زنجيره تلرانسي

Chart of tolerancesFor machining

Patrick CABAUD PSA/DPTA/DPMO/IDMT/IDPP april 2004

1/65

1 INTRODUCTION...................................................................................................3

1.1 MACHINING ANALYSE.............................................................................................3

1.2 ECONOMIC TOLERANCES......................................................................................3

2 DIMENSIONS.......................................................................................................4

2.1 CONDITION DIMENSIONS........................................................................................4

2.2 MACHINING DIMENSION WD MD TD......................................................................4

2.3 MINIMUM STOCK REMOVAL SR...........................................................................14

2.4 MINIMUM RAW DIMENSION RD............................................................................14

3 STARTING POINT AND CLAMPING.................................................................15

3.1 GENERALITY...........................................................................................................15

3.2 STARTING POINT...................................................................................................15

3.3 CLAMPING...............................................................................................................17

3.4 SYMBOLS................................................................................................................18

4 GENERAL REMARKS FOR THE MACHINING.................................................19

5 CHART OF TOLERANCES................................................................................20

5.1 PRINCIPE OF THE CHART OF TOLERANCES.....................................................20

5.2 EXAMPLES..............................................................................................................21

5.3 statistical calculate....................................................................................................65

2/65

1 INTRODUCTION

1.1 MACHINING ANALYSE

machining a part is deliver at the good dimensions asked by the study department

drawing at the minimum price. And for this the technician of the method department

define the different steps of the process from the raw to the finish part. They must

make a choice among the process and the means of the factory.

Machining a part is very expensive, so the technician of the method department must

try to:

avoid machining which don’t add functional value to the part (rough, semi

finish, temporary start point, …..)

Calculate the raw part dimensions according to the minimum stock removal of

each operation.

Machining the part directly with the final drawing dimensions.

Choose the machining means capable to carry out the asked tolerances.

1.2 ECONOMIC TOLERANCES

All machine setting at a precise dimension don’t make the parts at the tolerance of the

setting but at nearly dimensions depending of different parameters ( tool life,

repeatability of the machine, …..)

Each machine have a range into witch it machining the best , this is its economic

tolerance. Machining with more closed tolerance cost more. (reject, reworking, more

setting, ….)

Example for economic tolerances.

Rough Semi finish finish

milling 0.5 0.2 0.05

turning 0.5Ø and length 0.2Ø and length 0.05Ø and length

drilling 0.3 0.2 0.1

broaching 0.1 0.03 0.01

grinding 0.2 0.05 0.01

boring 0.3 0.1 0.03

3/65

2 DIMENSIONS

2.1 CONDITION DIMENSIONS

This is the dimension of the final drawing and this is the dimension to respect

2.2 MACHINING DIMENSION WD MD TD

Each operation of machining need a setting of the tool, either from stopper on machine, either between two tools or from machining fixture.

To be capable of setting machine, the technician of the method department have to put these dimensions on the process sheets.

3 types of machining dimensions :

Working dimension ( moving of the tool)Machine dimension ( distance between two holes,….)Tool dimension ( diameter, step, ….)

Example

4/65

Tool dimension

Tool

dim

ensi

on

Wor

king

dim

ensi

on

Machine dimensionWorking dimension

5/65

Working dimension

Working dimension

Working dimension

Working dimension

Tool dimension

Tool dimension

7/65

Working dimension

Tool dimension Working dimension

Tool dimension

Wor

king

dim

ensi

on

Wor

king

dim

ensi

on

Wor

king

dim

ensi

on

Wor

king

dim

ensi

on

Working dimension

Working dimension

Tool dimension

Tool dimension

Tool dimension

Tool dimension

9/65

TD

WD

WD

TD

TD

WD

WD

TD

TD

WD

TD

TD

WD

TD

TD

TD

11/65

Sol 1

Sol 2WD

TD

TD

WD

WD

Sol 1

Sol 2WD

TD

TD

WD

WD

Sol 1

Sol 2WD

TD

TD

WD

WD

WD

WD

TD

13/65

WD

WD

WD

WD

WD

WD

MD

MD

WDWD

WD WD

TD

TD TD

TD

TDTD

2.3 MINIMUM STOCK REMOVAL SR

For make a good working with a tool it is necessary to have a minimum thickness , under this minimum thickness , the tool don’t cut, the material is crushed and the dimension isn’t realized. The name of this thickness is the minimum stock removal.

