EXPERIMENT - 1
AIM: TO FIND OUT CRITICAL SPEED EXPERIMENTALLY AND TO COMPARE THE WHIRLING SPEED OF A SHAFT.
EQUIPMENTS: TACHOMETER, SHAFT, END FIXING ARRANGEMENT ETC.
THEORY: THIS APPARATUS IS DEVELOPED FOR THE DEMONSTRATION OF A WHIRLING PHENOMENON.
THE SHAFT CAN BE TESTED FOR DIFFERENT END CONDITIONS.
THE APPARATUS CONSISTS OF A FRAME TO SUPPORT ITS DRIVING MOTOR, END FIXING AND SLIDING BLOCKS ETC.
A SPECIAL DESIGN IS PROVIDED TO CLEAR OUT THE TESTING OF BEARING OF MOTOR SPINDLE FROM THESE TESTING SHAFTS. THE SPECIAL DESIGN FEATURES OF THIS EQUIPMENT ARE AS FOLLOW:
A. COUPLING
A FLEXIBLE SHAFT IS USED TO DRIVE THE TEST SHAFT FROM MOTOR.
B. BALL BEARING FIXING ENDS.
THE END FIXES THE SHAFT WHILE IT ROTATES. THIS CAN BE REPLACED WITHIN A SHORT TIME WITH THE HELP OF THIS UNIT. THE FIXING ENDS PROVIDE CHANGE OF END FIXING CONDITION OF THE ROTATING SHAFT AS PER THE REQUIREMENT.
SHAFT SUPPLIED WITH THE EQUIPMENT
POLISHED STEEL SHAFT IS SUPPLIED WITH THE MACHINE. THE DIMENSIONS BEING AS UNDER :
SHAFT NO.
|
DIAMETER (APPROX)
|
LENGTH(APPROX)
|
1.
|
4.0 MM
|
900 MM
|
2.
|
4.7 MM
|
900 MM
|
END FIXING ARRANGEMENT
AT MOTOR END AS WELL AS TAIL END DIFFERENT END CONDITIONS CAN BE DEVELOPED BY MAKING USE OF DIFFERENT FIXING BLOCKS.
- SUPPORTED END CONDITIONS - MAKE USE OF END BLOCK WITH SINGLE SELF ALIGNING BEARINGS.
- FIXED END CONDITION - MAKE USE OF END BLOCK WITH DOUBLE BEARING.
GUARDS D1 AND D2 :
THE GUARDS D1 AND D2 CAN BE FIXED AT ANY POSITION ON THE SUPPORTING BAR FRAME WHICH FITS ON SIDE SUPPORTS F. ROTATING SHAFTS ARE TO BE FITTED IN BLOCKS IN A AND B STANDS.
SPEED CONTROL OF DRIVING MOTOR:
THE DRIVING MOTOR IS 230V, DC 1/6 HP, 3000 RPM, UNIVERSAL MOTOR AND SPEED CONTROL UNIT IS A DIMMER STATE OF 240V, 2 AMPS, 50 C/S.
MEASUREMENT OF SPEED:
TO MEASURE THE SPEED OF THE ROTATING SHAFT A SIMPLE TACHOMETER MAY BE USED ON THE OPPOSITE SIDE OF THE SHAFT EXTENSION OF THE MOTOR.
WHIRLING OF ELASTIC SHAFT:
IF L = LENGTH OF THE SHAFT IN CMS.
I = 2ND MOMENT OF INERTIA OF THE SHAFT CM4
W = WEIGHT OF THE SHAFT PER UNIT LENGTH KG/CM.
G = ACCELERATION DUE TO GRAVITY OF CMS/SEC2
= 981
THEN THE FREQUENCY OF VIBRATION FOR THE VARIOUS MODES IS GIVEN BY THE EQUATION:
E.I.G
F = K X --------
W.L.4
END CONDITION
|
VALUE OF K
| ||
1ST MODE
|
2ND MODE
| ||
FIXED , SUPPORTED
FIXED , FIXED
|
1.47
1.57
|
2.56
2.46
| |
DATA:
SHAFT DIA
|
I = CM4
|
W = KG/CM
|
3.8 MM
5.0 MM
|
X 10-4
X 10-4
|
0.15 X 10-2
0.28 X 10-2
|
CALCULATIONS:
a) BOTH ENDS OF SHAFTS FREE (SUPPORTED) 1ST AND 2ND MODE OF VIBRATION CAN BE OBSERVED OF SHAFTS WITH 3/16” DIA AND ¼” DIA.
b) ONE END OF SHAFT FIXED AND THE OTHER FREE; 1ST AND 2ND MODE OF VIBRATION CAN BE OBSERVED ON SHAFT WITH 3/16” DIA.
c) BOTH ENDS OF SHAFT FIXED- 2ND MODE OF VIBRATION CANNOT BE OBSERVED ON ANY OF THE SHAFTS AS THE SPEEDS ARE VERY HIGH AND HENCE BEYOND THE RANGE OF THE APPARATUS.
FIXED – FIXED
DIAMETER OF BRASS ROD = 0.4 CM
WEIGHT = 150 GRM = KG/CM = 0.0015
YOUNG MODULUS E = 2.06 X 106
S.NO.
|
SPEED RPM
1ST MODE
|
VALUE OF K
|
I=(ΠD4)/64
|
WEIGHT IN GRAMS
|
FTH =
K.(EIG)/W
|
FACT =
RPM/TIME
|
1
| ||||||
2
|
DIAMETER OF BRASS ROD = 0.47 CM
WEIGHT = 190 GRAM = KG/CM = 0.0019
YOUNG MODULUS E = 2.06 X 106
S.NO.
|
SPEED RPM
2ND MODE
|
VALUE OF K
|
I=(ΠD4)/64
|
WEIGHT IN GRAMS
|
FTH =
K.(EIG)/W
| |||
1
| ||||||||
2
| ||||||||
SUPPORTED – FIXED
DIAMETER OF BRASS ROD = 0.4 CM
WEIGHT = 190 GRAM = KG/CM = 0.0019
YOUNG MODULUS E = 2.06 X 106
S.
NO.
|
SPEED RPM
1ST MODE
|
SPEED RPM
2ND MODE
|
VALUE OF K
|
VALUE OF K
|
I=(ΠD4)/64
|
WEIGHT
IN GRAMS
|
FTH =
K.(EIG)/WL4
|
FTH =
K.(EIG)/WL4
|
FACT=
RPM/TIME
|
FACT=
RPM/TIME
| |
1.
| |||||||||||
2.
| |||||||||||
DIAMETER OF BRASS ROD = 0.47 CM
WEIGHT = 140 GRAM = KG/CM = 0.0014
YOUNG MODULUS E = 2.06 X 106
S.NO.
|
SPEED RPM
1ST MODE
|
SPEED RPM
2ND MODE
|
VALUE OF K
|
VALUE OF K
|
I=(ΠD4)/64
|
WT.
IN GRAMS
|
FTH =
K.(EIG)/WL4
|
FTH =
K.(EIG)/WL4
|
FACT=
RPM/TIME
|
FACT=
RPM/TIME
| ||
1.
| ||||||||||||
2.
| ||||||||||||
EXPERIMENT - 2
AIM: TO FIND EXPERIMENTALLY THE GYROSCOPIC COUPLE ON MOTORIZED GYROSCOPE AND COMPARE WITH APPLIED COUPLE.
APPARATUS USED: MOTORIZED GYROSCOPE, TACHOMETER.
