Investigating the Effect of Design Parameters on the Mechanical Performance of Contact Wave Springs Designed for Additive Manufacturing

Abstract

Additive manufacturing (AM) enables design freedom to fabricate functionally graded wave springs designed by varying design parameters, which are not possible in traditional manufacturing. AM also enables optimization of the wave spring design for specific load-bearing requirements. Existing wave springs are manufactured by metal with constant dimensions (width and thickness of the strip, diameter) using customized traditional machines in which design variations are almost impossible. This study aims to investigate the effect of wave height, the overlap between the two consecutive coils, and the number of waves per coil on the mechanical properties, for example, load-bearing capacity, stiffness, and energy absorption of contact wave springs. Two designs, that is, rectangular and variable thickness wave springs, were chosen and the design of experiment was devised using Minitab software, resulting in 24 samples. HP MultiJet Fusion (MJF) printer was used to manufacture the samples for performing uniaxial compression tests up to 10 cycles and 90% of the compressible distance to study the variation in mechanical properties due to changes in parameters. Experimental and simulation results showed that variable thickness wave springs have better load bearing, stiffness, and energy absorption compared with the rectangular counterparts. In addition to that, the number of waves per coil and the overlap are directly proportional to the load-bearing capacity as well as stiffness of the wave springs, while the constant wave height is responsible for more uniformly distributed stresses throughout the coils. Load-bearing capacity was increased by 62%, stiffness by 37%, and energy absorption by 20% once the number of waves per coil is increased from 5 to 6 in rectangular wave springs. Overall, the parametric variations significantly affect the performance of wave springs; thus, designers can choose the optimized values of investigated parameters to design customized wave springs for specific applications as per load/stiffness requirements.

Introduction

Wave springs are unique in design by having a shorter height than helical springs but possess more advantages over other types of springs.¹ At present, wave springs are fabricated by traditional manufacturing processes using customized machines with constant width and thickness of metal strip.^2,3 Wave springs having variable dimensions and different geometric shapes were successfully manufactured by additive manufacturing (AM) and concluded that strip thickness is an important parameter, that is, variable thickness wave spring has better mechanical properties than all other variations.⁴

Furthermore, a detailed parametric study was conducted by designing and manufacturing functionally gradient wave springs by incorporating the coils of different cross sections in a single wave spring, resulting in improved mechanical properties including load bearing, stiffness, and energy absorption.⁵

Methods of AM have been developed according to the demand of manufacturing complex structures with a better surface finish.^6,7 In parallel to that, researchers are paying special attention to the material design of cladding layers, feedstock materials, the metallurgical behavior during the manufacturing process, and the resulted microstructures and properties.^8,9 Relatively, powder bed technology either with metal or polymer is the most popular of all AM methods because of its applications and industrial functional parts mostly in aerospace,^10–12 in the medical field.¹³ Three-dimensional (3D)-printed lattices were also investigated for mechanical and biological characteristics,¹⁴ including AM models to understand acetabular fractures.¹⁵

MultiJet Fusion (MJF) is a highly efficient powder bed fusion AM technique as the study concluded that MJF-printed parts have a better surface finish and higher tensile strength in Z orientation once compared with other powder bed techniques, for example, selective laser sintering.¹⁶ Due to these fundamentals of MJF, a lot of research has been carried out where this process was used to manufacture different parts by this process, for example, pressurized vessels¹⁷ and glass bead composites.¹⁸ Researchers even enhanced the mechanical strength of MJF-printed PA 12 (polyamide) through high-temperature annealing and also investigated the deformation of PA 12 printed parts, which concluded that deformation was influenced by the load rate and control methodology.^19,20

The design freedom of AM enables the researcher to design and fabricate different structures with enhanced capabilities of energy absorption. Auxetic structures, which are negative Poisson's ratio,^21,22 and graded Auxetic structures with graded materials²³ were studied by different researchers to enhance the energy absorption properties.^24,25 Xiong et al. concluded that narrowing the porosity gradient pattern improves the yield strength as well as elastic modulus of the structure.²⁶ Functionally gradient lattice structures were also investigated and found that variation in density resulted in deformation starting from the least dense layer to the densest layer during compression testing.²⁷

Other than different structures, springs were considered to be better energy absorbers than all as having different types as per load, shape, and applications.^28,29 Research had been carried out to investigate the mechanical properties of helical springs, the natural frequency of different helical springs of arbitrary shape, for example, conical, barrel, and hyperboloidal, by the transfer matrix method.³⁰ Other than uniform dimension springs, studies had been conducted by varying the different parameters to study their effect on the mechanical properties of springs.

