1final Project - Design of A Concrete Vibrating Table

 

UNIVERSITY OF NAIROBI

SCHOOL OF ENGINEERING

DEPARTMENT OF MECHANICAL & MANUFACTURING ENGINEERING

PROJECT CODE: SMK/01

PROJECT TITLE: DESIGN OF A CONCRETE VIBRATING TABLE

AUTHORS

Kiseu Emmanuel Kimuyu

Njira Alex

A project submitted pursuant to the regulations in partial fulfillment for the award of:

B.Sc. Mechanical & Manufacturing Engineering 1  

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DECLARATION AND CERTIFICATION We declare that this our own original work and to the best of our knowledge and has never been presented elsewhere for academic  purposes.

AUTHORS

NAME: Kiseu Emmanuel Kimuyu Reg.No:F18/2429/2009

NAME: Njira Alex Reg. No: F18/28451/2009

SIGN:

SIGN: 

DATE:

DATE: 

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SUPERVISOR

This project has been submitted for examination as partial satisfaction of B.Sc. Mechanical & Manufacturing Engineering with my approval as the student’ student’s supervisor.

NAME: MR. S.M. KABUGO

SIGN:

DATE:

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ACKNOWLEDGEMENTS

We are humbled and grateful to all the people who supported us in the successful completion of this  project. We wish to pass our sincere gratitude to the Department of Mechanical Engineering under the leadership of Dr. J.M Ogolla, the Workshop Staffs headed by Mr. Aduol for being of great assistance to us. In a special way we appreciate our project supervisor Mr. S. M. Kabugo for his guidance and support throughout this project. We would also wish to appreciate our colleagues and lectures that were not reluctant to give us both constructive advice and criticism in the course cou rse of the project.

Above all, glory to God Almighty. Almighty.

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ABSTRACT

Concrete is a composite mixture of aggregate, water and cement. When mixed together in specific ratios, they form a mass fluid which can be easily molded into different shapes for various functions. After exposure to air, it forms a hard matrix like structure that resembles stone that is widely used for infrastructure and construction. In order to attain the specific required strengths, concrete con crete needs to be free of entrapped air and voids. This is done by consolidation of concrete. Consolidation is the process of removing entrapped air from freshly placed concrete. Several methods and techniques are available, the choice depending mainly on the workability of the mixture, placing conditions, and degree of air removal desired thus in the process inducing a closer arrangement of the solid particles in freshly mixed concrete or mortar, some form of vibration is usually employed in effort to achieve proper consolidation. Many Man y of these products require the use of a vibration table in order to remove air and water trapped within the concrete. Removal of the these se voids improves the outside surface of the molded concrete, and also allows the use of a lower water to cement ratio, allowing a much stronger finished product. This project is tasked with the mandate of designing d esigning a concrete vibrating table that effectively ensures consolidation of concrete to give a better finished product. These concrete can be used for producing roof tiles and concrete paving bricks from the concrete molds. There are several ex existing isting vibrating tables, however, our task was to design from scratch and possibly fabricate an improved vibrating table from readily available local materials.

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TABLE OF CONTENTS

DECLARATION AND CERTIFICATION........................................................................................................................ 2 1.1INTRODUCTION .................................................................................................................................................. 9 1.2 BACKGROUND ............................................................................................................................................. 10 1.3 PROBLEM STATEMENT ................................................................................................................................ 13 1.4 PROJECT OBJECTIVE .................................................................................................................................... 13 1.5 METHODOLOGY .......................................................................................................................................... 14 1.6 METHODS OF CONSOLIDATION .................................................................................................................. 15

2.1 TYPES OF CONCRETE VIBRATORS .................................................................................................................... 19 Internal vibrators .............................................................................................................................................. 19 2.1.1 Flexible shaft type ................................................................................................................................ 19 2.1.2 Electric motor-in-head type ................................................................................................................. 22

2.2 Form Vibrators  ............................................................................................................................................ 23 2.2.1 Types of form vibrators ........................................................................................................................ 24 2.3 VIBRATING TABLES ...................................................................................................................................... 25 2.4 Management plan ....................................................................................................................................... 26 2.5 EXISTING PRODUCTS ................................................................................................................................... 27

3.1 DESIGN DEVELOPMENT .................................................................................................................................. 28 ............................................................................................................................................. Motor + eccentric load  29 3.2 TABLETOP ........................................................................................................................................................ 30 3.2.1 Spring Suspension System: ...................................................................................................................... 30 3.2.2 Rubber Mount Suspension System: ......................................................................................................... 31 3.2.3 Air Cushion Suspension System: .............................................................................................................. 32 3.3 Development Test Plan: .............................................................................................................................. 34 7  

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4.1 DESIGN OF PARTS ............................................................................................................................................ 35 4.1.1Design Of Helical Springs; ......................................................................................................................... 35 ECCENTRIC LOAD............................................................................................................................................... 44 DESIGN OF TABLE TOP ...................................................................................................................................... 45 ASSEMBLY ......................................................................................................................................................... 46

5.1 CONCLUSION .................................. ................. ................................... ................................... .................................. ................................... .................................... ................................... ......................... ........ 49 5.2 RECCOMENDATION RECCOMENDAT ION ................................. ................ .................................. ................................... ................................... .................................. ................................... ................................... ................. 49

5.3 REFERENCES  ............................................................................................................................................... 50

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CHAPTER 1

1.1INTRODUCTION Concrete vibrating tables are used to reduce the porosity of concrete and enhancing its bond to the reinforcement. Concrete quality is directly dependent on the consolidation of the concrete. conc rete. A freshly  prepared batch of concrete is honeycombed, with entrapped air. If allowed to harden in this condition, the concrete will be non-uniform, weak, porous, p orous, and poorly bonded to the reinforcement. It will also have a poor appearance. The mixture must be consolidated if it is to have the properties normally desired and expected of concrete. Consolidation is the process of inducing a closer arrangement of the solid particles in freshly mixed concrete or mortar during placement by b y the reduction of voids, usually b by y vibration, centrifugation, rodding, tamping, or some combination of these the se actions; it is also applicable to similar manipulation of other cementitious mixtures, soils, aggregates. Drier and stiffer mixtures require greater effort to achieve proper consolidation. By using certain chemical admixtures, consistencies requiring reduced consolidation effort can be achieved at lower water content. As the water content of the th e concrete is reduced, concrete q quality uality (strength, durability, and other properties) improves, provided it is properly consolidated. Alternatively, Alterna tively, the cement content can be lowered, reducing the cost while maintaining the same quality. If adequate consolidation is not  provided for these drier or stiffer mixtures, mixtures, the quality of the in place concrete drops off rapidly. Equipment and methods are now available for fast and efficient consolidation of concrete over ove r a wide range of placing conditions. Concrete with relatively low water content can be readily molded into an unlimited variety of shapes, making it a highly versatile and economical construction material. When good consolidation practices are combined with good formwork, concrete surfaces have a highly  pleasing appearance.

