Abstract
Springs are one of the most popular means of mechanically storing and issuing energy, and they can be found in a wide variety of machines and products. Most springs are made of metal, and nowadays, there are many new alloys to choose from, but nonmetallic materials, such as the reinforced plastics and ceramics, have been appearing worldwide. The research problem is the performance for circular cross-sectional springs with the same geometry and manufactured with three different materials: steel, composite, and functionally graded material (FGM) under stable loading using finite element analysis. This paper intends to guide mechanical designers in considering different material options for a spring design as well as to provide a methodology through finite element analysis for selecting the most favorable material option for the application required. The findings of this research show that some feature performances of compression springs made of carbon steel are improved by using FGM and composite materials. Enhanced capabilities include higher load to failure: 1.48 times in an FGM spring and 1.1 times in a composite spring, as well as increased energy storage: 1.53 times in an FGM spring and 6.84 times in a composite spring and less weight representing only 61% in an FGM spring and 24% in a composite spring.
1. Introduction
Springs are one of the most popular means of mechanically storing and issuing energy, and they can be found in a wide variety of machines and products. Most springs are made of metal, and nowadays, there are many new alloys to choose from, but nonmetallic materials, such as the reinforced plastics and the ceramics, have been appearing worldwide.
The research aim focuses on contributing to the mechanical design of a spring considering the selection of its manufacturing material. In this sense, it will carry out an analysis of two springs made with two new types of materials used worldwide for manufacturing them, comparing the performance of a spring made of FGM with a spring made of composite materials, and these results will be contrasted with a traditional spring made of carbon steel. For completing the evaluation, a finite element analysis will be carried out using the commercial software ANSYS Workbench. Three computational cases will be performed with the same geometric model of a helical spring of circular cross section and subjected to compression. It will vary only on the material used in each computational case; for comparing the spring performance made of each of three materials analyzed in this study, FGM, composite material, and carbon steel were used.
First, it will corroborate the computational model of carbon steel spring, comparing the finite element analysis (FEA) results with mathematical models of spring design from [1]. Then, it will validate the computational model of a carbon fiber spring (composite materials) considering the experimental results published in the international literature. These validations will allow corroborating the methodology used for the FEA of each of the cases assessed in this study and will ensure the reliability of the results issued.
2. Methodology
The following phases were considered for the numerical analysis of circular cross-sectional spring with steel, FGM, and composite materials. (i)Validation analysis(ii)Computational models
2.1. Validation Analysis
Some researchers [2–6] have demonstrated that the mechanical behavior of composite materials, as well as FGM, can be simulated satisfactorily. This research intends to simulate the mechanical behavior of three springs taking into account several experimental research results as well as international standards to demonstrate the reliability of the FEA results in the present investigation.
According to [1, 7], the design calculation for steel spring in the case of compression load without initial tension refers to the following equations.
2.1.1. Deflection of Spring
where is the number of active coils or number of active turns, is the mean diameter of coil (mm), is the load (force) acting on spring (N), is the modulus of rigidity ( for steel spring), and is the diameter of the material (mm).
2.1.2. Spring Constant ()
2.1.3. Energy Stored in Spring ()
Equation (1) will be used to validate the deflection result of the numerical analysis in the case of a steel spring with a circular cross section.
Equations (2) and (3) will be used to evaluate the spring performance in each of the three cases assessed in this study.
2.1.4. Composite Spring
According to [8], develop an experimental investigation into the mechanical behaviors of helical composite springs made of preimpregnated fibers fabricated with fibers along with ±45° directions. Then, pack, coil, and outer braid one layer with resin-impregnated 3K carbon fiber. The present paper will focus only on the “BU” preformed composite bar structure shown by [8] (see Figure 1).
The experimental results of this research [8] considering a cylindrical helical spring with a square cross section will be used in this paper only for validation purpose to corroborate the mechanical behavior of the composite spring made of 3K carbon fiber outer braid with a “BU” preformed structure.
Figure 2 and Table 1 show the geometrical dimensions of the square cross section for the computational model used in the validation of composite spring.
Considering the manufacturing methodology of carbon fiber composite spring described by [8], Figure 2 shows the square cross-sectional compound for a core made of preimpregnated fibers fabricated with fibers along with ±45° directions with an outer braided one layer of 3K carbon fiber. This 3K carbon fiber lamina with a length of 37.5 cm is coiled 14 times, as shown in Table 1.
The total side length of the square cross section is 10 mm, after coiling 14 times the 3K carbon fiber lamina according to the description in Table 1 and considering a carbon fiber lamina thickness of 0.22 mm. Table 2 shows the properties of 3K carbon fiber that were used in the numerical simulation.
Figure 3(a) shows the experimental investigation spring model [8] in comparison with the geometrical model developed in the module ACP (pre) from ANSYS Workbench of the composite spring used for validation purposes (Figure 3(b)).
