Piano Guidance
Piano Guidance
Photo: Roberto Nickson
The Kennedy key consists of two square keys. The hub is bored off the centre and the two keys force the hub and the shaft to a concentric position. Kennedy key is used for heavy duty applications.
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Read More »ANALYTICAL SOLUTION The key is designed by solving the considered application analytically complying with the theory of machine design. The key is analysed by its free body diagram. The forces acting on the Kennedy key are shown in Fig. 2. The shear stress and the compressive stress are given by = NUMERICAL SOLUTION The key is initially designed according to the specifications of application considered and using the analytical solution as well. The designing is done in SolidWorks which is a 3D CAD design software developed and marketed by Dassault Systèmes while the analysis is carried out in Ansys which is an engineering simulation software developed and marketed by Ansys, Inc. to obtain a numerical solution. and = 2 respectively [1]. 2 A. Permissible compressive and shear stresses = = 380 = 126.67 /2 3 According to distortion energy theory of failure, = 0.577 = 0.577(380) = 219.26 /2 = = 219.26 = 73.09 /2 3 Fig. 3. Kennedy Key fitted in keyway in a shaft Finite Element Analysis FEA is a method in which the model is discretized into small elements, properties of which are then evaluated using Torque transmitted by shaft [60 × 106 × ()] [60 × 106 × 35] general equations of motion and boundary conditions specified during a test. This involves solution of the equation: = = 2 2(300) [Reaction] = [Stiffness] [Displacement] + [Load] Key length = 1114084.6 Boundary Conditions The boundary conditions in finite element analysis Using the formula of shear stress on the key, we get comprises of the loads and constraints applied over a region = = 1114084.6 = 26.95 or part in which a set of differential equations needs to be solved. 2 2(40)(10)(73.09) And using the formula of compressive stress, we get In the case of Kennedy key in application, shear and compressive loads are being applied while the movement of 2 2(1114084.6) = = (40)(10)(126.67) = 31.10 the key is constrained in particular directions due to the shaft and hub between which it is fitted. The loading diagram of the key is shown in Fig. 4. Thus, from the analytical solution obtained above we can estimate the length of the key to be approximately 30mm to get a factor of safety of 3. Fig. 2. Forces acting on Kennedy Key Fig. 4. Boundary Conditions applied on Key Mesh Generation This process involves the solid model of key being discretized into small elements and thus equations are solved on nodes resulting from meshing of elements. To obtain a more accurate solution, a fine mesh is generated in Ansys Mechanical which consists of elements of very small size as shown in Fig. 5. The mesh statistics are given in Table-4. Fig. 5. Mesh TABLE 4. MESH STATISTICS Nodes 118712 Elements 27342 Size Function Proximity and Curvature Relevance Center Fine Span Angle Center Fine Minimum Edge Length 1.e-002 m Solution The mesh obtained is solved for the applied boundary conditions using finite element solvers to obtain an accurate solution in terms of equivalent stress, normal and shear stress and the factor of safety. The results are displayed below. Fig. 6. Equivalent Stress Fig. 7. Normal Stress Fig. 8. Shear Stress Fig. 9. Total Deformation Fig. 10. Factor of Safety EFFECT OF VARIATIONS IN LENGTH AND CROSS-SECTION To develop a better understanding of stress distribution, stress concentration and the resulting factor of safety, a comparative study is conducted by varying the length and cross section of the Kennedy Key and subsequently plotting graphs of equivalent stress, normal and shear stress, factor of safety versus the varying length and cross-section as shown in Fig. 11 and Fig. 12. Conclusions are based upon the interpretation of these graphs. Thus, from these graphs optimum length and cross-section of the Kennedy Key can be determined for a specific application for complying with the recommended minimum value of factor of safety to be kept while designing the key according to industrial standards. Fig. 11. Variations in stress with length for different cross-sections Fig. 12. Variations in factor of safety with length for different cross- sections
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Read More »CONCLUSIONS The Kennedy Key is designed based upon the analytical calculations and then analysed through the finite element analysis in Ansys Workbench with relevant boundary conditions. The numerical and analytical solutions differ by a considerable amount for the compressive stress, shear stress as well as the factor of safety. An increase in the magnitude of normal and shear stresses from the analytical results in an increase in equivalent stress and eventually a reduction in factor of safety from a value of 3 as per the key is designed to a value of 1.1 which is obtained through the FEA solution. This is due to the fact that in analytical solution the part is assumed to have uniform factor of safety throughout the body but it varies throughout the regions of part due to varying geometrical sizes and thickness. The region having lowest factor of safety is most likely to fail or fatigue during the part lifetime. Hence, the key should be designed such that the factor of safety in no region falls below 1.5 which is taken as reference to industrial standards. Hence, for the particular application considered, the dimensions of the Kennedy Key has to be changed to increase the minimum factor of safety from 1.1 to 1.5. This iterative process can be assisted by the comparative study in which variations in equivalent stress and factor of safety with length have been plotted on the graph for different cross-section areas. The graphs can be interpreted to select the optimum dimensions of cross-section and length of the Kennedy Key for obtaining required magnitudes of factor of safety required for the specific application.
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