The overall project is to design an adjustable vibration table with a rigid tabletop and suspension 9  

system .This will be used locally to create employment emplo yment for people constructing in relatively remote areas. The table will be used in an important step in producing con concrete crete paving bricks and roof tiles from molds. Vibrating the concrete reduces the number nu mber of voids in the mix mixture, ture, which in turn reduces School of Engineering | www.uonbi.ac.ke © Emmanuel and Alex

 

the water to cement ratio (w/c). This allows for a stronger finished product and maximizes the use of materials. Vibration also improves outside surface finish, which allows the product to look better and last longer by reducing the chances chan ces of cracks forming from foreign contamination. The existing vibration table does not currently meet the th e necessary requirements that are desired. The current design includes a flexing tabletop that resembles rese mbles the head of a drum. This provides uneven vibration which may result in a non-uniform non -uniform finished product. The current vibration table is also incompatible with the current tray design. Therefore, the molds must be placed directly on the vibration table, which reduces the mold life span considerably due to the mold not being supported by a more rigid tray. Additionally, edges of the molds occasionally crack under the stress of the concrete while transferring from the table to the cooling stack.

1.2 BACKGROUND Our initial research consisted of finding existing vibration tables that might perform the task of this consolidating concrete. From our research, several different categories of table design emerged. For suspension, three different types were present. These categories are springs, rubber rubb er mounts and air cushions. The springs were used in two different configurations, including hanging h anging springs (in tension) and vertically aligned compressed springs designs that used springs in tension generally allowed vibrations in the horizontal plane, while the compressed springs allowed for vertical vibrations. The ASTM standard for concrete vibration states that the tabletop vibrators must operate in the vertical direction. This standard limits the spring suspension design to vertically compressed springs. Solid rubber mounts in compression, were less widely used, as they did not allow as much movement as the other two. However, they are generally the least expensive, and may be used if low amplitude vibrations are desired. Rubber mounts can also be mounted in such a way as to only experience shearing forces. The effective spring rate can be calculated from the dimensions of the rubber moun mountt and the shear modulus of the rubber. This configuration is also good for low amplitudes of vibration, and when a moderate mode rate amount of damping is required. Rubber mounts used in shear can be seen on the Syntron Vibratory Equipment 1

vibration table. In a few instances, rubber mounts mou nts were also used as a centering pivot point for inverted  pendulum based vibration tables. This configuration allowed for horizontal movement only and

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therefore cannot be used in our design. The last suspension category, air cu cushion, shion, was the most common. Air cushion suspension was seen in most of the higher end vibration tables. All the designs seen using this type of suspension were configured with a rigid table mounted with air cushions in the four corners. Air cushions are generally more expensive and less readily available than tha n the other suspension types listed. However, these air cushions are very adjustable, as air can be easily added or removed from the system. The change in air pressure will change both spring rate and d damping, amping, which is an important quality to have in our design since such a wide range of loads will be used on the tabletop. As well as researching the different types of suspension, many different sources of vibration were found. However, our design requirement of using a 12 volt DC motor limited the list of sources to a few viable options. Sources of vibration were limited to using a rotating shaft with an eccentricity or using u sing cams. Both options allow for adjustable vibration amplitudes. The rotation of an eccentric mass was the most common source of vibration seen. This design is easy to fabricate, has minimal wear, and can be relatively easy to adjust. Alternatively, cams will provide constant amplitude of vibration, regardless of load (unlike a design using an eccentricity). However, cams will be difficult to machine because according to the ASTM handbook for concrete vibration table design, vibration amplitudes should range from 0.3 to 0.4 mm at a frequency of 3900±200 RPM. Also, our low torque motor will be unable to lift the heavy loads required of it. Therefore, the most viable source of vibration is the rotating eccentricity. Steel was almost exclusively used in the construction of vibration tables. We feel that steel is the best b est option for our design as well, due to its durability, relatively low cost, rigidity, and high availability. Steel is also a very forgiving metal to weld, unlike aluminum, which usually requires a h heat eat treatment  process after welding. In addition to researching existing products, we contacted co ntacted various local concrete production facilities, which provided us with valuable information from the industry. We found that vibration tables used in industry are designed for a specific concrete mixture. This is  because desired amplitudes, frequencies, and vibration times change with specific mixtures and are all taken into consideration when choosing table components. Therefore, we found that it is important to 1

keep the mixture constant between batches in order to have a uniform product. One method to control consistency is the use of of a slump cone and associated slump test. Concrete strength is determined determined

 

almost entirely by the components in the mixture. Vibration of the concrete is onl only y used to improve School of Engineering | www.uonbi.ac.ke © Emmanuel and Alex

 

the surface finish, or cosmetics of the product. We learnt that the ‘throw’ of the tabletop is a very v ery important design consideration. The term throw refers to the ability of the table to disperse the aggregate in a desired direction within the concrete mixture. Improper throw can cause non non-uniform -uniform distribution of aggregate. For this reason, most concrete vibration tables have h ave two opposing eccentric masses, in order to cancel out any an y horizontal force seen by the tabletop. This will be considered in our design, but may not end up being cost effective. There are a re also other ways to induce uniform throw over the entire concrete mold, such as having the user rotate the mold manually during the vibration  process. Knowing the throw of the table is important because it determines how the aggregate is displaced within the mold after vibration. A simple way wa y to check the throw of the table is to put sand on the table and see how it is displaced when the table is vibrating. If there is no ex extreme treme tendency for the sand to shift in a preferential direction the aggregate within the mold should aalso lso be fairly evenly dispersed. Besides using traditional vibration, many concrete production facilities are transitioning to using self-consolidating concrete (SCC) exclusively. SCC contains a mix additive which replaces most of the water normally used in the mix. This additive reduces the w/c ratio, increases the strength, and eliminates the need to use vibration

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1.3 PROBLEM STATEMENT The design problem in our context is improving the design of a concrete vibrating table such that we acquire finished product of better quality while ensuring en suring the machine is cost effective and more durable than the existing vibrating table locally locall y available.  The high speed of operations operation s as well as the excessive vibration of the vibratory table tends to reduce  both efficiency and at the same time allowing excessive noise.

1.4 PROJECT OBJECTIVE The goal of this project is to create c reate a rigid vibration tabletop and suspension system with adjustable amplitude. Our design will be used for increasing the t he lifespan of the molds, reducing the number of voids in the concrete which consequently reduces the water to cement rat ratio. io. This improves the aesthetics and therefore the life span of the finished product. This vibration allows for an overall better finished product. The vibration table must have the characteristics stated in the design goals.

Design Goals

  Must vibrate the whole tabletop, not just the center

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  Tabletop must not flex more than 0.4 mm under load 

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  Compatible with wooden crates and molds ranging in size from 300 x 300 mm to 650 x 650

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mm

  Be able to work in a adverse environmental conditions , including concrete, moisture and dust

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  Durable; must last without major breakdown for 3-5 years

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  Must be easily built and repaired using locally available ava ilable materials and components

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(Lathe, drill press, arc welder, and various hand power p ower tools)

  Must run for 3-5 work days on one fully charged 12 volt battery  

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1.5 METHODOLOGY We proposed use of a 12 volt D.C motor which was mounted beneath the tabletop by use of connecting rods which secured it in place. The power transmitted from the rotating D.C. motor moves the eccentric load which in turn moves the tabletop vertically. The vibration results from the tension and compression of the spring suspension system. The resulting vibrations from the vibration table cause the consolidation of the concrete molds resulting in a better a consistent surface finish.

