INCREASING THE EFFICIENMO

ПОВЫШЕНИЕ ЭФФЕКТИВНОСТИПОДВИЖНЫ

Ass.Prof. PhDepartment of Mechatro

Abstract: The influence of type of mechanical drive ois considered in the work. An analytical comparison oon friction and capacity of motors are accepted. It is devices made of light alloys or plastics. KEYWORDS: ENERGY, TORQUE, FRICTION, RAC

1. Introduction

It is often necessary to obtain exact concentratio

in chemical and food-processing industry. Using difdevices it can be achieved. The automation of sucusually made by two ways:

- dosing-head is positioned stationary, vesselconveyer;

- vessels are positioned stationary, dosing-heaThere are positive and negative aspects in both these of them is depending on production specificity.

It also is often needed strong positioning of a capin case of using poisonous or volatile substances. process becomes complicated owing to necessity ofinstallation of the cap.

The article discusses increasing the efficiency ofmoving dosing-head. Attention pays not only to achiegreatest speed of head moving but also to increasefficiency of the device. The analysis of change of spinvariable useful work of the device for differmechanical drives is carried out.

2. Theoretical background and research As an example of research object can be u

analyzing system [3]. The system (Fig.1) is controlleallows make various types of analyses using several A control block receives information about chemicand concentration of liquid in vessels. Then the sigpumps and dilutors for changing volume and conliquid. Efficiency of measurement realization dependtests moving, viscosity of liquid, processing of receive

Fig. 1. Spice diagram of analyzing system

CY OF CASTING AND DOSING DEVICES WITH BILE DOSING-HEADS

РАЗЛИВОЧНОГО И ДОЗИРУЮЩЕГО ОБОРУДОВАНИЯ С МИ ДОЗИРУЮЩИМИ ГОЛОВКАМИ

D. Penkov I. and Ass.Prof. PhD. Strizhak V. nics, Tallinn University of Technology, Tallinn, Estonia

n efficiency of casting and dosing devices and value of maximal load on moving links f rack-gear and ball-screw drives is carried out where as criterion the link speed, loss shown that a ball-screw is a very effective type of drives especially in instruments and

K-GEAR, BALL-SCREW.

n of solutions ferent dosing h systems is

s move along

d moves. cases and use

on the vessel The batching removal and

systems with vement of the e the general ent energy on ent types of

object

sed a BOD d on-line and types of tests. al compound nal is sent to centration of s on speed of date etc.

The control block provides accurate moving of tests on given co-ordinates and software provides processing of measurement results.

The system serves several tens vessels for one running cycle therefore one of the basic parameters of overall performance of similar devices is decreasing processing time for one set of vessels. It can be achieved by following methods:

- software improvement; - increasing through-put of hydro-systems; - increasing speed of test or dosing-head moving.

The first increases productivity of the device by decreasing of processing time of measurement results. The second depends on productivity of pumps and dilutors, types of tubes and liquid viscosity. These parameters do not depend directly on instrument design and investigation of their influence is not a purpose of this work. In this investigation the influence of mechanical parts of the device is considered.

The basic parameters of quality of the device are reliability and durability of units and details at action of rated loads and also speed, smoothness and noiselessness of the tests moving. These characteristics depend on many parameters including kinetic energy of mechanism, design parameters of drive elements, capacity and rotation frequency of engines etc.

The test or dosing head makes linear moving on three directions and have rotating freedom. For realization of these movements various types of mechanical drives can be used: ball-screws, cogged belts, rack-gears etc.

Let us consider the change of device productivity when the engine elements of links are ball-screws or rack-gears. Kinetic energy of mechanisms is determined from following equation [2]

( )

∑∑==

⋅++=

k

i

iiiin

i

ii

rmJvmE

1

22

1

2

22ω

(1)

.

where mi is mass of the mechanism link, vi is linear speed of gravity center of the link, Ji is moment of inertia concerning the gravity center of the link, ri is distance between the center of rotation and the gravity center of the link, ωi is tangential velocity of the link.

Mass of links, without taking into account a motor-reductor, is designated mi. In case of using rack-gears the motors are placed into kinematic pairs and links mass is increased on Δmi. In case of using lead-screws the motor is placed on a frame and does not move together with the link. Having determined by Eq. (1) the kinetic energy of the link with ball-screw ES and rack-gear EG and having accepted ES = EG the linear speed of the link with a lead-screw can be obtained as follows

i

iGS m

mvv ii

Δ+= 1 (2)

89

where index S designates the ball-screw and index G designates the rack-gear. Equation (2) shows that for achievement of identical kinetic energy the links with ball-screw must move faster than links with rack-gear.

3. Results and discussion

Let us consider the efficiency of mechanical drives caused first

of all by loss on friction. The dosing head has no steady movement therefore it is possible to lead only a conditional comparative analysis of efficiency of the kinematic pairs. In this case use of term “efficiency of kinematic pair” is justified since each pair is actuated by separate motor.