INTRODUCTION:
a) AXIS OF SPAN
IF A BODY IS REVOLVING ABOUT AN AXIS, LATTER IS KNOWN AS AXIS OF SPIN.
b) PRECESSION
PRECESSION MEANS THE ROTATION ABOUT THE THIRD AXIS OZ WHICH IS PERPENDICULAR TO BOTH THE AXIS OF SPIN OX AND THAT OF COUPLE OY.
C) AXIS OF PRECESSION
THE THIRD AXIS OX IS PERPENDICULAR TO BOTH THE AXIS OF SPIN OX AND THAT OF COUPLE OY IS KNOWN AS AXIS OF PRECESSION.
d) GYROSCOPE
IT IS A BODY WHILE SPINNING ABOUT AN AXIS IS FREE TO ROTATE IN OTHER DIRECTION UNDER THE ACTION OF EXTERNAL FORCE.
EXAMPLE: LOCOMOTIVE, AUTOMOBILE AND AEROPLANE MAKING A TURN. IN CERTAIN CASES THE GYROSCOPIC FORCES ARE UNDESIRABLE WHEREAS IN OTHER CASES THE GYROSCOPIC EFFECT MAY BE UTILIZED IN DEVELOPING DESIRABLE.
e) GYROSCOPIC EFFECT
TO A BODY REVOLVING ABOUT AN AXIS SAY OX(REFER FIG. 1) IF A COUPLE REPRESENTED BY A VECTOR OY PERPENDICULAR TO OX IS APPLIED, THEN THE BODY TIES TO PROCESS ABOUT AN AXIS OZ WHICH IS PERPENDICULAR BOTH TO OX AND OY. THUS THE PLANE OF SPIN, PLANE OF PRECESSION AND PLANE OF GYROSCOPIC COUPLE ARE MUTUALLY PERPENDICULAR.
THE ABOVE COMBINED EFFECT IS KNOWN AS PROCESSIONAL OR GYROSCOPIC EFFECT.
GYROSCOPIC COUPLE OF A PLANE DISC
LET A DISC OF WEIGHT ‘W’ HAVING MOMENT OF INERTIA I BE SPINNING AT AN ANGULAR VELOCITY ABOUT AXIS OX IN ANTI-CLOCKWISE DIRECTION VIEWING FROM FRONT (REFER FIG.2). THEREFORE THE ANGULAR MOMENTUM OF THE DISC IS I. APPLYING RIGHT HAND , SCREW RULE, THE SENSE OR VECTOR REPRESENTING THE ANGULAR MOMENTUM OR THE DISC WHICH IS ALSO A VECTOR QUANTITY WILL BE IN THE DIRECTION OX AS SHONE . A COUPLE WHOSE AXIS IS OY PERPENDICULAR TO OX AND IS THE PLANE Z, IS NOW APPLIED TO PROCESS THE AXIS OX.
LET AXIS OX TURN THROUGH A SMALL ANGULAR DISPLACEMENT FROM OX TO OX’ IN TIME Δ T. THE COUPLE APPLIED PRODUCES A CHANGE IS DUE TO THE VELOCITY OF PRECESSION. THEREFORE OX REPRESENTS THE ANGULAR MOMENTUM AFTER TIME Δ T.
CHANGE OF ANGULAR MOMENT = OX’-OX =XX’
OR RATE OF CHANGE OF ANGULAR MOMENTUM= ANGULAR DISPLACEMENT/TIME
= XX’/T = OX* ΔΘ/ΔT
AS XX’=OX *Δ Θ IN DIRECTION OF XX’
NOW AS RATE OF CHANGE OF ANGULAR MOMENTUM
=COUPLE APPLIED =C=T
WE GET
T = O × δ θ /ΔT
BUT OX = I.Ω
WHERE I = MOMENT OF INERTIA OF DISC AND
Ω = ANGULAR VELOCITY OF DISC. AND IN THE LIMIT WHEN IS VERY SMALL, WE HAVE —
Θ/T = DΘ/DT
AND DΘ/DT = ΩP = ANGULAR VELOCITY OF PRECESSION OF YOKE AT VERTICAL AXIS.
THUS WE GET T = I × Ω × WP
THE DIRECTION OF THE COUPLE APPLIED ON THE BODY IS CLOCKWISE WHEN LOOKING IN THE DIRECTION XX AND IN THE LIMIT IS PERPENDICULAR TO THE AXIS OF Ω AND ΩP. THE REACTION COUPLE EXERTED BY THE BODY ON ITS FRAME IS EQUAL IN MAGNITUDE TO THAT OF C, BUT OPPOSITE IN DIRECTION.
RULE NO. 1
“THE SPINNING BODY EXERTS A TORQUE OR COUPLE IN SUCH A DIRECTION WHICH TENDS TO MAKE THE AXIS OF SPIN COINCIDES WITH THAT OF THE PRECESSION”.
TO STUDY THE RULE OF GYROSCOPE BEHAVIOR FOLLOWING PROCEDURE MAY BE ADOPTED:
(a) BALANCE THE INITIAL HORIZONTAL POSITION OF THE ROTOR.
(b) START THE MOTOR BY INCREASING THE VOLTAGE WITH THE AUTO-TRANSFORMER, AND WEIGHT UNTILL
IT ATTAINS CONSTANT SPEED.
(c) PRESS THE YOKE FRAME NO.2 ABOUT VERTICAL AXIS BY A APPLIED NECESSARY FORCE BY HAND TO
THE SAME (IN THE CLOCKWISE SENSE SEEN FROM ABOVE).
(d) IT WILL BE OBSERVED THAT THE ROTOR FRAME SWINGS ABOUT THE HORIZONTAL AXIS Y.Y MOTOR
SIDE IS SEEN COMING UPWARDS AND THE WEIGHT PAN SIDE GOING DOWNWARDS.
ROTATE THE VERTICAL YOKE AXIS IN THE ANTI-CLOCKWISE DIRECTION SEEN FROM ABOVE AND OBSERVE THAT THE ROTOR FRAME SWING IN OPPOSITE SENSE (AS COMPARED TO THAT IN PREVIOUS CASE FOLLOWING THE ABOVE RULE).
RULE NO. 2:
“ THE SPINNING BODY PROCESSES IN SUCH A WAY AS TO MAKE THE AXIS OF SPIN COINCIDE WITH THAT OF SPIN COINCIDE WITH THAT OF THE COUPLE APPLIED, THROUGH 90 TURN”
a) BALANCE THE ROTOR POSITION ON THE HORIZONTAL FRAME.
b) START THE MOTOR BY INCREASING THE VOLTAGE WITH THE AUTO-TRANSFORMER AND WAIT TILL THE DISC ATTAINS CONSTANT SPEED.
c) PUT WEIGHT (0.5 KG, 1KG OR 2KG) IN WEIGHT PAN, AND START STOP WATCHTO NOTE THE TIME IN SECOND REQUIRED FOR PROCESSION, THROUGH 60 OR 45 ETC.
d) THE VERTICAL YOKE PROCESSES ABOUT OZ AXIS AS PER THE RULE NO. 2.
e) SPEED MAY BE MEASURED BY THE TACHOMETER PROVIDED ON THE CONTROL PANEL.
f) ENTER THE OBSERVATION IN THE TABLE.
MOTORIZED GYROSCOPE APPARATUS
M WEIGHT OF DISC 4.800 KG
D DIA OF THE PLATE 28.5 CM
DISTANCE WEIGHT POINT TO DISC CENTER 22.5 CM
TIME 60 SEC.
G 9.81 M/S
S.