Concrete Workability  

Workability of freshly mixed concrete is that property that determines the ease e ase and homogeneity with which it can be mixed, placed, consolidated, and finished. Workability is a function of the rheological  properties of the concrete. Workability may be divided into three main aspects: 1. Stability (resistance to bleeding and segregation). 2. Ease of consolidation. 3. Consistency, affected by the viscosity and cohesion of the concrete and angle of internal friction. Workability is affected by grading, particle shape, proportions of aggregate ag gregate and cement, use of chemical and mineral admixtures, air content, and water content of the mixture. Consistency is the relative mobility or ability of freshly mixed concrete to flow. It also largely determines the ease with which concrete can c an be consolidated. Once the materials and proportions are selected, the primary control over work ability is through changes chan ges in the consistency brought aboutby abou tby minor variations in the water content. The slump test (ASTM C 143) is widely used to indicate consistency of mixtures used in normal construction. The Vebe test is generally recommended for stiffer mixtures.

Workability requirements;

The concrete should be sufficiently workable so that consolidation equipment, properly used, will give adequate consolidation. A high degree of flowability may be undesirable because it may increase the cost of the mixture and may reduce the quality of the hardened concrete. Where such a high degree of flowability is the result 1

of too much water in the mixture, the mixture will generally be unstable and will probably segregate during the consolidation process.

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Mixtures having moderately high slump, small maximum size aggregate, and an d excessive fine aggregate are frequently used because the high degree of flowability means less working placing. At the other extreme, it is inadvisable to use mixtures that are too stiff for conditions of consolidation. They will require great consolidation effort and even then may not be adequately consolidated. Direction and guidance are often required to achieve achiev e the use of mixtures of lower slump or fine aggregate content, or a larger maximum size aggregate, so as to give a more efficient use of the cement. Concrete containing certain chemical admixtures may be placed in forms with less consolidation effort. It is the workability of the mixture in the form that determines d etermines the consolidation requirements. Workability may be considerably less than at the mixer because of slump loss due to high temperature, false set or delays.

1.6 METHODS OF CONSOLIDATION The consolidation method should be compatible with the concrete mixture, placing conditions, form intricacy, amount of reinforcement, etc. Many manual and mechanical methods are available.

Manual methods 

Some consolidation is caused by gravity gravit y as the concrete is deposited in the form. This is particularly true for well proportioned flowing mixtures where less additional consolidation effort is required. Plastic or more flowable mixtures may be consolidated by b y rodding. Spading is sometimes used at formed surfaces — a flat tool is repeatedly inserted and withdrawn adjacent ad jacent to the form. Coarse  particles are shoved away from the form and movement of air voids and water pockets toward the top surface is facilitated, thereby reducing the number and size of bug holes in the formed concrete surface. Hand tamping may be used u sed to consolidate stiff mixtures. The concrete is placed in thin layers, and each layer is carefully rammed or tamped. This is an effective consolidation method, but laborious and costly. The manual consolidation methods are generally only used on smaller nonstructural concrete placement. 1

The most widely used consolidation method is vibration. It will receive the most attention in this report. Vibration may be either internal, external, or both.

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Power tampers may be used to compact stiff concrete in precast units. In addition to the ramming or tamping effect, there is a low-frequency vibration that aids in the consolidation. Mechanically operated tamping bars are suitable for consolidating stiff mixtures for some precast  products, including concrete blocks. Equipment that applies static pressures to the top surface may be used to consolidate thin concrete slabs of plastic or flowing consistency. Concrete is literally squeezed into the mold, and entrapped air and part of the mixing water is forced out. Centrifugation (spinning) is used to consolidate concrete in concrete pipe, piles, poles, and other hollow sections. Many types of surface vibrators are available for slab construction, including vibrating v ibrating screeds, vibratory roller screeds, plate and grid vibratory tampers, and vibratory finishing tools. Shock tables, sometimes called drop tables, are suitable for consolidating low-slump concrete. The concrete is deposited in thin lifts in sturdy molds. As the mold is filled, it is alternately raised a short distance and dropped on to a solid base. The impact causes the concrete to be rammed into a dense mass. Frequencies are 150 to 250 drops per min., and the free fall is 1/8 to 1/2 in. (3 to 13 mm). Under some conditions, a combination of two or more consolidation methods gives the best results. Internal and external vibration can often be combined to advantage in precast work and occasionally in cast-in-place concrete. One scheme uses form vibrators for routine consolidation and internal vibrators for spot use at critical, heavily reinforced sections prone to voids or poor bond with the reinforcement. Conversely, in sections where the primary consolidation is by b y internal vibrators, form vibration may also be applied to achieve the desired surface appearance. Vibration may be simultaneously applied to the form and top surface. This procedure is frequently used in making precast units on vibrating tables. The mold is vibrated while a vibratory plate or screed working on the top surface exerts additional vibratory v ibratory impulses and pressure. Vibration of the form is sometimes combined with static pressure applied to the top surface. Vibration under pressure is particularly useful in concrete block production where whe re the very stiff mixtures do not react favorably to vibration alone. Centrifugation, vibration, and rolling may be combined in the  production of concrete pipe and other hollow sections. 1

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CONSOLIDATION OF CONCRETE BY VIBRATION

Vibration consists of subjecting freshly placed concrete to rapid vibratory impulses which liquefy the mortar and drastically reduce the internal friction between aggregate a ggregate particles. While in this condition, concrete settles under the action of gravity (sometimes aided by other forces). When vibration is discontinued, friction is reestablished.

Vibratory motion

A concrete vibrator has a rapid oscillatory motion that is transmitted to the freshly placed concrete. Oscillating motion is basically described in terms of frequency (number of oscillations or cycles per unit of time) and amplitude (deviation from point of o f rest). Rotary vibrators follow an orbital path caused by rotation of an unbalanced weight or eccentric inside a vibrator casing. The oscillation is essentially simple harmonic motion, Acceleration, a measure of intensity of vibration, can be computed from the frequency and amplitude when the they y are known. It is usually expressed by gravity  gravity which is the ratio of the vibration acceleration acc eleration to the acceleration of gravity. Acceleration is a useful parameter for external vibration, but not for internal vibration where the amplitude in concrete cannot be measured readily. For vibrators other than the rotary type, reciprocating vibrators v ibrators for example, the principles of harmonic motion do not apply. However, the basic concepts described here are still useful.