Nazir et al. investigated the stiffness and energy absorption for the variable-dimension helical spring manufactured by MJF, and concluded that wire diameter, pitch, and overall diameter of the spring had a significant effect on the mechanical properties of helical spring.³¹ The same variable-dimension helical springs were used to additively manufacture shoe midsole by selecting the appropriate dimensions to bear the foot pressure.³² Multihelical springs with variable dimensions were also investigated for mechanical properties and resulted that stiffness has a direct proportion with the number of helix, the difference in pitch, and wire diameter of spring.³³

Parametric variations affect the mechanical properties greatly as design for AM enables the researchers to design and fabricate the parts far more quickly than the traditional manufacturing with modification/variation of any parameter to investigate its effect on the mechanical performance of the part. Several parametric studies had been conducted on helical springs and other energy-absorbing structures; however, the effect of wave spring parameters on the mechanical performance is still absent from the literature. Hence, the motivation and objective of this work are to study the effect of three design parameters, that is, the number of waves, wave height, and overlap between the two consecutive coils on the mechanical properties such as load-bearing capacity, stiffness, and energy absorption of wave springs as these design parameters were not considered in the other previous studies.

Two contact wave spring designs, that is, rectangular (constant width and thickness of strip) and variable thickness, were selected. The design of experiments (DOE) was devised by using Minitab software³⁴ while each spring was compressed within the elastic range up to 10 cycles of load–unloading. Finite element analysis (FEA) was performed for each design to compare with experimental results.

Materials and Methods

Designing of contact wave springs

Contact wave springs having coils merged with each are designed by using SolidWorks software (Dassault Systems SolidWorks Corporation).³⁵ The same authors had already designed different designs of contact and noncontact wave springs in their previous study,⁴ and so, the same method has been adopted to design the wave spring.

Two major designs are included in this study, that is, the rectangular design, having constant width and thickness of the strip, while the other one is variable thickness, that is, variation among the strip thicknesses of each coil, and that design was proved to be better of all designs in terms of load-bearing capacity, energy absorption, and stiffness.⁴ The parameters that can affect the performance of wave springs are shown in Figure 1.

FIG. 1.

Variable of wave spring on which performance of wave spring is dependent.

Three variables, that is, the number of waves per coil, overlap, and wave height were selected to study the effect on the performance of wave spring. The number of waves is responsible to increase the load-bearing capacity as more waves increase more points or morphology area, which can bear load within the elastic range and bring the spring back to its original position after removal of load. The wave height of wave spring is the same as the pitch of helical springs, as when the wave height is more the compressible distance between the coils will be more, which will enhance the capacity of load bearing. Apart from the wave height and number of waves per coil, the overlap distance is also important for wave spring performance. There is a direct proportion between the stiffness of the wave spring and the overlap distance.

Noncontact wave spring had low stiffness as well as its load-bearing capacity was also less than contact wave spring.⁴ The springs were designed by varying these three parameters, that is, number of waves per coil, wave height, and overlapping distance between the contacting points of two consecutive coils. Minitab software (Pennsylvania State University)³⁴ was used to establish the DOE. The full factorial approach was used to set the number of experiments to study the above-defined three parameters. The summary of number of levels along with the details of variables is shown in Table 1.

Table 1.

Summary of Variables and Number of Levels Shows 24 Combinations to Be Designed and Tested

No.	Variables	No. of levels				Total no. of levels
1	No. of waves per coil	5	6		9	3
2	Design morphology	Rectangular		Variable thickness		2
3	Wave height (mm)	3		Variable (1–2.50)		2
4	Overlapping (mm)	0.3		0.5		2
Total no. of experiments						24

The number of waves was noninteger in noncontact wave springs as half-wave is common between two consecutive coils,⁴ while for the contact wave springs, the number of waves per coil must be an integer. By keeping in view, the possible number of waves per coil can be 2, 3, 4, 5, 6, and 9 by dividing the complete circle into segments at an angle of 90, 60, 45, 36, 30, and 20, respectively. The coils having 2 and 3 waves per coil can be ignored because of instability in the wave spring and cannot balance properly. The design of a single coil with different possible numbers of waves is shown in Figure 2.