NO.
|
RPM
|
Φ2
|
Φ1
|
Φ =
(Φ2-Φ1)
|
WT.
|
I=MXD2/8G
|
W=(2ΠN/60)
|
WP=ΠΦ/180T
|
TTH=IXWXWP
|
TACT=X
DISTANCE
|
1
| ||||||||||
2
| ||||||||||
3
|
EXPERIMENT - 3
AIM: TO PERFORM THE EXPERIMENT THE UNBALANCED COUPLE AND FORCE.
DESCRIPTION: THE APPARATUS BASICALLY CONSIST OF A STEEL SHAFT MOUNTED IN BALL BEARING IN A STIFF RECTANGULAR MAIN FRAME. A SET OF SIX BLOCKS OF DIFF. WEIGHTS IS PROVIDED AND MAY BE CLAMPED IN ANY POSITION ON THE SHAFT AND ALSO BE EASILY DETACHED FROM THE SHAFT.
A DISC CARRYING A CIRCULAR PROTECTOR SCALE IS FITTED ON ONE SIDE OF THE RACTANGULAR FRAME. SHAFT CARRIES A DISC AND RIM OF THE DISC IS GROOVED TO TAKE A LIGHT CORD PROVIDED WITH TWO CYLINDERICAL METAL CONTAINERS OF EXACTLY THE SAME WEIGHT.
A SCALE IS FITTED TO THE LOWER MEMBER OF THE MAIN FRAME AND WHEN USED IN CONJUCTION WITH THE CIRCULAR PROTACTOR SCALE, ALLOWS THE EXACT LONGITUDINAL AND ANGULAR POSITION OF EACH ADJUSTABLE BLOCK TO BE DETERMINED.
THE SHAFT IS DRIVEN BY A 230 VOLTS SINGLE PHASE 50 CYCLES ELECTRIC MOTOR, MOUNTED UNDER THE MAIN FRAME, THROUGH A BELT.
FOR STATIC BALANCING OF INDIVIDUAL WEIGHTS THE MAIN FRAME IS SUSPENDED TO THE SUPPORT FRAME BY CHAINS AND IN THIS POSITION THE MOTOR DRIVING BELT IS REMOVED.
FOR DYNAMIC BALANCING OF THE ROTATING MASS SYSTEM THE MAIN FRAME IS SUSPENDED FROM THE SUPPORT FRAME BY TWO SHORT LINKS SUCH THAT THE MAIN FRAME AND THE SUPPORTING FRAME ARE IN THE SAME PLANE.
PROCEDURE
STATIC BALANCING
REMOVE THE DRIVE BELT. THE VALUE OF WR. FOR EACH BLOCK IS DETERMINED BY CLAMPING EACH BLOCK IN TURN ON THE SHAFT AND WITH THE CORD AND CONTAINER SYSTEM SUSPENDED OVER THE PROTACTOR DISC, THE NUMBER OF STEEL BALLS, WHICH ARE OF EQUAL WEIGHT, ARE PLACED INTO ONE OF THE CONTAINERS TO EXACTLY BALANCE THE BLOCK ON THE SHAFT. WHEN THE BLOCK BECOMES HORIZONTAL, THE NUMBER OF BALLS ‘N’ WILL GIVE THE VALUE OF WR. FOR THE BLOCK.
FOR FINDING OUT ‘WR’ DURING STATIC BALANCING PROCEED AS FOLLOWS:
1. REMOVE THE BELT.
2. SCREWED THE COMBINED HOOK TO THE PULLEY WITH GROOVE (THIS PULLEY IS DIFFERENT THAN THE BELT PULLEY).
3. ATTACH THE CORD – ENDS OF THE PANS TO THE ABOVE COMBINED HOOK.
4. ATTACH THE BLOCK NO. 1 TO THE SHAFT AT ANY CONVENIENT POSITION AND IN VERTICAL DOWNWARD DIRECTION.
5. PUT STEEL BALLS IN ONE OF THE PANS TILL THE BLOCK STARTS MOVING UP (UPTO HORIZONTAL POSITION).
6. NUMBER OF BALLS GIVE THE ‘WR’ VALUE OF BLOCK 1. REPEAT THIS 2-3 TIMES AND FIND THE AVERAGE NO. OF BALLS.
7. REPEAT THE PROCEDURE FOR OTHER BLOCKS
- STATIC & BALANCING OF 4 BLOCKS.
OBTAIN STATIC BALANCE OF A SET OF FOUR BLOCKS WITH UNBALANCE AS SHOWN BY PROPERLY POSITIONING THEM IN ANGULAR AND LATERAL POSITION ON THE SHAFT.
NO.
|
UNBALANCE (WR. PRODUCT)
|
1.
|
124
|
2.
|
122
|
3.
|
120
|
4.
|
117
|
DISTANCE BETWEEN EACH BLOCK IS 2 CM. THE ARRANGEMENT IS AS SHOWN IN FIG.
ANGULAR POSITION OF NO. 3 BLOCK IS OBTAINED FROM THE FORCE POLYGON AND ITS MAGNITUDE IS ALSO OBTAINED
F3 = 70. ADJUST ALL ANGULAR AND LATERAL POSITION PROPERLY AND FIND THAT THE SHAFT ROTATES WITHOUT VIBRATION.
FORCE POLYGON
S.NO.
|
WT. NO.
|
WT.
|
DISTANCE
|
COUPLE
|
ANGLE
|
1
|
4
|
124
|
0
|
0
|
189
|
2
|
3
|
122
|
2
|
244
|
0
|
3
|
2
|
120
|
4
|
480
|
33
|
4
|
1
|
117
|
6
|
702
|
206
|
EXPERIMENT - 4
OBJECTIVE: TO FIND THE SPEED AND TORQUE OF DIFFERENT GEARS IN AN EPICYCLIC GEAR TRAIN.
SPECIFICATONS:
1. GEAR TRAIN : SUN GEAR : 14 TEETH
1. PLANT GEAR : 21 TEETH (2 NOS.)
2. INTERNAL GEAR WITH : 56 TEETH
TORQUE MEASUREMENT
2. INPUT TORQUE – MOTOR CURRENT CALIBRATED FOR MOTOR TORQUE.
3. PLANT CARRIER - PULLEY OF 50 MM DIA AND SPRING BALANCE.
4. INTERNAL GEAR - PULLEY, 120 MM DIA AND SPRING BALANCES.
a. BOTH PULLEYS ARE PROVIDED WITH ROPE OF 12
b. MM DIA
5. DRIVE MOTOR - 1HP DC MOTOR RPM MOTOR OPERATING ON 220 VOLTS
a. 50 HZ SUPLLY, DRIVING THE SUN GEAR.
MOTOR CALIBERATION CHART
CRURENT(AMPS)
|
TORQUE
|
1.00
|
0.5
|
1.20
|
1.5
|
1.40
|
2.5
|
1.60
|
3.0
|
1.80
|
4.0
|
2.00
|
5.0
|
2.20
|
6.0
|
THEORY:
WHENEVER THE DISTANCE BETWEEN THE DRIVING AND DRIVEN MEMBER,(BOTH SHAFTS ARE NOT OPERATING ON THE SAME AXIS)IS SMALL OR WHEN A POSITIVE SLIP LESS DRIVE IS REQUIRED , GEAR DRIVES ARE USED .SUCH A COMBINATION OF TWO OR MORE GEARS IS CALLED GEAR TRAIN .GEAR TRAINS MAY BE SIMPLE , COMPOUND OR EPICYCLIC GEAR TRAINS .THE AXIS OF GEARS HAVE FIXED POSITION RELATIVE TO EACH OTHER. BUT IN EPICYCLIC GEAR TRAINS, THE AXIS OF GEARS MAY HAVE RELATIVE MOTION TO EACH OTHER.
