Design and Analysis of Globoidal Cam Index Drive

International Journal of Scientific Research Engineering & Technology (IJSRET)Volume 2 Issue3 pp 163-168 June2013 www.ijsret.org ISSN 2278 – 0882

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Design and Analysis of Globoidal Cam Index DriveSuresh Sanap1, Ketan Jagtap2 and Keshav Nandurkar3

1-2 Government Polytechnic, NashikE Mail: [email protected] and [email protected]

3K.K.W.I. E. E. & R NashikE Mail: [email protected]

ABSTRACTIn Globoidal cam mechanism, index motion issmooth and they are specially designed tominimise vibrations. A globoidal cam withcylindrical rollers radially mounted at its turret isone of the mechanisms employed for angularindexing motion control. As operating speed ishigh, there should be finite and low value ofjerk. Present paper focuses the different motioncurves. After studying the two different casesregarding the same input values of inputparameters, peak output torque and jerk aredetermined. The results were discussed aftercomparing with the graphs obtained from thecentesimal scales. Finally appropriate motioncurves are suggested for the given applications.

Keywords - Cam Indexer, Globoidal Cam,Modified Constant Velocity Curve, ModifiedSine Curve, Modified Trapezoid curve, Surfacebased modelling

1. INTRODUCTIONCompare to other cam-follower mechanisms, thestructure of globoidal cam follower mechanismsare relatively compact. These mechanisms alsohave some special features such as: high loadingcapacity, low noise, low vibration, and highreliability. Hence globoidal cams have widelybeen used in various automatic equipments inindustry. Typical usages of globoidal cammechanisms are in machine tools, automaticassembly lines, paper processing machines,packing machines, and many other automatedmanufacturing devices. In selecting a globoidalcam-turret device for a specific application,generally the parameters for its index time and

Fig. 1 Cam Indexer for intermittent action

inertial moments of work pieces with its tableloaded at the output shaft must first be specified.Then, the required total output torque containingthe inertia torque, the friction torque, and thework torque can be calculated. To meet the totalrequired output torque, the cam shaft torque atthe demanded rotational speed should beestimated based on the number of dwells of acomplete circle at the output shaft, index period,dimensional parameters, and the selected orsynthesized turret motion. In addition, to ensurea proper design for such a cam-turretmechanism, the cam profile has to bedetermined so that its pressure angles, surfacecurvatures, contact stresses, and load–life can becharacterized. As a result, a motor and itsreducer with an appropriate rotational speed andtorque can be decided to satisfy the totalrequired output torque of a globoidal cam-turretdevice. For driving the output shaft andsatisfying the required output torque, the neededgloboidal cam shaft torque is transmitted to itsturret through the direct contact between the cam


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and its engaged cylindrical rollers. During anindexing period, it is clear that the cylindricalrollers mounted at the turret must bear the inputtorque and the contact stress with the cam. Fig. 1shows schematic diagram of Cam Indexer forintermittent action.

Ching Huan Tseng et al. (1999) investigatednew concept of introducing pairs of rollersinstead of single roller in adjacent cam ribs.They claimed increased accuracy and stability,reduced contact stresses and improvement inpreload. In their patent they claimed improvedarrangement and geometry design of globoidalcam index mechanism. Fu Yang Ming et al.(2000) designed the contour surface of thegloboidal cam with the aid of computer. Hewrote a program in Visual BASIC Language.The program adopts the form of person-computer dialogue. He also prepared optimummathematical model of the cam with minimumvolume. He also discussed the problem ofpressure angle of the globoidal cam mechanismin detail and put forward a new concept ofequivalent pressure angle. Jie Shing Lo et al.(2001) studied bearing contact of roller gearcams which is useful to understand contactnature, and contact stresses of the roller gearcam, which are considered as design indices forperformance consideration and especially forlubrication of cam. Vu-Thinh Nguyen et al.(2007) described synthesis method of designingflexible cam profiles by using smoothing splinecurves. He presented a very flexible cam profilesynthesis method that uses smoothing splinecurves. The proposed method can control thedisplacement, velocity and acceleration of a camprofile simultaneously. Inherent characteristicsof the smoothing spline curve guarantee thesmoothness of the designed cam profile. Thenumerical results for the simulated dynamicresponse histograms of the high speed operatingGC system are in good agreement with theexperimentally measured by Huang et al. (2007).Tuong et al. (2008) described a computer-aideddesign for design of the concave globoidal camwith cylindrical rollers and swinging follower.Four models with different modeling methodswere made from the same input data. The inputdata was angular input and output displacements