FIG. 2.

Illustration of single coil design with (a.i) 3, (a.ii) 4, (a.iii) 5, (a.iv) 6, (a.v) 9 waves, (b) assembly of wave spring with 9 waves per coil, (c) variable thickness wave spring with constant wave height having 0.5 mm overlap, and (d) rectangular wave spring showing the direction of increasing wave height.

Four waves per coil with a constant wave height of 2 mm had been studied in the previous study of the same author,³⁶ and so, 5, 6, and 9 waves per coil have been selected for this study for rectangular and variable thickness wave springs. Similarly, an overlapping of 0.3 and 0.5 mm with a constant wave height of 3 mm between the coils were selected. In addition to that, the same with variable wave height with constant variation of 0.5 mm between the consecutive coils, were also selected parameters for this study. The combination of designed parameters set by DOE is tabulated in Table 2.

Table 2.

Summary of Designs Set by DOE Showing Each Variation Along with Designed Mass and Height of Each Spring

No.	Design	No. of coils	Wave height (mm)	Overlap (mm)	Height (mm)	Mass (g)	Width of strip (mm)	Thickness of strip (mm)
1	Rectangular	9	3	0.5	13.93	14.2	5	1
2		6	3	0.5	13.78	14.15	5	1
3		6	3	0.3	13.78	14.77	5	1
4		9	3	0.3	13.93	14.7	5	1
5		5	3	0.5	13.76	14.21	5	1
6		5	1.0–2.50	0.5	12.7	14.21	5	1
7		6	1.0–2.50	0.5	12.73	14.21	5	1
8		5	1.0–2.50	0.3	13.5	14.21	5	1
9		5	3	0.3	13.76	14.8	5	1
10		9	1.0–2.50	0.3	13.44	14.31	5	1
11		9	1.0–2.50	0.5	12.7	14.31	5	1
12		6	1.0–2.50	0.3	13.6	14.21	5	1
13	V. thickness	5	3	0.3	13.55	14.01	4	1.9–1.7
14		5	3	0.5	13.13	14.01	4	1.9–1.7
15		5	1.0–2.50	0.3	12.8	14.59	4	1.9–1.6
16		5	1.0–2.50	0.5	12.15	14.59	4	1.9–1.6
17		6	1.0–2.50	0.3	12.9	14.61	4	1.9–1.6
18		6	1.0–2.50	0.5	12.3	14.61	4	1.9–1.6
19		9	3	0.3	13.83	14.59	4	1.9–1.7
20		9	3	0.5	13.51	14.6	4	1.9–1.7
21		9	1.0–2.50	0.3	12.92	14.65	4	1.9–1.6
22		9	1.0–2.50	0.5	12.5	14.65	4	1.9–1.6
23		6	3	0.3	13.47	14.05	4	1.9–1.7
24		6	3	0.5	13.2	14.05	4	1.9–1.7

Source: Nazir and Jeng.

The designed wave springs with the abovementioned variations are shown in Figure 3. All the springs were designed by keeping the mass and height of each as constant.

FIG. 3.

All the designed wave springs for this study showed the variation of number of waves per coil, overlapping, and wave height for rectangular (1–12) and variable thickness wave springs (12–24).

The wave springs with variable parameters were manufactured by the MultiJet fusion (MJF) technology, a fast process compared with other processes of AM, which can build parts with good quality, functionality, and dimensional accuracy.¹⁶ This process involved the deposition of a thin layer of polymer powder, an application of a fusing and detailing agent, followed by exposure to infrared radiation (IR). The fusing agent absorbs the IR and increases the thermal energy that sinters the polymer powder together, while the detailing agent inhibits powder fusion and controls the geometrical outline of the printed part. After the completion of the first layer, the next layer of material is deposited, and the process repeats until the complete fabrication of part.³⁷ MJF (HP, MJF 4200)³⁸ had been used to manufacture these springs without any support structures as residual powder provides support to these parts.

PA 12 (Nylon 12) polymer material was used to print the parts, and the properties of the material are tabulated in Table 3.³⁹

Table 3.

