Final Analysis Report MIE 313 Design of Mechanical Components Juliana Amado Charlene Nestor Peter Walsh
Table of Contents Abstract:...iii Introduction:... 4 Procedure:... 5 Results:... 6 Reliability:... 8 Redesign:... 8 Conclusion:... 9 Table of Figures Figure 1: Table saw Fence Assembly... 4 Figure 2: Clamp Block Assembly... 4 Figure 3: Critical Stress Locations... 6 Figure 4: Stress Intensity for fast fracture... 7 Figure 5: Existing Clamp Block... 8 Figure 6: Redesigned Clamp Block...8 Tables Table 1: Stress Analysis Results... 6 Table 2: Critical Stress Redesign vs. Original... 9 i
Appendices Appendix A: Energy Analysis of Input Force... I Appendix B: Force Model & Hand Calculations... III Clamp Block: Simplified Stress Calculations... IV Lifter: Simplified Hand Calculations...VII Dog: Simplified Hand Calculations...VIII Appendix C: FEA Loads and Constraints... X Clamp Block... XI Lifter...XII Dog...XIII Appendix D: FEA (Existing Design)... XIV Appendix E: FEA (Redesign)...XVIII Appendix F: Reliability Calculations...XX Existing Clamp Block... XXI Redesigned Clamp Block... XXI Appendix G: Engineering Drawings...XXIII Clamp Block... XXIV Lifter...XXV Dog...XIII ii
Abstract: The part being analyzed is the Clamp Block component of the clamping mechanism of a table saw fence assembly. The clamping system acts as a spring and applies normal force to the fence rails. This normal force results in friction forces that prevent the fence from sliding horizontally along the fence rails. The Clamp Block has failed by fast fracture near an abrupt change in geometry. The overall objective of this project is to analyze the mode of failure of the Clamp Block and redesign it accordingly. Finite element analysis was used in conjunction with hand calculations to determine the cause of failure of the Clamp Block. Three critical locations were identified in the area of fracture. The most highly stressed was at an inside corner on a horizontal web that spans between the two sides of the Clamp Block. The magnitude of stress was not above the yield of the material at this location, but statistical analysis shows that the failure rate was approximately 5%. The concentration of stress at this critical point may have caused cracks to propagate causing fast fracture on subsequent loading cycles. To improve the reliability, changes were made in the geometry of the Clamp Block near the critically stressed area. These included increasing the thickness of the web from 4mm to 5mm, and adding a 3mm radius at an inside corner. These changes did not interfere with the other components in the system, and increased the reliability to a level of 99%. iii
Introduction: The focus of this analysis and redesign project is the clamp block component of the clamping mechanism of a table saw fence assembly. The in use operational purpose of the fence is to set the cutting width of the saw. It moves on two pipe rails that are perpendicular to the fence and saw blade. The user sets the cutting width, then clamps the fence to the rails by applying force to the hand lever. Once the user has rotated the hand lever to the locked position the system acts as a spring, storing the applied energy. This spring energy is what maintains the normal force on the rails that is necessary to keep the fence from sliding sideways. Figure 1: Table saw Fence Assembly The component in this system that has failed is the clamp block. It has fractured as shown below in Figure 2. Figure 2: Clamp Block Assembly 4
Objectives: The objective of this project is to analyze the mode of failure of the Clamp Block and redesign it accordingly. Issues that will be addressed are: static loading, dynamic loading, fatigue, and reliability. To reach this end, the previously developed solid and force models will be the basis for finite element analysis using the Pro-Mechanica software package. The FEA will be verified using simplified hand calculations, and the results of both techniques of stress analysis will be used as a foundation for decisions about the redesign. FEA analysis will also be run on the Lifter, and Dog components that are in direct contact with the Clamp Block in order to see if they are being stressed close to the limits of their capacities. Procedure: Design Analysis: 1. Solid model representations of critical components. Simplify solid models if necessary. Develop force model based on solid geometry and conditions of use. 2. FEA critical components Model loads using information developed in the solid and force models. Constrain components against motion in a manner that simulates the actual boundary conditions. Plot graphical results of the FEA. Validate FEA results using simplified hand calculations. Determine the critical locations and magnitudes of stresses in the Clamp Block Redesign: Assess significance of static versus dynamic loading as factors contributing to failure. Assess significance of fatigue as a factor contributing to failure. Assess reliability of existing part using FEA and hand calculation results. Determine desired reliability of the redesigned part. Redesign to meet desired reliability parameters. 5
