Tiêu đề ES-MDSP FORMULAS (EXCLUSIVE FOR ES REVIEWEES ONLY) (1).pdf ✅

P C I � KINEMATICS OF MACHINE ELEMENTS � = 3 2 � − 2 � = 2� − 4 “AW KLEIN’S EQUATION” � + � 2 >=< 3 2 � − 2 LHS>RHS (Locked or Structure) LHS=RHS (Constraint) LHS1 (Unconstraint) FOUR-BAR MECHANISM GRASHOFF’S RULE � + � ≤ � + � CASE (s+l) VERSUS (p+q) SHORTEST BAR TYPE 1 < Frame Double- crank 2 < Side Rocker- crank 3 < Coupler Double- rocker 4 = Any Change- point 5 > Any Triple- rocker VELOCITY ANALYSIS NUMBER OF INSTANTANEOUS CENTERS � = �(� − 1) 2 ; � =! �" KINEMATICS VELOCITY ANALYSIS �! = �!" �!" �# = �#$ �#$ �# �$ �#! S VELOCITY ANALYSIS WITH INSTANTANEOUS CENTER �! = �!% �#! �# = �#% �#! � S ACCELERATION ANALYSIS VELOCITY ANALYSIS WITH INSTANTANEOUS CENTER • FOR ROTATING WHEEL (CENTER) �# = �! ; � = � � • FOR DISK ROLLING �" = �& ; �' �"% = �& �&% At any edge (P) �& = )(�")( + (�")( − 2�'�' cos � TANGENTIAL AND RADIAL ACCELERATION �) = �� = 2�� �% = ��" = �" � �! = +�" $ + �% $ �! = Absolute/Normal Acceleration � = Angular Acceleration (if not given use 2��) � = Angular Velocity CAMS AND FOLLOWERS LIFT = MAXIMUM POSITION – MINIMUM POSITION SLIDER CRANK MECHANISM �. �. = � � � = tan&'(�. �. ) Crank Length = 1⁄2 Stroke of Slider ROLLING CYLINDERS CYLINDERS ROLLING OPPOSITE DIRECTION • Tangential Speed �' = �" = ��'�' = ��"�" • Relation of Diameter and Speed �'�' = �"�" • Speed Ratio �� = &'(() *+ ,%-.(% &'(() *+ "/( ,%-.(0 = 1! 1" = ," ,! • Cylinder Distance �$ + �2 = �$ + �2 2 CYLINDERS ROLLING SAME DIRECTION • Tangential Speed �' = �" = ��'�' = ��"�" • Relation of Diameter and Speed �'�' = �"�" • Speed Ratio �� = &'(() *+ ,%-.(% &'(() *+ "/( ,%-.(0 = 1! 1" = ," ,! • Cylinder Distance �$ − �2 = �$ − �2 2 MECHANICAL ADVANTAGE � = ��� ��� ; ��� = ���� ������ ; ��� = �������� ����h� FOR JACKSCREW ��� = 2�� � FOR WHEEL AND AXLE ��� = � � FOR INCLINED PLANE ��� = 1 � � + �( �
STRENGTH OF MATERIALS CONSTANTS MODULUS OF ELASTICITY (E) �*)++, = 30 × 10- ��� �*)++, = 207 ��� �#,./01./ = 2 3 �*)++, MODULUS OF RIGIDITY (G) �*)++, = 11.5 �� 12 × 10- ��� �*)++, = 80 �� 83 ��� SPECIFIC WEIGHT (ɣ) �*)++, = 7850 45! /" = 0.284 ,6! 01" POISSON’S RATIO (�) �!"##$ = 0.25 �� 0.30 Use 0.30 if not given COEFFICIENT OF THERMAL EXPANSION/ CONTRACTION (�) �*)++, = 6.5 × 107-/°F �*)++, = 11.7 × 107-/°C AXIAL STRESS (�) TENSILE/COMPRESSIVE STRESS � = � ��������� ���� For Solid Circular: � = )*! + For Hollow: ),-"!&-$ !. + BEARING STRESS (�/ , �/) �6 = � ��������� ���� FLEXURAL / BENDING STRESS (�( , �() �( = �� � = � � ; � = � � • Flexural Stress on Solid Shaft �+ = 32� ��3 = � 8 � 29 ��4 64 • Flexural Stress on Rectangle �+ = 6� �h$ = � 8 h 29 �h3 12 • Bending Stress of Steel Bandsaw �+ = �� 2� = �� � 8 � 29 � MAXIMUM BENDING MOMENT (M) • For Simply Supported Beam with Load At the Center � = �� 4 • For Simply Supported Beam with Load At Every 1/3 of the Length � = �� 3 • For Simply Supported Beam with Uniform Distributed Load � = ��$ 8 • For Cantilever Beam with Load At End � = �� • For Cantilever Beam with Uniform Distributed Load � = ��$ 2 POLAR MOMENT OF INERTIA (J) • For Solid Circular Beam � = ) 1"�+ • For Hollow Circular Beam � = ) 1" (�2 + − �3 +) POLAR SECTION MODULUS (�') �4 = � � • For Solid Circular Beam �4 = � 16�1 • For Hollow Circular Beam �4 = ) '5- (�+ − �+) COMBINED BENDING AND AXIAL STRESSES � = 8 # ± 9' % (+) Tension ; (-) Compression THERMAL STRESS (�6) �):+;/<, = ��∆� THERMAL DEFORMATION (�6) �):+;/<, = ��∆� SHEAR STRESS (�) THERMAL STRESS (�6) � = � ��������� ���� COMBINED TENSILE AND SHEAR STRESS MAXIMUM TENSILE STRESS �=(9BEAMS THEORIES OF FAILURE VARIABLE AND FLUCTUATING STRESSES GERBER METHOD 1 �� = �� f �< �= g " + �> �8 SODERBERG METHOD G HI = I? I@ + �J IA IB (For Ductile) GOODMAN METHOD G HI = I? IC + �J IA IB (For Brittle) ASME ELLIPTIC METHOD h�� �< �: i " + f�� �> �8 g " = 1 (��) (��) STRESS RATIO (R) � = �/01 �/(F = �� � • FOR SOLID SHAFT �D2G3* = 16� ��1 = � k � 2l � 32 (�+) • FOR HOLLOW SHAFT �H2GG2I = 16�� �(�+ − �+) = � k � 2l � 32 (�+ − �+) POWER TRANSMITTED � = �� ������ SI ENG P kW HP T N-mm lb-in N rpm rpm Factor 9.549 × 105 63025 TORSIONAL DEFLECTION (�) TORSIONAL DEFLECTION / ANGLE OF TWIST � = �� �� SHORTCUT FORMULAS • For Shearing Stress in the Shaft �*(2�) = ��� • For Angular Deflection with Given Shaft Diameter � = 584�� �+� = 584�� (�+ − �+)