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TRAINING MANUALMECHANICAL
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UNITS IN THIS COURSE
UNIT 1 BEARING
UNIT 2 LUBRICATION
UNIT 3 COUPLING
UNIT 4 CLUTC !"
UNIT # CA$"
UNIT % C AIN" AN& B!LT &RI'!
UNIT 7 G!AR"
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TABLE OF CONTENTS
Para Page
1.0 OBJ!CTI'!". 3
1.1 INTRO&UCTION. 4
1.2 (RICTION. 4
1.3 T ! (UNCTION O( B!ARING". #
1.4 T)P!" O( B!ARING. %
1.4.1 Pla*+ ,ea *+g . %
1.4.2. " l* ,ea *+g 9
1.4.3. A+ *- * * + ,ea *+g 11
1.# T)P!" O( ROLLING CONTACT B!ARING". 14
1.#.1 Ball ,ea *+g . 14
1.#.2. R lle ,ea *+g . 1#
1.%. BALL AN& ROLL!R B!ARING ALIGN$!NT 17
1.7. B!ARING $OUNTING" 1
1. . B!ARING LUBRICATION. 20
1.9. IN"TALLATION O( B!ARING". 20
1.10 R!$O'ING B!ARING". 2#
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1.0 OBJECTIVES.
T5e a*+ee 6*ll ,e a,le
&e *+e 5e u+ * + a ,ea *+g.
&e *,e 5e e a *+g + ,ea *+g .
I8e+ * y va * u y e ,ea *+g a+8 a e 5e* a l* a * + .
I8e+ * y va * u ,ea *+g u+ *+g a+8 a e 5e* a l* a * +.
&e *,e e 5 8 u e8 u+ *+g a ,ea *+g + a 5a .
&e *,e 5 6 l8 u+ a ,ea *+g + a 5a u *+g a 5y8 aul* e .
&e *,e 5 6 5 u+ a ,ea *+g + a 5a u *+g a+ *l ,a 5 5ea e .
&e *,e 5 6 8e e *+e l* ,ea *+g lea a+ e u *+g la *-gauge
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1.1 INTRODUCTION
Bea *+g a e u e8 u a *+g a u 5 a 5a : a;le a+8 *v . A,ea *+g 6*ll al e8u e 5e * * + ,e 6ee+ v*+g a+8 a * +a y a 5*+e a .T5ey a e ea *ly e la e8: av*+g 5e e; e+ *ve a 5*+e a .
1.2 FRICTION.
T5e e a e 5 ee y e * * + ve e8 *+ 5* u e< 5ey a e l*8*+g: ll*+g a+8lu*8 * * +. = ee *gu e 1.1>.
Figure 1 1.
A la*+ ,ea *+g * a+ e;a le 65e e 5e e * l*8*+g * * +. A ,all ,ea *+g * a+e;a le 65e e 5e e * ll*+g * * +. T5e 5* 8 y e * * + * lu*8 * * +.T5* u 65e+ e al e al + a * av *8e8 ,y la *+g a *l *l ,e 6ee+
5e 6 u a e . T5e e +ee8e8 ve e all 5e e y e * * + va *eg ea ly.
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1.! THE FUNCTION OF BEARINGS.
T5e u+ * + a ,ea *+g * e8u e 5e * * + ,e 6ee+ 6 v*+g a : ,e 6ee+ a v*+g a a+8 a a * +a y a . T5ey a+ e8u e 5e * * + + 5a
a *+g a 5*g5 ee8 : a+8 + +e a y*+g 5eavy l a8 . T5ey al u a+8al*g+ =?ee *+ l*+e> 5a a+8 5e v*+g a . T 8 5e e 5*+g 5e ,ea *+g
u ve e 5e e 8u e8 65e+ 5e 5a a e . T5e a*+ e a *+g+ a ,ea *+g a e a ll 6
Ra8*al e - a *+g a 90 5e 5a a;* = 5e e+ e 5e 5a >.
A;*al = 5 u > e - a *+g a allel 5e 5a a;* .
Figure 1 2.
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1." T#PES OF BEARING.
