Interchangeability and Measurement Techics - APS
1 Hole and Shaft
1.1 Size
- nominal size / basic size
- Limit size
- size of real figure
- maximum material condition MMC
- maximum material size MMS
- least material condition LMC
- least material size LMS
- local size
1.2 Deviation
- actual D
- limit D
- upper D : $ES=D_{max}-D, es=d_{max}-d$
- lower D : $EI=D_{min}-D, ei=d_{min}-d$
fundamental deviation : shaft (up), hole(low)
size tolerance : $T_D=|ES-EI|, T_d=|es-ei|$
- zero line
- tolerance zone
1.3 fit
variation fit : $T_f=X_{max}-X_{min}=Y_{min}-Y_{max}=T_h+T_s$
Clearance fit
- minimum clearance : $X_{min}=EI-es$
- maximum clearance : $X_{max}=ES-ei$
- $X_{av}$
- Interference fit
- maximum interference : $Y_{max}=D_{min}-d_{max}$
- minimum interference : $Y_{min}=D_{max}-d_{min}$
- $Y_{av}$
- Transition fit
- $X_{max}$
- $Y_{max}$
- $X_{av}/Y_{av}$
- fit system
- shaft-basis system of fits : $d_{max}=d$
- hole-basis system of fits : $D_{min}=D$
1.4 Standard Tolerance
- standard tolerance grades
GB/T 1800.1
can be calculated, but we just look up in the grades table
- normal : IT5-13
- high precision : IT5-7
- low precision : IT11-13
Shaft
- a-g $\rightarrow$zero line
- h : $es=0$
- j-zc
- $js=\pm IT_n/2$
Hole
- A-G $\rightarrow$zero line
- H : $ES=0$
- J-ZC : <IT8, ES+$\Delta$
Hole-basis
- size>IT8, same grade : H9/h9, H10/d10
- size<IT8, higher grade : H7/m6, H6/k5
- =IT8, same/higher : H8/m7,H8/h8
2 Length measurement
2.1 gauge block
- manufacture 5 grades : $\rightarrow$0,1,2,3,k
- use 6 classes : $\rightarrow$1,2,3,4,5
2.2 Measurement error
- Absolute error : $\delta=l-L$
Relative error : $f=\dfrac{\delta}{L}$
random error : Normal distribution $f=\dfrac{1}{\sqrt{2\pi\sigma^2}}e^{-\dfrac{(x-\mu)^2}{2\sigma^2}}$
- average : $\bar{L}=\dfrac{\sum l_i}{n}$, residual error : $v_i=l_i-\bar{L}$, absolute error : $\sigma_i=l_i-L$
- SD(standard deviation) : $\sigma=\sqrt{\dfrac{\sum v_i^2}{n-1}}$, experimental SD : $s=\sqrt{\dfrac{\sum v_i^2}{n-1}}$
- limit deviation : $\sigma_{lim}=\pm 3s$
systematic error
Indirect error method
parasitic error : $|v_i|>3\sigma$
3 Geometric tolerance
3.1 Feature
- integral feature : outfit
- derived feature : center point/line
- true feature
- real feature
- extracted feature
- associated feature
3.2 Symbol
Form
- straightness
- flatness
- circularity
- cylindricity
Profile
- profile of a line
- profile of a surface
Orientation
- parallelism
- perpendicularity
- angularity
Location
- concentricity
- symmetry
- position
Run-out
- circular run-out
- total run-out
3.3 Label
- datum feature-Benchmark
- toleranced feature
- integral f
- derived f
3.4 Tolerance zone
3.5 Tolerance principle
External function size : $D_{fe},d_{fe}$
$D_{fe}=D_a-ERROR\d_{fe}=d_a+ERROR$
Internal function size : $D_{fi},d_{fi}$
MMC maximum material condition
- MMS : $D_M=D_{min},d_M=d_{max}$
- Boundary : MMB
- MMVC maximum material virtual condition
- MMVS : $D_{MV}=D_{min}-t_M\d_{MV}=d_{max}+t_M$
- MMVB
- LMC least material condition
- LMS : $D_L=D_{max},d_L=d_{min}$
- LMB
- LMVC
- LMVS : $D_{LV}=D_{max}+t_L\d_{LV}=d_{min}-t_L$
- LMVB
- IP independency principle : every tolerance need to be required
- Related requirements
- ER envelope requirement :extracted integral feature <MMB, local size >LMS
- MMR MMVS
3.6 Detection
- Shape : change is minimal, minimum envelope zone
- integral feature
- derived feature
4 Surface roughness
It is quantified by the deviations in the direction of the normal vector of a real surface from its ideal form
4.1 Evaluation parameter
- sampling length : $l_r$
- evaluation length : $l_n=5l_r$
- mean line for the roughness profile : $\sum Z(x)^2=min$
profile peak
- profile peak height : $Z_p$
profile valley
- profile valley depth : $Z_v$
profile element : peak+valley
- element height : $Z_t$
- element width : $X_s$
Maximum height of profile : $R_z=max{Z_{pi}}+max{Z_{vi}}$
arithmetical mean deviation of the assessed profile : $R_a=\dfrac{1}{n}\sum|Z_i|$
mean width of the profile element : $R_{sm}=\dfrac{1}{m}\sum X_{si}$
material ratio of the profile : $R_{mr(c)}=\dfrac{Ml(c)}{ln}=\dfrac{\sum Ml_i}{ln}$
4.2 Symbol
5 Gauges
plain limit gauge
- [Hole] go/no go gauge T,Z
- [Shaft] calliper
Taylor princple
- $D_m\ge D_{min}\d_m\le d_{max}$
- $D_d\le D_{max}\d_a\ge d_{min}$
6 Rolling bearing
Tolerance and fit
grade 0,6,5,4,2
- normal : P0
- high : P6 P6x
- precise : P5
- preciser : P4
- Highest : P2
Tolerance zone
- Outside ring
- shaft-basis fit system
- transition
- shaft IT5-7
- Inside ring :
- hole-basis fit system
- transition/ interference
- hole IT6-IT8
- Outside ring
7 Screw Thread tolerance
- Major diameter : $D,d$
- Minor d : $D_1,d_1$
- [&] Pitch d : $D_2,d_2$
- [&] Pitch : $P$
- [&] Included angle : $\alpha$
- Flank angle : $\phi$
7.1 Tolerance zone
Deviation
- external thread : upper deviation, es, efgh
- internal thread : lower deviation, EI, HG
- length : S / N / L
- choose : H/g, H/h, G/h
7.2 Qualification
8 Cylindrical gear precision
13 grades : 0-12
8.1 Requirements
- Transmission accuracy
- Transmission smoothness
- Load distribution uniformity
- Transmission backlash
8.2 Machining error
- Geometric eccentricity : $e_g$
- Motion eccentricity : $e_m$, tooth shape changed by error from tool, Indexing turbine
- Drive chain
- Tool installation error
8.3 Evaluation index
Transmission accuracy
total cumulative pitch deviation : $\Delta F_p$
cumulative pitch deviation : $\Delta F_{pk}$ k teeth
Transmission smoothness
single pitch deviation : $\Delta f_{pt}$
total profiler deviation : $\Delta F_\alpha$, the distance in$L_\alpha$
Load distribution uniformity
total helix deviation : $\Delta F_\beta$,
Transmission backlash
thickness deviation of teeth : $\Delta f_{sn}$
- Vernier caliper
base tangent length deviation : $\Delta E_{bn}$