Example for minimum stock removal

rough 0.5Semi finish 0.2Finishing with tool 0.1Grinding 0.05Super finish 0

2.4 MINIMUM RAW DIMENSION RD

The minimum raw dimension is the dimension necessary to make a good part.With this dimension the raw department put his tolerance to define the raw drawing.

Example

14/65

MSR for rough

MSR for semi finish

MSR for finish

Fin

ish

tole

ranc

e

Sem

i Fin

ish

tole

ranc

e

Rou

gh to

lera

nce

MIN

IMU

M R

AW

3 STARTING POINT AND CLAMPING

3.1 GENERALITY

- The positioning and the clamping of the part during the machining are the principal conditions to make a good part an also in mass production for insure a good repeatability .- The starting points in the control mean must be the same than the fixture in the machine. (dimensions, positioning and form)

3.2 STARTING POINT

generally for positioning a part you need 6 points in space you have 6 possible moving : 3 translatory motion and 3 rotations.

3.2.1 PRISMATIC PART

3 points define a plane : you delete 1 tranlatory motion and 2 rotations.

2 points you delete 1 tranlatory motion and 1 rotation.

15/65

1 point you delete 1 translatory motion

3.2.2 Cylindrical parts

Short V 2 points delete 2 translatory motions

Long V 4 points delete 2 translatory motions and 2 rotations

Concentric Chuck 5 points delete 2 translatory motions and 3 rotations

16/65

Center 3 points delete 3 translatory motions

Center and counter center 5 points delete 3 translatory motions and 2 rotations

Important remarks

THE STARTING POINTS IN THE MACHINE FIXTURE MUST BE SMALLEST AS POSSIBLE

THE STARTING POINTS IN THE CONTROL MEAN MUST BE THE SAME THAN THE FIXTURE IN THE MACHINE. (DIMENSIONS, POSITIONNING AND FORM)

3.3 CLAMPING

TO AVOID THE BUCKLING OF THE PART , THE CLAMPING POINTS MUST BE DIRECTLY OPPOSED TO THE STARTING POINTS.

17/65

3.4 SYMBOLS

18/65

4 GENERAL REMARKS FOR THE MACHINING

At the first step of the machining it’s necessary to use raw surfaces. The used raw surfaces must generally stay on the finish part and generally they have a dimension to a machining surface on the study department drawing.For the following machining we use for starting point the surfaces machining at the previous operations.

Example

19/65

60±0.1 38±0.2

20±0.0520±0.1

15±2

BA

Study department drawing OP10 OP20

5 CHART OF TOLERANCES

5.1 PRINCIPE OF THE CHART OF TOLERANCES

It’s not still possible to carry out the positioning of the part to machining directly the dimensions of the final drawing. In this case the surface for the starting points aren’t the surfaces of the final drawing dimensions. So it’s necessary to make some calculations.

THIS CALCULATIONS IS CALLED CHART OF TOLERANCES

Principles of calculations.

Every time that the machining of a surface need for the tool setting a different dimension than the final drawing dimension , there are a chart of tolerance.

The final drawing dimension witch not used in machining is nevertheless the dimension that it’s imperatively to carry out. The final drawing dimension is called “condition dimension” and generally drawing with a positive arrow whith a double line like this.

The machining dimensions necessary to obtain the condition dimension are the links of the chart of tolerances. This chart of tolerances answer at two equations :

TOL CD > OR = TOL WD

Tolerance of the condition dimension = sum of the tolerances of the Working dimensions to make the condition dimension.

WD = CD

Sum of the chain vector for working dimensions = vector of the condition dimension (this is true only when you used the average dimensions)

The methods of the chart of tolerance consist in :

- Find the condition dimension ( all the final drawing dimension and all the minimum stock removal)

- Find the chain with the links of the chart of the tolerances ( one chain per condition dimension)

- Calculate the tolerances of the machining dimensions.

- Calculate the machining dimensions (rough, semi finish and finish) and the raw dimensions.