PA 12 Properties Which were Used for Printing and Validating the Experimental Results of Wave Springs³⁹

Density (g/cm3)	Young's modulus (MPa)	Poisson's ratio
1.01	1250	0.3

The printed designs of wave springs are shown in Figure 4a as three samples of each design were printed. The visual check was made to witness the quality of critical areas of the springs. The waves were printed with minimum layer effect as even a maximum of 9 waves per coil were printed smoothly and had a good surface finish. Similarly, the overlapping and variable wave height were also printed without any significant error, which cannot affect our results. The enlarged images of the abovementioned critical areas are shown in Figure 4b.

FIG. 4.

(a) Wave spring printing did not need support structure and showed less dimensional variations without any cracks or defects. (b) Illustration of printed critical areas (b.i), wave printing (b.ii), variable wave height (b.iii) overlap, good quality, profile, as well as minimum layer effect.

Apart from visual testing, the dimensional variation has been checked for the designed and printed parts by taking the average values of dimensions for three samples. A comparison for height, mass, and outer diameters for designed and printed wave springs is made in Figure 5.

FIG. 5.

Comparison of (a) height, (b) mass, and (c) outer diameter for designed and printed wave springs showed minimum variation.

The above comparison showed the minimum variation between the designed and printed dimensions, which can be neglected for further analysis.

Compressible distance for each design had been calculated as the same author used this approach in the previous study by measuring the distance between each wave of each design as it is the maximum distance up to which a spring can be compressed and all the waves are fully in-contact with each other. Each design had a different compressible distance, as recorded in Table 4. For uniform criteria of testing, each specimen had been compressed up to 90% of its compressible distance. The strain endpoint was calculated by the ratio of 90% compressible distance to total height for each design, which was a required input value for the compression testing machine.

Table 4.

Compressible Distance for Each Printed Wave Spring Showed Variation Along with Its Mass

Design no.	Mass (g)	Height (mm)	Compressible distance (mm)	90% of compressible distance (mm)	Ratio with total height	Strain endpoint
1	13.9	19.9	8.4	7.6	38.0	0.38
2	14	19.1	8.2	7.4	38.6	0.39
3	14.9	20.5	9.6	8.6	42.1	0.42
4	14.1	21.2	9.2	8.3	39.1	0.39
5	14.3	21.2	9.3	8.4	39.5	0.39
6	14.8	20	7.3	6.6	32.9	0.33
7	14.3	19.1	7.2	6.5	33.9	0.34
8	14	20.6	9.6	8.6	41.9	0.42
9	14.5	21.3	9.6	8.6	40.6	0.41
10	14.1	20.7	9.5	8.6	41.3	0.41
11	14.6	20	7.3	6.6	32.9	0.33
12	14.4	19.1	7.3	6.6	34.4	0.34
13	13.8	19.9	7.3	6.6	33.0	0.33
14	14.1	19.4	7.2	6.5	33.4	0.33
15	14.8	19.2	5.2	4.7	24.4	0.24
16	15.1	18.6	5.1	4.6	24.7	0.25
17	13.7	19.2	5.7	5.1	26.7	0.27
18	13.7	18.6	5.1	4.6	24.7	0.25
19	14.5	20.3	7.3	6.6	32.4	0.32
20	14.3	19.9	7.1	6.4	32.1	0.32
21	14.7	19.2	5.4	4.9	25.3	0.25
22	14.9	18.7	4.9	4.4	23.6	0.24
23	13.9	19.8	7.1	6.4	32.3	0.32
24	13.9	19.5	7	6.3	32.3	0.32

Uniaxial compression testing (loading–unloading) was performed for the three samples of each designed wave spring. The MTS Insight universal testing machine (MTS System Corporation)⁴⁰ was used to carry out the testing at room temperature, as shown in Figure 6. The crosshead speed was 300 mm/min, which was high for compression testing because the energy absorption and energy returned at high speed will result the damping capacity of these designed springs.

FIG. 6.

Uniaxial loading–unloading compression testing setup uniform for all designs by fixing the bottom plate and applying displacement from the top.

Each specimen of each designed spring was tested up to 10 cycles of loading–unloading as literature review suggested that loading–unloading was required to ensure a steady-state hysteresis, that is, a <3% change in hysteresis loop (area of hysteresis loop) between the two consecutive cycles.⁴¹ This was attained in the eighth cycle in the presented research. The graphs presented in this study were based on the average value of load and compression, stiffness, and energy absorption.