@5e+ a 5*+e y a+8 e u* e+ * a8e 5e y e ,ea *+g u ,e 8e *8e8. T5ey e ,ea *+g 5 e+: 8e e+8 + 5e l a8 +8* * + : ee8 a+8 e a *+ge u* e e+ * 5a 6 ? u+8e . T5e e a e 6 a*+ y e ,ea *+g < la*+ a+8
a+ *- * * +. A+ *- * * + ,ea *+g a e e* 5e ,all lle ,ea *+g . Ce a*+ y e ,ea *+g a e u e8 + l 5e 8* e e+ l a8 a *+g + 5e 5a . T5* * 8 +e a
ll 6
Ra$ia% %&a$'. T5e e a+ ,e + lle8 ,y u *+g u +al a+ *- * * +,ea *+g = lle ,all y e>.
A(ia% %&a$'. T5e e a+ ,e + lle8 ,y u *+g 5 u ,ea *+g . T5e e a ea+y y e 5 u ,ea *+g . T5e a*+ +e a e +ee8le: 5e * al:
a+8 *l *+g a8. T5ey a e u e8 a, , 5 u l a8 8u e8 ,y
a *+g 5a . A )&*+i,a-i&, & a(ia% a,$ ra$ia% %&a$'. T5e e a+ ,e + lle8 ,y u *+g
a e e8 lle a+gula + a ,ea *+g . T5ey 8 5e 6 ? u +al a+8 5 u ,ea *+g .
1.".1 P%ai, Beari,g'
A /%ai, +eari,g * * ly a leeve 5a * a u+8 a 5a . "5a a+8 a;le a eal6ay *+ + a 6* 5 5e u a e a la*+ ,ea *+g. ( 5* ea + 5ey 8u e
l*8*+g * * +.
Pla*+ ,ea *+g 5 ul8 al6ay ,e a e a e *al 5a+ 5e 5a . T5* * a*+ly8ue 5e e la e e+ . "5a a e + ally a8e 5a 8e+e8 eel
eve+ e; e *ve 6ea . A la*+ ,ea *+g * al6ay ea *e a+8 5ea e e la e5a+ 5e 5a . I ay + ,e *,le ll 6 5e 5a 8e+*+g e8u e *+ 5ea*+ e+a+ e 6 ? 5 .
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T5e +a e u +al e e 5e a 5e 5a 5a * *+ + a 6* 5 5e ,ea *+g.= ee *gu e 1.3>.
Figure 1 !.
A laye lu, * a+ * +e e a y e8u e 5e l*8*+g * * + ,e 6ee+ 5e ,ea *+g:a+8 5e *;e8 +e+ a . Ba * ally a la*+ ,ea *+g * a yl*+8 * al 5 le l*+e86* 5 ,ea *+g e al * e8 6* 5 a ,ea *+g ,u 5. A ,ea *+g l*?e 5* a+ 6ea,e au e l*8*+g * * + ,e 6ee+ 5e 5a a+8 5e ,ea *+g u a e . Lu, * a * +
e8u e 5e a u+ 6ea *+ 5e ,ea *+g. I 5e e * e lu, * a * +: 5elu, * a+ 6*ll e a a e 5e 5a 5e ,ea *+g. T5e lu, * a+ + +ly lu, * a ea+8 l : ,u al l a e 5e 5a . !ve+ *+ 5e l e * e8 ,ea *+g 5e lu, * a+6*ll l a e 5e 5a . @5e+ 5e 5a * u +*+g * 6*ll + u 5 5e ,ea *+g.
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@5e+ a 5a a+8 ,ea *+g * a *+ * + 5ey a e *+ e al e al + a a+8l*8*+g * * + u . @5e+ 5e 5a ea 5e * a;* u ee8 a+ *l *l
*+ 5e all a e ,e 6ee+ 5e 5a a+8 ,ea *+g. T5e l*8*+g * * + * e la e8 ,ylu*8 * * +. = ee *gu e 1.4>.
Figure 1 ".
A 5e 5a a a e: 5e *l l* , u 5e *8e 5e 5a : *+ 5e 8* e * +* e 5e a * +. T5e laye *l + 5e l 6ly u +*+g 5a * ? 5e u
a e a+8 u + 6* 5 * . A 5e *l * a *e8: * e a a e 5e ,ea *+g u a e *+ a+ *+u u laye . = ee *gu e 1.#>.
