Roda Gigi (Gear)
Perencanaan Material
Daya yang ditransmisikan
Kecepatan
Geometri (jumlah gigi, involute teeth)
Efisiensi
Gear Box
Perencanaan poros
Friction Wheels Gerak dan daya yang ditransmisikan oleh gigi adalah setara dengan yang dikirimkan oleh roda. untuk memahami bagaimana gerakan dapat ditularkan oleh dua roda bergigi, mempertimbangkan dua roda melingkar polos A dan B dipasang pada poros.
Velocity Ratio
2 N 2 d1 T1 1 N1 d 2 T2
Gear Drives Advantages 1. Dapat mentransmisikan rasio kecepatan yang tepat. 2. Dapat digunakan untuk mengirimkan daya yang besar. 3. Memiliki efisiensi tinggi. 4. Memiliki tata letak yang kompak. Disadvantages 1. Karena pembuatan gigi memerlukan peralatan dan perlengkapan khusus , oleh karena itu lebih mahal dari drive lainnya. 2. Kesalahan dalam pemotongan gigi dapat menyebabkan getaran dan kebisingan selama operasi. 3. Hal ini membutuhkan pelumas yang sesuai dan metode yang dapat diandalkan untuk menerapkannya, untuk operasi yang tepat dari drive.
Klasifikasi Kecepatan Roda Gigi 1. Low velocity ( < 3 m/s )
2. Medium velocity ( 3 - 15 m/s ) 3. High velocity ( > 15 m/s )
Bentuk Gigi CYCLOIDAL
INVOLUTE
Bentuk Gigi CYCLOIDAL 1. 2.
Lebih kuat pada pitch yang sama dengan involute Tidak terjadi interference (lebih smooth)
INVOLUTE 1.
Pressure angle konstan
2.
Velocity ratio tidak berubah dengan berubahnya ukuran gigi
Sistem Gigi 1.
14 1/2 ° Composite
2.
14 1/2 ° Full depth involute
3.
20 ° Full depth involute
4.
20 ° Stub involute
Sistem Gigi
Interference Gigi Involute
Interference Gigi Involute
Interference Gigi Involute
Material Roda Gigi Pertimbangan dalam pemilihan material roda gigi
1.
Kekuatan ijin
2.
Noise
3.
Keausan
4.
Dan lain-lain
Material roda gigi 1.
Metallic
2.
Non-Metallic Table 28.3. Properties of commonly used gear materials
Pertimbangan Desain Roda Gigi 1. Kekuatan yang ditransmisikan, 2. Kecepatan dari roda gigi penggerak, 3. Kecepatan dari roda gigi yang digerakkan atau rasio kecepatan, dan 4. Jarak titik pusat. Syarat yang harus dipenuhi : 1. Gigi pada roda gigi harus memiliki kekuatan yang cukup sehingga tidak rusak dibawah beban statis dan beban dinamis. 2. Gigi pada roda gigi harus memiliki karateristik keausan yang tinggi. 3. Penggunaan ruang dan material harus ekonomis. 4. Penyelerasan gigi dan defleksi pada poros harus diperhatikan karena berpengaruh pada kinerja pada roda gigi. 5. Pelumasan roda gigi harus cukup.
28.17 Kekuatan Batang Gigi pada Roda Gigi – Lewis Equation
28.18 Tengangan Izin yang bekerja untuk roda gigi pada Persamaan Lewis Tegangan kerja yang diizinkan ( σw) dalam persamaan Lewis tergantung pada bahan yang tegangan statis yang diijinkan ( σo) dapat ditentukan. Tegangan statis yang diijinkan adalah tegaangan pada batas elastis bahan. Hal ini juga disebut tegangan dasar.
Mekanisme gigi sepeda mengganti rantai antara sprocket ukuran yang berbeda di pedal dan roda belakang. Naik bukit, depan kecil dan sproket belakang yang besar yang dipilih untuk mengurangi tekanan diperlukan untuk pengendara. Pada tingkat, depan dan belakang besar kecil. sproket digunakan untuk mencegah Pembalap harus mengayuh terlalu cepat
28.19 Beban Dinamis pada Gigi Faktor kecepatan digunakan untuk membuat perkiraan koreksi untuk efek pembebanan dinamis. Beban dinamis disebabkan berikut : 1. Ketidakakuratan dari jarak gigi, 2. Penyimpangan dalam profil gigi, dan 3. Lendutan gigi bawah beban.