Process of consolidation

When low-slump concrete is deposited in the form, it is in a honeycombed condition, consisting of mortar-coated coarse-aggregate particles and irregularly distributed pockets of entrapped air. It is see seen n that the volume of entrapped air depends d epends on the workability of the mix mixture, ture, size and shape of the form, amount of reinforcing steel and other items of congestion, and method of depositing the concrete. It is generally in the range of 5 to 20 percent. The purpose of consolidation is to remove practically all 1

of the entrapped air because of its adverse effect on concrete properties and surface appearance. Consolidation by vibration is best described as consisting of two stages — the the first comprising

 

subsidence or slumping of the concrete, and the second a desecration (removal of entrapped School of Engineering | www.uonbi.ac.ke © Emmanuel and Alex

 

air bubbles). The two stages may occur simultaneously, with the second stage under wa way y near the vibrator before the first stage has been completed at a t greater distances. When vibration is started, impulses cause rapid disorganized movement of mixture particles within the vibrator’s radius of influence. influence. The mortar is temporarily liquefied. Internal friction, which enabled the concrete to support itself in its original honeycombed condition, is reduced drastically. The mixture becomes unstable, and seeks a lower level and denser condition condition.. It flows laterally to the form and around the reinforcing steel and embedment. At the completion of this first stage, honeycomb has been eliminated; the large voids between the coarse aggregate are now filled with mortar. The concrete behaves somewhat like a liquid containing suspended coarse-aggregate particles However, the mortar still contains any entrapped air bubbles, ranging up to perhaps 1 in. (25 mm) across and amounting to several percent of the concrete volume. After consolidation has proceeded to a point po int where the coarse aggregate is suspended in the mortar, further agitation of the mixture by vibration causes entrapped air bubbles to rise to the surface. Large air bubbles are more easily removed than small ones because of their greater buoyancy.

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CHAPTER 2

2.1 TYPES OF CONCRETE VIBRATORS Concrete vibrators can be divided into two main classes- internal and external. External vibrators may  be further divided into form vibrators, surface vibrators, vibrators, and vibrating tables.

Internal vibrators Internal vibrators, often called spud or poker vibrators, have a vibrating casing or head. The head is immersed in and acts directly against the concrete. In most cases, internal vibrators depend on the cooling effect of the surrounding concrete to prevent overheating. All internal vibrators presently in use are the rotary type The vibratory impulses emanate at right angles to the head.

2.1.1 Flexible shaft type This type of vibrator is probably the most widely used. The eccentric is usually driven b by y an electric or  pneumatic motor, or by a portable internal combustion engine.

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 Fig - Flexible shaft vibrators; electric electric motordriven type (top); gasoline engine-driven type (middle; andcross section through head (bottom)

For the electric motor-driven type, a flexible drive shaft leads from the electric motor into the vibrator head where it turns the eccentric weight. The motor generally has universal, 120 (occasionally 240) volt, single-phase, 60 Hz alternating- current characteristics. Fifty Hz AC current c urrent is used in some countries. The frequency of this type of vibrator v ibrator is quite high when op operating erating in air   — generally generally in the range of 12,000 to 17,000 vibrations per min (200 to 283 Hz) (the higher values being for the smaller head sizes). However, when operating in concrete, the frequency is usually reduced by about one-fifth. Frequency is given in hertz in the For the engine-driven types, both gasoline and diesel, the engine speed is usually about 3600 revolutions per min (60Hz). A V-belt drive or gear transmission is used to step up this speed to an acceptable frequency level. Another type of unit uses a 2-cycle gasoline engine operating at a no-load speed of 12,000 RPM so the need for a step-up transmission is eliminated as shown in the figure below.

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 Back pack two-cycle gasoline engine-driven vibrator

This unit is portable and is usually carried on a back pack. Again a flexible shaft leads into the vibrator head. While larger and more cumbersome than electric motor-driven vibrators, engine-driven vibrators are attractive where commercial power is not readily available. For most flexible-shaft vibrators, the frequency is the same as the speed of the shaft. However, the roll-gear (conical-pendulum) type is able to achieve high vibrator frequency with modest electric motor and flexible shaft speeds. The end of the pendulum strikes the inner ho housing using in a star-shaped  pattern, giving the vibrator head a frequency higher than the shaft driving it. Motor speeds are usually about 3600 revolutions per min with 60 Hz current (about 3000 revolutions per min with 50 Hz current). A single induction or three-phase squirrel-cage motor is generally used. u sed. The low speed of the flexible shaft is favorable from the standpoint of maintenance

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2.1.2 Electric motor-in-head type Electric motor-inhead vibrators have increased in popularity in recent years (see Fig. below). 

Since the motor is in the vibrator head, there is no separate motor and flexible drive to handle. A substantial electrical cable, which also acts as a handle, ha ndle, leads into the head. Electric motor-in-head vibrators are generally at least 2 in. (50 mm) in diameter. This type of vibrator is available in two designs. One uses a universal motor and the other o ther a 180 Hz (high-cycle) three phase motor. In the latter, the energy is usually supplied by a portable gasoline engine-driven generator; however, commercial power passed through a frequency converter may be 2

 

used. The design uses an induction-type motor that has little drop-off in speed when immersed in concrete. It can rotate a heavier eccentric weight and develops a greater centrifugal force than current universal motor-in-head models of the same diameter. Vibrator motors operating on 150 or 200 Hz. School of Engineering | www.uonbi.ac.ke © Emmanuel and Alex

 

Pneumatic neumatic vibrators are operated by compressed air, the pneumatic motor Pneumatic vibrators — P generally being inside the vibrator head. The vane type has been the most common, with both the motor and the eccentric elements supported on bearings. Bearingless models, which generally require less maintenance, are also available. A few flexible-shaft pneumatic models, with the air motor outside the head, are also available. Pneumatic vibrators are attractive where compressed air is the most readily available source of power. The frequency is highly dependent on o n the air pressure, so the air p pressure ressure should always be maintained at the proper level, usually that recommended by b y the manufacturer. In some cases, it is desirable to vary the air pressure to obtain a different frequency.

H ydr ydr auli ulicc vibrat vibrato or s — Hydraulic Hydraulic vibrators, using a hydraulic gear motor, are popular on paving machines. Here the vibrator is connected to the paver’s hydraulic system by means of hi high gh-pressure -pressure hoses. The frequency of vibration can be regulated by varying the rate of flow of hydraulic fluid through the vibrator. The efficiency of the vibrator is dependent on the pressure and flow rate of the hydraulic fluid. It is, therefore, important that the hydraulic system be checked frequently.

2.2 Form Vibrators

Form vibrators are external vibrators attached to the outside o utside of the form or mold. They vibrate the form, which in turn transmits the vibration to the concrete. Form Fo rm vibrators are self-cooling and may be of either the rotary or reciprocating type. Concrete sections as thick as 24 in. (600 mm) and up to 30 in. (750 mm) deep have been effectively vibrated by form vibrators in the precast concrete industry. For walls and deeper placements, it may ma y be necessary to supplement a form vibrator with internal vibration for sections thicker than 12 in. (300 mm).