Figure 1 .
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Pla*+ ,ea *+g a e e * e u e8 65e e 5a al*g+ e+ * le * a+ : a+865e+ 5e R.P.$. * l 6. T5ey a?e u le a e 5a+ a+ *- * * + ,ea *+g a+8:,e au e 5ey a+ ,e a8e u* e ea *ly: 5e* e la e e+ * u 5 le . T5e
a e *al u e8 la*+ ,ea *+g u al6ay ,e e 5a+ 5e 5a . T5ey a+ ,ea8e +e l*8 *e e *+ 6 5alve : alle8 l* ,ea *+g .
1.".2 . S/%i- +eari,g'
S/%i- +eari,g' a e u e8 65e e * * 8* * ul *+ all a+8a 8 ,ea *+g . T5e e *u ually le a?e a a e la e l* ,ea *+g . T5ey a e 5el8 *+ la e ,y a,ea *+g a . = ee *gu e 1.%>.
Figure 1 .
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" l* ,ea *+g a e +ly u e8 *+ e * a *+g e+g*+e a+8 + ea+? 5a . T5e lea a+ e ,e 6ee+ 5e l* ,ea *+g a+8 5e 5a a+ ,e
ea u e8 ,y u *+g la *-gauge. T5* * 8 +e ,y * e v*+g 5e ,ea *+g a :5e+ a 5*+ * la *-gauge * la e8 al +g 5e 5a u +al. T5e a *e la e8 a+8 5e , l a e ue8 = *g5 e+e8>. @5e+ 5e a * e ve8 5e 6*8 5
5e e e8 la *-gauge a+ ,e ea u e8 6* 5 5e gauge v*8e8. T5elea a+ e a+ ,e , a*+e8 a 5a u *+g 5e 6*8 5 5e la *-gauge. = ee*gu e 1.7>.
Figure 1 .
T5e e a u+ lea a+ e a+ ,e e ,y *+ e *+g e v*+g 5* = 5*+*e e e al>. = ee *gu e 1. >.
Figure 1 3.
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1.".!. A,-i ri)-i&, +eari,g'
A,-i ri)-i&, +eari,g' a e u+8 *+ *+8u *al a 5*+e a+8 e u* e+ 65e e5e e a e v*+g +e+ . T5* * ,e au e 5ey a+ 5a+8le a va *e y l a8
a+8 ee8 +8* * + . T5ey a e * * +e8 ,e 6ee+ 5e 5a a+8 5e *;e8a 5*+e a .
A+ *- * * + ,ea *+g + * 5e ll 6*+g
T5e i,,er ra)e 65* 5 * a l*g5 e * + 5e 5a .
T5e /re)i'i&, gr&u,$ +a%%' &r r&%%er'.
T5e )age 5a ?ee 5e ,all lle e ually a e8.
T5e &u-er ra)e 65* 5 * a l*g5 e * *+ 5e ,ea *+g 5 u *+g. = ee *gu e1.9>.
Figure 1 4.
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*g5 ee8 a *+g 5a a e ly u e8 ,y ,all lle ,ea *+g . B 5y e ,ea *+g u, * u e ll*+g * * + l*8*+g * * + 5a * e e+ *+ la*+
,ea *+g . "*+ e ll*+g * * + * u 5 le 5a+ l*8*+g * * +: ,all a+8 lle,ea *+g a e e e8 a a+ *- * * + ,ea *+g . A a a8va+ age 5ey 5ave ve
la*+ ,ea *+g * 5a 5ey e u* e le 6e a 5e a * +.
T5e a*+ u+ * + 5e age a e
T 8* *,u e 5e ,all lle eve+ly a u+8 5e * u e e+ e 5e,ea *+g.
T eve+ 5e ,all lle u 5*+g +e a+ 5e .
T ?ee 5e 65 le e ,ea *+g ge 5e 65e+ y u a e a e ,l*+g,ea *+g 5a a+ ,e 8* a+ le8..