Results: The results of the FEA and hand calculations agree closely, and indicate that there are three critical locations in the area of the fracture. Figure 3: Critical Stress Locations The most highly stressed was point C on a horizontal web that spans between the two sides of the clamp block. This is the result of the 773 N load causing compressive stress, yy, along the web. The change in section of the web at point C causes a significant stress concentration. An examination of the broken part showed small cracks originating from corners at point C, and extending towards the area of point B. The part was broken cleanly along the red line indicated between points A and B. FEA e (Mpa) Hand e (Mpa) S y (Mpa) Clamp Block: A (Grey Cast Iron) 0.183 41.7 41.6 152 Clamp Block: B 0.183 41.7 31.8 152 Clamp Block: C 83.4 125 145 152 Lifter (HR Steel) 736-883 795 910 Dog (HR Steel) 842-947 844 910 Table 1: Stress Analysis Results 6
One explanation for the failure is that the cracks originating at point C reached the area of point B and caused fast fracture to occur along the line A-B. Using the relationships for stress intensity factors k i and k ic, the plausibility of fast fracture as a failure mode can be assessed. k i =. 8 1 c g and kic =. 0 c y 2 (Juvinall-Marshek eq. 6.1 & 6.2 pg 209) where k I is stress intensity factor and k ic is the fracture toughness of the material. When k I k ic fast fracture will occur. Assuming a maximum crack length of 7 mm, g = max stress on section = 125Mpa, and y = yield strength of grey cast iron = 152 Mpa. 3 3 2 2 k i = 1.8 0.007 125 = 19N m k ic = 2 0.007 152 = 25.5N m Figure 4: Stress Intensity for fast fracture Although k i is not greater that k ic,, it is close enough that fast fracture is clearly possible given that the material properties of the casting will vary from sample to sample. This issue of reliability will be explored in the next section of this analysis. Fatigue due to cyclic loading was considered as a possible cause of failure, but, because this is a hand operated system, and is used relatively infrequently, it is unlikely that the Clamp block component experienced 10 6 loading cycles More likely on the order of 10 3 cycles. Likewise, because the input energy is applied to the system rather slowly by a human hand dynamic loading was also dismissed as a possible cause of failure. The stress analysis results listed in Table (1) indicate that the Dog and Lifter are also being stressed close to their limits. These components may also need redesign in order to achieve an adequate level of reliability for the system as a whole, but since the analysis was primarily on the Clamp Block, the redesign of the Lifter and the Dog were not addressed in this report. 7
Reliability: Reliability is a concept closely related with the factor of safety. In industrial production, reliability factor plays an important role; the goal is to obtain a product with a high reliability avoiding failure. The clamp block of the table saw was subjected to a load of 125 MPA. The yield strength of the ASTM 20 Grey Cast Iron is 152 MPA. This means that failure will not always occur under these loading conditions. The interference theory of reliability prediction was used to approximate the failure percentage that would be expected from the original design. The clamp block was found to be 95% reliable and with a factor of safety equal to 1.22. (See Appendix F: Reliability Calculations) Redesign: To improve its reliability the Clamp Block was redesigned. Geometric changes were made in the area of point C as follows: The thickness of the web was increased from 4mm to 5mm, and a 3mm radius replaced the sharp inside corner at point C. The results of an FEA on the redesigned part, and reliability analysis showed that the stress in the critical locations was reduced, and that the component as redesigned is 99% reliable with a factor of safety of 1.4. (See Appendix F: Reliability Calculations) Figure 5: Existing Clamp Block Figure 6: Redesigned Clamp Block 8