FEA framework

FEA was performed using ANSYS 19.2 for all the designs. The same material properties as for printing, described in Table 3, were used in FEA. Although the experiment was performed up to the elastic region of wave spring and did not need many details regarding stresses induced after yield point, but still, the nonlinear properties of the PA 12 material were also considered for the simulations. Frictional contacts were applied between the waves and in plate-to-wave, with a friction coefficient of 0.20⁴² as these contacts were also nonlinear in behavior. The setup for the simulation was similar to the experimental setup in terms of boundary conditions by fixing the bottom plate and applying the displacement from the top plate.

A convergence check was made to find the optimal mesh size to be used for each design, as presented in Figure 7. The results showed that the variation in results was negligible as the mesh size changed from 1 to 2 mm although the number of nodes had been increased, as shown in Figure 7b. Consequently, a 2-mm mesh size was used for FEA of each of the designed wave springs.

FIG. 7.

Convergence check results. (a) Variation in equivalent stress by changing the mesh size from 1 to 2 mm. (b) The variation in equivalent stress was 5% as mesh size changed from 1 to 2 mm would not affect the results.

Results and Discussion

The results were reported for the load-bearing capacity, stiffness, energy absorption, and energy loss in each designed wave spring, which were also compared with the FEA results.

The experimental results showed that the designed springs became stable in terms of load-bearing capacity after the eighth cycle of loading–unloading as there was a considerable difference between the first and subsequent cycles. The energy required for material setting and to deform the microcavities was different for each design, which was greater in the first cycle of loading–unloading. Similarly, there was a variation of compressible distance, as described in Table 4, due to which the deformation produced in each spring was different.

In addition, the printer parameters, as well as the residual powder, create the variation in stiffness in different regions of the same structure, which also played an important part in the considerable variation in properties during the first and second cycles of loading–unloading. The comparison of the first and second cycles for designs 1 and 2 is shown in Figure 8a, while the comparison for the 9th and 10th cycles for the same is shown in Figure 8b.

FIG. 8.

(a) The comparison of first and second cycles of loading–unloading for designs 1 and 2 showed significant changes. (b) Cycles 9 and 10 of loading–unloading had almost zero variation.

The above trend was seen in every designed wave spring, that is, variation among the 1st and 10th cycles was considerably large, which will affect the analysis. By comparing and keeping in view the above scenario, it was concluded that the 10th cycle of loading–unloading would be considered for further analysis as this cycle gives stable results, which were more reliable and helpful for the uniformity of comparison for all the designs.

For rectangular wave springs, the comparison of the 10th cycle of uniaxial loading–unloading for each spring was compared with each other, as shown in Figure 9.

FIG. 9.

Comparison of 10th cycle of loading–unloading of each design investigated the effect of (a.i) number of waves per coil along with (a.ii) the compression stages of design 5, (b.i) overlap (b.ii) compression of design 8, (c.i) wave height (c.ii) stages of compression of design 11, (d.i) combined effect of overlap and variable height on the performance of wave spring (d.ii) compression of design 12 showed no permanent deformation (units mm).

The load-bearing capacity of wave spring was directly proportional to the number of waves per coil, as illustrated in Figure 9a, but at the same time, the maximum material setting considered permanent deformation was also observed, that is, at the end of the 10th cycle, design 9 has achieved the strain up to 21%, design 6 and design 5 showed 14% and 13%, respectively, calculated by the following Equation (1):

$$\%Changeinheightorstrain=\frac{Changeinheight}{Origionalheight}X100$$ (1)

The curves showed the three distinct regions as marked in Figure 9a.i, the first region was a linear region (I) that comprised the concave curve, representing all the waves in contact with each other with a maximum energy absorption. The second region (II) was recorded as the transition phase of linear to densification state, while the third region (III) was densification in which all the coils were fully compressed and showed as a sudden spike/increase in the load-bearing capacity, as shown in Figure 9a.i. The spring returns to its original position while unloading. All these three regions are shown in Figure 9b.ii for one of the designs (design 5), as the same trend was observed for all the springs.

