Kayış Kasnak Mekanizmaları Hareket İletim Mekanizmaları Makine Elemanları II İ.T.Ü. Makine Fakültesi (Belt and Pulley mechanism)

Kayış tipleri

Kayış tipleri Comparison of flat belt and V belt

Kayış Kasnak Mekanizmaları Düz kayış V- kayışları Dişli kayışlar Zincir mekanizmaları Sürtünmeli çarklar

Dişli Çarklar ve Kayış Kasnak

Teorik Esaslar Çevrim oranı sarım açısı ile sınırlıdır. Bu şekildeki sarım açısı 100o kadardır.

Kayış Kuvvetleri Normal Doğrultu: sin(dβ/2)≈dβ/2

Kayış Kuvvetleri Normal Doğrultu: sin(dβ/2) ≈ dβ/2

Kayış Kuvvetleri Teğetsel Doğrultu: Cos(dβ/2≈1

Kayış Kuvvetleri dN reaksiyon, gelen kuvvetler FT1 ve FT2 , Eytelwein - Grashof

Çevre Kuvveti Çevre Kuvveti Yatak Kuvveti (Aks Kuvveti) β = 180o ise β ≠ 180o ise

Aks Kuvveti Çevre Kuvveti Yatak Kuvveti (Aks Kuvveti) β = 180o ise

Kayış Gerilmeleri A : Kayış kesiti ; Faydalı gerilme

(Santrifüj) Merkezkaç Kuvvet Tesiri Çevre hızı sebebi ile σf santrifrüj gerilmesi ve FTf kayış kuvveti meydana gelir.

Merkezkaç Kuvvet Tesiri Merkezkaç kuvvetler sebebi ile σf gerilmelerinin tayini için kayış elemanı üzerindeki kuvvetler

Merkezkaç Kuvvet Tesiri FTf kayış kuvvetleri ile bileşke Ff merkezkaç kuvveti arasındaki denge

Merkezkaç Kuvvet Tesiri Ff gelen, FTf reaksiyon kuvvetleri

Merkezkaç Kuvvet Tesiri Merkezkaç kuvveti tesiri dikkate alınırsa ifadesi kullanılmalıdır. Bileşke kuvvet Ff , ΔFf kısmi kuvvetlerinin toplamıdır.

Eğilme Gerilmesi σb eğilme gerilmesinin tayini için kayış elemanındaki geometrik oranlar s, dk'ya göre küçük olduğundan;

Eğilme Frekansı z kasnak sayısı, v kayış hızı ve L kayış uzunluğunun fonksiyonudur.

Kayış üzerindeki gerilmeler

Toplam Gerilme ; birim alana gelen güç

Optimum Kayış Hızı Nispeten küçük bir gerilme olan σb hesaba katılmaz ise faydalı güç; A=b.s kesidine orantılı P/A=σnv gücünün v çevre hızına bağlı olarak değişimi

Optimum Kayış Hızı Nispeten küçük bir gerilme olan σb hesaba katılmaz ise faydalı güç; olduğu yerde optimum hız elde edilir. vopt = 38 m/sn (kösele kayış)

v hızına bağlı kayış gerilmeleri v çevre hızına bağlı olmak üzere kösele kayıştaki gerilmeler

Kayış Mekanizmaları Kayış uzunluğu geometrik eğrilerin toplamıdır.

Düz kayışların boyutlandırılması Kayış uzunluğu

Boyutlar a: eksenler arası mesafe β: sarım açısı

Boyutlar x a α a

Kayış iç uzunluğu ve alınarak

Çok tabakalı düz kayışlar Kayış Genişliği P1 = 1 cm genişliğe gelen güç c1 = yük faktörü c2 = açı faktörü Extremultus Kayışlar Uzama : ; 80 tipi için

Mil Kuvveti FA1 ; birim genişlikteki çekme kuvveti Poliamid kayışlar yüksek elastikdir. Sonradan bir kontrol lüzumlu değildir.