T5e age * gu*8e8 ,y: 5e ,all lle : a+8 5e *++e a+8 u e *+g < a+8 a?e+ a *+ 5e 6e a+ * * +. ( + al e a *+g +8* * + 5ey a e u ually
a8e e e8 eel: al 5 ug5 e * e 5ey a e a8e ge8 e al. (all ,ea *+g : , a *, e a+ ,e u e8 a?e 5e age. = ee *gu e 1 . 10>.
Figure 1 10.
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Bea *+g 5a 5ave e *al e u* e e+ : ,e au e 5*g5 l a8 ee8 e .: 5 ul8,e a8e l*8 age . " l*8 age a e + ally a8e , a : l*g5 e al
la * . = ee *gu e 1.11>.
Figure 1 11.
T5e ,ea *+g a e a e 5e a 5e ,ea *+g 5a u 5 5e a 5*+e y a . T5eyl a e 5e ,all lle *+ * * + ,u all 6 5e ve eely.
A+ *- * * + ,ea *+g a+ ,e la * *e8 ,y 5e 5a e 5e ll*+g a = lle ,all>.T5e 5a e 6*ll 8e e+8 + 5e a u+ a+8 y e l a8: a+8 5e ee8 5a 5ey
5ave 6 ? u+8e . = ee *gu e 1. 12>.
Figure 1 12.
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1. T#PES OF ROLLING CONTACT BEARINGS.
T5e e a e a+y y e ,ea *+g . I * + ea y 5 e a u* a,le ,ea *+g ag*ve+ ,. @e u 8e *8e: 5e e e: 65a y e l a8 * 6*ll 5ave a?e< a;*al:
a8*al: eve+ 5 ? l a8 . Al : 65a y e ve e+ 6*ll u 8u *+g *e a * +. @5e+ 6e 5ave 8 +e 5a : 6e 6*ll 5ave e *8ea 65* 5 y e
,ea *+g 6*ll 8 5e , ,e .
1. .1 Ba%% +eari,g'.
Ball ,ea *+g a+ 6 ? u+8e 5*g5 ee8 ,u +ly l*g5 l a8 . T5ey a e u ually elal*g+*+g 5ey a e ea *e *+ all 5a+ lle ,ea *+g .
T5e e a e u ,a * y e ,all ,ea *+g . T5ey a e
Si,g%e r&5 ra$ia% +eari,g' - a*+ly u e8 u a8*al l a8 +ly.
Si,g%e r&5 a,gu%ar )&,-a)- +eari,g' - u e8 u , 5 a8*al l a8 :a+8 5 u l a8 *+ +e 8* e * +.
D&u+%e r&5 a,gu%ar )&,-a)- +eari,g' - u e8 u , 5 a8*al a+85 u l a8 *+ , 5 8* e * + .
T6ru'- +eari,g' - + u e8 a e a;*al l a8 *+ +e 8* e * + +ly.
Figure 1 1!.
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1. .2. R&%%er +eari,g'.
A lle ,ea *+g * 8e *g+e8 a?e 5eav*e l a8 5a+ a ,all ,ea *+g: ,u 5e l*8*+g* * + * g ea e . B 5 ,all a+8 lle ,ea *+g a e u ually lu, * a e8 6* 5 g ea e
e8u e * * + a+8 6ea a *+* u . R lle ,ea *+g a e a8e *+ 5e a e 6aya a ,all ,ea *+g: e; e 5e 5a e 5e ll*+g ele e+ * 8* e e+ . T5e e a e
5 ee a*+ lle . T5ey a e
P%ai, r&%%er- yl*+8 * al *+ 5a e a+8 ll *+ a la a e6ay. T5ey all 6 a;* uu 5e a8*al l a8: ,u + u 5 u l a8. = ee *gu e 1. 14>.
Figure 1 1".
S/6eri)a% r&%%er al alle8 a ,a el lle . I 5a a u ve8 + a u a e5a * *+ a + ave a e6ay: 8u *+g 6 a+gula *+
+ a . I v*8e la ge l a8 u : ,u +ly a l* le 5 u u*+ e* 5e 8* e * +. T5ey a+ 5ave 8 u,le *+gle 6 lle .= ee *gu e 1. 1#>.
