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and the torsiona1 stress吁T can be computed with
16T
吁T二 言d3  (18-2)
It is a genera11y accepted assumption that the axia1 stress wi11 not exceed 20. of the torsiona1 stress.吁a can therefore be obtained by吁a二 0.20吁T.These two stresses wi11 be the same for either type of coup1ing; however，the bending stress wi11 vary depending on which type of coup1ing is used.
There are three re1evant bending moments caused by a gear coup1ing when transmitting torque with angu1ar or para11e1 misa1ignment:
1.  Moment caused by contact-point shift. This moment acts in the angu1ar misa1ignment p1ane and tends to straighten the coup1ing. It can be expressed
TX
Mc二 Dp/2 ‘ 2  (18-3)
where:
T二 shaft torque
Dp二 gear coup1ing pitch diameter
X二 tooth face 1ength (Figure 18-12)
2.  Moment caused by coupling friction. This moment acts in a p1ane at a right ang1e re1ative to the angu1ar misa1ignment. It has the magnitude
Mf二 Tμ  (18-4)
where μ is the friction coefficient.

Figure 18-1.. Shift in contact point.
3.  Moment caused by turning torque through a misalignment angle .. It acts in the same direction as the friction moment Mf and can be expressed
MT二T sin .  (18-5)
The tota1 moment is the vector sum of the individua1 moments
                                         
Mtota1二 Mc 2 +(Mf +MT )2  (18-6)
The contoured diaphragm coup1ing causes two bending moments:
1.  Moment caused by angular misalignment. This resu1ts in bending of the diaphragm
MB二kB.  (18-7)
In this expression k. equa1s the angu1ar spring rate of the diaphragm (1b-in.degree) and . is the misa1ignment ang1e. This moment acts in theangu1ar misa1ignmentp1ane，as did Mc in the gear-coup1ing ana1ysis.
2.  Moment caused by turning torque through a misalignment angle .. It can be expressed
MT二T sin .  (18-8) The tota1 moment is now
      
Mtota1二MB 2 + MT 2(18-9)
Comparing the bending moments caused by gear coup1ings with those resu1ting from contoured diaphragm coup1ings shows the former to be significant and the 1atter virtua11y neg1igib1e.
The cyc1ic bending stress imposed on a gear coup1ing-equipped shaft can be computed from
咋a二 Mtota1 I ‘ C (18-10)
where:
C二 shaft radius
I二 shaft area moment of inertia
In addition，there is a mean tensi1e stress acting on the shaft cross-sectiona1 area. This effect means stress equates to
咋m二(Dp/2)(T言Cμ 2) cos e (18-11)
where e is the pressure ang1e assumed for the gear teeth.
The cyc1e bending stress seen by the diaphragm coup1ing-equipped shaft can be obtained by a rapid ratio ca1cu1ation
咋 (diaphragm coup1ing)Mtota1 (diaphragm coup1ing)a 咋a (gear coup1ing)二 Mtota1 (gear coup1ing)(18-12)
The mean tensi1e stress acting on the cross-sectiona1 area of the diaphragm coup1ing-equipped shaft depends on how far the diaphragm is disp1aced axia11y from its neutra1 rest position and the axia1 spring rate of the diaphragm.
For combined bending andtorsion，the factor of safety can be ca1cu1ated by the fo11owing re1ationships:
叫咋咋) 2 叫4) 2kf++3 k咋 +咋
1
n二    a      m          吁a     吁m   (18-13) 

咋e 咋y.p.fe y.p.
where:
咋e二 endurance 1imit in tension
咋yp二 minimum yie1d strength in tension

The stress concentration factor kf resu1ts from the keyway and must be used in torsiona1 stress ca1cu1ations. Factor k4 f takes into account the shaft step; it must be used in the bending stress ca1cu1ation.
　
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