Conclusion: The results of this analysis indicate that the most critically stressed location on the Clamp block is in the area of points C and B. An inspection of the failed part showed small cracks emanating from point C toward the area of point B. This observation, coupled with FEA and hand calculations, led to the conclusion that the Clamp block cracked under load near point C, and that these cracks caused fast fracture of the section along a line from point B to A on subsequent loadings. (See Figure 3: Critical Stress Locations) While the levels of stress intensity at the critical locations do not exceed the yield strength of grey cast iron, an analysis of the reliability of the Clamp block using the interference theory of reliability prediction showed that as originally designed and under the assumed loading conditions, the Clamp block had a failure rate of approximately 5%. This is a relatively high rate of failure the component was redesigned to reduce the stress at critical locations and give a failure rate of 1%. The stress at point C is primarily due to direct compressive stress on the web between the two sides of the Clamp block. At point C there is a sharp corner that causes a significant stress concentration. This group s recommendation for redesign is that the thickness of the web be increased from 4mm to 5mm, and that the sharp corner at point C be replaced with a 3mm radius. These changes in geometry should not cause any interference with the other components in the system, and an FEA run on the modified part indicates that the stress at the critical location has been reduced enough that the 99% reliability target has been reached. Graphical plots of the redesigned FEA are in Appendix E. Original Design FEA e (Mpa) S y (Mpa) %Fail S.F Clamp Block: C 83.4 125 152 5% 1.22 Redesign Clamp Block: C 75.7-113 152 1% 1.40 Table 2: Critical Stress Redesign vs. Original 9
Appendix A: Energy Analysis of Input Force I
Work Analysis of Applied Force The force being applied to the hand lever results in forces acting on the Clamp Block, Lifter, and Dog. In order to find these forces and develop FBD s for the Clamp Block, Lifter, and Dog, the tension in linking rod must be established. 45 Figure 3. Work Analysis At the beginning of the hand lever rotation the entire system is at rest- there is no elastic energy stored in the system and so the initial applied force is zero. As the hand lever is rotated the components of the system are stretched and the required input force increases until it reaches a maximum at the locked position. Using Data from Human Factors Design Handbook, an applied force of F=80 N has been established as the upper range of force that an average person can easily apply when pushing down on a lever from a standing position. Assuming the force varies linearly from 0 N to 80 N over the displacement then F av =40 N. Using the principle of conservation of energy, the work applied at the hand lever equals the work done on the linking rod. W lever = W rod Sf θf π/4 F ds = T ds = F av cos θ r dθ T rod (.003m) = (-40 N) (0.100m) cos θ dθ Si θi 0 4 sin (π/4) = T rod (0.003m) T rod = 943 N II
Appendix B: Force Model & Hand Calculations Clamp Block Lifter Dog III
Clamp Block: Simplified Stress Calculations Stress at (A): Bending stress zz at extreme fiber. M A M A = 773 (35 + 10) + 73 10 + 1230 (26 15) 1230 (30 15) = 31975 N mm I A 3.5 38 = 2 12 3 2 20 3.5 + (19 15) + 12 3 + 13 2 4 I A = 322816mm K t 2.8 (From Juvinall-Marshek Figure 4.39, pg 133) zz 31975 15 = 2.8 32281 zz = e = 41. 6 Mpa IV
Stress at (B): Combined bending stress zz at extreme fiber and axial compressive stress yy from 773 N contact force. zz : M B = 773 (35 3) + 773 3 1230 19 M B = 3685 N mm I B 20 14 = 12 3 13 6 12 3 4 I B = 4105mm C=-7mm zz 3685 ( 7) = 4105 zz = 6. 31Mpa yy : 773 = 4 14 yy k t k 2.5 (From Juvinall-Marshek Figure 4.41, pg. 135) t yy = 773 2.5 4 14 yy = 34. 5Mpa e : e = 1 2 2 [ 6.31 + 34.5 6.31 34.5] 2 e = 31. 8Mpa V
Stress at (C): Combined bending stress zz, axial compressive stress yy. zz : M C = 773 35 1230 19 M C = 3790 N mm 4 I C = 4105mm c = 8mm zz yy : 3790 8 = 4104 zz = 3. 7Mpa 773 = 4 14 yy k t k 10 (From Juvinall-Marshek Figure 4.41, pg. 135) t yy = 773 10 4 6 yy = 147Mpa e : e = 1 2 2 [ 3.7 + 147 3.7 147] 2 e = 145Mpa VI
Lifter: Simplified Hand Calculations M x =M y at the element is 53 N-m 1 : = = M x c 1 x I I 2(14) = 12 12 3 3 4 = bh = 457mm c = 7mm 2 : = = M y c y I 28.3x10 (7) 457 3 x = = 434 N mm 3 3 4 2 I bh = = 288mm 2 = 2(12) c = 6mm 12 12 28.3x10 (6) 288 3 y = = 590 N mm 2 x y, but both are positive so there is no need to use a Mohr circle to find combined stress, instead will use x and y to calculate Von Mises stress. VII