THE APPARATUS CONSIST OF SUN AND PLANET GEAR TYPE EPICYCLIC GEAR TRAIN .A DRIVING MOTOR DRIVES THE SUN WHEEL. THE PLANATORY GEARS, WHICH MESH WITH THE SUN GEAR AND MOUNTED ON PINS, WHICH ARE FITTED TO PLANET CARRIERS PULLEY .EXTERNALLY, PLANET GEAR MESH WITH THE INTERNAL GEAR WHICH IS MOUNTED OVER A SHAFT .THIS SHAFT ALSO CARRIES A PULLEY. BOTH PULLIES ARE PROVIDED WITH ROPE BRAKE WITH SPRING BALANCES, SO THAT EITHER PLANET CARRIES PULLEY OR INTERNAL GEAR PULLEY CAN BE HELD STATIONARY AND OUTPUT TORQUE WITH HOLDING TORQUE CAN BE MEASURED .INPUT TORQUE HAS BEEN CALIBERATED IN TERMS OF MOTOR CURRENT
PROCEDURE
1. CHECK THE NUT BOLTS FOR TIGHTENING (NORMALLY ALL NUT-BOLTS ARE TIGHTENED) CONNECT THE ELECTRICAL SUPPLY TO THE UNIT AND START THE UNIT.
2. TIGHTEN THE ROPE ON PLANET CARRIER PULLEY SO THAT IT DOSE NOT ROTATE. NOW, SLIGHTLY TIGHTEN THE ROPE OVER INTERNAL GEAR PULLEY.
3. NOTE DOWN THE OBSERVATIONS. REPEAT THE PROCEDURE FOR DIFFERENT TORQUES.
(NOTE: WHEN ROPE ON INTERNAL GEAR PULLEY IS TIGHTENED, PLANET CARRIER STARTS ROTATING. KEEP THE TENSION OF THE ROPE OVER THE PULLEY (INTERNAL GEAR PULLEY) SO THAT IT JUST DOSE NOT ROTATE)
4. NOW, HOLD THE CARRIER PULLEY AND LET INTERNAL GEAR PULLEY TO ROTATE.
REPEAT THE SAME PROCEDURE FOR DIFFERENT TORQUES AND COMPLETE THE OBSERVATION TABLE.
CALCULATIONS
LET US CALOCULATE THE SPEED RATIO, USING TABULAR METHOD.
ASSUME PLANET CARRIER ‘C’ LOCKED AND SUN GEAR GIVEN ONE REVOLUTION.
S. NO.
|
OPERATION
|
PLANET CARRIER
C
|
SUN GEAR S 14
|
PLANET
GEAR
P 21
|
INTERNAL GEAR
I 156
|
01.
|
PLANET CARRIER LOCKED SUN GEAR GIVEN 1 ROTATION
|
0
|
+1
|
-TS
---------
TP
|
-TS TP -TS
--- --- = -----
TP T1 T1
|
02.
|
MULTIPLY BY ‘X’
|
0
|
X
|
-TS
--------- X
TP
|
-TS
-------- X
T1
|
03.
|
ADD ‘Y’ TO ALL COLUMNS
|
0
|
Y + X
|
Y -(TS/TP)
X
|
Y - (TS/T1) X
|
1. CONDITION 1 ( PLANET CARRIER LOCKED )
IN THIS CONDITION, INTERNAL GEAR MAKES [ -(TS T1) X ] REVOLUTIONS OF SUN GEAR.
HENCE, ANGULAR VELOCITY RATIO.
NS WS X T1
---- = ---- = ---------- = ----
N1 W1 (-TS/T1) X TS
-T1 56
= ---- = -------- = -4
TS 14
HENCE, INTERNAL GEAR MAKES ONE REVOLUTION FOR 4 REVOLUTIONS OF SUN GEAR. THE NEGATIVE SIGN INDICATES THAT BOTH THE GEARS REVOLUTION IN REVERSE DIRECTION.
2. CONDITION-2 (INTERNAL GEAR LOCKED)
IN THIS CONNECTION, LET US TAKE ONE REVOLUTION OF PLANET CARRIER.
.: Y=1 & Y -TS/T1 X=0
.: Y = TS/T1
PUTTING THE VALUE OF ‘Y’
TS/T1 X=1
.:X=T1/14 = 56/ =4
ALSO, PLANET CARRIER MAKES ‘Y’ REVOLUTIONS FOR (Y+X) REVOLUTIONS OF SUN GEAR.
HENCE, ANGULAR VELOCITY RATIO.
NS/NC= WS/WC= Y+X/Y
WHERE ‘NS’ AND ‘NC’ ARE THE SPEEDS OF SUN AND PLANET CARRIER RESPECTIVELY.
=4+1/1 =5 3. TORQUE
LET, TS = INPUT TORQUE
TC = TORQUE ON PLANET CARRIER
T1 = TORQUE ON INTERNAL GEAR
IF FRICTION IS NEGLECTED.
INPUT POWER = OUTPUT POWER.
.: TSWS +TCWC + TIWI = 0
EITHER WC OR WI WILL BE ZERO
HENCE3, TS.WS = TC.WC (OR TI.WI)
4. WITH THE CALIBRATION CHART OF MOTOR, FIND OUT TORQUE AT THE CURRENT READING.
TS.
(a) TORQUE ON THE PLANET CARRIED
TC = [0.05+0.012/2]X 9.81XS.B.
DIFFERENCE
(b)TORQUE ON INTERNAL GEAR
TI = [0.120+0.022/2]X9.81XS.B.
DIFFERENCE
.: TC = TS + TI
PRECAUTIONS:
1. DO NOT LOAD THE MOTOR ABOVE 1.9AMP. CURRENT
2. BEFORE STARTING THE EXPERIMENT , PUT SOME LUBRICATING OIL TO GEARS & BEARINGS
3. OPERATE ALL THE SWITCHES AND CONTROLS GENT.
EXPERIMENT - 5
AIM:-TO PERFORM EXPERIMENT ON WATT AND PORTER GOVERNORS TO PREPARE PERFORMANCE CHARACTERISTIC CURVES, AND TO FIND STABILITY & SENSITIVITY.
APPARATUS USED: - WATT AND PORTER GOVERNORS.
INTRODUCTION & THEORY: - THE FUNCTION OF A GOVERNOR IS TO REGULATE THE MEAN SPEED OF AN ENGINE, WHEN THERE ARE VARIATIONS IN THE LOAD E.G. WHEN THE LOAD ON AN ENGINE INCREASES, ITS SPEED DECREASES, THEREFORE IT BECOMES NECESSARY TO INCREASE THE SUPPLY OF WORKING FLUID. WHEN THE LOAD ON THE ENGINE DECREASES, ITS SPEED INCREASES AND THUS LESS WORKING FLUID IS REQUIRED. THE GOVERNOR AUTOMATICALLY CONTROLS THE SUPPLY OF WORKING FLUID TO THE ENGINE WITH THE VARYING LOAD CONDITIONS AND KEEPS THE MEAN SPEED WITHIN CERTAIN LIMITS.
THE GOVERNORS MAY, BROADLY, BE CLASSIFIED AS
- CENTRIFUGAL GOVERNOR
- INERTIA GOVERNOR
THE CENTRIFUGAL GOVERNORS MAY FURTHER BE CLASSIFIED AS FOLLOWS:
1. PENDULUM TYPE (WATT GOVERNOR)
2. LOADED TYPE
(I) DEAD WEIGHT GOVERNOR (PORTER GOVERNOR AND PROELL GOVERNOR)
(II) SPRING CONTROLLED GOVERNORS (HARTNELL GOVERNOR, HARTUNG GOVERNOR, WILSON-HARTNELL GOVERNOR AND PICKERING GOVERNOR).
