonly exploited in mechanical systems for years and their behavior is considered as well identified. Nevertheless, it appears that, even though old research studies suggest correcting the rate formula, the main industrial software dedicated to spring design exploits the uncorrected one. In order to evaluate the accuracy of the analytical formulae for spring behavior, an experimental study was performed, which tried to cover the common design space. This study was done using the two common coil ends: closed and ground ends, and closed and not ground ends. Moreover, the accuracy of the load–length relation was investigated whereas older studies focused only on the spring rate. It appears that the common uncorrected formulae give satisfactory results only when large numbers of coils are involved. We also highlight, for the first time, that it is interesting to correct not only the spring rate but also the free length of the spring.

Advanced leaf spring design and analysis with respect to vehicle kinematics and durability

Purpose – The purpose of this paper is to provide sound understanding of the mutual interactions of the major leaf spring design parameters and their effects on both the stress behavior of the designed leaf and the steering behavior of the vehicle. Design/methodology/approach – Finite elements analyses have been performed referring to the design of a high performance monoleaf spring used for the suspension of the front axle of a serial heavy truck. Design parameters like eye type, eye lever, spring rate and arm rate difference have been parametrically examined regarding the stress performance and their influence on the wheel joint kinematics. The effect of each design parameter is exhibited both qualitatively and quantitatively. Findings – Eye lever and eye type affect significantly the wheel joint kinematics and therewith the steering behavior of the vehicle. Spring rate and arm rate difference affect solely the stress performance of the leaf spring. Practical implications – Design engineers may use the outcomes of this research as a guide to achieve optimal leaf spring design ensuring its operational strength in conjunction with accurate steering performance of the vehicle. Originality/value – The international literature contains only few, mostly qualitative data regarding the effect of single design parameters on the leaf spring and the corresponding axle kinematics. The present work contains a comprehensive and systematic study of all major leaf spring design parameters, and reveals their effect on both the stress behavior and the steering behavior of the vehicle qualitatively and quantitatively.