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2.2.1 Types of form vibrators

R otar y   Rotary form vibrators produce essentially simple harmonic motion. The impulses have components   both perpendicular to and in the plane of the form. This type may be pneumatically, hydraulically, or electrically driven.  In the pneumatically and hydraulically driven models, mod els, centrifugal force is developed by a rotating cylinder or revolving eccentric mass (similar to internal vibrators). These vibrators generally work at frequencies of 6000 to 12,000 vibrations per min (100 to 200 Hz). The frequency may be varied by adjusting the air pressure on the pneumatic models or the fluid pressure on the hydraulic models. The electrically driven models have an eccentric mass attached to each end of the motor shaft. Generally, these masses are adjustable. In most cases, induction motors are used and the frequency frequenc y is 3600 vibrations per min (60 Hz AC, or 3000 vibrations per min for 50 Hz AC). Higher frequency vibrators operating at 7200 or 10,800vibrations per min (120or 180 Hz) are also available (6000, 9000, or 12,000 vibrations per min [100, [100 , 150, or 200 Hz] in Europe). These higher frequency vibrators require a frequency converter. There are also electric form vibrators with frequencies of 6000 to 9000 vibrations per min (100 to 150 Hz) that are powered by single-phase unive universal rsal motors.

The manufacturer’s catalog should include physical dimensions, mass, and eccentric moment. For  pneumatically driven models, frequency in air and approximate frequency under load should be given. For electric models, the frequency at the rated electric load should be stated. The centrifugal force at the given frequency values should be provided. In addition, the catalog should provide data needed for  proper hookup of the vibrators.

Reciprocating   In reciprocating vibrators, a piston is accelerated in one direction, stopped (by impacting against a steel plate), and then accelerated in the opposite direction. This type is pneumatically driven, 2

and frequencies are usually in the range of 1000 to 5000 vibrations  per min (20 to 80 Hz).

 

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These vibrators produce impulses acting perpendicular to the form. The principles of simple harmonic motion do not apply.

2.3 VIBRATING TABLES A vibrating table normally consists of a steel or reinforced concrete table with external vibrators rigidly mounted to the supporting frame. The table and frame are isolated from the base by steel springs, neoprene isolation pads, or other means. The table itself can be part of the mold. However, a separate mold usually rests on top of the table. Vibration is transmitted from the table to the mold and thence to the concrete. There is a difference of opinion as to the advisability of fastening mold to th thee table. Low frequency (below 6000 vibrations per min [100 Hz]), high amplitude (over 0.005 in. [0.13 mm]) vibration is normally preferred, at least for stiffer mixtures. The effectiveness of table vibration is largely a function of the acceleration imparted to the concrete conc rete by the table. Accelerations in the range of 3 to 10 g (30 to 100 m/sec2) are generally recommended, the higher values being needed for the stiffer mixtures. In addition, the amplitude should not be less than 0.001 in. (0.025 mm) for plastic p lastic mixtures, or 0.002 in. (0.050 mm) for stiff mixtures. Acceleration of the table is a function of the vibrational force as related to the mass of form and concrete activated. The following empirical formulas have been be en useful in estimating the required centrifugal force of the vibrators 1. Rigid vibrating table or vibrating beams, with with form  placed loosely on the table: Centrifugal force = (2 to 4) [(mass of table) + 0.2 (mass of form) + 0.2 (mass of concrete)]. 2. Rigid vibrating vibrating table, with form form attached to the table: Centrifugal force = (2 to 4) [(mass of table) + (mass of form) + 0.2 (mass of concrete)]. 3. Flexible vibrating table, continuous over several supports: Centrifugal force = (0.5 to 1) [(mass of table + 0.2 2

(mass of concrete)]. The choice of vibrators and spacing should be based on the preceding formulas and previous

 

experience. Frequency and amplitude should be checked at several points on the table, with a School of Engineering | www.uonbi.ac.ke © Emmanuel and Alex

 

micrograph or other suitable device. The actual acceleration may then be computed. The vibrators should be moved around until dead spots are eliminated and the most uniform vibration is attained. When concrete sections of different sizes are to be vibrated, the table should have variable amplitude. Variable frequency is an added advantage. If the vibrating table has a vibrating element containing only one eccentric, a circular vibrational motion may be obtained which imparts an undesirable rotational movement to the concrete. This may ma y be prevented by mounting two vibrators side by side in such a manner that their shafts rotate in opposite oppo site directions. This neutralizes the horizontal component of vibration, so the table is subjected to a simple harmonic motion in the vertical direction only. onl y. Very high amplitudes may be obtained in this manner.

2.4 Management plan As our design team consists of two members, working together to gether has shown, in many project tasks, to have the highest efficiency and create the highest quality product. However there have been several areas of the design process that dividing the work load has worked best if. These areas include the CAD drawings, initial calculations for our respective design concepts, in-depth in -depth calculations for subsystems of our selected design, and construction of the prototype. The schedule of our o ur time management plan and project flow path in an easy to read format which displays the order in which the various tasks must be completed, which tasks are related to each other, important due dates, and  projected amount of time allocated for individual tasks.

2

 

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2.5 EXISTING PRODUCTS

Star trace spring vibrating table

kinergy spring vibrating table

Vibco electric air cushion vibrating table

tabletop vibrator

2

(www.themouldstore.com)  

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CHAPTER 3

3.1 DESIGN DEVELOPMENT The first of the designs was a rigid tabletop that had a cam directly attached to the motor shaft. This design would have the benefit be nefit of keeping constant amplitude of vibration for an any y load size. After refining our background research we found that the amplitudes of the tabletop should be between 0.3 and 0.4 mm. From this we determined that machining a cam for that range of amplitudes would be extremely difficult and no longer a viable design solution with the given tools available. The next two  brainstorming ideas involved the tabletop sliding horizontally on glide bearings positioned on the top of the frame. These designs have the advantage of taking the preload from the concrete off of the springs. The first design consisted of one vertically aligned car spring in tension. A positive aspect of this design was that the amplitude could be change easily. This spring wo would uld act in the transverse direction, so a transverse spring constant equation, based b ased on the physical dimensions of the spring, could be seen from Castigliano’s Theorem.  Theorem. 

2

 

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Concept layout in various suspension systems.

Motor + eccentric load Helical spring

Pre-load adjustment

2

The horizontal design ideas showed to be viable design solutions. Further background research of conventional standards for tabletop concrete vibrators ruled out both of the designs, stating that

 

tabletop vibrations are required to act in the horizontal direction. From this analysis we acquired a School of Engineering | www.uonbi.ac.ke © Emmanuel and Alex

 

useful tool for calculating the horizontal displacement of our ou r tabletop with a vertically aligned suspension. After more specific background research, the concepts for our prototype design were narrowed down to three viable solutions. All three designs have a rigid tabletop reinforced with angle iron. These Th ese designs share a common four point contact vertical v ertical displacement tabletop design, but differ in suspension type. The first design uses four vertically aligned springs in compression, the second design uses four rubber mounts acting in shear, and the third design uses aair ir cushions or air cylinders. We have also proposed using a single bike inner tube in place of four air cushions. This has the advantage of a lower initial cost, increasing contact con tact area (less relative tabletop deflection), and keeping keepi ng uniform pressure distribution. With the single inner tube suspension design the tabletop will not have to have angle iron reinforcement because of the increased contact area.