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5.2 EXAMPLES

5.2.1 EXAMPLE 1 :AXLE WITH 2 DIAMETERS

Final drawing

For the chart of tolerances it’s necessary to use the average dimensions

21/65

20+0.10 20 -0.2

0

CD 120.05 ± 0.05

CD 219.9 ± 0.1

Machining of the part

This part is machining in turning machine

Starting points

Concentric chuck 5 points1 stop 1 point

Machining dimensions

22/65

1-2 3-4

2-41-3

SS

6

55

WD 1

WD 2

Principle of the chart of tolerances

Dimension to respect

Working dimension

Dimensions machining

WD1 = 20.05±0.05

23/65

CD 120.05±0.05

WD 1

- +

CD 1 maxi = WD1 maxi = 20.1

CD 1 mini = WD1 mini = 20


Working dimensions

to make CD2 it’s necessary to use 2 working dimensions.

We know WD1 = 20.05

CD2 = WD2 – WD1

We know : WD1 = 20.05 CD2 = 19.9

19.9 = WD2 – 20.05

WD2 = 19.9 + 20.05 = 39.95

24/65

WD 2WD 1

CD 219.9±0.1

Variation of CD2

We can see here that the variation of CD2 depend of the variation of WD1 and of WD2

TOL CD2 = TOL WD1 + TOL WD2

We know :

TOL CD2 = ±0.1TOL WD1 = ±0.05

± 0.1 = ±0.05 + TOL WD2

TOL WD2 = ±0.1 - ±0.05 = ±0.05

WD2 = 39.95 ± 0.05

25/65

- +

- +

WD 2

WD 1

- +

- +

CD 2 maxi

CD 2 mini

Other solution

We know :

WD1 20.05 ± 0.05WD1 mini = 20WD1 maxi = 20.1

CD2 19.9 ±0.1CD2 mini = 19.8CD2 maxi = 20

CD2 maxi = WD2 maxi – WD1 mini20 = WD2 maxi – 20WD2 maxi = 20 + 20 = 40

CD2 mini = WD2 mini – WD1 maxi19.8= WD2 mini – 20.1WD2 mini = 19.8 +20.1 = 39.9

WD2 = 39.95±0.05

26/65

- +

- +

CD 2 mini

- +

- +

CD 2 maxi

WD 1 mini

WD 2 maxi

WD 1 maxi

WD 2 mini

Building of the chart of tolerance

Recap of the dimensions

Name Dim Tol mini maxi

CD 1CD 2

20.0519.9

± 0.05± 0.1

2019.8

20.120

WD 1WD 2

??

??

??

??

27/65

Condition dimensions

Working dimensions

Calculation of the value of the working dimension

WD = CD


CD 1CD 2

20.0519.9

± 0.05± 0.1

2019.8

20.120

WD 1WD 2

20.0539.95

??

??

??

CD1 CD1WD1

20.0520.05

± 0.05 20 20.1 WD = CDWD1 = CD1WD1 = 20.05

CD2 CD 2WD1WD2

19.920.0539.95

± 0.1 19.8 20 WD = CD-WD1+WD2 = CD1-20.05 + WD2 = 19.9WD2 = 19.9 + 20.05WD2 = 39.95

28/65


Working dimensions

-+

Calculation of the tolerance of the working dimension

Tol CD > or = Tol WD


CD 1CD 2

20.0519.9

± 0.05± 0.1

2019.8

20.120

WD 1WD 2

20.0539.95

??

??

??

CD1 CD1WD1

20.0520.05

± 0.05± 0.05

2020

20.120.1

CD2 CD 2WD1WD2

19.920.0539.95

± 0.1± 0.05± 0.05

19.82039.9

2020.140

29/65


Working dimensions

-+



CD 1CD 2

20.0519.9

± 0.05± 0.1

2019.8

20.120

WD 1WD 2

20.0539.95

±0.05±0.05

2039.9

20.140

CD1 CD1WD1

20.0520.05

± 0.05 20 20.1

CD2 CD 2WD1WD2

19.920.0539.95

± 0.1 19.8 20

30/65


Working dimensions

-+

±0.05 ±0.05

±0.05

±0.1

5.2.2 Example 2 :Prismatic part

5.2.2.1 1st process

Final drawing

40±0.2

20±0.210±0.1

CD1

CD3CD2

31/65

Machining process

OP10

OP20

OP30

WD1

WD2

WD3

32/65


Working dimension

(WD1 = 40±0.2)

