(1.6.3)--3.2材料力学材料力学.ppt

Chapter 3 Torsion Mechanics of Materials3.2 Torsional moment diagramTortional moment diagramTransmission of Power by Circular ShaftsThe power is transmitted through the rotary motion of the shaft.Power is the rate at which work is done.Shaft transmitting a constant torque T at an angular speed.The work W done by a torque of constant magnitude is equal to the product of the torque T and the angle through which it rotates.Tortional moment diagramTransmission of Power by Circular Shaftsn-the number of revolutions per minute(rpm)xTortional moment diagramInternal torsional momentThe moment of internal forces acting in arbitrary section of the member in torsion.MMeMMeMMeT TDesignated by“T”.MMexT TSign conventionsAn internal torque is positive when its vector points away from the cut section and negative when its vector points toward the section.Tortional moment diagramTortional moment diagram(TMD)Sketch that expresses the law of change of the torque in each cross section along the axis.xTPurpose uThe law of change of the torque uValue of|T|max and the position of its section Tortional moment diagramExample 1 A shaft is driven by a gear at C that transmits 50 kW to the shaft at 200rmp.The gears at B and D drive machinery requiring power equal to 35 kW and 15 kW,respectively.It turns freely at A and E.Try to plot the TMD.Tortional moment diagramExample 1 Solution：Calculate the external torqueTortional moment diagramExample 1 Solution：Determine the internal torque（suppose it is positive）The internal torques in the end segments(AB and DE)are zero,since any friction in the bearings at the supports is assumed to be too small to consider.TAB=0 TDE=0Tortional moment diagramExample 1 The internal torque is assumed to be positive;therefore,its vector points away from the cut section.The positive sign in the result means that TCD acts in the assumed positive direction.Tortional moment diagramExample 1 TBC has an negative sign,which means that its direction is opposite to the direction shown in the figure.Tortional moment diagramExample 1 Plot the Tortional moment diagramEach of these torques is constant throughout the length of its segment.xTQ:Is it reasonable to change the position of gear B and C?Tortional moment diagramEnd