WATT GOVERNOR: - THE SIMPLEST FORM OF A CENTRIFUGAL GOVERNOR IS A WATT GOVERNOR. IT IS BASICALLY A CONICAL PENDULUM WITH LINKS ATTACHED TO A SLEEVE OF NEGLIGIBLE MASS. THE ARMS OF THE GOVERNOR MAY BE CONNECTED TO THE SPINDLE IN THE FOLLOWING THREE WAYS:
- THE PIVOT P MAY BE ON THE SPINDLE AXIS.
- THE PIVOT P MAY BE OFFSET FROM THE SPINDLE AXIS AND THE ARMS WHEN PRODUCED INTERSECT AT O.
- THE PIVOT P MAY BE OFFSET, BUT THE ARMS CROSSES THE AXIS AT O.
PORTER GOVERNOR: - THE PORTER GOVERNOR IS A MODIFICATION OF A WATT’S GOVERNOR, WITH CENTRAL LOAD ATTACHED TO THE SLEEVE. THE LOAD MOVES UP DOWN THE CENTRAL SPINDLE. THIS ADDITIONAL DOWNWARD FORCE INCREASES THE SPEED OF REVOLUTION REQUIRED TO ENABLE THE BALLS TO RISE TO ANY TO ANY PRE-DETERMINED LEVEL.
OBSERVATION :-
· MASS OF THE BALL (M) = ————-KG.
· WEIGHT OF THE BALL (W)=————NEWTONS
· HEIGHT OF THE GOVERNOR (H) = ——- METRES
· MINIMUM EQUILIBRIUM SPEED (N1) = —— R.P.M.
· MINIMUM EQUILIBRIUM SPEED (N2) = —— R.P.M.
· FRICTIONAL FORCE (F) = ————- NEWTONS
· MEAN EQUILIBRIUM SPEED (N) = (N1 + N2)/2 IN R.P.M
· MASS OF THE CENTRAL LOAD = ———KG.
· WEIGHT OF THE CENTRAL LOAD (W) = ——–N
· ANGLE OF INCLINATION OF THE ARM TO THE VERTICAL (Α ) = ——
· ANGLE OF INCLINATION OF THE LINK TO THE VERTICAL (Β ) = ——
CALCULATION:-
- N2 = 895/H (FOR WATT GOVERNOR)
- N2 = ((M + M (1+Q)/2)/M) X (895/H) (FOR PORTER GOVERNOR ), WHERE, Q = TAN Β/ TAN Α
- SENSITIVENESS OF THE GOVERNOR = 2(N1 – N2)/ N1 + N2 = 2 (Ω2 – Ω1)/ Ω2 + Ω1
- A GOVERNOR IS SAID TO BE STABLE WHEN FOR EVERY SPEED WITHIN THE WORKING RANGE THERE IS A DEFINITE CONFIGURATION I.E; THERE IS ONLY ONE RADIUS OF ROTATION OF THE GOVERNOR BALLS AT WHICH THE GOVERNOR IS IN EQUILIBRIUM. FOR A STABLE GOVERNOR, IF THE EQUILIBRIUM SPEED INCREASES, THE RADIUS OF GOVERNOR BALLS MUST ALSO INCREASE.
OBSERVATION TABLE
WATT GOVERNOR (WITHOUT WEIGHT)
LENGTH OF EACH LINK L=120MM
INITIAL HEIGHT OF GOVERNOR H0=110MM
INITIAL RADIUS OF ROTATION RO=135MM
WEIGHT OF SLEEVE W=1.8 KG
S.
NO.
|
SPEED‘N’
|
SLEEVE DISP.‘X’
|
HEIGHT H =H0-(X/2)
|
FINDα
COSα
=H/L
|
RADIUS OF ROTATION R = R0=L SINΑ
|
W=(2ΠN/T)
|
FORCE F =(W(W2XR))/G
| |
1
| ||||||||
2
| ||||||||
3
| ||||||||
UNIVERSAL GOVERNOR APPARATUS
PORTER GOVERNOR (WITH WEIGHT)
LENGTH OF EACH LINK L=120MM
INITIAL HEIGHT OF GOVERNOR H0=110MM
INITIAL RADIUS OF ROTATION RO=135MM
WEIGHT OF BALLS+ SLEEVE W=1+1.8 KG=2.8KG
S.NO.
|
SPEED‘N’
|
SLEEVE DISP.‘X’
|
HEIGHT H =H0-(X/2)
|
FINDΑ COSΑ=H/L
|
RADIUS OF ROTATION R=R0=L SINΑ
|
W=(2ΠN/T)
|
FORCE F =(W(W2XR))/G
|
1
| |||||||
2
| |||||||
3
|
UNIVERSAL GOVERNOR APPARATUS
HARTNELL GOVERNOR
LENGTH OF EACH LINK A=75MM
LENGTH OF EACH LINK B=155MM
INITIAL RADIUS OF ROTATION RO=160MM
WEIGHT OF SLEEVE W=1.8 KG
T = 60SEC
S.NO.
|
SPEED‘N’
|
SLEEVE DISP.‘X’
|
HEIGHT R = (RO+(A/B).X)/10
|
W=(2ΠN/T)
|
FORCE F = W.W2.R
|
1
| |||||
2
| |||||
3
|
UNIVERSAL GOVERNOR APPARATUS
PROELL GOVERNOR
LENGTH OF EACH LINK L=125MM
INITIAL HEIGHT OF GOVERNOR H0=100MM
INITIAL RADIUS OF ROTATION RO=135MM
WEIGHT OF BALLS W=0.5 KG
EXTENSION OF LENGTH BG= 75MM
S.NO.
|
SPEED‘N’
|
SLEEVE DISP.‘X’
|
HEIGHT H =H0-(X/2)
|
FINDΑ COSΑ=H/L
|
RADIUS OF ROTATION R=R0=L SINΑ
|
W=(2ΠN/T)
|
FORCE F =(W(W2XR))/G
|
1
| |||||||
2
| |||||||
3
|
PRECAUTIONS:-
- TAKE READING CAREFULLY.
- MEASURE THE ANGLE VERY CAREFULLY.
- MEASURE THE HEIGHT OF GOVERNOR CAREFULLY.
- SPEED OF GOVERNOR MEASURE ACCURATE.
EXPERIMENT - 6
OBJECTIVE: TO FIND CORIOLLIS COMPONENT OF ACCELERATION AND VERIFY THE RESULT.
THEORY: IF A POINT IS MOVING ALONG A LINE, WITH THE LINE HAVING ROTATIONAL MOTION THE ABSOLUTE ACCELERATION OF THE POINT IS VECTOR SUM OF –Ω
1) ABSOLUTE ACCELERATION OF COINCIDENT POINT OVER THE LINK RELATIVE TO FIXED CENTRE.
2) ACCELERATION OF POINT UNDER CONSIDERATION RELATIVE TOP COINCIDENT POINT AND
3) THE THIRD COMPONENT CALLED CORIOLLIS COMPONENT OF ACCELERATION.
CONSIDER THE MOTION OF SLIDER ‘B’ ON THE CRANK OA.LET OA ROTATE WITH CONSTANT ANGULAR VELOCITY OF Ω RAD/SEC AND SLIDER B HAVE A RADIAL OUTWARD VELOCITY V M/SEC RELATIVE TO CRANK CENTRE ‘O’.