3.2 TABLETOP Although angle iron reinforcements were not implemented into the final design choice for modified design, the following section summarizes the analysis performed on the reinforced tabletop design that is common between the three/ four corner suspension type design options. The tabletop for our design has to be very rigid because the amplitudes of vibration are between 0.3 and 0.4 mm. Since the amplitudes are so small, the flex of table due to the forces from the eccentricity coupled with the weight of concrete and acceleration forces must be limited to less than 0.2 mm. This is to ensure that the tabletop does not vibrate only the center of the table, as with the previous design. To accomplish this required rigidity and to minimize cost, we decided dec ided to keep the existing ex isting tabletop thickness of 4 mm, while adding angle steel structural supports in an optimized location.

3.2.1 Spring Suspension System: The spring concept design will feature four springs mounted in the contact points. points . In order to predict 3

the required spring rate needed to match the frequency (3900±200 RPM) and amplitudes (0.3 to 0.4 mm) desired for our system design, spring constant, damping, load, frequency of rotation, and m*e are

 

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all variables we considered to create a more efficient design. Additionally, we assumed a v very ery low damping value to model a system with springs only. At low spring rate values, k, the natural frequency of the system is greatly reduced from the 3800±300 RPM requirement but with larger values of k, the natural frequency matches the input frequency of the motor. In this situation there is a secondary/ beat frequency frequenc y that emerges; this frequency is undesirable  because the amplitude of vibration varies with time in a periodic manner. Therefore in order to obtain the desired output of the system, a damper d amper must be present. With a damper damper,, the secondary frequency disappears and the system has constant amplitude with a frequency equal to that o off the drive shaft. However, the damper does directly affect the amplitude of vibration and therefore, for the same amplitude, a different eccentricity is required.

Assumptions made in the design   The tabletop is a perfectly rigid member 



an d that all four springs vibrate   The motions of the springs are restricted to the vertical axis, and synchronously. In actuality, the rotating mass will put a changing chan ging horizontal force on the

springs and therefore induce a horizontal vibration. This horizontal force will translate to a horizontal deflection of the tabletop

3.2.2 Rubber Mount Suspension System: In our rubber mount suspension concept for the new design, four rubber mounts will be attached at the same contact points, they may also be configured in a circular housing, like a motor mount. The rubber mount suspension design is very similar to that of the spring suspension, but the there are two key differences. First, unlike the springs, the rubber rub ber mounts will have an inherent damping da mping associated with them. This is a positive aspect of this design d esign since, as previously described, damping is desired in our system. Unfortunately, once a mount is selected, the amount of damping cannot be easily changed to account for differences differences in mold sizes. Secondly, with the rubber mount 3

configuration, vibrations can be limited to the vertical v ertical direction. This is also beneficial for our System.

 

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3.2.3 Air Cushion Suspension System: As with the other two suspension types, the air cushion cush ion design concept for the MODIFIED DESIGN consists of four air cushions/shocks mounted in the same location. Air cushions/shocks also have an effective spring rate associated with them. If the spring rate is unknown un known it can be calculated for a cylindrical shock based on the dimensions and pressure, but for an air cushion of irregular shape the spring rate may not be linear and would therefore have to be determined experimentally. The benefits to an air suspension system is that the damping/spring rate can be easily changed by inflating or deflating the suspension. This would be a simple way to control the vibration amplitudes for various mold sizes. Additionally, in some instances, depending on the shock/cushion, the vibration can be limited to the vertical direction. The figure below shows an example of a vibration vib ration table with an air cushion type suspension.

Vibco Electric Air Cushion Vibration Table 

3

 

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Eccentricity Assembly:

The eccentricity assembly in our concept design is similar to the one used in the previous design. However, the input shaft has increased to 0.5 in diameter so as to allow a wider selection of bearings. In order to prevent unnecessary bearing impact loads, the input shaft is press fit with both of the  bearings and the bearings are press fit into their seats. Furthermore, the eccentricity itself will be changed slightly from the eccentricity used in the former design, in order to allow for the amplitudes of vibration to remain within specifications. Two primary eccentricity options were we re considered. The first option is having an eccentricity that is easily adjustable and will function as the primary p rimary variable in tuning the amplitudes of vibration for different mold sizes. While the previous design required the user to disassemble the vibration box assembly in order to remove and then reposition the cylindrical eccentricity, the new one allows the user to change both the mass and radius of mass to center without disassembly. A ratchet coming into the assembly through the bottom can thread additional nuts or plates on to the U-Bolt, thus changing the forces exerted b by y the spinning mass. This change in force results in a change in tabletop amplitude and frequency.

The second option uses the same eccentricity as the previous vibrating table but with slightly different dimensions. This option is not adjustable but is fine tuned to work with the other chosen cho sen design variables (tube height, shaft speed, or Damping Mass).

Rheostat:  Rheostat:  Another available option which will change the amplitude of the tabletop is a rheostat. A rheostat

(variable resistor) can be connected in series with the motor in order to provide a different voltage drop through the line. This voltage drop d rop means the motor itself will receive less than 12 V. Therefore, even though the battery is outputting a constant voltage, the motor will only be able to use a certain  percentage of it, due to the voltage drop across the rheostat. By manually changing the resistance across the rheostat, the motor will be able to change from a rated speed of 4500 RPM to about 500 RPM (based upon the max resistance available on the rheostat). By changing the speed, the amplitude 3

of vibration of the tabletop will also change.

 

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However, there are some problems in using a rheostat in our system. During use, and depending on the resistance setting, the rheostat may get very hot. The rheostat would have to be placed in such a location that the heat will not affect the user. Also, because the rheostat is removing en energy ergy from the system by way of non-usable heat, the efficiency of the system drops depending on the rheostat resistance setting. Output torque will also drop as the rheostat’s resistance increases, and may ma y reach aa    point to where the motor can no longer rotate the eccentricity. Small variations in speed can have large effects on the amplitude. The exact change in efficiency, speed, and torque for a change in resistance cannot yet be determined, as the armature resistance and other motor characteristics are not yet known.

Damping Mass:

Additional mass can also be used to change the amplitudes of the tabletop. By varying the size of the mass hanging from the bottom of the tabletop depending on the mold size, the effective mass that the tabletop sees can be maintained to a relatively constant value. For instance if the tabletop were designed to reach the desired amplitude and frequency for a 40 kg mold, the operator would add 15 kg to the tabletop when a 25 kg mold is vibrated. Therefore, for each case the vibrator will respond similarly. For each case, small amplitude variations will result from differences in weight distribution. Testing will determine the minimum number of masses and their respective sizes needed in order to maintain the amplitudes within specification for all mold sizes.

3.3 Development Test Plan Plan:: Since the three suspension types (spring, rubber mounts, and air cushions) were all viable options for the final design of the modified vibrating table, we decided that to pick a spring suspension system. Although it would have been beneficial to build and test each design and then compare results,  because of time limitations and cost considerations, we decided to start with the spring suspension design since it has the most desirable characteristics. These characteristics include damping, maximum weight distribution, easier operability, low cost, availability and size of added add ed mass to optimize 3

 performance with different mold sizes. 

 

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CHAPTER 4

4.1 DESIGN OF PARTS 4.1.1Design Of Helical Springs; Mechanical springs have varied use in different types of machines. Briefly discussed are some of the applications, followed by design aspects of springs in general. Definition of a spring: Springs act as a flexible flexible joint in between two parts or bodies Objectives of spring: The main objectives of a spring when used as a machine member are as

follows: 1.  Cushioning, absorbing, or controlling of energy due to shock and vibration.