28.20 Beban Statis pada Gigi Beban statis gigi (disebut juga kekuatan batang atau kekuatan daya tahan pada gigi) diperoleh dari rumus lewis dengan mengganti batas ketahanan lentur dan batas tegangan elastis (σe) pada tegangan izin (σw) yang bekerja.
Untuk keamanan, terhadap kerusakan gigi, beban statis (WS) harus lebih besar dibandingkan beban dinamis (WD). Buckingham menyarankan mengikuti hubungan antara WS dan WD Untuk steady loads, WS ≥ 1,25 WD Untuk pulsating loads, WS ≥ 1,35 WD Untuk shock loads, WS ≥ 1,5 WD Note : Untuk baja, batas ketahanan lentur (σe) dapat diperoleh dengan menggunakan hubungan berikut :
Causes of Gear Tooth Failure 1.
Bending Failure
Every gear tooth acts as a cantilever. If the total repetitive dynamic load acting on the gear tooth is greater than the beam strength of the gear tooth, then the gear tooth will fail in bending, i.e. the gear tooth will break. The module and face width of the gear is adjusted so that the beam strength is greater than the dynamic load. 2.
Pitting The failure occurs when the surface contact stresses are higher than the endurance limit of the material. The dynamic load between the gear tooth should be less than the wear strength of the gear tooth.
Causes of Gear Tooth Failure 3.
Scoring
The excessive heat is generated when there is an excessive surface pressure, high speed or supply of lubricant fails. By properly designing the parameters such as speed, pressure and proper flow of the lubricant, so that the temperature at the rubbing faces is within the permissible limits. 4.
Abrasive Wear The foreign particles in the lubricants such as dirt, dust or burr enter between the tooth and damage the form of tooth.
By providing filters for the lubricating oil or by using high viscosity lubricant oil which enables the formation of thicker oil film.
Causes of Gear Tooth Failure 5.
Corrosive Wear
The corrosion of the tooth surfaces is mainly caused due to the presence of corrosive elements such as additives present in the lubricating oils. Proper anti-corrosive additives should be used.
Spur Gear Construction a.
The dedendum circle diameter is slightly greater than the shaft diameter, then the pinion teeth are cut integral with the shaft
Spur Gear Construction a.
If the pitch circle diameter of the pinion is less than or equal to 14.75 m + 60 mm (where m is the module in mm), then the pinion is made solid with uniform thickness equal to the face width
b.
Small gears up to 250 mm pitch circle diameter are built with a web, which joins the hub and the rim. The web thickness is generally equal to half the circular pitch or it may be taken as 1.6 m to 1.9 m, where m is the module. The web may be made solid.
Gear with Arms
Gear with Arms
Gear with Arms
The hub diameter: 1.
1.8 times the shaft diameter for steel gears
2.
Twice the shaft diameter for cast iron gears
3.
1.65 times the shaft diameter for forged steel gears used for light service.
The length of the hub is kept as 1.25 times the shaft diameter for light service and should not be less than the face width of the gear.
Gear with Arms
Design of Shaft for Spur Gears
Design of Shaft for Spur Gears
Design of Arms for Spur Gears 1. The cross-section of the arms is calculated by assuming them as a cantilever beam fixed at the hub and loaded at the pitch circle. 2. It is also assumed that the load is equally distributed to all the arms. 3. It may be noted that the arms are designed for the stalling load. 4. The stalling load is a load that will develop the maximum stress in the arms and in the teeth. This happens at zero velocity, when the drive just starts operating.
Design of Arms for Spur Gears Stalling load
Design of Arms for Spur Gears Maximum bending moment on each arm
Design of Arms for Spur Gears Section modulus of arms for elliptical cross-section
Helical Gear
Definisi 1. A helical gear has teeth in form of helix around the gear.
2. The helixes may be right handed on one gear and left handed on the other. 3. Helical gears give smooth drive with a high efficiency of transmission.
Helical Gear Type 1. Single helical gear menghasilkan gaya aksial pada gigi
2. Double helical gear terjadi keseimbangan gaya aksial
Nomenclature 1. Helix angle. It is a constant angle made by the helices with the axis of rotation. 2. Axial pitch. It is the distance, parallel to the axis, between similar faces of adjacent teeth. The axial pitch may also be defined as the circular pitch in the plane of rotation or the diametral plane. 3. Normal pitch. It is the distance between similar faces of adjacent teeth along a helix on the pitch cylinders normal to the teeth. It is denoted
Face Width of Helical Gears
Face Width of Helical Gears
Formative or Equivalent Number of Teeth for Helical Gears
Proportions for Helical Gears American Gear Manufacturer's Association (AGMA)
Strength of Helical Gears
Strength of Helical Gears
Strength of Helical Gears
Contoh
Contoh
Contoh
Contoh
Contoh
Bevel Gears
Introduction Used for transmitting power at a constant velocity ratio between two shafts whose axes intersect at a certain angle. The pitch surfaces for the bevel gear are frustums of cones. The elements of bevel gear pitch cones and shaft axes must intersect at the same point.
