زنجيره تلرانسي

Chart of tolerancesFor machining

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

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

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

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

Tool dimension

Machine dimensionWorking dimension

Working dimension

Tool dimension

Working dimension

Tool dimension Working dimension

Tool dimension

Working dimension

Tool dimension

Sol 2WD

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

MSR for rough

MSR for semi finish

MSR for finish

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.

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

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.

3.4 SYMBOLS

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

60±0.1 38±0.2

20±0.0520±0.1

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.

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

20+0.10 20 -0.2

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

1-2 3-4

2-41-3

Principle of the chart of tolerances

Dimension to respect

Working dimension

Dimensions machining

WD1 = 20.05±0.05

CD 120.05±0.05

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

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

CD 2 maxi

CD 2 mini

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