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§14-3圆轴扭转强度与刚度计算

①若是阶梯轴，由于各段Wn不同，需分段计算才能确定max。

②[ ]——材料的许用扭转切应力。

③该强度条件可解决圆轴扭转构件的三类强度问题。

M1

M2

M3

50

80

C

B

A

Mn

0

-

x

1.8kNm

5kNm

①画轴的Mn图

②计算各段的最大切应力值。

AB段：

BC段：

max = 73.4MPa＞[ ]

1)试校核AB轴的强度。

2)如将AB轴改为实心轴，试在相同条件下确定轴的直径。

3)比较实心轴和空心轴的质量。

①校核AB轴的强度

②计算实心轴直径D1

D1=53mm

③比较实心轴和空心轴的重量

Mnmax≤[ ]GI/180

MB

MC

MD

MA

d

B

A

D

C

477.5

Mn/Nm

0

x

+

-

159.2

477.5

①计算外力偶矩

MA=159.2Nm； MB=318.3Nm； MC= 955Nm ； MD=477.5Nm

②画扭矩图

③强度计算

④刚度计算

①在外力偶矩一定的情况下，增大Wn或I的值即可提高圆轴扭转的强度和刚度。对于圆轴，采用空心轴较适宜。

②在轴形状、尺寸一定的情况下，降低Mnmax值即可提高圆轴扭转的强度和刚度。

-

-

+

A

C

B

D

D

C

B

A

b)

a)

1170Nm

351Nm

351Nm

468Nm

351Nm

351Nm

468Nm

1170Nm

Mn/Nm

468

Mn/Nm

0

0

x

x

315

315

702

702

1170