V- Kayış Mekanizmaları Kayışın yuvaya şekil ve kuvvet bağlı olması halinde sürtünme katsayısı μ’nün tayini için kuvvetler

V- Kayış Mekanızmaları ΔF: öngerilme kuvveti ΔN: normal kuvvet μ ΔN: sürtünme kuvveti

Çevre Kuvveti Sürtünme katsayısı

Dar V-Kayışları Sarım Açısı: a

Çalışma Uzunluğu 630...12500 mm arasında Lw : öngerilme verildikten sonra ölçülür bw : tarafsız eksendeki kayış genişliği Ld = Lw + 2πhw : dış uzunluk 

Takribi çalışma uzunluğu

V Kayış özellikleri Dar V-kayışlarında h/b~1/1,123'dir, (Normal~1/1,6). Eğilmeye karşı daha elastiktir. Daha küçük kasnak çaplarında kullanılabilirler, yer ve ağırlık tasarrufu sağlanır.

Kayış Mekanizmaları Dişli kayış

Belt tensions

Belt tensions

Selection procedure Belt type: initial Selection Estimates of belt speed and speed ratio can be used as shown below to make an initial Selection of the type of belt required. If a constant speed ratio is important, use a Toothed belt if belt speed < 30 m/s, use a Vee belt

Belt type: initial Selection if belt speed < 40 m/s and, - speed ratio < 7:1, use a Vee belt - speed ratio < 8:1, use a Wedge belt otherwise, if speed ratio > 8:1 or belt speed > 40 m/s, use a Flat belt

Duty/Service factor Types of duty are categorised as follows: Light duty Medium duty Heavy duty Extra heavy duty The type of duty determines the service factor involved (S).

Duty/Service factor Service factors for typical driving and driven machines and for a variety of duties are shown in the table below. Further allowacne may be required if the consequences of failure are particularly serious. Some manufacturers' catalogues may give further advice on suitable values.

Duty/Service factor

Nominal speed ratio The speed ratio is a function of the pulley sizes. The minimum recommended pulley size for a given section depends on the flexibility of the belt and the mass/unit length. Pulleys are normally manufactured in standard sizes so the choice of the driving pulley should be the smallest standard size which is recommended for the chosen belt section such that the ratio obtained is near to the required value when matched with a larger standard size pulley.

Nominal speed ratio Pulley sizes are normally based on a pitch diameter, which may be less than the outside diameter. Minimum pulley diameters recommended for a range of belt types are as follows: Vee 67 mm Wedge 60 Flat 40 Polyvee 18 Timing 16

Belt length Belt Length (L) is a function of shaft center distance and pulley diameters. Most belts are made in standard lengths which are cheaper and easier to obtain than non- standard ones. Some (particularly plain flat belting) can be supplied in straight lengths which can be joined round the pulleys.

Belt length

Belt length However, these are recommended only if the assembly of a continuous belt is difficult. The nominal length calculated above should be modified to the nearest standard length, and the shaft centre distance amended to suit. Manufacturers’ catalogues should be consulted to determine the standard lengths available for specific belt types.

Power factors Allowable Power per Belt (Pb) is a function of the dimensions of the belt section and is obtainable from the manufacturer's catalogue. Plain flat belting is often rated as power per width dimension (kW/mm).

Power factors Power Correction Factors may be required to compensate for: Speed ratio Length of belt/pulley contact Total length of belt Appropriate manufacturers' catalogues will provide values and method of application.

Number of belts Number of Belts (X) refers to the total number of separate belts or the total width of (flat) belt required. This is given by: X = P'/Pb In the case of Vee type belts the value of X should be rounded up to the nearest whole number. For flat belt types the value of X should be rounded up to the nearest standard belt width available from the manufacturer.

Other factors Further refinement of the belt choice will result from consideration of commercial and reliability factors such as cost, availability etc, and belt life, pulley wear etc.

Select the type of belt required Optimising the choice of a suitable element is now a process of finding the best compromise (in the opinion of the designer) between the priorities of the system and the availability of the hardware. Select a suitable belt type, using 'best match" criteria.

Select the type of belt required As far as the factors involving numerical data are concerned, some yield a 'go/no-go‘ situation which will eliminate those which are too costly, too heavy, too big etc. The table below indicates the maximum performance to be expected from different belt types

Typical belt performance

Installation During the design of the installation for a belt drive, particular attention should be paid to the following: Maintenance of initial tension (where required), Adjustability of tension, Pulley alignment, Ease of removing and fitting belt, Protection from pollutants (lubricants, acids, grits etc) , Guarding from interference with operators' clothing, person etc

Belt types and features Five main types of belt are currently available. Details of their construction and performance are shown in the table below. An initial Selection of belt type should be made at an early stage of the design, based on estimates of speed and speed ratio.