(a) Experimental investigation spring model
(b) Numerical simulation spring model
Considering the maximum compression load in the elastic range of the spring (250 kgf or 2452 N) obtained experimentally by [8]. Figure 4 shows the boundary conditions and mesh used in the numerical simulation. Spring mesh was refined until achieving the convergence. The final mesh sizing was 0.8 mm (0.031 in) using second-order solid elements.
(a) Boundary conditions
(b) Mesh
Another aspect for validating is the failure load in the elastic range for the composite spring; hence, it will consider the results obtained experimentally by [8] related to the failure behavior of this coil spring.
2.2. Computational Models
After validating the methodology used for simulating, three geometric models were carried out using ANSYS Workbench considering the following general features described in Table 3.
2.2.1. Computational Model 1
Mechanical and physical properties of the material (carbon steel with ) used for numerical simulation are shown in Table 4.
Figure 5 depicts the boundary conditions and mesh used in computational model 1. It highlighted a load compression force of 981 N (220.54 lbf), which is the maximum load in the elastic range.
(a) Boundary conditions
(b) Mesh
2.2.2. Computational Model 2
Figure 6 shows the difference in compositions and properties between an ordinary composite material and FGM. There is a distinct interface between metals and ceramics in an ordinary composite material, but not in an FGM. This difference corresponds to the distribution of properties. An ordinary composite material contains a sudden change in properties at the interface, while an FGM presents a gradual change inside it.
For developing the numerical simulation of the FGM compound by carbon steel with less than 0.5% of C in addition with aluminum oxide (Al2O3), the research developed by [13] was considered, as well as [14, 15] to determine the material properties [14]. Describe that properties () are dependent on the temperature and are expressed in the form
where , , , and are constants in the cubic fit of the material property and is the temperature in kelvin. For this paper, is equivalent to 298 K.
Besides, reference [14] states that, to model the material properties of FGM effectively, the properties must be both temperature-dependent and position-dependent. The combination of these functions gives rise to the effective material properties of FGMs and is expressed as where is the effective material property of FGM, and are the temperature-dependent properties of the metal and ceramic, respectively, and is the volume fraction of the metal constituent of the FGM. In addition, reference [14] mentions that a simple power-law exponent of the volume fraction distribution is used to provide a measure of the amount of metal in FGMs. For an axisymmetric cylinder, the expression for the volume fraction of ceramic is where is the outer radius of the cylinder, is the inner radius, is the radial coordinate (), and is the power-law index ().
According to the preceding distribution, the outer surface of the cylinder is ceramic-rich and the inner surface is metal-rich. Table 5 shows the modulus of elasticity of aluminum oxide (Al2O3) in Pa, considering Equation (4). Table 6 shows the Poisson’s ratio of aluminum oxide (Al2O3), considering Equation (4).
For this paper, it was considered a power-law index () equivalent to 1. In this case, the mechanical and physical properties of the FGM compound by carbon steel with less than 0.5% of C in addition with aluminum oxide (Al2O3) and considering Equations (4)–(6) are shown in Table 7.
According to [16], develop an algorithm to simulate properties of FGM for the design optimization in a dental implant for bone remodeling. In this sense and to estimate the mechanical and physical properties, which are position-dependent, an algorithm was developed to simulate this computational model in the ANSYS Workbench.
Figure 7 depicts the boundary conditions and mesh used in computational model 2. It highlighted a load compression force of 1450 N (325.97 lbf), which is the maximum load in the elastic range.
(a) Boundary conditions
(b) Mesh
2.2.3. Computational Model 3
Considering the same methodology explained in Section 2.1 about the validation of composite spring simulation, Figure 8 shows the geometrical dimensions of the circular cross section for computational model 3.
Table 8 shows the geometrical dimensions of the circular cross section for computational model 3.
The final diameter of the circular cross section is 10 mm, after coil 14 times the 3K carbon fiber lamina according to the description in Table 8 and considering a carbon fiber lamina thickness of 0.22 mm. Table 2 shows the properties of 3K carbon fiber that will be used in the numerical simulation.
Figure 9 depicts the boundary conditions and mesh used in computational model 3. It highlighted a load compression force of 1070 N (240.55 lbf), which is the maximum load in the elastic range.
(a) Boundary conditions
(b) Mesh
3. Results and Discussion
3.1. Validation Analysis
Figure 10 shows the maximum displacement in the elastic range for the carbon steel spring considering a compression load of 981 N (220.54 lbf).
(b) Final condition
(a) Initial conditions
Equation (1) represents the deflection of the spring according to international standard [1]. Considering Equation (1), the theoretical maximum deflection in the elastic range for the carbon steel spring is 2.3 mm, and the FEA result in Figure 10 shows a maximum displacement equivalent to 2.4 mm; in consequence, the relative error is 4.19%. Hence, results about displacement demonstrate that numerical simulation of the steel spring can represent very well the spring theoretical behavior. Figure 11 shows the maximum displacement in the elastic range for the composite spring with a square cross section.