of the cam and the follower and some othergeometrical parameters of the globoidal cammechanism. Tuong et al. (2009) proposed someimportant tasks which are necessary in themodeling procedure of globoidal cams. Thesetasks are modeling and virtual animation of thegloboidal cam mechanism for checkinginterference between components of the system.The correlation between the dynamic responseof a globoidal cam (GC) system and the motordriving speed is investigated numerically andexperimentally investigated J H Kuang et al.(2010).

2. METHODOLOGY ANDDEVELOPMENT

There are applications in which the motion of amechanism is dictated by a special function ithas to perform or by the motion of an associatedmechanism. If cam is used to move a drillforward at a constant feed rate the shape of thecam must be designed with the regard togeometry of the follower and transmission toprovide a constant velocity. Those sections ofsuch cam which are governed purely by dynamicconsiderations (accelerations and deceleration)require the selection of suitable law. There areapplications which are the majority requiringsimply moving a mass of mechanism from oneposition to another in a certain time. If the speedof operation is very slow it matters little whichmotion law is chosen. However, for high speedsefficient performance is essential to select adynamically suitable cam motion law.

2.1 Motion Laws (Motion Curves)

The output motion is a normalized function ofthe input rotation. Mathematical expressions toproduce suitable follower motions are known ascam laws. There are well-known laws used forcam motions, all of which has virtues and vices.The problem is to decide which law is bestsuited for a particular application, or which lawcan be used as a standard for a wide variety ofapplications in different machines withoutdeparting vary from ideal. In the design of agloboidal cam-turret mechanism, the desiredturret motion of its roller-follower must be welldefined. Motion curves for index drives provide


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superior velocity, acceleration and inputcharacteristics. The acceleration and inputcharacteristics greatly affect the accuracy andlife of index drives. Improvement of thesecharacteristics is necessary for high-speed andhigh-accuracy index drives. Three motioncurves considered for the study which are as perindustry standards are,

Modified Constant Velocity (MCV) Modified Trapezoid (MT) Modified Sine (MS)In case of globoidal cam, the relationship

between input and output motion is expressed bytwo rotary motions.

Modified Constant Velocity Curve (MCV)The constant velocity curve has a straight linedisplacement at a constant slope. It also has thesmallest cam for a given rise and provides a longstroke action. The cycloidal curve or paraboliccurves have been utilized depending on the camspeed, mass of the follower, and work performedby the machine. To obtain a lower peak figure ofvelocity, the peak of the velocity curve shouldbe flattened. This is to provide the constantvelocity period with acceleration of zero.

Modified Sine Curve (MSC)The modified sine curve is a combination ofquarter sine wave curves. In terms of itstorsional action, the change from positive tonegative torque occurs in over 40 percent of thetravel time. This attribute makes this curveattractive as a choice in moving large massessuch as indexing intermittent turrets. Its lowertorque and power demand make the modifiedsine curve one of the best choices of curves.

Modified Trapezoid Curve (MTC)A trapezoidal acceleration curve is composed ofa parabolic motion combined with the cycloidalcurve. This combination reduces the maximumacceleration at the expense of somewhat higherjerk values. The modified trapezoidal curve ispopular in industry. However, it has oneobjectionable characteristic: the torque goesfrom positive maximum to negative maximumin 20 percent of the travel time. If dynamic

TABLE IINPUT DATA FOR TWO DIFFERENT CASES

Sr.No. Data Symbol Unit Case

ICaseII

1ApplicationType

- -StartStop

StartStop

2Cam IndexPeriod

degree 270 270

3Weight ofthe dialplate,

Wd kg 40 225

4Diameterof dialplate

D m 0.95 1.2

5Total Wt.of workstation

Ws kg 35 200

6Radius ofwork circle

Rs m 0.34 0.55

7No. ofstations

S - 4 4

8 Index time sec 1.61 2.87

forces represent a significant part of the load onthe cam, this sudden release of energy may bedetrimental to the cam-follower systemperformance and limit the operating speeds.Much better torque characteristics can beobtained with the modified sine curve.