IN THE VELOCITY DIAGRAM OA REPRESENT TANGENTIAL VELOCITY SLIDER AT CRANK POSITION OA, AND AB REPRESENT RADIAL VELOCITY OF SLIDER AT SAME CRANK POSITION .OA IS THE TANGENTIAL VELOCITY OF SLIDER AT CRANK POSITION OA AND AB REPRESENT RADIAL VELOCITY OF SLIDER AT SAME POSITION.
HENCE BB’ REPRESENT THE RESULTANT CHANGE OF VELOCITY OF SLIDER.THIS VELOCITY HAS TWO COMPONENT B’T AND BT IN TANGENTIAL AND RADIAL DIRECTIONS RESPECTIVELY.
NOW, THE TANGENTIAL COMPONENT, B’T
=B’S+ST
=VSINDѲ +(Ω(R+DR)-ΩR)
=VDѲ+ΩDR
THERE FORE RATE OF CHANGE OF TANGENTIAL VELOCITY
=VDѲ/DT + ΩDR/DT
=VΩ+ΩV
=2VΩ
EQUATIN REPRESENT CORIOLLIS COMPONENT OF ACCELERATION .THIS ACCELERATION IS MADE UP OF TWO COMPONENTS, ONE DUE TO INCREASE IN RADIUS AND OTHER FROM CHANGE IN DIRECTION OF CRANK.
HYDRAULIC ANALOGY
CONSIDER A SHORT COLUMN OF FLUID OF LENGTH DR AT RADIUS R FROM AXIS OF ROTATION OF THE TUBE.THEN IF VELOCITY OF FLUID RELATIVE TO TUBE IS V AND ANGULAR VELOCITY OF TUBE ISΩ THEN CORIOLLIS COMPONENT OF ACCELERATION IS 2V Ω IN A DIRECTION PERPENDICULAR TO ROTATION OF TUBE.THE TORQUE DT APPLIED BY THE TUBE TO PRODUCE THIS ACCELERATION IS THEN
DT=DW.2VΩR/G
WHERE DW IS WEIGHT OF SHORT COLUMN OF FLUID.
IF W BE THE SPECIFIC WEIGHT OF FLUID AND A IS CROSSECTIONAL AREA OF TUBE, THEN
DW=WADR
DT=WADR/G=2VRΩ
AND TOTAL TORQUE APPLIED TO COLUMN OF LENGTH L.
T=2WL\G.VΩ.A.R.DR
T=W\G.2ΩV.A.L
THEREFORE, CORIOLLI’S COMPONENT OF ACCELERATION.
CA= 2GT\2WAL
THE APPARATUS:
T HE APPARATUS USES HYDRAULIC ANALOGY TO DETERMINE CORIOLLI’S COMPONENT OF ACCELERATION.
THE APPARATUS CONSIST OF TWO BRASS TUBES CONNECTED TO A CENTRAL ROTOR DISTRIBUTOR. THE
DISTRIBUTOR IS ROTATED BY A VARIABLE SPEED D.C MOTOR. WATER IS SUPPLIED TO A DISTRIBUTOR BY A PUMP THROUGH. WHEN TUBES ARE ROTATING WITH FLOWING THROUGH TUBES WITH VARIOUS EASUREMENTS PROVIDED, CORIOLLI’S COMPONENT CAN BE DETERMINED EXPERIMENTELY AND THEORETICAAY.
PROCEDURE
FILL- UP SUFFICIENT WATER IN TANK. ROTATE THE COUPLING TO ENSURE FREE ROTATION. CHECK NUT BOLTS FOR TIGHTENING. START THE MOTOR AND SET THE SPEED AS REQUIRED, E.G SAY 150 RPM. MEASURE THE TORQUE REQUIRED FOR FREE ROTATION OF TUBES AT THAT SPEED.
NOW START THE PUMP AND ADJUST THE FLOW RATE WITH HELP OF BY- PASS VALVE, SO THAT WATER DOES NOT OVERFLOW THROUGH CENTRAL GLASS TUBE AND ALSO PIPES RUN FULL OF WATER. NOW ADJUST THE SPEED TO PREVIOUS
VALUE AND MEASURE THE TORQUE. NOTE DOWN WATER FLOW RATE. REPEAT THE PROCEDURE AT DIFFERENT SPEEDS.
OBSERVATION TABLE
DIAMETER OF FLOW TUBE=6MM =0.006M
ARM LENGTH =200MM=0.2M
G=9.81KG/M2
W=DENSITY OF WATER =1000KG/M2
EXPERIMENT - 7
AIM: TO STUDY THE AUTOMATIC TRANSMISSION UNIT
GEAR BOX OR TRANSMISSION
‘TRANSMISSION’ WORD IS GENERALLY USED FOR GEAR BOX. TRANSMISSION IS A MECHANISM WHICH PROVIDES US VARIATION IN SPEED AND TORQUE AS REQUIRED. THE TRANSMISSION MAY BE MANUAL OR AUTOMATIC.
FUNCTIONS OF GEAR BOX OR TRANSMISSION
1) A LOT OF VARIATION IN TORQUE IS REQUIRED AT ROAD WHEEL OF A VEHICLE. A GEAR BOX SERVES THIS PURPOSE. IT PROVIDES HIGH TORQUE AT STARTING AND HIGH SPEED WHILE RUNNING.
2) GEAR BOX ALSO PROVIDES MEANS TO REVERSE THE DIRECTION OF THE VEHICLE.
3) IT PROVIDES A NEUTRAL POSITION, THE POSITION AT WHICH THE POWER FLOW TO ROAD WHEELS IS DISCONNECTED.
NECESSITY OF TRANSMISSION
THERE ARE MANY RESISTANCES FACED BY VEHICLE WHILE RUNNING. ALSO WHEN VEHICLE IS ON THE VERGE TO MOVE, THERE ARE ALSO RESISTANCES WHICH OPPOSE ITS MOVEMENT. TO OVERCOME THESE RESISTANCES, TRANSMISSION IS A MECHANISM WHICH IS NECESSARY TO BE USED.
THE FOLLOWING RESISTANCE ARE FACED BY THE VEHICLE:
- ROLLING RESISTANCE
IT IS OBSERVED THAT MORE FORCE IS REQUIRED TO MOVE A STATIONARY VEHICLE AND ONCE IT STARTS MOVING OR ROLLING, THE FORCE REQUIRED TO KEEP IT MOVING IS LESSER. THE RESISTANCE, WHICH COMES INTO PLAY HERE, IS CALLED ROLLING RESISTANCE. IT DEPENDS UPON THE FOLLOWING FACTORS:
a) CONDITION OF ROAD
b) CONDITION OF TYRES
c) TYRE INFLATION
d) VEHICLE LOAD INCLUDING CARRIAGE
e) TYPE OF TYRES
- AIR RESISTANCE
WHEN THE VEHICLE IS STATIONARY, IT FACES THE RESISTANCE OF BLOWING AIR ONLY. TO START MOVING, IT HAS TO OVERCOME THIS RESISTANCE. BUT WHEN THE VEHICLE IS MOVING, THE AIR RESISTANCE INCREASES, BECAUSE VELOCITY OF AIR STRIKING THE VEHICLE IS INCREASED. THIS RESISTANCE IS PROPORTIONAL TO THE SQUARE OF THE VELOCITY OF THE AIR. SO, IF THE AIR VELOCITY IS DOUBLED, THE AIR RESISTANCE INCREASES FOUR TIMES. TO LESSEN THIS RESISTANCE, THE VEHICLE’S FRONT BODY SHAPE IS MADE STREAMLINED.
- GRADIENT RESISTANCE
THIS RESISTANCE IS DUE TO THE INCLINATION OF THE ROAD TO HORIZON. WHEN CLIMBING UP, THE VEHICLE FACES MORE RESISTANCES THAN DOWN-HILL MOVEMENT.