Increasing the overlap between the two consecutive coils affects the stiffness of the spring and increased the load-bearing capacity, as shown in Figure 9b.i. There was no permanent deformation during the compression of these designs as Figure 9b.ii shows the smooth loading–unloading of design 8. The results shown in Figure 9a and b had the same number of coils, wave height, and strip thickness while only the overlap was changed, which resulted in the load-bearing capacity increased up to 19% and 10% by increasing the overlap from 0.3 to 0.5 mm in design 8 and design 10, respectively. The stiffness of spring is also related to the damping coefficient as researchers studied and devised the linear models to estimate the damping force, with direct proportion with overlap as well as contact duration.^43,44

Hence, the maximum overlap will result in high damping force as well as high stiffness. The overlapping of coils also behaved as a thick solid section, which causes torsional stiffness to change, and moving away from solid cross sections results in a relatively large torsional stiffness corresponding to a small area.⁴⁵

Wave height is another parameter that affects the properties of wave spring, that is, higher wave height resulted in higher compressible distance due to which load bearing, as well as energy absorption, was increased. Figure 9c.i shows the results of designs that had variable wave heights for each consecutive coil. The comparison of these with the constant wave height designs is shown in Figure 9a.i, and it was found that the load-bearing capacity was decreased from 416 to 403 N for design 1, from 1072 to 940 N for design 11, and from 300 to 253 N for design 6. Also, the material setting or strain produced inside the wave spring was reduced to 2 mm for design 11, 1.5 mm for design 1, and 1 mm for design 6 compared with uniform wave height designs.

The combined effect of variable wave height and increase in overlap distance is shown in Figure 9d.I, which explained the linear behavior of the designs having less stiffness and increase in overlap along with variable wave height increased the load-bearing capacity by 13% in design 7, 33% in design 2, and 29% in design 12 compared with the results of the designs shown in Figure 9c.i. The wave height behaves like the pitch of helical spring, which increases the number of active coils during loading to enhance its load-bearing capacity.^33,46,47 The wave spring with more waves initially had a linear characteristic with a first lower spring rate, namely, primary spring rate, but with the increase of force, these came into contact with the next larger relative maxima and relative minima at the contact surfaces.

At this moment, the characteristic of the spring changes to a substantially linear spring force. Hence, waves possessed a markedly higher spring rate after contact with each other.⁴⁸

The deformation, that is, change in height at the end of the 10th cycle for each design is shown in Figure 10, which was due to the deformation of microcavities that provided resistance to coils to come to the original position. These microcavities or porosity is also dependent on the build orientation of specimens as MJF-fabricated parts have the highest porosity in horizontal orientation. The parts manufactured in a vertical orientation in this study had lesser porosity than in a horizontal orientation, and more than in 45 orientation.³⁷ The microcavities caused the instability regions, which resulted in a change in stiffness, orientation, and relative spacing between spring coils, while the equally spaced and identical spring sets suppress several of the instabilities.^.49

FIG. 10.

The comparison of the change in height (in mm) for each design (1–12) showed the material setting, but not splitting or cracking of any coil.

The comparison of load against compression for variable thickness wave springs (designs 13–24) is shown in Figure 11. Generally, the load-bearing capacity was higher in each design of variable thickness wave springs compared with the rectangular (constant thickness) wave springs. The same trend can be seen while increasing the number of waves per coil, overlap, and wave height, while the variable wave height resulted in the reduction of strain or material setting along with lowering the load-bearing capacity of the springs, as can be noted in Figure 11a and b.

FIG. 11.

Load-bearing capacity of each design showed variation as per varying (a) wave height, (b) overlap, (c) number of waves per coil, (d) overlap and variable wave height.

Load-bearing capacity had a direct proportion to the number of waves per coil and wave height as the compressible distance was higher once both were increased. Due to this, more load can be borne within the elastic limit. However, more waves per coil resulted in higher deformation or material setting. The comparison of load-bearing capacity for rectangular and variable thickness wave springs is shown in Figure 12.

FIG. 12.

The load-bearing capacity of each design for (a) rectangular (b) variable thickness wave springs shows that parametric changes influence the spring properties significantly.

All springs showed smooth behavior within the elastic range as no permanent deformation is produced except in designs 19 and 20, as shown in Figure 13.

FIG. 13.

The (a) design 19 (b) design 20, appeared with cracks (permanent deformation) during loading–unloading and were considered failed designs.