With indexing motion, unlike constant speedmotion, the moving parts have to be acceleratedfrom rest to a maximum velocity and deceleratedto rest again once every indexing cycle. Toaccelerate the mass a torque is exerted by themechanism to overcome the inertia of the load.This torque is the function of the indexing speed,the cam motion law and the mass and size of theindexed parts. Inertia torque is as determined forthe given input parameters. For comparisonapplications where cam index period andnumber of stations are same are selected. Table Ishows the values of input parameters for Case Iand Case II.


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3. RESULTS AND DISCUSSIONGloboidal cam indexing mechanism producescontrolled output acceleration /decelerationbecause its output shaft is at all times tightlyconnected to its input shaft, making the outputrotation a strict function of the input rotation,determined by the shape of the cam profile. Thecams are designed to have the required indextime, dwell time and number of stations, and tomeet the requirements of static and dynamicloading, rigidity and accuracy. As part ofdynamic loading the torque imposed on theoutput shaft during the index period and the jerkdeveloped during start-stop indexing are selectedas the performance parameters. The results forthree motion curves for two differentapplications are presented in Table II.

TABLE IIIRESULTS FOR THREE MOTION CURVES

MotionCurve/parameter

Modified Sine(MS)

ModifiedTrapezoid(MT)

ModifiedConstantVelocity(MCV)

DataI

DataII

DataI

DataII

DataI

Data II

Inertia IKg-m²

8.559101.00

8.559101.000

8.559101.0

AngularAccelerationε -rad/sec²

5.9599

1.8755

5.2702

1.65850

8.6328

2.716

PeakOutputTorque TNm

51.008

189.43

45.105

167.509

73.884

274.3

Radius ofgyrationK

0.3378

0.4875

0.3378

0.48750.3378

0.487

InputTorqueT i/p - Nm

30.058

111.63

26.579

98.7107

43.538

161.6

InputPowerP i/p - hp

0.2347

0.4889

0.2075

0.43238

0.3399

0.708

MaximumJerk

m/

1741.7

307.75

1540.1

272.132

5049.4

888.3

From the above Table II it can be seen that forthe same input parameters the values of peak

output torque and jerk are minimum for MTcurve for both applications. Time period 1 isassumed for both the data in which index angleis 270 degree for input motion and 90 degree foroutput motion. From the centesimal scalesprepared for Modified Sine, ModifiedTrapezoid, Modified Constant Velocity motioncurves graph of cam angle and jerk values areobtained. The graphs obtained are shown inFig 2.

Fig. 2 Non Dimensional Time Vs Jerk

Index drives utilize the dual-dwell curves toperform the cycle of the dwell-index-dwell. TheMT, MS and MCV curves are the mostcommonly used motion curves at present. MThas lowest peak acceleration and is known to be

MSC

MTC

MCV


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suitable for high-speed applications. The MS hasa reasonable and also, the lowest

provides the advantage of the

lowest input shaft rotational irregularity. Thiscurve is estimated as the best compromise, and70% of cams for index mechanisms utilize thiscurve. Though the MCV has the lowest and

is known to be suitable for low speed and heavyload applications, it is also often used forapplications requiring the constant velocityperiod.

Generally the higher increases the pressure

angle of cam, and the cam size should beincreased to obtain the desired torque. Thehigher reduces the curvature radius of the

cam and might cause an undercut. Therepresents the input shaft torque and

the lower figure of this allows a drive motorwith a smaller rated output. Considering allthese factors, the most suitable motion curveshould be selected. This is a real example but itsmodeling procedures can be applied for othersituations when the angular input/output areknown. For the two different inputs from thecustomers the values obtained from calculationsof various components are analyzed. The resultof this study is very useful in terms of modelingand manufacturing globoidal cam.

