Technology of watch production - part 94

An axial clearance x between the pinion-journal shoulder and the jewel

face is necessary, in addition to the radial clearance in the jewel, in order
to enable the third- wheel pinion to revolve freely.

We will calculate the dimensional chain resulting from the firs t process

variant (Figure 3 , a ), where the plate and bridges are machined using equip

ment available for watch production. The face is machined to dimensions
D 1

and D2 on the S - 1 8 8 machine to an accuracy of 0 . 0 1 0 mm . The S - 5 0

machine is used for machining the recess e s t o dimensions d 1 and d2 t o an
accuracy of 0 . 0 1 5 mm .

Using formula ( 1 ), we obtain the following limiting values for

x :

max =

(2. 7

+ 1 .2 + 0. 1 6) - (0.485

2. 1 1 + 1 .385)

0.08

mm.

Xmin

(2.69

1 . 1 9

0. 1 5) - ( 1 .40

0.5

2. 1 3)

B_.. = Xmax - Xmin =

0.08 - 0

0.08

mm.

The clearance in the ass embly must lie within the limits from 0 . 02 to

0 . 0 7 mm according to specifications; thus

Xmax

0.07

mm and

Xm;n =

0.02

mm and

0.05

mm .

It follows that the processing method described will lead to a certain

amount of rejects . The proportion of rejects can be calculated using the

theoretical - probability m ethod . We assume that the scatter of dimensions
for each link in the chain conforms to the law of normal distribution. It

follows from the probability theory that the scatter in the resultant dimension

will likewise conform to the law of normal distribution, and that its range,

or tolerance

8_..

v'ill be equal to

6 ox .

The standard deviation will therefore

�...

0.08

0 1 3

ox = 6

= 6 =

mm.

We will plot the normal - distribution curve for the given case (Figure 4 ) .

The area which repres ents the probability o f obtaining acceptable assemblies

can be split into two parts (A and B ). The s haded areas repres ent the pro
bability of obtaining rejects . The probability of obtaining acceptable as

semblies can be dete rmined using the formula

( 3)

where the values o f

<l>

(z) are taken from the table i n Appendix 1 and z

= � .

We obtain for

0 . 02 mm,

0 . 03 m m , and

ox =

0 . 0 1 3 mm

3 7 3

F rom the same table

<1>

(zA)

0 . 8 7 6 4 , and

<l>

(z8)

0 . 97 8 6 . Substituting

in ( 3 ) we obtain:

w =

0 . 5 ( 0 . 8 7 6 4 + 0 . 9 7 8 6 )

0 . 9 2 7 5 .

The probability o f obtaining acceptable ass emblies i s thus 92 . 7 5 o/o. The

remaining 7 . 2 5 o/o of the assemblies must be adjusted , that is the dimension
C must be altered by displacing the jewel . This is the p rocedure actually

used in the assembly shops of watch plants . This type of adjustment does

no t require chip removal o r shape alteration, as in the case with fitting
operations, and its us e is advisable where incomplete interchangeability

is practiced.

FIGURE 4. Dimension-distribution curve for the first

process variant

FIGURE 5 . Diagram of a plane dimensional chain

it is required to achieve complete interchangeability and to observe

the clearance limits of 0 . 02 - 0. 07 mm, the plate and bridges should be ma
chined according to the s econd process variant (Figure 3 , b ). Here the

recesses are machined to dimensions A and B from the reference surfaces

M, or they are machined in the same chucking as the surfaces M themselves .

The machining accuracy for dimensions A and B is higher than the accuracy

of machining dimensions d 1 , d2 . The dimensional chain in the second var

iant is the shortest possible , as it is made up of four dimensions for the four

parts: plate, b ridge, j ewel, and pinion. The maximum and minimum values

of the resultant are (according to formula ( 1 ) ):

Whence

Xmu

= 1 .3 1 + 0.71 + 0. 1 6 -

- 2. 1 1 = 0.07 mm;

Xmln

= 1 .30 + 0.70

0. 15 -

- 2. 1 3 = 0.02 mm .

8z = 0.07 - 0.02 = 0.05 mm .

The limit calculation shows that all assemblies machined according to

the s econd variant will be acceptable. The design of machines which will

process plates and bridges according to this variant is a m atter of time only.