(a) Initial conditions
(b) Final condition
Considering the data issued by [8], the maximum deflection for the composite spring during the experiment in the elastic range is 16.23 mm, and the FEA result in Figure 11 shows a maximum displacement equivalent to 17.12 mm; hence, the relative error is 5.48%.
When the experimental behavior of failure (Figure 12(b)) is compared with results obtained by FEA (Figure 12(a)), it can be noticed that there is a correspondence in the failure location.
(a) Numerical simulation of failure
(b) Experimental behavior of failure
The maximum stress ratio (1.2) in FEA results matches the experimental location of a crack at the opening end of the coil spring. With this compressive load (1452 N), the spring in the numerical simulation exhibits an orange color in most coils of spring that represent a stress ratio near to one, being the value of 1 the limit of the stress ratio for the failure in the elastic range. Stress ratio values equal to or more than one represent a failure by yield strength.
In consequence, results about not only displacement but also failure behavior demonstrate that numerical simulation of the composite spring can represent very well the composite spring behavior during experimental investigation.
3.2. Computational Models
3.2.1. Computational Model 1
Figure 10 shows the steel spring maximum displacement in the elastic range, and this displacement was validated with Equations (1) and (2) that represents the theoretical behavior.
Figure 13 exhibits the stress ratio obtained in the numerical simulation, considering that stress ratio equivalent or more than 1 represents the failure in the elastic range of the material.
In this case, Figure 13 shows a maximum stress ratio equivalent to 1.025, which means that the material reaches the yield strength; hence, the compression load used in this numerical simulation (981 N) is considered as the maximum load in the elastic range.
3.2.2. Computational Model 2
Figure 14 shows the FGM spring maximum displacement in the elastic range. It can be noticed that a maximum displacement is equivalent to 2.48 mm considering a compressive load of 1450 N (325.97 lbf).
(a) Initial conditions
(b) Final condition
Figure 15 shows the stress ratio obtained in the numerical simulation, with a maximum stress ratio equivalent to 1.03; it means that the material reaches the yield strength; hence, the compression load used in this numerical simulation (1450 N) is considered as the maximum load in the elastic range.
3.2.3. Computational Model 3
Figure 16 exhibits the composite spring maximum displacement in the elastic range. It can be noticed that a maximum displacement is equivalent to 15.07 mm (0.59 in) considering a compressive load of 1070 N (240.55 lbf).
(a) Initial conditions
(b) Final condition
Figure 17 shows the stress ratio obtained in the numerical simulation, obtaining a maximum stress ratio equivalent to 1.05; it means that the material reaches the yield strength; hence, the compression load used in this numerical simulation (1070 N) is considered as the maximum load in the elastic range.
Table 9 shows the performance comparison between these three computational models, which will help to better understand how new development in materials such as FGM and composite can enhance the capability and potential use of springs.
As shown in Table 9, springs made of FGM and composite outperform springs made of carbon steel in some characteristics. Regarding load-to-failure performance, an FGM spring outperforms a carbon steel spring 1.48 times, while a carbon fiber spring outperforms its carbon steel counterpart by 1.1 times.
Regarding weight and for industrial applications that require it, such as in the manufacturing of vehicles and automobiles [17, 18], this performance characteristic also shows its advantages for FGM and composite springs. As shown in Table 9, the weight of an FGM spring represents only 61% of the mass of a carbon steel spring, while its similar one made of composite has a weight equivalent to 24% of the weight carbon steel spring [19–21].
Another favorable feature is about the energy storage in the coil spring, where again both springs, FGM and composite, outperform their carbon steel counterpart by 1.53 times and 6.84 times, respectively. In the same sense, the characteristic about specific energy stored in the coil spring that relates the energy stored in the spring with the weight of the spring demonstrates that a composite spring can store more energy per mass unity, 11.3 times more than an FGM spring and 28.2 times more than a steel spring.
On the other hand, for applications that require high stiffness or higher spring constant, the best option is an FGM spring, followed by a carbon steel spring, and at last a composite material spring. This characteristic intrinsically linked to the deflection of the spring is modifiable in a composite material spring by selecting laminates of carbon fiber with mechanical properties superior to those used in the present work [22, 23].
4. Conclusions
Three computational models were carried out to compare the spring performance considering three different kinds of materials: carbon steel, FGM compound by carbon steel+aluminum oxide, and composite material. Validation of these computational models was confirmed considering international standards and international publications.
The results of this work show that some feature performances of compression springs made of carbon steel are improved when using FGM and composite materials. Enhanced capabilities include higher load to failure (1.48 times in an FGM spring and 1.1 times in a composite spring) as well as increased energy storage (1.53 times in an FGM spring and 6.84 times in a composite spring) and less weight (representing 61% in weight in an FGM spring and 24% in a composite spring).
Data Availability
The data used to support the findings of this study are included within the article.
Conflicts of Interest
The author declares that there are no conflicts of interest.