1 A B
2 C
3 n D
T2 = −m2 − m3 = −(4.78 + 4.78) = −9.56kN⋅ m
10
③绘制扭矩图 Draw the torque diagram
T max = 9.56 kN ⋅ m
BC段为危险截面。 段为危险截面。 段为危险截面 Section BC is dangerous section .
目 的
①确定扭矩变化规律 To determine the rule of change of the torque |T| max 截面 的确定
purposes
To determine the location of dangerous section
8
[例1]已知：一传动轴， n =300r/min，主动轮输入 P1=500kW，从动轮输出 P2=150kW， 例 已知 一传动轴， 已知： ， ， ， P3=150kW，P4=200kW，试绘制扭矩图。 ， ，试绘制扭矩图。 Example 1 The transmission shaft is shown as Fig.the input power of driver wheel C is 500KW The export powers of driven wheel A,Band D are 150KW,150KW,200KW.To draw the torque diagram of the transmission shaft .
3
8–1 扭转的概念及外力偶矩的计算
Concepts of torsion and how to calculate the external couple moment 轴：工程中以扭转为主要变形的构件。如：机器中的传动轴、钻杆等。 工程中以扭转为主要变形的构件。 机器中的传动轴、钻杆等。 Shaft :the members create torsion deformation due to subjected to the external moments.such as the transmission shafts and drill pipes of the machines . 扭转的外力特点：外力的合力为一力偶， 扭转的外力特点：外力的合力为一力偶，且力偶的作用面与直杆的轴线 垂直。 垂直。 external forces:Two couples that have the same magnitude moment, the opposite direction and the plane of couples perpendicular to the axial line 变形特点： 变形特点：各横截面绕轴线发生相对转动 The deformation is that the external loads tend to twist one segment of the body with respect to the other
Chapter objectives In this chapter we will discuss the effects of applying a torsion loading to a long straight member such as a shaft or tube. Initially we will consider the member to have a circular cross-section. we will show how to determine both the stress distribution within the member and the angle of twist when the material behaves in a linear-elastic manner. Lastly, we will consider the design of shafts based on the torsion moments and twist angles.
一、等直圆轴扭转实验观察： 等直圆轴扭转实验观察： To observe the torsion experiment of straight circle shaft
1.实验前：before test 实验前： 实验前
绘纵向线，圆周线； 绘纵向线，圆周线；②施加一对外力偶 m。 。 Draw longitudinal and transverse lines adding a pair external couples
2
本目标
本章讨论圆轴承受扭转载荷时的变形和内力,讲述圆轴横截面上的应力分布及 本章讨论圆轴承受扭转载荷时的变形和内力 讲述圆轴横截面上的应力分布及 扭转角计算问题,最后讲述扭转强度 刚度条件在工程设计中的应用. 最后讲述扭转强度\刚度条件在工程设计中的应用 扭转角计算问题 最后讲述扭转强度 刚度条件在工程设计中的应用
解：①计算外力偶矩 Solution to calculate the external moments
m2
m3
m1
m4
P 500 m = 9.55 1 = 9.55⋅ 1 n 300 A = 15.9(kN ⋅ m )
n B C D
P 150 m2 = m3 = 9.55 2 = 9.55⋅ = 4.78 (kN ⋅ m ) n 300 P 200 4 m4 = 9.55 = 9.55⋅ = 6.37 (kN ⋅ m ) n 300
A
B
O
A m
γ
O ϕ B
4
m
工 程 实 例
Engineering examples
5
二、传动轴的外力偶矩
The calculation of external couple moment
其中： 功率，千瓦（ 转速， 分 其中：P — 功率，千瓦（kW）n — 转速，转/分 ） （rpm） ） Here Prep resents power,the unit is KW,n represents rotate speed,the unit is rpm.
∑mx = 0 T −m = 0 T =m
3
x
m m
Principal of torque calculation
扭距计算法则
m
T
扭距=截面一侧所有外力距的代数和 扭距 截面一侧所有外力距的代数和 Torque equals the scalar sum of all external moments of one side of section 外力偶距正负可用右手定则来判定 The signs of external couple moments are determined by the right-hand rule 4 右手四指弯向沿外力距转向，则拇指指向与截面内法线同向着为正，反向者为负。 右手四指弯向沿外力距转向，则拇指指向与截面内法线同向着为正，反向者为负。 It is positive if the thumb indicates the same direction to the internal normal line of section when the fingers are curled with the sense of rotation, opposite it is negative.
6
二、扭矩及扭矩图Torque and torque diagram 扭矩及扭矩图 1 2 扭矩：构件受扭时，横截面上的内力偶矩，记作“ 。 扭矩：构件受扭时，横截面上的内力偶矩，记作“T”。 The internal force in cross-sections of twisting-shaft are called torque. 截面 法求扭矩 To calculate the torque by using the methods of section
9
应用截面法计算扭矩
applying the methods of section to calculate the torque
∑mC = 0 , T + m2 = 0 m2 1 T = −m2 = −4.78kN⋅ m 1
1
m3
2
m1
3
m4
T2 + m2 + m3 = 0 , T3 − m4 = 0 , T2 = m4 = 6.37kN⋅ m
m2
m3
m1
m4
n A T
⊕ – 4.78 – 9.56
11
B
C
D
6.37
x
若将C论与 论位置对调 画扭距图。 若将 论与D论位置对调 画扭距图。 论与 问哪种布置合理？ 问哪种布置合理？ Draw the torque diagram in Fig 8-2 after melody the steel C and D. Think over Which distribution is reasonable? Summary ：To master the drawing of torque diagram, because it is basis of the design of transmits shafts. 扭矩图的简单画法 The simple method to draw torque diagram
P m = 9.55 (kN ⋅ m ) n
P m = 7.024 (kN ⋅ m ) n
其中：P — 功率，马力（PS） n — 转速，转/分 其中： 功率，马力（ ） 转速， 分 （rpm） ） Here Prep resents power,the unit is PS,n represents rotate speed,the unit is rpm.
13
扭转时横截面上的应力： 二 扭转时横截面上的应力： The stress in cross section of Torsion shaft