SHAFTS static moment by sanmelody


									CHAPTER 15            SHAFTS
   A shaft is one of the most important components in machines. Shafts are used
to support rotating elements. And transmit rotational motion and power.

The types of shafts
   According to the shapes, there are crank shaft, the axis is not at a horizontal line;
straight shaft: The axis is at a horizontal line; flexible shaft, convoluted by groups of
steel wire ,goodflexibility.
   According to the straight shafts, there are plain shaft, no-diameter-change shafts,
simple, is prone to machining, inconvenient to install the components on the shafts;
stepped shaft: inconvenient to install the components on the shafts; hollow shaft and
solid shaft

   To machining technics, straight shafts are the best, but difficult to fixed. To the
forces on the shafts, equality intensity shafts are good, but difficult to machining and
install. Hence, there are all stepped shafts.
   The word “shaft” covers numerous variations and according to the loads exerted
on the shafts, the shafts can be classified into three groups:
(a) Shafts with only bending moments, usually called axle;
(b) Shafts with only torsional moments, usually called spindle.
(c) Shafts with bending and torsional moments;
    rotating axle              fixed axle

                     Spindle                                    Rotary shaft

              (a) shaft                                   (b) axle

                                            (c) spindle
The material of shafts
① Carbon steel
In common use:30、40、45steel
② Alloy steel
③ Cast steel
   Selecting the material and heat treatment of the shafts mainly accord to the
strength and wearing resistance, but not the bending and tension rigidity.

1. The factors relative to the configuration of shafts
   The location and modality of the shafts installing on machine ;
   The types, size, amount of elements on the shaft ;
   The character, magnitude orientation and distributing of load on the shaft;
   The types, size, collocation of bearing;
   The roughcast and machining technics of shafts;
   The assembly project of elements on shaft.
2、The conditions the configure of shafts should to satisfy
   The elements on the should have exact working location, convenient for to
dismantle and install and rectify, Have good machining technics.
3、The names of segments of shaft

4、The ways of shaft design
  When select the project, it is possible to reduce the quantity of elements on shaft
and deadweight of shaft, have good machining technics and proper forces on it.
                                     955 10 4 P n
                              T                   [ T ]
                                         0.2d 3

                       955 104 P      955 104 3 P          P
                    d  3           3                A0 3
                        0.2[ T ]n      0.2[ T ]   n        n
Where n—rotate speed of shaft(r/min)
     P—the power transmitted by the sh(kW)
     [τT]—the permissible shear stress for the shaft(MPa)
     A0—coefficient,Table 15—3
                    d  A0 3
                             n(1   4 )
To hollow shaft:

When d>100mm:
 single key groove aggrandize3%, double key groove aggrandize7%;
When d≤100mm:
 single key groove aggrandize5~7%, double key groove aggrandize10~15%
The location of elements on shaft

  Orientation by sleeve
  Used for orientation between two elements, inconvenient to locate the elements
with big distance, not feasible for the occasion where rotational speed is high.
  Orientation by retaining rings
  Orientation by nuts

Orientation by bearing cover
Orientation by flexible retaining rings
Orientation by fixed screw
Orientation by fixed retaining rings
Orientation by cone
  Peripheral orientation of elements on shaft, key、spline、interference-fit joint、fixed

The location of elements on shaft
  In order to ensure the fixed position of elements on the shaft, it is needed to fix
each element on the shaft radially and axially
Radial location of shafts
Key joints   Spline joints
        Pin joints   interference-fit joints
Axial   location

        Locknut                   Shoulder fillet

         Locknut                 Snap ring
    End plate              Screw
configuration technics of shaft
   As long as possible to aggrandize the transition fillet radius, as soon as possible to
unify the fillet radius of shaft. For install elements conveniently, we should wipe off
the burr, the ends of the shaft should be 45, there must be grinding wheel outre groove
to grind and cut rounding chamfer. To machining screw thread by lathe, there should
be a groove for the reamer exit. The groove for keys should be in a horizontal line

①Calculate accord to bending-torsion strength.
   To ensure horizontal forces and vertical forces
   Calculate bending moment MH and MV

   Draw torque moment diagram(T)
   Calculate bending moment
         Mca  M2  ( T)2

 Checking the strength

              Mca   M2  ( T)2
        ca                    [ 1 ]
              W        W

② Checking exactly according to fatigue strength
                          S S
               Sca                 S
                         S  S2

Only normal stress
                              1
               S                     S
                       K  a    m

Only torsional shear stress
                              1
               S                      S
                       K  a     m

  Safety factor
 When even material, precise calculated load and stress ,S=1.3~1.5
 When uneven material, low precise calculated load and stress, S=1.5~1.8
 When even material, lowest precise load and stress, or the diameter of shaft d>
200mm, S=1.8~2.5
  The measure when calculating dissatisfy
   Lower concentrative stress effect when configuration design;
   Aggrandize fillet radius;
   Machining with crew thread on unload region;
   Loosen combination of shaft and elements.
  Intensify mechanical property
   Minish the roughness of the surface
   Surface preening
   Roller compaction, rotoblast the surface
  Using the material with high strength, or increase the diameter of shaft
② Checking according to static strength
Condition of strength            SS SS
                        SSca               SS
                                SS  SS
                                  2      2

SSca— static strength calculated safety factor of the jeopardy section

SS—Calculate design safety factor according to yield strength
                         SS          S
                                  M     F
                                 ( max  max )
                                   W     A

SSσ—the safety factor when only consider bending and axial force

SSτ—the safety factor when only consider torque
                            SS 

2、Checking calculate rigidity of shaft
①check by bending rigidity of shaft
  y  [y]       [ ]         dv  z
                                       di4

                                       i 1 i

li—the length of the i segment of stepped shaft

di—the radius    of the i segment of stepped shaft L—the calculated length of stepped

z—the number of segments of shaft in calculated length
[y]—allowable flexivity of shaft,Table 15—5
[θ]—allowable deflection angle of shaft,Table 15—5
② Check the torsional rigidity of shaft
plain shaft :                      T
                     5.73 104         [ ]
Stepped shaft:                    GI P
                                            1 z Ti li
T—the torque on shaft        5.73 104         [ ]
                                           LG i 1 I Pi
G—shear elasticity modulus of material of shaft

Steel G=8.1×104

IP—polar moment of inertia of shaft section        I P   d 4 32

L—the length of the shaft supporting torque
Ti、li、IPi—the torque, length, polar moment of inertia of i segment of shaft

z—the number of segments of stepped shaft
[φ]—allowable torsion angle per mile of shaft

 Configuration design of shaft
 Three calculation methods of shaft strength
 Rigidity calculation of shaft, stability of vibration, etc.

  Stepped shaft design , strength and rigidity checking

Example 15.1 A transmission shaft ,given: transmitted power p=10kw,rotational
speed n=120r/min,estimate the
diameter of shaft.

Example 15.2 There is a shaft system shown in Fig.15.6, and there are some errors
and unsuitable points, mark them by order, and make a brief illustration.

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