Parametric optimization and design validation based on finite element analysis of hybrid socket adapter for transfemoral prosthetic knee

Background

Above-knee prosthetics attempt to replace knee function in transfemoral (TF) amputees. In recent years, there have been significant advancements in this field. New materials such as glass fiber–reinforced plastic (GFRP) and oil-filled nylon have allowed artificial limbs to become stronger and lighter, minimizing the amount of energy required to operate the limb. In addition to new materials, the use of electronics is also becoming popular.^1,2 The development of lower limb prosthetics through the years has led to better joint mechanisms and structures. ³ A TF amputation affects the balance and strength of the muscles around the affected hip joint. ⁴ As a result, proper prosthetic alignment has been emphasized to enhance residual limb comfort and improve walking capabilities in persons with this kind of amputation.^5–10 It has been found through observations in the field of lower limb prosthetic rehabilitation that many TF prostheses show signs of wear on some components of the knee unit. ¹¹ The usual way to attach a prosthetic limb to the body is with a socket. Discomfort and other problems resulting due to the socket fit are common and have been shown to adversely affect the quality of life and mobility. ¹² The adapter should help to provide a better natural gait pattern and a reduction in energy expenditure in walking. ¹³

Consequently, a good and efficient design of socket adapter becomes very crucial because the adapter provides a coupling between the socket and prosthetic knee, so its properties such as strength, length,^14,15 weight, ¹⁶ and stress–strain ^17,18 limits become important design parameters. ¹⁹ This article deals with validation of design of a new kind of socket adapter developed by the authors for a TF prosthetic device, which would be henceforth referred to as hybrid adapter. The finite element analysis (FEA) of the adapter has been carried out on the software Autodesk Inventor Professional Ver. 2011. As the complexity of the structure increases, the difficulty in obtaining an acceptable understanding of the real loading also increases. ²⁰ FEA involves a complex system of points called nodes, which make a grid called a mesh. This mesh is programmed to contain the material and structural properties that define how the structure will react to certain loading conditions. Nodes are assigned a certain density throughout the material depending on the anticipated stress levels of a particular area. Regions that receive large amount of stress usually have a higher node density than those that experience little or no stress. Points of interest may consist of fillets, corners, complex detail, and high stress areas. FEA allows the users to validate component design by testing the part’s or assembly’s performance under forces and torques. The tools available as per classical mechanics are not suitable for irregular structure and contouring such as in the case of prosthetic knees. The powerful finite element method (FEM) is able to evaluate stresses in designs of intricate shape, variable loading, and material behavior. ²¹ FEM software provides a wide range of simulation options for controlling the complexity of both modeling and analysis of a system. Similarly, the desired level of accuracy required and associated computational time requirements can be managed simultaneously to address most engineering applications. FEM allows entire designs to be constructed, refined, and optimized before the design is manufactured. FEMs are extensively used in the field of biomedical engineering, especially biomechanics for computing stress and strain in complex systems. This article discusses the stress and strain distribution in the hybrid adapter (in isolation as well as when it is in the assembly) taking into account the loading character, the effect of material properties, and adapter geometry with the aim of contributing to the improvement of adapter design.

Although there are many articles based on the finite element modeling of socket–limb interaction, only a few are there which discuss this method for the analysis of lower limb prosthetic components, especially the socket adapter. ²² The socket adapter should allow for maximum range for knee flexion angle during the swing phase (flexion and extension). ²³ FEA also helped to identify the regions of an artificial prosthetic, which contribute to faster fatigue. ²⁴

Thus, this article focused on parametric optimization based on material selection, weight, strength during static and dynamic gait, and cost. This analysis gives an insight for design of an efficient adapter with the help of an FEM to investigate stresses in load-bearing components, which could help to improve the functioning and comfort level of TF prosthetic users.

Methods

This work involved the static and dynamic stress analysis of a TF prosthesis adapter. The need of a hybrid adapter was felt because the knee flexion angle range of up to 60° could be achieved with the male pyramid adapter. So to increase the knee flexion angle, a new design of a socket adapter was conceptualized incorporating the features of a male pyramid as well as those of the female pyramid adapter. Its three-dimensional (3D) model was developed on Autodesk Inventor Professional Ver. 2011, which is shown in Figure 1.