CD1 = 40 ± 0.2

WD1

CD1 maxi = WD1 maxi = 40.2

CD1 mini = WD1 mini = 39.8+-

33/65


Working dimension

To make CD2 it’s necessary to use 2 working dimensions

CD2 = WD1 – WD3

We know WD1 = 40 and CD2 = 10

10 = 40 – WD3

WD3 = 40 – 10 = 30

Variation of CD2

-The variation of CD2 depend of the variation of WD1 and WD3- Tol WD1 + Tol WD3 = Tol CD2-We know Tol WD1 = 0.4 (±0.2) and Tol CD2 = 0.2 (±0.1) 0.4 + Tol WD3 = 0.2-Tol WD3 = 0.2 – 0.4 = -0.2 < 0 it’s not possible to have a negative tolerance.

2 solutions to respect the tolerance of CD2 :

-Take for tolerance of WD1 and WD3 ± 0.05 ( Tol CD2 = Tol WD1 + Tol WD3 0.2 = 0.1 + 0.1)

- Change the process for machining CD2

CD2 = 10±0.1

+WD1

-WD3

Op10Op30

34/65

For the example we use the first solution WD1 = 40±0.05

+-

+ -

+ -

+WD1

-WD3

-WD3

35/65

CD2 mini = WD1 mini – WD3 maxi9.9 = 39.95 – WD3 maxiWD3 maxi = 39.95-9.9 = 30.05

CD2 maxi= WD1 maxi – WD3 mini10.1 = 40.05 – WD3 miniWD3 mini = 40.05-10.1 = 29.95

+-

+ -

+ -

+ WD1

-WD3

-WD3

WD

1 m

ini –

WD

3 m

ini

WD

1 m

axi –

WD

3 m

ini

WD

1 m

axi –

WD

3 m

axi

WD

1 m

ini –

WD

3 m

axi

CD2 mini

CD2 maxi WD1 maxi – WD3 mini

WD1 mini – WD3 maxi

36/65


Working dimension

To make CD3 it’s necessary to use 3 working dimensions

CD3 = WD3 + WD2 – WD1

We know WD1 = 40, WD3 = 30 and CD3 = 20

20 = 30 + WD2 – 40

WD2 = 40 +20 – 30 = 30

Variation of CD2

-The variation of CD3 depend of the variation of WD1,WD2 and WD3- Tol WD1 + Tol WD2 +Tol WD3 = Tol CD2-We know Tol WD1 = 0.1 (±0.0.5) Tol WD3 = 0.1 (±0.05) and Tol CD3 = 0.4 (±0.2) 0.1 + Tol WD2 + 0.1 = 0.4-Tol WD2 = 0.4 – 0.1 – 0.1 = 0.2

WD2 = 30±0.1

CD3 = 20±0.2

-WD1

+WD3

Op10Op30Op20

+WD2

37/65

+-

+ -

+ -

-WD1

+WD3

+WD3

+WD2

38/65

CD3 mini = - WD1 maxi + WD3 mini +WD2 mini19.8 = -40.05+ 29.95+ WD2 miniWD2 mini = 19.8 - 29.95 + 40.05 = 29.9

CD3 maxi= - WD1 mini + WD3 maxi + WD2 maxi20.2 = -39.95+ 30.05 + WD2 maxiWD2 maxi = 20.2 - 30.05 + 39.95 = 30.1

+-

+ -

+ -

+WD3

+WD3

- W

D1

min

i + W

D3

min

i

- W

D1

max

i + W

D3

min

i

- W

D1

max

i + W

D3

max

i

- W

D1

min

i + W

D3

max

i

CD3 mini

CD3 maxi- WD1 mini + WD3 maxi + WD2 maxi

- WD1 maxi + WD3 mini + WD2 mini

-WD1

+WD2

+-

WD

2 m

ini

WD

2 m

axi

39/65




CD 1CD 2CD 3

401020

± 0.2± 0.1± 0.2

39.89.919.8

40.210.120.2

WD 1WD 2WD 3

???

???

???

???


Working dimensions

40/65


WD = CD


CD 1CD 2CD 3

401020

± 0.2± 0.1± 0.2

39.89.919.8

40.210.120.2

WD 1WD 2WD 3

???