With the modified trapezoid curve the torquegoes from positive maximum to negativemaximum in 20 % of travel time, the suddenrelease of energy is detrimental to the camfollower system performance. This limits theoperating speed for MT curve.

Comparatively MS curve exhibits betterperformance for different combinations ofapplication parameters. For the same inputpower requirement and output torque may belittle bit higher (the same electric motor may berequired) but performance and life of the systemis better. For the Application I studied inputpower required is 0.235 hp with MS curve and0.208 hp with MT curve and for Application IIinput power 0.488 hp and 0.432 hp respectivelywhich indicates that the motor of 0.5 hp is

required. In such situations MS curve should bepreferred. From the result Table 2 it is clear thatResults for MT and MS curve are closer, it isclear that there is a choice between these curves.The MCV is suitable for very low speed andheavy load applications and where operationdemands uniform velocity.

4. CONCLUSIONConsidering the problems faced by themanufacturers of indexing mechanism indeciding the appropriate cam motion laws, threemotion curves MS, MT and MCV are selectedfor the study. The input data is from real lifeapplications. From the result and analysis ofmotion curves, it is observed that for high loadsand high speeds modified trapezoid is suitable,for low load and high speed modified sine is thebest choice and for high load conditions and lowspeeds modified constant velocity is preferable.For other combinations modified sine givesbetter results. From the numerical analysisvalues of torque and jerk are minimum and inputpower required is also low, for the applicationschosen for the study the modified trapezoidmotion curve seems to be suitable. As values areso closer modified sine curve is better choice forboth the applications.

ACKNOWLEDGEMENTThe authors are grateful to Orbital Systems Pvt.Ltd., Nashik (MS), India for providing theexperimental facility. Also thankful to thesupport of Prof. D. R. Nandanwar, Principal ofGovernment Polytechnic Nashik (MS), India.

REFERENCES

[1] Ching-Huan Tseng and Wei-Han Wang,“Indexing Mechanisms Using Pairs ofradially Disposed Rollers Engaged betweenAdjacent Cam Ribs”, U.S. Patent,No.5960668, 1999.

[2] FU Yan Ming, “Analysis and Design of theGloboidal Indexing Cam Mechanism”,Journal of Shanghai University, Vol. 4, No.1 Mar. 2000, pp 54-59.

[3] Jie-Shing Lo, Ching-Haun Tseng, Chung-Biau Tsay, “A Study on the bearing contact


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of roller gear cams”, Computer Methods inApplied Mechanics and Engineering, Vol.190, No. 3, 2001, pp 4649-4662.

[4] Vu-Thinh Nguyen, Do-Joong Kim,“Flexible Cam Profile Synthesis methodusing smoothing spline curves”, Mechanismand Machine Theory, Vol.42, 2007, pp.825-838.

[5] Kuang-Yuh Huang, Pei-Chuan Lin andSheng-Fu Tsai, “Magnetic TorqueCompensating Methods for Cam IndexingDevices”, IEEE Transaction of Magnetics,Vol.43, No.3, March 2007, pp 1061-1071.

[6] Nguyen Van Tuong, and Premysl Pokorny,“Modeling Concave Globoidal Cam withSwinging Roller Follower: A Case Study”,Journal of World Academy of Science,Vol.32, 2008, pp 150-156.

[7] Nguyen Van Tuong, and Premysl Pokorny,“Virtual Animation For CheckingInterference of Globoidal Cam”, MachineManufacturers Science Journal, Oct 2009,pp 138-141.

[8] Jao-Hwa Kuang, Chao-Ming Hsu, Chin-CheHu, “Dynamic Behavior of Globoidal CamSystems with Torque CompensationMechanisms”, Mechanism and MachineTheory, Vol.45, 2010, pp 1201-1214.

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Design and Analysis of Globoidal Cam Index Drive