Belt types and features

Belt types and features

Power rating ranges for belt types The power rating charts for the following belt types are supplied with this guide (courtesy of J.H. Fenner Ltd):

Power rating ranges for Vee belt

Power rating ranges for belt types Wedge

Power rating ranges for Timing Belts (courtesy of J H Fenner & Co Ltd)

For each belt type, the range of powers covered by a given belt section is denoted by a thick line and designated by a code. The elements of the code for Vee and Wedge belts are as follows: a number (eg: 200) shows the pulley pitch diameter limit a number (eg: 2) shows the number of belts a letter (eg: C) shows the belt section size

For Timing belts, the code simply denotes the section size For Timing belts, the code simply denotes the section size. Other manufacturers may show similar information in a slightly different format. The rating chart for Timing belts shows similar information from the same manufacturer. This time, the chart is confined to a particular width of belt (25mm) and wider belts should be uprated pro-rata.

A rating chart for Flat belts is also supplied, courtesy of Stephens Miraclo Belting Co. Belt codes here denote section size, and power ratings are given per unit belt width.

A rating chart for Flat belts

Basic Timing Belt Parameters Classical Timing belts

HTD- Curvilinear

GT - Curvilinear

Power method Designing a Synchronous Belt System Belt design procedures can be based on torque calculations or they can be based on power calculations.

1) The driven speed and the maximum driven torque required (including inertia load, shock loads, friction, etc) are used to calculate the required driven power 2) From information on the driver, driven equipment and operating period a service factor is obtained - see below

3) A design power is obtained based on the product of the Driven Power required and the service factor . 4) A belt section is initially selected using a graph as typically shown below 5) A drive geometry is derived selecting suitable pulleys, and belt Centre Distance – Some Pulley sizes are provided below

6) A Basic Power for the belt is calculated and a mesh factor is calculated - see below 7) A suitable belt width is selected -Using a table as provided below- Some iteration may be required

Torque Method The classical MXL belt and the Curvilinear more advanced belt options are designed based on torque levels. The outline method for the MXL drive is provided below. The method used for the HTD and other modern belt options will be provided at some future date...

The MXL belts operate generally at relatively low belt speeds so the torque levels are similar for the normal range of pulley rotational speed. Torque ratings can be calculated of each of the MXL belt widths as follows: I have converted an imperial formula to a metric formula and minor differences with the original formulae results.. Torque ratings of belts Tr (Nm) at P2 PCDs (mm

Zincir Dişli Mekanizmaları

Zincir Dişli Mekanizmaları Chordal speed variation %

Zincir Dişli Mekanizmaları Chordal speed variation %

Sürtünmeli Çark Mekanizmaları Sürtünmeli çark mekanizmaları birbiri ile temasta bulunan ve kuvvet bağı ile güç ve hareket ileten çark mekanizmalarıdır

Sürtünmeli Çark Mekanizmaları Kaymadan yuvarlanma halinde çevrim oranı: tek kademede: i  6 (14) Kayma hesaba alınırsa: kayma: = 0.005.....0.5

Sürtünmeli Çark Mekanizmaları Kaymadan yuvarlanma olması için normal kuvvet:  : sürtünme katsayısı Sürtünmeli Çark Tipleri: Evans Friction Cone Toroidal CVT

Ders Kitabı (Notu) Ders Notları mevcut Diğer Kaynaklar Joseph Edward Shigley, Mechanical Engineering Design, McGraw-Hill International Editions, First Metric Edition, 1986. Tochtermann/Bodenstein, Konstruktionselemente des Machinenbaues 1,2, Springer-Verlag Juvinall, R.J. and Marshek, K.M., Fundamentals of Machine Component Design, 3rd Edition, John Wiley & Sons, 2000. Deutschman, A.D., Wilson,C.E and Michels, W.J., Machine Design, Prentice Hall, 1996. Erdman, A.G. and Sandor, G.N., Mechanism Design Analysis and Synthesis, Vol. 1, 3rd Edition, Prentice Hall, 1997. Shigley, J.E., Uicker, J.J., Theory of Machines and Mechanisms, Second Edition, McGraw-Hill, 1995.