???

???

???

CD1 CD1WD1

4040

± 0.2 39.8 40.2 WD = CDWD1 = CD1WD1 = 40

CD2 CD 2WD1WD3

104030

± 0.1 9.9 10.1 WD = CDWD1-WD3 = CD240 - WD3 = 10WD3 = 40 - 10WD3 = 30

CD3 CD 3WD 3WD 1WD 2

20304030

± 0.2 19.8 20.2 WD = CDWD3-WD1+WD2 = CD330-40+WD2 = 20WD2 = 40–30+20WD2 = 30

-+


Working dimensions

41/65

Calculation of the tolerance of the working dimensionTol CD > or = Tol WD


CD 1CD 2CD 3

401020

± 0.2± 0.1± 0.2

39.89.919.8

40.210.120.2

WD 1WD 2WD 3

403030

???

???

???

CD1 CD1WD1

4040

± 0.2 39.8 40.2

CD2 CD 2WD1WD3

104030

± 0.1 9.9 10.1


20304030

± 0.2 19.8 20.2

-+


Working dimensions

42/65



CD 1CD 2CD 3

401020

± 0.2± 0.1± 0.2

39.89.919.8

40.210.120.2

WD 1WD 2WD 3

403030

???

???

???

CD1 CD1WD1

4040

± 0.2 39.8 40.2

CD2 CD 2WD1WD3

104030

± 0.1 9.9 10.1


20304030

± 0.2 19.8 20.2

-+


Working dimensions

± 0.2 ± 0.1 ± 0.1

±0.2

±0.3

±0.4

With this table we can see that the sum of the working dimension tolerance are no good to carry out the tolerance of the condition dimensions

43/65



CD 1CD 2CD 3

401020

± 0.2± 0.1± 0.2

39.89.919.8

40.210.120.2

WD 1WD 2WD 3

403030

±0.05±0.1±0.05

39.9529.929.95

40.0530.130.05

CD1 CD1WD1

4040

± 0.2 39.8 40.2

CD2 CD 2WD1WD3

104030

± 0.1 9.9 10.1


20304030

± 0.2 19.8 20.2

-+


Working dimensions

± 0.05

± 0.1±

0.05

±0.05

±0.1

±0.2

We see here that the tolerance of WD1 and WD3 are so closed.

this is due to the changing of starting point at the op 30.

Now we try another process for op30.

44/65

5.2.2.2 2nd process Final drawing

Machining process

OP10

OP20

OP30

CD1 =40±0.2

CD3 = 20±0.2CD2 = 10±0.1

WD1

WD2

WD3

45/65



Name Dim Tol mini maxiCondition dimensions

Working dimensions

46/65


WD = CD


CD 1CD 2CD 3

401020

± 0.2± 0.1± 0.2

39.89.919.8

40.210.120.2

WD 1WD 2WD 3

???

???

???

???

CD1

CD2

CD3

-+


Working dimensions

47/65



CD 1CD 2CD 3

401020

± 0.2± 0.1± 0.2

39.89.919.8

40.210.120.2

WD 1WD 2WD 3

403010

CD1 CD1WD1

4040

± 0.2 39.8 40.2 WD = CDWD1 = CD1WD1 = 40

CD2 CD 2WD 3

1010

± 0.1 9.9 10.1 WD = CDWD3 = CD2WD3 = 10

CD3 CD 3WD 3WD 2

201030

± 0.2 19.8 20.2 WD = CD-WD3 + WD2= CD3WD2 = CD3 + WD3WD2 = 20 + 10 = 30

Calculation of the tolerance of the working dimension

-+


Working dimensions

48/65



CD 1CD 2CD 3

401020

± 0.2± 0.1± 0.2

39.89.919.8

40.210.120.2

WD 1WD 2WD 3

403030

???

???

???

CD1 CD1WD1

4040

± 0.2 39.8 40.2 WD = CDWD1 = CD1WD1 = 40

CD2 CD 2WD 3

1010

± 0.1 9.9 10.1 WD = CDWD3 = CD2WD3 = 10

CD3 CD 3WD 3WD 2

201030

± 0.2 19.8 20.2 WD = CD-WD3 + WD2= CD3WD2 = CD3 + WD3WD2 = 20 + 10 = 30

-+


Working dimensions

±0.2 ±0.1 ±0.1

±0.2

±0.1

±0.2

49/65

5.2.2.3 Conclusion

First process Second process 1 > 2Op10 Tol WD1 ± 0.05 ±0.2 X 4Op 20 Tol WD2 ± 0.1 ± 0.1 0Op 30 Tol WD3 ± 0.05 ±0.1 X 2

We can see in this example that is very important to try to keep the same start points in all the process.

