Design of Mechanics - APS

五维生物

2015-12-03

APS, ME

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1. Design criteria

Strength c
Stiffness c
Life c
Vibration stability c
Reliability c

2. Component Strength

Failure: can not reach working requirment

Damage $\rightarrow$ Failure

2.1 Load Classification

2.2.1 Load Classification

static l
variable l
- periodic
- aperiodic

Nominal l : F
Actual l
Calculated l : $F_{ck}=kF$
- k : load factor

2.2.2 Stress Classification

Static Stress $\leftarrow$ Static l
Variable Stress $\leftarrow$ S/V l
- periodic s
- aperiodic s
  - regular s
  - irregular s

2.2.3 Stress

$\sigma_{max}=\sigma_m+\sigma_a\\sigma_{min}=\sigma_m-\sigma_a$

Stress ratio : Cycle characteristics $r=\dfrac{\sigma_{min}}{\sigma_{max}}$
- $-1\leq r\leq1$

One-way asymmetric cyclic stress
Static s
Pulsating cyclic stress
Bidirectional asymmetric cyclic stress
Symmetric cyclic stress

2.2 Component Design Criteria

$\sigma\leq [\sigma]=\dfrac{\sigma_{lim}}{[S]}$

$\sigma_{lim}$：Ultimate s
- Static s
  - Ductile material : $\sigma_{s}$ yield Strength
  - Brittle material: $\sigma_b$ ultimate Strength
- Variable s
  - $\sigma_{rN}$ Fatigue limit
$[S]$：Safety factor

2.3 Fatigue strength

2.3.1 $\sigma-N$ Fatigue Curve

CD : $\sigma^m_{rN}N=C$
D : $\sigma_{rN}=\sigma_\infty$
$\sigma_{rN}=\sigma_r \sqrt[m]{\dfrac{N_0}{N}}\\quad=K_N\sigma_r$
- $K_N$ : Life factor
- m : experiment 6-20
- $N_0$ : 10^6 magnitude

2.3.2 Equal life Curve A’G’C

A : r=-1, s.c.s
D : r=0, p.s

A’G’: $\sigma_{-1}=\sigma_a’+\varphi_\sigma\sigma_m’$

CG’ : $\sigma_m’+\sigma_a’=\sigma_s$

2.3.3 Comprehensive influence coefficient

$K_\sigma=(\dfrac{k_\sigma}{\varepsilon_\sigma}+\dfrac{1}{\beta_\sigma}-1)\dfrac{1}{\beta_q}$

$k_\sigma=1+q_\sigma(\alpha_\sigma-1)$ : Effective stress concentration factor
$\varepsilon_\sigma$ : Size f
$\beta_\sigma$ : Surface quality factor
$\beta_q$ : Enhancement factor

2.3.4 Component AGC

$\sigma_{-1e}=\dfrac{\sigma_{-1}}{K_\sigma}$

r=C

$S_{ca}=\dfrac{\sigma_{max}’}{\sigma_{max}}$
$\sigma_m=C$
$\sigma_{min}=C$

3. Key

Sunk Key
- Flat Key
- Woodruff K [Torque]
- Taper
Saddle Key
Spline

4. Threaded connection

4.1 Parameter

d : Major diameter
$d_1$ : Minor diameter
$d_2$ : Pitch diameter
P : Pitch
$P_n$ : lead
$\alpha$ : angle
$\phi$ : flank angle
h : depth

4.2 Connection

Bolt
Stud
Screw

Nut

4.3 Force analysis

Preload $F_0$ - Wrench

Horizontal
- Reamer bolt : $F=\dfrac{F_\sum}{zz}$
- normal : $F_0\ge \dfrac{K_s F_\sum}{fzi}$
- $K_s$ : Skid resistance coefficient
- z : number
- i : number of joint surface
- f : Coefficient of friction
Torque
- Reamer Bolt : $F_{max}=\dfrac{Tr_{max}}{\sum r^2}$
- normal : $F_0\ge\dfrac{K_sT}{f\sum r}$
Axial : $F=\dfrac{F_\sum}{z}$
Overturning moment : $F_{max}=\dfrac{ML_{max}}{\sum L^2}$
- No gap

4.4 Strength

Loose b : $\sigma=\dfrac{F}{\pi d^2_1/4}\le[\sigma]$
Tight b
- $F_0$
- $F_0+Work$
  - $C_b$ : Bolt Stiffness
  - $C_m$ : Material Stiffness
  - $\lambda_b$ : Bolt Elongation
  - $\lambda_m$ : Material Elongation
  - $F_1$ : Residual preload
  - up $\Delta F\downarrow$ : $C_b\downarrow, C_m\uparrow,F_0\uparrow$
- Shear force
  
  $\sigma_p=\dfrac{F}{d_0L_{min}}\le[\sigma_p]\\tau=\dfrac{F}{\pi d^2_0/4}\le[\tau]$

4.5 Material

Q235, 35, 45

15Cr, 40Cr

4.6 Allowable stress

5.Belt drive

simple, absorb vibration, Overload protection

transmission ratio is unstable

5.1 Classification

flat
V
Toothed
Rund

5.2 V-Belt Parameter

Cross-sectional area
thickness
width
wedge angle

5.3 Force Analysis

$F_e$ : effective pull
Ultimate $F_1=F_2e^{f\alpha}$$\rightarrow F_{ec}$

5.4 Stress Analysis

Tensile stress
Bending stress
Centrifugal tensile stress

5.5 Design

Pca=KaP
- Work factor
V belt type : ABCDE YZ(Pca, n)
- recalculate n$\rightarrow$v
set center distance a $\rightarrow$ L from kind
P$\rightarrow$number z
Pca, z,v$\rightarrow$F0
$F_p=2zF_0sin\frac{\alpha}{2}$

5.6 Material

HT150

HT200

5.7 V Pulley

0-2.5d : Solid
2.5d-300mm: Web
300-400:Orifice plate
400+ : Spoke

6. Gear

Gear accuracy :12
Pressure angle : 20
Soft tooth surface <2=350HBS/38HRC
- HBS : Hardened steel ball
- HRC : 120degree diamond cone

6.1 Material

Forged steel: 20CrMnTi
Cast steel
Cast iron
Non-metal

6.2 Force Analysis

Circumferential force Ft
Radial force Fr
Axial f

6.3 Design

6.3.1 Root bending fatigue strength [Hard]

tooth shape f Yfa$\leftarrow$Modification coefficient
Stress correction factor Ysa$\leftarrow$Modification coefficient
Coincidence coefficient $Y_\varepsilon$

6.3.2 Tooth surface contact fatigue strength [Soft]

Regional coefficient Zh
Elastic influence coefficient
Coincidence coefficient Z

6.4 Design

material
z,$\phi_b=b/d_1$,K
Contact Fatigue Strength$\rightarrow$d
adjust the smaller Index circle diameter
Root bending strength$\rightarrow$m
- adjust m
get the final d1 d2, a

helical gear

add Helix angle coffeint in RBS, and TCS
add $cos^2\beta$ in RBS

7.Worm gear

$\eta=\eta_1\eta_2\eta_3$
- engagement friction
- bearing friction
- Splashing oil

7.1 Classification

Cylinder
- ZA
- ZN
- ZI
- ZK
ZC
Cone worm

7.2 Parameters

mt=ma : end modulus, axis modulus
$\alpha_t=\alpha_a $：pressure a, za=20 nik
- $tan a_a=\dfrac{tan a_n}{cos\gamma}$
- gamma :Lead angle
q=d1/m for worm
z1:1,2,4,6
a