Car springs or railway buffers are used to control energy, springs-supports and vibration dampers. 2.  Control of motion

Maintaining contact between two elements (cam and an d its follower).In a cam and a follower arrangement, widely used in numerous applications, a spring maintains contact between the two elements. It primarily controls the motion and also creates the necessary pressure in a friction device (a brake or a clutch). A person driving a car uses a brake or a clutch for controlling the car motion. A spring system keep the brake in disengaged position until applied to stop the car. The clutch has also got a spring system (single springs or multiple springs) which engages and disengages the engine with the transmission system. Restoration of a machine part to its normal position position when the applied force is withdrawn (a governor or valve). A typical example is a governor for turbine speed control. A governor system uses a spring controlled valve to regulate flow of o f fluid through the turbine, thereby controlling the turbine speed. 3. Measuring forces; This achieved by use of spring balances and gauges. 4.  Storing of energy; - i.e. in clocks or starters - The clock has spiral type of spring which is

wound to coil and then the stored energy helps gradual recoil of the spring when in operation. 3

 Nowadays we do not find much use of the winding clocks. Before considering the design aspects of springs we took a quick look at the

 

spring materials and manufacturing methods involved. School of Engineering | www.uonbi.ac.ke © Emmanuel and Alex

 

Commonly used spring materials

One of the important considerations in spring design is the choice of the spring material. Some of the common spring materials are given below.

H ar d-draw -drawn nw wii r e: This is cold drawn, cheapest spring steel. Normally used for low stress and static load. The material is not suitable at subzero temperatures or at temperatures above

.

OilOi l-te tem mper ed wir e: It is a cold drawn, quenched, tempered, and general purpose spring steel. Ho However, wever, it is not suitable for fatigue or sudden loads, at subzero temperatures and at temperatures above

.

When we go for highly stressed conditions then alloy allo y steels are useful.

C hr hro ome Vana Vanad di um: This alloy spring steel is used for high stress conditions and at high temperature up to

 . It is

good for fatigue resistance and long endurance for shock and impactloads.

C hr hro ome Si lico li con n: This material can be used for highly stressed springs. It offers excellent service for long life, shock loading and for temperature up to

.

 Music wi re: This spring material is most widely used for small springs. It is the toughest and has highest tensile strength and can withstand repeated loading at high stresses. However, it cannot be used at subzero temperatures or at temperatures above

.

 Normally when we talk about springs we found that the music wire is a common choice for springs. springs. 

3

 Staii nle  Sta nless ss ste steel:  Widely used alloy spring materials.

 

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P ho hosp spho horr B r onz nze e / Spri Spring ng B r ass: It has good corrosion resistance and electrical conductivity. That’s the reason it is commonly used for contacts in electrical switches. Spring brass can be used at subzero temperatures.

Spring manufacturing processes:

If springs are of very small diameter and the wire diameter is also small then the springs are normally manufactured by a cold drawn process through a mangle. However, for very large springs having also large coil diameter and wire diametermone has to go for manufacture by hot processes. First, one has to heat h eat the wire and then use a proper mangle to wind the th e coils. There are two major types of springs which are mainly used, helical springs and leaf springs. In our case we have considered the design aspects of two types of springs. Helical spring: -

The figures below show the schematic representation of a helical spring acted upon by b y a tensile load F (Fig.1) and compressive load F (Fig.2). The circles circl es denote the cross section of the spring wire. Th Thee cut section, i.e. from the entire coil somewhere we make mak e a cut, is indicated as a circle with shade.

3

 

Figure 1

figure 2

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If we look at the free body diagram of the shaded region onl only y (the cut section) then do we see that at the cut section, vertical equilibrium of forces will give us force, F as indicated in the figure. This F iiss the shear force. The torque T, at the cut section and it’s direction is also marked in the figure. There is no horizontal force coming into the picture because b ecause externally there is no h horizontal orizontal force present. So from the fundamental understanding of the free body bod y diagram one can see that any section of the spring is experiencing a torque and a force. Shear force will always be associated with a bending moment. However, in an ideal situation, when force is acting at the centre of the circular spring and the coils of spring are almost parallel to each other, oth er, no bending moment would result at any section of the spring ( no moment arm), except torsion and shear force.

Stresses in the helical spring wire:

From the free body diagram, we have found out the direction of the internal torsion T and internal shear force F at the section due to the external load F acting at the centre of the coil.

The cut sections of the spring, subjected to tensile and compressive loads respectively, are shown separately in the Fig. below. The broken arrows show the shear stresses (

 ) arising due to the torsion

 due to the force F. It is observed that for both tensile loads as well as compressive load on the spring, maximum shear stress (   ) always occurs at the

T and solid arrows show the shear stresses

inner side of the spring. Hence, failure of the spring, in the form of crake, is alwa always ys initiated from the inner radius of the spring. As indicated on the sketched figures below, 3

 

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The radius of the spring is given by b y D/2. Note that D is the mean diameter of the spring. The torque T acting on the spring is

       If d is the diameter of the coil wire and polar moment of inertia,

  , the shear strstress ess in the spring

wire due to torsion is

               Average shear stress in the spring wire due to force F is

        Therefore, maximum shear stress the spring wire is

OR

OR 3

 

Hence;

                        where, C= ,          

    

where,

      

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is called the spring index.

 

The above equation gives maximum shear stress occurring in a spring.

 is the shear stress correction

factor. Stresses in helical spring with curvature effect 

What is curvature effect? Let us look at a small section of a circular spring, as shown in the Fig. Below Suppose we hold the section b-c fixed and give a rotation to the section a-d in the anticlockwise direction as indicated in the figure, then it is observed ob served that line a-d rotates and it takes up another  position, say a'-d'. The inner length a-b being smaller compared to the outer length c-d, the shear strain Y at the inside of the spring will be more than the shear strain

 at the outside of the spring.

Hence, for a given wire diameter, a spring with smaller diameter will experience more difference of shear strain between outside surface and inside surface compared to its larger counterpart. The above

 

 phenomenon is termed as cur curva vatur ture e effect . So more is the spring index (C= ) the lesser it will be the curvature effect. effect. For example, the suspensions in the railway carriages carriages use helical springs. These springs have large wire diameter compared to the diameter of the spring itself. In this case curvature effect will be predominantly high.

To take care of the curvature curva ture effect, the earlier equation for maximum shear stress in the spring wire is modified as,

       4

Where,  

is Wahl correction factor, which takes care of both curvature effect and shear stress

correction factor and is expressed as, School of Engineering | www.uonbi.ac.ke © Emmanuel and Alex

 

        Deflection of helical spring

(B)

(A)

Fig. (A) and Fig. (B) Show a schematic view of a spring, a cross section of the spring wire and a small spring segment of length dl. It is acted upon by a force F. From simple geometry we will see that the deflection, d, in a helical spring is given by the formula,  

       4

Where, N is the number of active turns and G is the shear modulus of elasticity. The force F cannot  just hang in space, it has to have some material contact with the spring. Normally the same spring wire

 

e will be given a shape of a hook to support the force F. The hook etc., although is a part of the spring, School of Engineering | www.uonbi.ac.ke © Emmanuel and Alex

 

they do not contribute to the deflection of the spring. Apart from these coils, other coils which take  part in imparting deflection to the spring are known as active coils. coils.