5.2.3 Example 3 :Prismatic part with minimum stock removal

The same part but with CD3 = 20 ±0.05For this we decide to change the process in 4 operations.

Final drawing

Machining process

OP10

CD1 =40±0.2

CD3 = 20±0.05CD2 = 10±0.1

WD1

50/65

OP20

OP30

OP30

WD2

WD3

WD4 TD1

SR1

SR2

51/65



We take for the minimum stock removal of SR1 and SR2 : 0,1 mm


Stock removal

Working dimensions


52/65



CD 1CD 2CD 3

401020

± 0.2± 0.1± 0.05

39.89.919.95

40.210.120.05

SR1SR2

0.10.1

WD 1WD 2WD 3WD 4TD 1

?????

?????

?????

?????

CD1

CD2

CD3

-+


Working dimensions

Stock removal

53/65


CD 1CD 2CD 3

401020

± 0.2± 0.1± 0.05

39.89.919.95

40.210.120.05

SR1SR2

0.10.1


40??1020

?±0.1±0.1??

?????

?????

CD1CD1WD1

4040

CD2CD2WD4

1010

CD3CD3TD1

2020

-+


Working dimensions

Stock removal

±0.1 ±0.1

54/65


CD 1CD 2CD 3

401020

± 0.2± 0.1± 0.05

39.89.919.95

40.210.120.05

SR1SR2

0.10.1


40??1020

±0.2±0.1±0.1±0.1±0.05

39.8??9.919.95

40.2??10.120.05

CD1CD1WD1

4040

± 0.2±0.2

39.839.8

40.240.2

CD2CD2WD4

1010

± 0.1±0.1

9.99.9

10.110.1

CD3CD3TD1

2020

± 0.05±0.05

19.9519.95

20.0520.05

SR1 SR1 0.1

SR2 SR2 0.1

-+


Working dimensions

Stock removal

±0.2 ±0.1 ±0.1 ±0.1 ±0.05±0.2±0.1±0.05

55/65


CD 1CD 2CD 3

401020

± 0.2± 0.1± 0.05

39.89.919.95

40.210.120.05

SR1SR2

0.10.1


40??1020

±0.2±0.1±0.1±0.1±0.05

39.8??9.919.95

40.2??10.120.05

CD1CD1WD1

4040

± 0.2±0.2

39.839.8

40.240.2

CD2CD2WD4

1010

± 0.1±0.1

9.99.9

10.110.1

CD3CD3TD1

2020

± 0.05±0.05

19.9519.95

20.0520.05

SR1SR1TD1WD4WD2

0.1

SR2

SR2 0.1WD3

WD4


Working dimensions

Stock removal

±0.2 ±0.1 ±0.1 ±0.1 ±0.05±0.2±0.1±0.05

56/65


CD 1CD 2CD 3

401020

± 0.2± 0.1± 0.05

39.89.919.95

40.210.120.05

SR1SR2

0.10.1


40

1020

±0.2±0.1±0.1±0.1±0.05

39.8

9.919.95

40.2

10.120.05

CD1 CD1WD1

4040

± 0.2±0.2

39.839.8

40.240.2

CD2 CD2WD4

1010

± 0.1±0.1

9.99.9

10.110.1

CD3 CD3TD1

2020

± 0.05±0.05

19.9519.95

20.0520.05

SR10.1= -20.05-10.1+WD2 miniWD2 mini = 20.05+10.1+0.1WD2 mini = 30.25

SR1 0.1TD1 20 ±0.05 20.05WD4 10 ±0.1 10.1WD2 30.35 ±0.1 30.25

SR20.1 = - WD3 maxi + 9.9WD3 maxi = 9.9 – 0.1WD3 maxi = 9.8

SR2 0.1WD3 9.7 ±0.1 9.8

WD4 10 ±0.1 9.9


Working dimensions

Stock removal

±0.2 ±0.1 ±0.1 ±0.1 ±0.05±0.2±0.1±0.05

57/65

5.2.4 Example 4 :Prismatic part with minimum raw dimension

Final drawing

CD1 =40±0.2

CD3 = 20±0.05CD2 = 10±0.1

RD 3

RD 2

RD 1

SR 1

SR 2SR 3

SR 6

SR 4SR 5

58/65

Machining process