Simplified Hand Calculations, Lifter contd. 2 2 1 e: 2 = + ) e ( x y x y 1 2 2 2 e = [434 + 590 434(590)] = 530 N mm 2 This calculation of Von Mises stress does not take into account the stress concentration due to the bore for the pin. Using the tabulated data for stress concentration factor k t, and the geometry of the lifter k t 2.3 d = 6 = 0.36 b 16.6 From Juninall/Marshek figure 4.40-a pg 134: k t 1.5 So, the e taking stress concentration into account is approximately: e max = e k t = 530(1.5) = 795 N mm 2 Dog: Simplified Hand Calculations VIII
3 3 12(4) N I = bh = = 64 c = 2mm 12 12 4 mm 3 27 10 (2) N 1 = 2 = Mc = x = 844 I 64 mm 2 2 2 ( ) 1 2 2 2 2 [( ) ( ) ( )( )] 1 N 1 + 2 1 2 = 844 + 844 844 844 844 2 e = = e max = 844 N/mm 2 mm IX
Appendix C: FEA Loads and Constraints Clamp Block Lifter Dog X
Clamp Block Figure 10. Loads and Constraints Applied to Clamp Block The Clamp Block has symmetry about the Y-Z plane so a half model was used as the basis for the FEA. Using a half model requires that the cutting plane through the part be constrained against translation along the X, and Y axes, but free to translate along the Z axis. It is free to rotate about the X, Y, and Z-axes. The top face of the Clamp Block is bolted to the fence extrusion, so in the FEA model it will be constrained against motion along all axes. There are four loads on the Clamp Block. The force magnitudes from the force model must be halved because this is a half model. The 1230-N load in the positive Z direction has been modeled as a line load along the points of contact with the fence rail. The 773-N force couple is modeled as line loads along points of contact with the Dog. The load at the pin is modeled as a distributed load over the surface of the pin bore. XI
Lifter Figure 11. Loads and Constraints Applied to Lifter The lifter was modeled as a solid. Although it is symmetrical about the Y-X plane, it was deemed to be simple enough in shape that using a half model was unnecessary. The bore of the pin is constrained against translation along the X, Y, and Z-axes, and against rotation about the X, Y, and Z axes. The lifter has three loads acting on it, a distributed load on the surface of the pin bore of 1550 N, and two line loads. The force in the Y direction is a result of the contact with the dog. They meet at a line; therefore, the force of 1230 N is distributed along this line of contact. The last force is 943 N in the X direction applied as a line load along the line of contact with the linking rod. XII
Dog Figure 12. Loads and Constraints Applied to Dog The Dog is modeled as a solid, and is constrained against translation along the X, Y, and Z-axes, and rotation about the X, Y, and Z-axes. The constraints are applied along two lines at points of contact with the Clamp Block. The dog has four loads acting on it, and all of them are line loads at points of contact with the clamp block, lifter, and fence rail. There are two force couples; one 1230-N couple in the y- direction and 773-N couple in the x-direction. XIII
Appendix D: FEA (Existing Design) Clamp Block Lifter Dog XIV
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Appendix E: FEA (Redesign) Clamp Block XVIII
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Appendix F: Reliability Calculations Existing Clamp Block Clamp Block Redesigned XX
Clamp Block Reliability: Interference theory of reliability prediction Figure 7, Reliability Calculations: Original Design Data: µ x = 152 MPA (Yield strength) x = 12.2 MPA (Standard deviation) µ y = 125 MPA (Load) y = 10 MPA (Standard deviation) The variance is 8 % of the mean. This is an assumed variance and more accurate variance can be obtained in a Material s Manual. Using: z = ( y ² + y ²) ½ z = [(12.2)² + (10)²] ½ = 15.8 MPA Knowing: µ z = µ x - µ y µ z = 152 MPA 125 MPA = 27 MPA Then: µ z - k z = 0 k = - 1.71 The Figure 6.20 from Juvinall on page 228 has a table which relate the failure of k (number of standard deviation) and % of reliability and % of failure. For k = -1.71 95 % of reliability or 5 % failure. XXI
Factor of safety = Significant strength of the material = SF Corresponding significant stress SF = 152 MPA = 1.22 125 MPA For the redesign the goal is to make a product, which is 99% reliable. Calculations: To achieve 99 % reliability the k factor should be equal to (-2.4). µ Y =? z = 15.8 MPA µ z - k z = 0 µ z = (2.4) x (15.8) = 38 MPA µ z = µ x - µ y 38 MPA = 152 MPA - µ y µ y = 114 MPA This is the maximum acceptable magnitude of stress for 99% reliability. The geometric changes made during the redesign stage meet its required stress intensity. And the component is 99% reliable. We tested our results by running a Finite Element Analysis of the component. Factor of safety = Significant strength of the material = SF Corresponding significant stress SF = 152 MPA = 1.4 114 MPA XXII
Appendix G: Engineering Drawings Clamp Block Lifter Dog XXIII
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