- TRACTIVE EFFORT
THE SUM OF ALL THE ABOVE THREE RESISTANCES IS CALLED TOTAL RESISTANCE OR TRACTIVE RESISTANCE.
TRACTIVE RESISTANCE = ROLLING RESISTANCE + AIR RESISTANCE + GRADIENT RESISTANCE.
TRACTIVE EFFORT IS THE DRIVING FORCE REQUIRED TO PROPEL THE VEHICLE I.E. TO OVERCOME THE TRACTIVE RESISTANCE. THIS EFFORT VARIES ACCORDING TO THE DRIVING CONDITIONS. TO MOVE A VEHICLE FROM STATIONARY OR CLIMBING A HILL, HIGH ENGINE SPEED IS REQUIRED. BUT THE ENGINE SPEED HAS ITS LIMITATIONS. SO A LOW GEAR HELPS TO MOVE A VEHICLE. THUS A GEAR BOX IS NECESSARY FOR A VEHICLE.
SELECTIVE TYPE GEAR BOX
IN THIS TYPE, ANY GEAR MAY SHIFTED FROM NEUTRAL POSITION AND EVERYTIME WHILE SHIFTING THE GEAR, WE HAVE TO GO TO NEUTRAL POSITION FIRST AND THEN TO THE OTHER GEAR POSITION.
SLIDING MESH GEAR BOX
CONSTRUCTION
THIS TYPE OF GEAR BOX IS SHOWN IN FIG.1. BY A SIMPLE DIAGRAM IN NEUTRAL POSITION. THERE IS A GEAR CALLED CLUTCH GEAR WHICH IS MOUNTED ON THE CLUTCH SHAFT. THIS GEAR BOX SHAFT IS ATTACHED TO THE CLUTCH. THE CLUTCH GEAR A IS ALWAYS MESHED WITH LAY SHAFT GEAR D. THE LAY SHAFT GEAR IS MOUNTED ON A SHAFT WHICH IS CALLED LAY SHAFT.
THERE ARE THREE OTHER GEARS E, F AND G, FIXED ON THE LAY SHAFT. THERE IS ALSO AN IDLE SHAFT ON WHICH A SMALL IDLE GEAR ‘H’ IS MOUNTED. THIS IDLE GEAR IS USED FOR REVERSING THE DIRECTION. THERE IS A MAIN SHAFTB WHICH IS ALIGNED TO THE CLUTCH SHAFT. TWO GEARS ‘B’ AND ‘C’ ARE MOUNTED ON THE MAIN SHAFT SUCH THAT THEY CAN SLIDE ON THE SHAFT.
WORKING
FIG. 1 SHOWS A SLIDING MESH GEAR BOX IS NEUTRAL POSITION. THE GEAR ‘A’ IS ALWAYS ROTATING WHEN THE CLUTCH IS ENGAGED. THE GEARS ‘D’ ‘E’ ‘F’ ‘G’ AND ‘H’ ALSO ROTATE WITH GEAR ‘A’. NEITHER GEAR ‘B’, NOR GEAR ‘C’ IS MESHED WITH ANY OF THE GEAR OF THE SHAFT.
SO NO POWER IS TRANSMITTED TO MAIN SHAFT. IN THIS POSITION THE GEAR BOX IS IN NEUTRAL POSITION.
FIRST GEAR: TO POSITION THE GEAR BOX IN FIRST GEAR (FIG.2.) THE GEAR C IS SLIDED ON THE MAIN SHAFT SUCH THAT IT IS MESHED WITH GEAR F. NOW THE MAIN SHAFT STARTS ROTATING. THE POWER IS TRANSMITTED FROM CLUTCH SHAFT THROUGH GEARS A,D,F AND C TO THE MAIN SHAFT.
SECOND GEAR: TO POSITION THE GEAR BOX IN SECOND GEAR. (FIG.3), THE GEAR B IS SLIDED ON THE MAIN SHAFT SUCH THAT IT IS MESHED WITH GEAR E. NOW THE POWER IS TRANSMITTED FROM CLUTCH SHAFT THROUGH GEARS A,D,E AND B TO THE MAIN SHAFT.
HIGH GEAR OR TOP GEAR: TO POSITION THE GEAR BOX IN HIGH GEAR (FIG.4), THE GEAR B IS SLIDED ON THE MAIN SHAFT SUCH THAT IT IS DIRECTLY ENGAGED TO GEAR THROUGH SPLINES. SO THE POWER IS TRANSMITTED TO MAIN SHAFT WITHOUT ANY REDUCTION.
REVERSE GEAR: TO POSITION THE GEAR BOX IN REVERSE GEAR (FIG.5), THE GEAR C IS SLIDED ON THE MAIN SHAFT SUCH THAT IT IS MESHED WITH THE IDLE GEAR H. BY DOING THIS THE GEAR H REVERSE THE DIRECTION OF ROTATION OF MAIN SHAFT. IN THIS POSITION POWER IS TRANSMITTED FROM CLUTCH SHAFT THROUGH GEARS A, D, G, H AND C TO THE MAIN SHAFT.
EXPERIMENT - 8
AIM: TO STUDY AND PREPARE REPOT ON THE CONSTRUCTIONAL DETAILS, WORKING PRINCIPLES AND OPERATION OF AUTOMOTIVE BRAKE SYSTEMS.
A) HYDRAULIC AND PNEUMATIC BRAKE SYSTEMS
B) DRUM BRAKE SYSTEM
C) DISC BRAKE SYSTEM
THEORY
LABELLED DIAGRAM, CONSTRUCTIONAL DETAILS, WORKING PRINCIPLE AND OPERATION OF THE ABOVE STEERING SYSTEMS.
PRINCIPLE
IT GOES WITHOUT SAYING THAT BRAKES ARE ONE OF THE MOST IMPORTANT CONTROL COMPONENTS OF VEHICLE. THEY ARE REQUIRED TO STOP THE VEHICLE WITHIN THE SMALLEST POSSIBLE DISTANCE AND THIS IS DONE BY CONVERTING THE KINETIC ENERGY OF THE VEHICLE INTO THE HEAT ENERGY WHICH IS DISSIPATED INTO THE ATMOSPHERE.
BRAKING REQUIREMENTS
1 THE BRAKES MUST BE STRONG ENOUGH TO STOP THE VEHICLE WITHIN A MINIMUM DISTANCE IN AN EMERGENCY. BUT THIS SHOULD ALSO BE CONSISTENT WITH SAFETY. THE DRIVER MUST HAVE PROPER CONTROL OVER THE VEHICLE DURING EMERGENCY BRAKING AND THE VEHICLE MUST NOT SKID.
2 THE BRAKES MUST HAVE GOOD ANTIFADE CHARACTERISTICS I.E. THEIR EFFECTIVENESS SHOULD NOT DECREASE WITH CONSTANT PROLONGED APPLICATION E.G. WHILE DESCENDING HILLS. THIS REQUIREMENT DEMANDS THAT THE COOLING OF THE BRAKES SHOULD BE VERY EFFICIENT.