OP10

OP20

OP30

OP40

OP50

WD1

WD3

WD4

WD5 TD1

WD2

59/65

Name Dim Tol mini maxiCD CD 1

CD 2CD 3

401020

± 0.2± 0.1± 0.05

39.89.919.95

40.210.120.05

SR SR1SR2SR3SR4SR5SR6

0.20.20.10.10.20.2

RD RD1RD2RD3

WD WD1WD2WD3WD4WD5TD1

±0.5

±0.1±0.1

±0.5 ±0.1 ±0.1±0.2±0.1±0.05

60/65

Name Dim Tol mini maxiCD CD 1

CD 2CD 3

401020

± 0.2± 0.1± 0.05

39.89.919.95

40.210.120.05

SR SR1SR2SR3SR4SR5SR6

0.20.20.10.10.20.2

RD RD1RD2RD3

41.7

30.159.6

WD WD1WD2WD3WD4WD5TD1

40.94030.359.71020

±0.5±0.2±0.1±0.1±0.1±.05

40.439.830.259.69.919.95

41.440.230.459.810.120.05

CD1 CD1WD2

4040

± 0.2± 0.2

39.839.8

40.240.2

CD2 CD2WD5

1010

± 0.1±0.1

9.99.9

10.110.1

CD3 CD3TD1

2020

± 0.05±0.05

19.9519.95

20.0520.05

SR1 SR1 0.2 0.2 = +wd1 mini –40.2wd1 mini = 40.2+0.2 = 40.4WD1 40.4

WD2 40.2SR2 SR2

RD2WD1WD2WD4

0.2 0.2 = -rd2 maxi +40.4-40.2+9.6rd2 maxi = -.2+40.4-40.2+9.6rd2 maxi = 9.6

9.640.4

40.29.6

SR3 SR3WD4WD5

0.1 0.1 =- wd4 maxi + 9.9wd4 maxi = 9.9-0.1= 9.89.8

9.9SR4 SR4

TD1WD5WD3

0.1 0.1 = - 20.05 – 10.1 + wd3 miniwd3 mini = 0.1+20.05+10.1wd3 mini = 30.25

20.0510.1

30.25SR5 SR5

WD3WD2WD1RD3

0.2 0.2 = -30.45+41.4-40.9+rd3 minird3 mini = 0.2+30.45-41.4+40.9rd3 mini = 30.15

30.4539.8

41.430.15

SR6 SR6WD1RD1

0.2 0.2 = -41.4 +rd1 minird1 mini = 0.2+41.4 = 41.641.4

41.6

±0.5 ±0.2 ±0.1 ±0.1 ±0.1 ±0.05±0.2±0.1±0.05

62/65

Machining process

OP10

OP20

OP30

OP40

OP50

40.9±0.5

30.35±0.1

9.7±0.1

10±0.1 20±0.05

40±0.2

63/65

Raw dimensions

30.15 mini

9.6 maxi

41.6 mini

64/65

5.3 statistical calculate

we know, in the work dimensions calculate, that the tolerance of the condition dimension is equal to the sum of the tolerances of the dimension of the chain.


This calculate is true if we consider that all the dimensions of the chain are at the limit (mini-maxi). In reality the probability that all the dimensions of a chain are at the limit is very small.And this reality is all the more true that the number of dimensions is big.

We can consider , with a limited risk , to increase the tolerance of the working dimension by a statistical calculate when we have some problems.

TOL CD > OR = (TOL WD)²

Be careful , generally we don’t use this method when we have less than 3 working dimensions.

Example :


±0.2 > ±0.1 + ±0.1 + ±0.1 not possible

TOL CD > OR = (TOL WD)²

±0.2 > ±0.1² + ±0.1² + ±0.1² = ±0.1732

±0.2

±0.1±0.1

±0.1

65/65

زنجيره تلرانسي

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