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Figure 1.

(a) 3D model of the hybrid adapter and (b) fabricated oil-filled nylon hybrid adapter.

Geometries

Figure 2 shows the full mechanical assembly model of the prosthetic knee. The mechanical assembly consists of a GFRP outer cover, hybrid adapter, pneumatic cylinder of aluminum, a helical compression spring made of spring steel, nylon bushes, and bolt–nut sub-assembly. The computer-aided design (CAD) model was designed on the basis of manual measurements. The assembly was simulated in the Inventor Dynamic Simulation environment to see its actual working and to generate loads to export and use in stress analysis.

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Figure 2.

3D model of the mechanical assembly.

Material properties

The FEA of hybrid adapter has been carried out on four types of materials: (1) mild steel, (2) carbon fiber, (3) Al-6061, and (4) oil-filled nylon.

The mechanical properties of all the above materials were taken to be linearly elastic, isotropic, and homogeneous. Linear material properties imply that the stress is directly proportional to the strain in the material, meaning no permanent yielding of the material. Linear behavior results when the slope of the material stress–strain curve in the elastic region (measured as Young’s modulus of elasticity) is constant. Isotropic behavior implies that the material properties are not dependent on the direction. The values of Young’s modulus, Poisson’s ratio, yield strength, and ultimate tensile strength were taken from standard datasheets. A load of 600 N has been considered throughout for the stress analysis. Table 1 summarizes the material properties of the components (other than hybrid adapter) used.

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Table 1.

Material properties of components used in TF prosthesis.

Component	Material	Young’s modulus (GPa)	Poisson’s ratio	Yield strength (MPa)
Outer cover	GFRP	13	0.34	148
Cylinder and rod eye	Aluminum	68.9	0.33	275
Spring	Spring steel	180	0.3	413
Bolt	Stainless steel	193	0.31	250
Nut	Mild steel	220	0.27	207
Bush	Nylon-6/6	2.93	0.35	82.75

TF: transfemoral; GFRP: glass fiber–reinforced plastic.

The total deformation is assumed to be small in comparison to the part thickness. For example, if studying the deflection of a beam, the calculated displacement must be less than the minimum cross section of the beam. The temperature is assumed not to affect the material properties so the results computed are temperature independent.

Numerical analysis

The finite element static and dynamic loading stress analysis was carried out on Autodesk Inventor Professional Ver. 2011. In the first phase of our analysis, the static stress analysis of the hybrid adapter (in isolation) was performed for all the four materials. In the second phase, the dynamic stress analysis of the full mechanical assembly was carried out by segregating the gait cycle in five stages taking the angle between the loading vector and the hybrid adapter as the standard parameter.

Static stress analysis

This was performed in three different orientations of hybrid adapter with respect to horizontal, that is, 0°, 45°, and 90°, for each of the four materials. Since FEA uses small elements to solve complex problems, a larger number of smaller elements can sometimes yield more accurate results. This is where convergence comes into play. Convergence in Inventor Stress Analysis is actually a series of settings that can be used to automatically make mesh elements smaller, and it helps to determine whether results are accurate. The basic concept is that the mesh will be automatically made of smaller elements and solved until the results of the refined mesh fall within a percentage of the previous mesh. The number of FE elements and nodes assigned was approximately 5226 and 8374, respectively. The number of refinement cycles for convergence was kept as five. The von Mises stress was the key parameter throughout the analysis.

Dynamic stress analysis

In this analysis, the force was resolved into two components with respect to the angle between the force vector and the adapter while specifying the load on the adapter. The angles considered were 124°, 149°, 157°, 161°, and 164° for a gait cycle. The number of FE elements and nodes assigned was approximately 75,763 and 145,432, respectively. The fixed boundary was given to the outer cover of the assembly and the adapter was loaded with the two mutually perpendicular resolved forces as well as the spring force in the axial direction of the pneumatic cylinder acting on the lower surface of the adapter. The spring force was calculated by using the equation F = kx, where k is the spring constant in Newton/millimeter and x is the compression in the spring in millimeter. The value of the spring constant was calculated by using equation (1):

k = G d 4 8 D 3 n

(1)

where G is the modulus of rigidity of spring material, d the wire diameter, D the mean coil diameter, and n the number of active coils which is the number of coils subjected to flexure. The number of refinement cycles for convergence was again kept as five.