Watch-movement dimension calculations frequently reduce to the calcu

lation of a plane dimensional chain. Such a chain can be solved either by

p rojection on a line, by a combined m ethod, by m eans of a coordinate system ,
o r analytically.

The first two - the projection and the combined methods - are used in

watch p roduction.

3 7 4

P r o j e c t i o n is a method of reducing a plane dimensional chain to a

linear chain. This is done by projecting all the dimensions on some line

(direction} which can be the resultant (x) direction, or any other direction

which is not perpendicular to any of the dimensions . By connecting the

parallel dimensions thus obtained, we obtain a linear chain closed by the

dimension (x). Figure 5 shows the projection of the plane dimensional chain

A BCDEX

as the linear chain

abcdex.

FIGURE

6 .

Sectional view of the

K-36

pocket watch through

the winding-stem axis

FIGURE 7. Schematic diagram of the plane

dimensional chain corresponding to Figure

This method is rarely used in watch-movement calculations . Plane

dimensional chains are usually calculated by combined methods , that is by

using the graphical- analytical m ethod.

As an example we will the assembly (operation } of the middle and back of

K- 3 6 pocket watches . Figure 6 is a s ection of the watch through the wind

ing-stem axis . The clearance

must be positive under all ass embly con

ditions . The corresponding dimensional chain (Figure 7 } is made up of

horizontal, vertical, and inclined dimensions . The clearance ( see F igure 7 }

x = o'c - o'b

2.8 -

o'a1.

The distance o'o

3 1 1 . 6- 2 . 8 3 08 . 8 mm, and therefore

3 7 5

(4 }

The values of ab and

o'a

are determined from the two linear dimensional

chains . The horizontal linear chain determines the m agnitude of ab

39,5_0,17

ab=

- 1 8,9 = 0,85_0,065 •

The vertical linear chain determine s the value of o'a :

o'anom

(31 1 .6

0.6

3.5) - (308 .2

2.4

2.2 + 0.5)

2 . 1 3 mm ;

o'amax =

(31 1 .6

0.6

3.5) - (308.2 + 2.34 + 2 . 1 4 + 0,44) = 2.31 mm ;

o'amln

(3 1 1 .6

0.54

3.42) - (308.2 + 2.4

2.2

0.5)

1 .99

m m .

o 'a

2.13

±g:l!

Substitution of the values obtained for

and o' a in expression (4 ) gives

xnom=

2.8 -

0.852

2. 1 3�

2.8 - 2 .29

0.51 mm;

xma.x =

2.8 -

1 .99�

2.8 - 2. 1 3

0.67 mm;

min =

2.8 -

0.852

2.3 1 2

2.8 - 2.47

0.33 mm.

The clearance

thus lies within the limits 0 . 6 7 and 0 . 3 3 mm, and is

therefore always a positive clearance . The assembly tolerance will be

.. =

0 . 6 7 - 0 . 3 3

0.34 mm .

Dimensional- chain calculation thus m akes it possible to establish the

most rational manufacturing and assembly processes for the watch move

ment.

SUBASSEMBLIES

Watch subassemblies are classified into the following groups according

to their ass embly c riteria: plates and bridges with their pins, s crews,
jewels and sleeves ; wheels and pinions; barrel, barrel cap, barrel arbor

and mainspring; pallet lever and balance; keyless work and hand-setting

parts and external parts .

We will consider s everal characteristic elements of the assembly of plate s

and bridge s , gear pairs, the barrel and the escapement regulator .

Pre s s -mounting the Sleeve s , Pins, and Jewels in

the Plate and Bri dges

Figure 8 shows the design of detachable j oints b etween plate and b ridge s .

The b ridge holes for the pins (2 ) have 0 . 0 1 - 0. 0 1 5 mm clearance , and tho s e

f o r the sleeve ( 1 ) have 0 . 1 - 0 . 1 5 mm clearanc e . Pins up to 1 mm i n diameter

are fitted into the plate with a negative allowance of 0 . 0 1 - 0 . 02 mm, corre

sponding to medium and heavy interference fits (GOST 304 7 - 4 7 ) . The pins

accurately position the bridge on the plate in the horizontal plane and ensure

3 7 6

Content .. 92 93 94 95 ..