Figure 1 1 .
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Ta/ere$ r&%%er - 5a e8 *+ 5e a +e: 65* 5 a+gula + a *+ .T5ey a+ u 5eavy a8*al l a8 a+8 8e a e 5 u l a8 *+ +e8* e * + +ly: a+8 a+ ,e 8 u,le *+gle 6. = ee *gu e 1. 1%>.
Figure 1 1 .
Nee$%e +eari,g' a+ e 6* 5 6* 5 u a age e a a e 5e lle . I 5ae lle *+ + a 6* 5 5e 5a : a+8 5e e * e * e + *++e a e:
e * e + u e a e. T5ey a+ u ve y 5eavy a8*al l a8 : ,u+ 5 u l a8 . T5ey a e al +ge 5a+ la*+ lle ,ea *+g . = ee *gu e1. 17>.
Figure 1 1
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T5e 6 a*+ a8va+ age +ee8le ,ea *+g a e
T5ey u 5eav*e a8*al l a8 .
T5ey a?e u le a e.
A + u e +ee8le ,ea *+g * 65e+ +e 5a u a e 6* 5*+ a+ 5e5a . = ee *gu e 1. 1 >.
Figure 1 13
1. . BALL AND ROLLER BEARING ALIGNMENT
Al*g+ e+ a ,all lle ,ea *+g 8e e+8 + a u a e a 5*+*+g a+8 a e ,ly." e * e 5* * + *,le 8ue 5e 8e *g+ 5e e u* e+ a+8 e a *+g
+8* * + . I+ 5e e * ua * + el -al*g+*+g ,ea *+g a e u e8 v*8e e5a u . T5ey a e 8e *g+e8 al*g+ 5e elve au a * ally 6* 5 5e 5a .
= ee *gu e 1. 19>.
Figure 1 14.
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1. . BEARING MOUNTINGS
Bea *+g a+ ,e *;e8 *+ * * + a+8 u e8 ,y ,ea *+g u+ *+g . Bea *+gu+ *+g a e u e8 65e+ * * * a+ 5a 5e ,ea *+g * 5el8 *+ a u a e
al*g+ e+ 6* 5 5e 5a a;* . C + y e ,ea *+g u+ *+g a e a ll 6
Pi%%&5 +%&)7 - u e8 e u e 5e ,ea *+g a u a e 5a * a allel 6* 55e 5a a;* . = ee 1.20>.
Figure 1 20.
F%a,ge *&u,-i,g' - u e8 e u e 5e ,ea *+g a u a e 5a *e e+8* ula 5e 5a a;* . = ee *gu e 1.21>.
Figure 1 21.
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Ta7e u/ *&u,-i,g' - u e8 65e+ 5e ,ea *+g * * + * va *a,le. = ee *gu e1.22>.
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Figure 1 22.
I,-egra% *&u,-i,g' - 5e ,ea *+g 5 l8e * a 5e a 5*+e: a+8 5el8 *+la e 6* 5 a l ? *+g: * l* . = ee *gu e 1 .23>.
Figure 1 2!.
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1.3. BEARING LUBRICATION.
All ,ea *+g +ee8 lu, * a * + ve e *+ e +al * * +: ve 5ea *+g: a+8 6ea :=e; e e la * >. "eale8 ,ea *+g 8 + +ee8 lu, * a * + e; e +ally. T5ey a e
* *la a + al ,all lle ,ea *+g: e; e 5a eal a e la e8 ve 5e a e,e 6ee+ 5e *++e a+8 u e *+g . T5e eal ?ee 5e lu, * a * + *+ *8e 5a 5a,ee+ *+ alle8 ,y 5e a?e : 5e l* e 5e ,ea *+g. = ee *gu e 1 .24>.
Figure 1 2".
1.4. INSTALLATION OF BEARINGS.
&u a+8 8* a+ 8e y 5e u a e a ,ea *+g ve y u* ?ly. Ne6 ,ea *+g5 ul8 ,e u+ a ?e8 u ,e e 5ey a e *+ alle8. T5ey 5 ul8 ,e ?e ve y lea+.