The above designs had 9 waves per coil and exhibited the highest load-bearing capacity, but cracks had been produced in the coils during compression testing. Experimental results of these had been considered for comparison, but they were considered failed designs for further FEA. Apart from permanent strain, these could be used where higher energy absorption, as well as higher load-bearing capacity, is required irrespective of plastic deformation.

Experimental testing revealed that the compression trend was different for the wave springs having constant wave height and the ones having variable wave height. The comparison between these two is shown in Figure 14.

FIG. 14.

The comparison of compression trend for wave height (a) constant in design 3 and (b) variable for variable thickness wave spring in design 14 shows variation.

The designs having constant wave height started compressing from the top and bottom coil, as shown in Figure 14a, and then compress the middle coil, while all the coils were compressed simultaneously in variable wave height wave springs, as shown in Figure 14b. Due to this reason, the constant wave height resulted in higher compressibility as the compressible distance was more, but also, more material setting or more strain is associated with a constant wave height of wave springs. In contrast, variable thickness showed lesser compressibility.

Energy absorption for each design is calculated by using Equation (2):

$$Energyloss=\frac{EnergyApplied-EnergyReturned}{EnergyApplied}X100$$ (2)

By comparing the results, it was found that the number of waves per coil and wave height had a direct effect on energy absorption/loss as the number of waves increased, the energy absorption was also increased. Similarly, higher wave height would emanate more energy absorption in the wave spring. Design 9 had the highest energy absorption among all the rectangular wave spring designs as it consisted of 9 waves per coil with a wave height of 3 mm, which was the highest for this study. The comparison of energy absorption is presented in Figure 15.

FIG. 15.

Comparison of energy absorption in each for (a) rectangular and (c) variable thickness designs showed the variation according to wave height and number of waves per coil, (b) energy absorption or loss trend for design 9 and (d) design 17 showed the constant energy loss after 8th cycle of loading–unloading.

For variable thickness wave springs, design 23 had the highest energy loss/absorption as it had the maximum wave height of 3 mm. Figure 15b and d shows the comparison of energy loss in each cycle of loading–unloading for designs 9 and 17, respectively. This comparison explained that energy absorption was constant after the eighth cycle, while more waves per coil and higher wave height resulted in higher energy loss or absorption in the wave spring.

A similar energy absorption trend was seen for variable thickness wave springs as energy absorption or loss was directly proportional to the number of waves per coil and wave height. Stiffness for each designed spring was calculated by using Equation (3):

$$Stiffnessofspring\left(k\right)=F∕x$$ (3)

F meant to be force/load, while x means compression or displacement, which was kept constant for all designs for the uniformity of comparison of all designs. Stiffness was calculated at 4 mm of compression for each design for the uniform comparison. Overall, the stiffness was much more for variable thickness wave springs than the rectangular or constant thickness wave springs, as presented in Figure 16.

FIG. 16.

Stiffness comparison for (a) rectangular (b) variable thickness wave springs showed considerable variation among each other.

By the above comparison, it was found that variable height and overlap were the most important factors to increase or decrease the stiffness of spring as there is a direct proportion between stiffness, wave height, and overlap between coils. In variable wave height, the compressible distance was less due to which, once all the waves were compressed, material resistance and frictional contact between the coils increased the stiffness of the spring. For the rectangular waves spring, designs 11, 12, and 22 of variable thickness wave spring had the highest stiffness as all these designs had variable wave height and maximum overlap of 0.5 mm due to which the stiffness of these designs was double and triple of the average stiffness values of other designs of rectangular and variable thickness wave springs, respectively.

Comparison of Experimental and Simulation Results

Figure 17 shows a comparison of the experimental and simulation results for the loading–unloading of designed rectangular wave springs, which had a close agreement and similar trend.

FIG. 17.

The comparison of experimental and Finite element analysis results (a–l) for rectangular wave springs (design 1–12) shows similar behavior and trend.

The results of the linear region of each spring were almost the same, but there was more deviation in the nonlinear region, which was due to buckling, the contact area for the designs, the residual powder at the interface of waves, and changes occur, that is, deformation of microcavities, which could not be incorporated in finite element analysis. The maximum deviation can be seen for designs 1 and 2 due to the opposite directions of printing the part and applying the load during experimental compression testing as both designs were almost same except having different overlaps between the coils.