HYDRAULIC BRAKES
MOST OF THE CARS TODAY USE HYDRAULICALLY OPERATED FOOT BRAKES ON ALL THE FOUR WHEELS WITH AN ADDITIONAL HAND BRAKE MECHANICALLY OPERATED ON THE REAR WHEELS. AN OUTLINE OF THE HYDRAULIC BRAKING SYSTEM IS SHOWN IN FIG. THE MAIN COMPONENT IN THIS IS THE MASTER CYLINDER WHICH CONTAINS RESERVOIR FOR THE BRAKE FLUID. MASTER CYLINDER IS OPERATED BY THE BRAKE PEDAL AND IS FURTHER CONNECTED TO THE WHEEL CYLINDERS IN EACH WHEEL THROUGH STEEL PIPE LINES, UNIONS AND FLEXIBLE HOSES. IN CASE OF HINDUSTAN AMBASSADOR CAR, ON FRONT WHEELS EACH BRAKE SHOE IS OPERATED BY SEPARATE WHEEL CYLINDER (THUS MAKING THE BRAKE TWO SHOE LEADING) WHEREAS IN CASE OF REAR WHEELS THERE IS ONLY ONE CYLINDER ON EACH WHEEL WHICH OPERATES BOTH THE SHOES (THUS GIVING ONE LEADING AND ONE TRAINING SHOE BRAKES.) AS THE REAR WHEEL CYLINDERS ARE ALSO OPERATED MECHANICALLY WITH THE HAND BRAKE, THEY ARE MADE FLOATING. FURTHER, ALL THE SHOES IN THE AMBASSADOR CAR ARE OF THE FLOATING ANCHOR TYPE.
THE SYSTEM IS SO DESIGNED THAT EVEN WHEN THE BRAKES ARE IN THE RELEASED POSITION, A SMALL PRESSURE OF ABOUT 50 KPA IS MAINTAINED IN THE PIPE LINES TO ENSURE THAT THE CUPS OF THE WHEEL CYLINDER ARE KEPT EXPANDED. THIS PREVENTS THE AIR FROM ENTERING THE WHEEL CYLINDERS WHEN THE BRAKES ARE RELEASED. BESIDES, THIS PRESSURE ALSO SERVES THE FOLLOWING PURPOSES.
(I) IT KEEPS THE FREE TRAVEL OF THE PEDAL MINIMUM BY OPPOSING THE BRAKE SHOE RETRACTION SPRINGS.
(II) DURING BLEEDING, IT DOES NOT ALLOW THE FLUID PUMPED INTO THE LINE TO RETURN, THUS QUICKLY PURGING AIR FROM THE SYSTEM.
DRUM BRAKES
IN THIS TYPE OF BRAKES, A BRAKE DRUM IS ATTACHED CONCENTRIC TO THE AXLE HUB WHEREAS ON THE AXLE CASING IS MOUNTED A BACK PLATE. IN CASE OF FRONT AXLE, THE BACK PLATE IS BOLTED TO THE STEERING KNUCKLE. THE BACK PLATE IS MADE OF PRESSED STEEL SHEET AND IS RIBED TO INCREASE RIGIDITY AND TO PROVIDE SUPPORT FOR THE EXPANDER, ANCHOR AND BRAKE SHOES. IT ALSO PROTECTS THE DRUM AND SHOE ASSEMBLY FROM MUD AND DUST. MOREOVER, IT ABSORBS THE COMPLETE TORQUE REACTION OF THE SHOES DUE TO WHICH REASON IT IS SOMETIMES ALSO CALLED TORQUE PLATE. TWO BRAKE SHOES ARE ANCHORED ON THE BACK PLATE AS SHOWN IN FIG. FRICTION LININGS ARE MOUNTED ON THE BRAKE SHOES. ONE OR TWO RETRACTOR SPRINGS ARE USED WHICH SERVE TO KEEP THE BRAKE SHOES AWAY FROM THE DRUM WHEN THE BRAKES ARE
NOT APPLIED. THE BRAKE SHOES ARE ANCHORED AT ONE END, WHEREAS ON THE OTHER ENDS FORCE F IS APPLIED BY MEANS OF SOME BRAKE ACTUATING MECHANISM WHICH FORCES THE BRAKE SHOE AGAINST THE REVOLVING DRUM, THEREBY APPLYING THE BRAKES. AN ADJUSTER IS ALSO PROVIDED TO COMPENSATE FOR WEAR OF FRICTION LINING WITH USE. THE RELATIVE BRAKING TORQUE OBTAINED AT THE SHOES FOR THE SAME FORCE APPLIED AT THE PEDAL VARIES DEPENDING UPON WHETHER THE EXPANDER (CAM OR TOGGLE LEVER) IS FIXED TO THE BACK PLATE OR IT IS FLOATING, WHETHER THE ANCHOR IS FIXED OR FLOATING AND WHETHER THE SHOES ARE LEADING OR TRAILING.
DISC BRAKES
AS SHOWN IN FIG. A DISC BRAKE CONSISTS OF A CAST IRON DISC BOLTED TO THE WHEEL HUB AND A STATIONARY HOUSING CALLED CALIPER. THE CALIPER IS CONNECTED TO SOME STATIONARY PART OF THE VEHICLE, LIKE THE AXLE CASING OR THE SUB AXLE AND IS CAST IN TWO PARTS, EACH PART CONTAINING A PISTON. IN BETWEEN EACH PISTON AND DISC, THERE IS FRICTION PAD HELD IN POSITION BY RETAINING PINS, SPRING PLATES ETC. PASSAGES ARE DRILLED IN THE CALIPER FOR THE FLUID TO ENTER OR LEAVE EACH HOUSING. THESE PASSAGES ARE ALSO CONNECTED TO ANOTHER ONE FOR BLEEDING. EACH CYLINDER AND CONTAINS A RUBBER SEALING RING BETWEEN THE CYLINDER AND THE PISTON.
WHEN THE BRAKES ARE APPLIED, HYDRAULICALLY ACTUATED PISTONS MOVE THE FRICTION PADS INTO CONTACT WITH THE DISC, APPLYING EQUAL AND OPPOSITE FORCES ON THE LATER. ON RELEASING THE BRAKES, THE RUBBER SEALING RINGS ACT AS RETURN SPRINGS AND RETRACT THE PISTONS AND THE FRICTION PADS AWAY FROM THE DISC.
FOR A BRAKE OF THIS TYPE
T = 2µPAR
WHERE
µ = COEFFICIENT OF FRICTION
P = FLUID PRESSURE
A = CROSS SECTIONAL AREA OF ONE PISTON
R = DISTANCE OF THE LONGITUDINAL AXIS OF THE PISTON FROM THE WHEEL AXIS
BRAKE SYSTEM FOR MARUTI (SUZUKI) 800 CAR
THE FRONT WHEEL BRAKES ARE OF THE DISC TYPE, WHEREAS FOR REAR WHEELS DRUM TYPE BRAKES (LEADING TRAILING SHOES) ARE EMPLOYED. PARKING BRAKE IS MECHANICALLY OPERATED BY A WIRE AND LINK SYSTEM AND WORKS ON THE REAR WHEELS ONLY. SAME BRAKE SHOES ARE USED FOR SERVICE AND PARKING BRAKES. THE LAYOUT OF THE SYSTEM IS SHOWN IN FIG.
A TANDEM MASTER CYLINDER IS EMPLOYED. THE HYDRAULIC PRESSURE PRODUCED THERE IS APPLIED TO TWO INDEPENDENT CIRCUITS. ONE CIRCUIT IS FOR FRONT LEFT AND REAR RIGHT BRAKES, WHEREAS THE OTHER IS FOR FRONT RIGHT AND REAR LEFT BRAKES. DUE TO THIS REASON, THE BRAKING SYSTEM IN THE MARUTI HAS GREATER SAFETY BECAUSE EVEN IF A PRESSURE LEAK OCCURS IN THE BRAKE LINE OF ONE CIRCUIT, THE OTHER BRAKING CIRCUIT WORKS, DUE TO WHICH A CERTAIN DEGREE OF BRAKING IS STILL AVAILABLE TO THE VEHICLE.
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