I+ alla * + e val 5 ul8 +ly ,e 8 +e ,y e +e 65 ?+ 6 a, u ,ea *+g .T5e+ 5e ,ea *+g 5 ul8 5ave a l +g a+8 u,le ee l* e.
T5e ll 6*+g * 5e e8u e *+ all*+g ,ea *+g
$a?e u e 5a 5e e la e e+ ,ea *+g * e;a ly 5e a e a 5e +e * *e la *+g. I ay l ? 5e a e ,u 5e 8* e+ * + ay va y l*g5 ly. C5e ? 5e
,ea *+g +u ,e + 5e u e a e 5e ,ea *+g. $a+u a u e a al gue 6*lle; la*+ 5e +u ,e *+g y e : a+8 65* 5 ,ea *+g u e.
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Be e *+ all*+g a+y ,ea *+g: lea+ 5e 5a 5 u *+g a+8 5e ? 5eu a e 8a age. & + * ,ea *+g a+y 8a age8 u a e..
a+8le 5e ,ea *+g a e ully: * 5a+8l*+g a+ a e * e * * + le a+ e . T5e ,ea *+g 5 ul8 ,e lea+: a+8 5ave a l*g5 ve *+g lu, * a+ .
T5e + a u a e 5e 5 u *+g 5a 5 ul8 ,e lea+e8 a+8 ve e86* 5 lu, * a+ . &* 5a ge + 5e ,ea *+g 8u *+g *+ alla * + 6*ll
a?e 5e u a e a, a *ve.
T5e * ,e 6ee+ 5e ,ea *+g a+8 5e 5a : 5 u *+g: 5 ul8 ,e l e. T5ee8ge , 5 5e *++e a+8 u e *+g 5ave a l*g5 ,evel 5a 5elal*g+ 5e ,ea *+g 8u *+g a e ,ly.
T5e e a e va * u e 5 8 u+ *+g ,ea *+g ,u 5ey u ually all *+6 g u : l8 5 u+ *+g. &u *+g l8 u+ *+g: al6ay e+ u e 5a5e e * a l*e8 +ly 5e e a e: 5e ,ea *+g 6*ll ,e 8a age8.
( e 5 ul8 +eve ,e a l*e8 5e ,all lle 8u *+g *+ alla * +. " all,ea *+g a+ ge+e ally ,e e e8 + 5e 5a : *+ 5e 5 u *+g: *+ a
l8 a e. C l8 u+ *+g a+ ,e 8 +e 6* 5 e* 5e a 5y8 aul* e : 6* 58 * u+ 5e . = ee *gu e 1.2#>.
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Figure 1 2 .
@5e+eve *,le: u e a 68$rau%i) /re'' u+ ,ea *+g . A 5y8 aul*e 6*ll ?ee 5e ,ea *+g ua e 5e 5a : 5e 5 u *+g.
&e *8e 65* 5 * 5e ,e 6ay e u 5e , + 5e e . U e a e al a ?*+g ,e 6ee+ 5e a a+8 5e ,ea *+g * 5e e * a*,*l* y 8a age 5e ,ea *+g.
"e u 5e 5a 5 u *+g + 5e ,a e 5e e .
Al*g+ 5e ,ea *+g *+ la e a+8 l 6e 5e a .
C5e ? 5a 5e a a e ua e ea 5 5e : a+8 5a 5e l a8 * g *+g e + 5e e a e.
Ge+ ly e 5e ,ea *+g + 5e 5a *+ 5e 5 u *+g.
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T5e a u+ 5ea *+g * 6*ll e u* e 6*ll 8e e+8 + * *De. ea *+g * e 6*ll va y +e 5 u eve al 5 u a la ge ,ea *+g. T5e a;* u e e a u e
5 ul8 + ,e e 5a+ 120 C. = ee *gu e 1.2%>.
Figure 1 2 .