Despite all these, the trend and behavior for experimental as well as FEA curves for all the designs were the same. The stress distribution in each coil of the designs after unloading is shown in Figure 18a, explaining that the considered parameter for this study affects the distribution of stresses although the overall equivalent stress in each design was almost the same.

FIG. 18.

(a) Stress distribution in each coil of rectangular wave spring designs (1–12) showed the variation after removal of load (b) the cross-sections of (b.i) design 9 with constant wave height and (b.ii) design 11 with variable wave height, showed more stress at the top in later.

Constant wave height between the coils resulted in the top coils being under more stress, while the subsequent coils had lesser stress, as illustrated in Figure 18b. This variation in stress distribution highlighted that increasing the number of waves per coil resulted in more stress concentration points, and variable wave height decreased the stress accumulated points, as shown in Figure 18b.ii.

The comparison of experimental and FEA results for variable thickness wave springs is shown in Figure 19.

FIG. 19.

Experimental and Finite element analysis curves (a–j) for variable thickness wave springs (design 13–24, excluding design 19 and 20) showed good agreement with each other.

The above comparison also showed some deviation as the maximum deviation can be seen in designs 21 and 22, which could be due to the highest stiffness of the spring and more material setting, that is, deformation of microcavities that cannot be incorporated during simulation. Also, as the number of waves per coil was increased, the permanent deformation was more, which is evident by the deviation in the experimental and FEA results. The stress distribution in each coil after unloading is illustrated in Figure 20.

FIG. 20.

(a) Equivalent stresses in each design after unloading showed that the variation in parameters affects the stress distribution trend in each coil. (b) Experimental and simulation of compression for design 21 exhibited uniform behavior.

The stress distribution along with the stress concentration points in each designed variable thickness wave spring is shown in Figure 20a, which highlighted that the stress distribution was uniform in variable thickness wave springs compared with rectangular wave springs, as presented in Figure 18a. The compression trend for experimental testing (first cycle of loading–unloading) and of simulation for design 21 is illustrated in Figure 20b, which showed a close resemblance as compression started from the top and transfered the load to subsequent coils, once compressed fully, which also resulted in uniform stress distribution among all the coils. Overall, the experimental and FEA compression trend was the same for all the designed wave springs.

It was evident during loading–unloading as well as in FEA that the contact points of coils were the stress concentration points in each design and considered critical points for design failure. Visual testing of the tested specimens showed that there was no crack formation or separation of these contact points. Also, Figure 21 presents the comparison of stress distribution at the contact points during FEA, and after 10 cycles of compression testing for the designs with maximum load-bearing capacity and stiffness showed no signs of crack propagation, that is, no design failed while compressing the spring within the elastic limit.

FIG. 21.

Comparison of the behavior of contact points of designs (a) 8 (b) 10 (c) 14 (d) 22, after 10 cycles of loading-unloading and during FEA showed uniformity.

Conclusions

In this study, wave springs with variations in design parameters were successfully printed with all details, which were considered by using MJF technology. In rectangular wave springs, the load-bearing capacity was increased by 62% as the number of waves was increased from 5 to 6 waves per coil, while this increase was 16% in variable thickness wave springs. The same trend was concluded for 9 waves per coil for both the designs of wave springs. The stiffness was increased by 89% while increasing the overlap distance from 0.3 to 0.5 mm in consecutive coils of rectangular wave springs, while the increase of stiffness was 24% in variable wave springs. Variable wave height resulted in 48% of energy loss/absorbed in rectangular wave springs, which were almost the same for variable thickness wave springs.

Overall, variable thickness wave springs and their embodiments for this study had more load-bearing capacity, stiffness, and energy absorption compared with rectangular wave springs. The number of waves per coil has a direct relationship with material setting properties, in which deformation of microcavities would be more, which resulted in permanent deformations.

Further investigation needs to be done by designing the variable number of waves in each coil of the same wave spring assembly and optimizing the three parameters studied in this work according to the application of wave spring and requirement in terms of load-bearing capacity, stiffness, strain, and energy absorption.

Author Disclosure Statement

The authors have no conflict of interest to declare.

Funding Information

This work was financially supported by the High-Speed 3D Printing Research Center (Grant No. 108P012) from the Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education (MOE) Taiwan.