How to compute the deflection of a helical spring

Consider a small segment of spring of length ds, subtending an angle of dß at the centre of the spring coil as shown in Fig. (B) above. Let this small spring segment be considered to be an active portion and remaining portion is rigid. Hence, we consider only the deflection of spring arising due to application of force F. The rotation, df, of the section a-d with respect to b b-c -c is given as,

                          sp ring O to rotate to O', shown in   will cause the end of the spring  Fig.(A). From geometry, O-O' is given as, O-O'=   The rotation,

However, the vertical component of O-O' only will contributes towards spring deflection. Due to symmetric condition, there is no lateral deflection of spring, i.e., the horizontal component of O-O' gets cancelled. The vertical component of O-O', d d , is given as,

           4

     

 

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

Total deflection of spring, , can be obtained by integrating the above expression for entire length of the spring wire.

        Simplifying the above expression we get,

       The above equation is used to compute the deflection of a helical spring. Another important design  parameter often used is the spring rate. It is defined as,

     

Here we conclude on the discussion for important design features, namely, stress, deflection and spring rate of a helical spring.

Example Problem

A helical spring of wire diameter 6mm and spring index 6 is acted by an initial i nitial load of 800N. After compressing it further by 10mm the stress in the wire is 500MPa. Find the number of active coils. G = 84000MPa. Solution:

       OR



     

Therefore shear force F =940.6

           

Hence, K=14N/mm

         Or,         4

Hence,

        

 

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ECCENTRIC LOAD An eccentricity that is easily adjustable and will function as the primary variable in tuning the amplitudes of vibration for different mold sizes. It also allows the user to change c hange both the mass and radius of mass to center without disassembly. A ratchet coming into the assembly through the bottom can thread additional nuts or plates on to the U-Bolt, thus changing the forces exerted by the spinning mass. This change in force results in a change chan ge in tabletop amplitude and frequency. As shown in the figure below:

The eccentricity itself is a U-bolt which allows for an easy eas y way to add mass and or change eccentric radius. This is accomplished by adding bolts to the free end of the U U-bolt, -bolt, and then using the threads to change the distance to the center .

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DESIGN OF TABLE TOP Deflection and stresses in Table Top 4 mm thick steel plate with sections of angle steel w welded elded to the underside. The steel angle line has dimensions of about 60x60x5 mm and is also made of steel. When the tabletop is at its lowest point, the springs are at a t their maximum compression. From our mass spring damper, we expect that this location will cause the maximum bending of the tabletop. At this location, spring forces and the eccentricity force are acting on the bottom of the tabletop, while the weight of the concrete and the acceleration forces are acting on the top of the tabletop. We assumed a distributed load of 400-600 N (40-60 kg of concrete) over an area of 75x75 cm, and the forces exerted by eccentricity are distributed across its contact area. This force was calculated using an m*e (mass times eccentric radius) of .00346Kg*m, which is approximately ap proximately 2.5 times greater than the eccentricity used on the previous design, can be varied and assumes a rotation speed of 3800 RPM. This force is caused  by the angular acceleration force of the mass imbalance and amounts to about 600N. The maximum displacement seen in the tabletop for the forces provided p rovided is 0.069 mm, located in the corners of the tabletop. This displacement is well below the required maximum deflections of 0.2 mm, and this is due to the high rigidity in the table. If the angle iron reinforced tabletop was chosen for our final design, further analysis would be done to minimize the size of the angle iron in order to reduce weight and overall cost. The stresses are negligible in the design of the tabletop. The design had a high factor of safety and this is because the tabletop is designed to be b e so rigid. Overall the deflections of the tabletop are what will drive the design. The stress and deflection analysis have a few notable differences between the design concept and the actual system. s ystem. The spring contact points are designed as stationary pivot points, when in actuality the springs/rubber mounts will be dynamic.

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 ASSEMBLY Design of assembly process was done with the ease of the assembly in mind. Th This is was achieved by using integrated parts that do need much orienting and utilize minimal fasteners. This eases part fabrication and assembly of individual components constituting the concrete vibration table. We proposed the use of 12V DC motor to transmit transmit the vibrations to the table top, steel which are welded together to form rigid rectangular stand as supports to the vibrating table top The motor is firmly anchored beneath the table top by use of bolt and pin. An eccentric load is attached to the motor to provide an imbalance so that the motor can vibrate as it rotates. The tabletop has shelled corners beneath it so as to accommodate the spring suspension system and rubber mountings on the upper side. These rubber mountings were used to reduce the noise generated by the vibrating table during its consolidation of concrete.

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Final design for the concrete vibrating table.  

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COST ESTIMATION OF THE MACHINE COMPONENTS

Machine Part

Number

Material

Cost(Ksh)

Tabletop 

1

Mild Steel

7500

Helical Spring

4

Stainless Steel

1200

Frame

1

Iron

5000

12V D.C. Motor

1

Eccentric Load

1

Iron

1500

Rubber Mountings

4

Rubber

400

Pin rod

5

Mild Steel

1750

Bush

8

Mild Steel

640

Seat

8

Steel

80

Bolt

10

Steel

200

1500

TOTAL

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18,270

 

DRAWINGS

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CHAPTER 5

5.1 CONCLUSION A study of the various methods of consolidation of o f concrete was done from which the design of a concrete vibrating table was done. A few modifications were taken into consideration such as damping of the noise by use of rubber rub ber mountings, use of adjustable speed motor and attaching an adjustable eccentric load to the motor. This enabled increase or decrease of the vibratory motion depending on the load. The whole table top vibrated and not just the center as per our design objectives. As per the initial design goals, we were able to meet all the deign objectives.

5.2 RECCOMENDATION With regards of the project design, the modifications made can easily be implemented and fabricated. Unfortunately, we did not manage to fabricate the concrete vibrating table due to time constraints. However, the design is feasible and to prevent experiencing the shortcomings we experienced, we recommend that prior to implementation adequate funds should be set aside for fabrication in a university setting. However, in a factory setting, the design implementation is fairly simple as the funds are present and the materials are all readily and locally available. The vibrating concrete table can be widely used in rural areas a reas to produce paving blocks and roofing tiles for better structural finishes.

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5.3 REFERENCES Analele P. 2004 - Concrete consolidation and vibration

www.ann.ugal.ro/im/anale-fib-2004-16.pdf

Bevan T. (2010). Design of a Vibrating Table for a CBVT Shetty M.S. (2005). Concrete Technology Ogot M. Okudan-Kremer, G. Engineering Design: A Practical Guide Tattersall, G.H. and Baker, P.H. 1989 –  Importance  Importance of An investigation on the effect of vibration on the workability of fresh concrete.

Zhu, W. Bartos, P.J.M. , 2003 - Cement and Concrete Research- Permeation Research- Permeation properties of self-compacting concrete

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