Results and discussion

This article discusses the design evaluation of hybrid adapter in various gait cycle angles. The FEM analysis is carried out to generate a stress profile of the adapter at various sections. The stress analysis is carried out in static and dynamic gait positions. Four material properties are evaluated for maximum and minimum stress. This evaluation gives the optimum material for the design of such hybrid adapters.

Static stress analysis

The aim of this analysis was to find a material best suited for the hybrid adapter minimizing the weight of the adapter keeping the maximum von Mises stress in mind as well as to achieve desired strength and knee flexion. It was evident from the analysis that the peak von Mises stress occurs at the neck of the adapter. Carbon fiber material experienced the maximum stress (Figure 3) and oil-filled nylon experienced the minimum stress (Figure 4) in all the three orientations. With respect to the weight parameter, machinability, and cost, oil-filled nylon was found to be the optimum material. Table 2 summarizes the peak von Mises stress for all the four materials.

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Figure 3.

Von Mises stress distribution of hybrid adapter (carbon fiber).

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Figure 4.

Section view of the adapter for oil-filled nylon.

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Table 2.

Peak von Mises stress during static gait (in megapascal).

Material	Weight (g)	Maximum stress (0°)	Maximum stress (45°)	Maximum stress (90°)
Carbon fiber	46	12.09	50.6	35.98
Oil-filled nylon	32.6	11.39	46.29	33.1
Al-6061	77.8	11.5	47.17	32.89
Mild steel	225.74	11.79	49.66	33.43

Dynamic stress analysis

This analysis was meant for checking the performance of the adapter under loading conditions when undergoing standard gait cycle. This analysis also revealed that the oil-filled nylon material gives the minimum value for the peak von Mises stress for all the five standard gait cycle angles. The peak von Mises stress was observed in the lower face of the adapter at the rod eye–adapter junction as shown in Figure 5. Table 3 summarizes the data obtained for peak von Mises stress for all the four materials with respect to the five angles.

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Figure 5.

Section view of the peak von Mises stress distribution in the full assembly.

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Table 3.

Peak von Mises stress for the full assembly (in megapascal).

Peak von Mises stress (in megapascal) at different flexion angle (in degrees)
Material	124°	149°	157°	161°	165°
Carbon fiber	49.2	58.45	60.03	61.67	61.89
Oil-filled nylon	24.5	34.3	35.21	35.51	35.66
Al-6061	34.37	44.53	46.89	47.06	47.75
Mild steel	30.39	37.53	38.78	39.33	39.98

Similar types of stress analysis using FEM as an evaluation tool were carried by many researchers. In the presented case, a different approach is taken first to design the hybrid adapter and evaluate the design on the basis of static and dynamic stress. The material properties were also evaluated for deciding the optimum material for fabrication of such adapters. More strength to the claims can be provided if dynamic stress analysis is carried out for whole gait cycle. We can have improved results of stress calculation and material optimization. The detailed cost analysis for each material is required to have affordable hybrid adapter.

Conclusion

The analysis presented in this article reflects the importance, capabilities, and use of FEM in parametric optimization and design evolution of an efficient hybrid socket adapter required for indigenously developed TF knee. The approach followed was a standard mechanical design validation process in which a 3D design is developed on CAD software; dynamic simulation is performed to assess its working, and finally, it is subjected to stress analysis to check its performance under variable loading conditions. Through this manner, design optimization is done with respect to weight, strength, material properties, and feasibility. A socket adapter was developed integrating the features of a male pyramid adapter and a female pyramid adapter. The FE analysis was carried out for four materials, namely, carbon fiber, oil-filled nylon, Al-6061, and mild steel, which are readily available in the market, and it was found that oil-filled nylon material gives the minimum value for peak von Mises stress, whereas carbon fiber gives the maximum corresponding value. The peak von Mises occurs in the neck region of the adapter in case of static stress analysis. In dynamic stress analysis, the peak is observed in the region constituting the lower face of the adapter where it is in contact with the rod eye. Oil-filled nylon was eventually found to be the best material among the four with respect to strength, weight, and machinability. The presented FEM model was thus found suitable for a parametric analysis of developed socket adapter.