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Be e 5e ,ea *+g * e ve8 5e *l 5ea e : lea+ 5e ea *+g u a e 6* 5 alea+ l 5 e ve *l. @5e+ 5e ,ea *+g 5a ea 5e8 5e e u* e8 e e a u e:e ve * 5e *l ,a 5 . @* e 5e *l *+ 5e , e a+8 e y 5e e a*+*+g *l
*+ 5e u e *+g. Pu + lea+ a ,e gl ve a+8 * e8*a ely * * + 5e ,ea *+g
+ * ea ,e au e 5e ,ea *+g 6*ll l u* ?ly. T5e+ u 5 5e ,ea *+g *+ la e:a *+g * l*g5 ly eve+ * *l *+g. I 5e ,ea *+g a ,e e ea 5*+g 5ee * * +: 6* 58 a6 * * e8*a ely a+8 e-5ea * .
T5e e a e a+y + aul 5a u ,e au e *+ e u+ *+g ,ea *+g 5 ug5 ,a8ly 8a age8 5a . = ee *gu e 1.27>.
Figure 1 2 .
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1.10 REMOVING BEARINGS.
@5e+ a ,ea *+g u ,e u e8 aga*+: y u u ,e a e ul + 8a age * 8u *+ge val. A ,ea *+g ulle : 5y8 aul* e * u e8 e ve ,ea *+g . ( e5 ul8 ,e a l*e8 ua ely 5e a e. I * aga*+ * a+ : 5 6eve : a ly 5e
e 5e e a e. Re v*+g a ,ea *+g ,y a ly*+g e 5e 6 +g a e6*ll 8a age * . T5e+ 5e ,ea *+g a++ ,e e-u e8. = ee *gu e 1.2 >.
Figure 1 23.
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@5e+ y u a e e v*+g ,ea *+g 6* 5 a ,ea *+g ulle y u u
"ele 5e u* a,le ulle 5e ,.
O*l 5e u a e eve+ a 5*+g u *+g 8u *+g e val. A a+ge 5e ulle *+ *8e u *8e 5e ,ea *+g a e u* e8.
(* 5e ulle a+8 *g5 e+ * 5 l8 * *+ * * +.
Eee 5e ulle lea 5e ea *+g.
C5e ? 5a 5e ulle * ua e: a+8 ull*+g +ly + 5e e u a e .
Pull 5e ,ea *+g l 6ly.
Eee 5e ,ea *+g ua e 5e ea *+g 8u *+g e val.
A 6* 5 u+ *+g ,ea *+g : 65e+eve *,le: u e a 5y8 aul* e e ve,ea *+g . Re e ,e : a 5y8 aul* e 6*ll ?ee 5e ,ea *+g ua e 5e 5a
5e 5 u *+g.
&e *8e 65* 5 * 5e ,e 6ay e 5e , u + 5e e . U e a e ala ?*+g ,e 6ee+ 5e a a+8 5e ,ea *+g * 5e e * a *,*l* y 8a age 5e
,ea *+g. T5e+
"e u 5e 5a 5 u *+g + 5e ,a e 5e e .
Al*g+ 5e ,ea *+g *+ la e a+8 l 6e 5e a .
C5e ? 5a 5e a a e ua e ea 5 5e : a+8 5a 5e l a8 * g *+g ,e e;e e8 + 5e e a e.
Ge+ ly e 5e ,ea *+g a6ay 5e 5a 5 u *+g.
$a?e u e 5a a 8 + all 5e l a+8 ,e e 8a age8.
O+ly e ve ,ea *+g 6* 5 a e al 8 * u+ 5 65e+ a 5y8 aul* e a++ ,eu e8. &e *8e 65* 5 * 5e ,e 6ay a 5e ,ea *+g a6ay 5e 5a 5 u *+g. I *,le u e a *e e u,e 5a 6*ll * ua ely + 5e e a e: a+8
ua e 5e ea *+g. Pla e a *?*+g ,l ? *e e la e ve 5e u,*+g. T5e+5* 5e *?*+g ,l ? u+ *l 5e ,ea *+g * lea 5e 5a ,ea *+g.
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@5e+ u *+g a 8 * e ve 5e ,ea *+g: a eve+ly a u+8 5e a e. Ta?e a e + *?e a+y 5e a 5e ,ea *+g. Eee 5e ,ea *+g ua e. I 5e ,ea *+g g e
u ua e: a 5e 5e *8e ua e * aga*+.
O 5e e val e 5 8 a e 5 6+ *+ *gu e 1.29.
Figure 1.24.
Recommended