Loss on friction in the rack-gear is given by the equation [4]

( ) 1

3.2costan

cosz

fkPdfd

fp

ttpp

tG ≈

++=

ωω

ω

ααα

ϑ

where f is friction factor in the rack-gear, z1 is teeth number of pinion, k is ratio dependent on addendum, P is pitch of teeth, αtω is pressure angle and dp is diameter of basic circle.

Loss on friction in the ball-screw is given by the equation [1]

ϕβϕϑ

tan1tan1 2

++

=S

where r

b

fd

2sinα

β = , ϕ is lead angle, db is ball diameter, α is

contact angle of balls and fr is factor of rolling friction. Having accepted loss on friction as the basic parameter of the

drive efficiency it is possible to determine the areas of more effective application for ball-screws or rack-gears. Accepting ϑG = ϑS, after transformations and leaving out of account of insignificant members the relationship between z1 and ϕ is found as follows

( )ϕϕα

21 tan1tansin15.1

+≈

r

b

ffkd

z

As the teeth number of pinion is an integer it is more expedient

to define a relationship between ϕ of ball-screw and z1 of rack-gear providing identical loss on friction. Then

( )r

r

fzfz

1

21

21tan

−−= − γγ

ϕ (3)

where αγ sin575.0 bfkd≈ .

Calculations by Eq. (3) show that use of ball-screws is more effective in comparison with rack-gears with small number of teeth. Therefore if it is necessary to develop a device having small dimensions of links and kinematic pairs then can be preferred a lead-screw. Especially effective is using ball-screws with large lead angle ϕ but it value is limited and most used ball-screws are produced with lead angle up to 18° [5]. Balls diameter influences essentially on drive efficiency. Friction in the rack-gear does not depend on teeth module but only on teeth number. Friction in the ball-screw changes with change of ball diameter, so the increasing the past one increases an advantage of ball-screws as compared with rack-gears.

Comparing two drives it also is important to compare of torque values. Remembering that mass of the link with the rack-gear is Δm greater than mass of the link with ball-screw the torque on the rack-gear can be presented as

( )

2FFd

T GG

Δ+= (4)

where F is a load on the mechanical drive without taking into account mass of the motor-reductor and dG is the diameter of the pitch circle.

The torque on the ball-screw is given by equation [4]

( ρϕ ′+= tan2

Fd

T SS ) (5)

where α

ρsin

2tan 1

b

r

df−=′ .

Solving foregoing Eqs. (4) and (5) together gives

( ρϕ ′+⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ−= tan

21S

GS dF

mzT

T ) (6)

where m is a rack-gear module. Equation (6) shows that relation between TS and TG depends on

value ΔF dependent on mass of the motor-reductor moving the link. Frames of most devices are usually made of light alloys or plastics therefore mass of the motor-reductor can be comparable with link mass and in this case using ball-screws is more expedient.

From calculations by Eq. (6) one can see that for moving an identical axial load the torque on the rack-gear must be several times more than torque on the ball-screw. It means that by using of a rack-gear a more powerful motor should be used. It influences on mass of the motor and the mechanism as a whole. Considering that gears in most casting and dosing devices are kinematics and do not move great loads, the additional value of ΔF can significantly increase the difference between values TS and TG.

Having known the relationship between torques on rack-gear and ball-screw it is possible to compare the capacity required for achievement identical axial moving. One turn of pinion gives length of axial moving equal to Gdl π= . For the same movement

of ball-screw the stroke will be equals ϕπ tanSdnnPl == ,

where P is pitch of screw thread, GSn ωω /= , ωS and ωG are tangential velocities of screw and pinion accordingly. Taking into account Eqs. (4) an (6) can be obtained

( )

ϕρϕ

tantan1

′+⎟⎠⎞

⎜⎝⎛

Δ+Δ

−=FF

FPP GS (7)

where PS and PG are required capacities for ball-screw and rack-gear accordingly.

Equation (7) shows that required capacity for the ball-screw is less as compared with the rack-gear and this difference increases with increasing of ΔF, i.e. in this case using ball-screws is more effective.

4. Conclusion Productivity of casting and dosing devices made of light alloys

and plastics can be increased with use of optimal type of mechanical drive. Both motor mass and relationship of this one to link mass have a great importance on the productivity. If it is necessary to minimize dimensions of links and kinematic pairs it is possible to recommend using ball-screws instead rack-gears having pinions with small teeth number. Increasing lead angle in ball-screw increases efficiency of drive and decreases loss on friction.

5. References

1. Andreev G. N., Markov B. N., Ped E. I. Theory of Mechanisms and Parts of Precision Instruments. Machinebuilding, Moscow, 1987.

2. Artobolevsky I. I. Theory of Machines and Mechanisms. Science, Moscow, 1988.

3. BOD Robotic Analyzer. www.skalar.com, January 2007. 4. Reshetov D. N. Machinery Parts. Machinebuilding, Moscow,

1989. 5. SKF Ground Ball Screws. www.skf.com, January 2007.

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