Classification of Bevel Gears Mitre gears
Angular bevel gears Crown bevel gears Internal bevel gears
Nomenclature
Nomenclature
Nomenclature
Determination of Pitch Angle for Bevel Gears
Proportions for Bevel Gear
Formative or Equivalent Number of Teeth for Bevel Gears
Formative or Equivalent Number of Teeth for Bevel Gears
Formative or Equivalent Number of Teeth for Bevel Gears
Strength of Bevel Gears
Strength of Bevel Gears
Forces Acting on a Bevel Gear
Design of a Shaft for Bevel Gears
Design of a Shaft for Bevel Gears
Contoh Soal 1:
Diketahui: 2 buah bevel gear 200 full depth steel dengan N1 = 40 gigi N2 = 60 gigi Pd = 4 pada diameter luar b = 2,5 in b’ = 1,5 in BHN = 300 AGMA quality No.8
Ditanyakan: 1. Kecepatan ( Vb )? 2. Daya transmisi ( hp ) ? Apabila gear beroperasi dalam kapasitas maksimum Keterangan : N = Number of teeth Pd = diameter pitch b = face width of tooth b’ = thickness thickness bevel gears BHN = Brinell Hardness Number AGMA = American Gear Manufacturers Association
Flowchart :
A Mulai
Pitch cone angle of bevel gears
α
2 buah bevel gear 200 full depth steel N1 = 40 ; N2 = 60 ; Pd = 4 b = 2,5 in ; b’ = 1,5 ; BHN = 300 AGMA quality no.8
Pitch radius r1 Pitch diameter d1
Outside radius of pitch cone
Factor in wear equation Q’
ro1 dan ro2 A
B
B
C
Pitch radius, formative gear
Limit Load for wear
r’1
Fw
Konstanta ( dari grafik )
Dynamic tooth load
K
C
Fd
Perbandingan jml gigi C
D
D
E
Massa ekuivalen dari 2 gear
Spring konstans k
Typical error in tooth outline e
Speed of rotation n
me
E
F
F
Kecepatan ( Vb ) Daya transmisi ( hp )
Selesai
Penyelesaian:
Keterangan : ro = outside radius of pitch cone (in) α = pitch cone angle (o) r1 = pitch radius (in) d1 = diameter pitch (in)
BHN = 300 maka K= 136 ( dari Grafik/tabel) Dengan interpolasi
Keterangan: Q’ = factor in wear equation of bevel gears r’1 = pitch radius formative gears (in) Fw = limit load of wear (lb)
Jika power maksimum maka:
Keterangan: Fd = dynamic tooth load (lb) Fp = horsepower force C = perbandingan jml gigi me = massa ekuivalen dari 2 gear ( lb sec2 / in) γ = weight per unit volume ( 0,283 lb/in3 )
e = 0,0035 + 0,0036 = 0,0071 ( dari tabel ) k = 1.667.000 x 2,5 = 4.167.000 lb/in
Contoh Soal 2:
Bevel gear pada soal pertama mentransmisikan 100 horsepower pada saat beroperasi pada kapasitas maksimum. Carilah BHN dan kecepan maupun kecepatan putaran gear tersebut harus dioperasikan. Ditanya : BHN = ? Vb = ? n1 = ?
Flowchart : Mulai A hp = 100 e = 0,0071 N1 = 40 gigi k = 4.167.000 lb/in me = 304 ( lb sec2 / in) d1 = 8,612 in φ= 20 derajat
Wear Capacity of tooth
Fw
Konstanta
K Dynamic force
Fd B A
B
BHN Kecepatan ( Vb ) Kecepatan putaran (n1 )
Selesai
Penyelesaian:
Subtitusi persamaan 1 dan 2
Jika power maksimum :
= 153
BHN = 318 ( dari grafik / tabel ) dengan cara interpolasi
Worm Gears
Introduction Transmit power at high velocity ratios up to 300:1 Lower efficiency The worm gearing is mostly used as a speed reducer The worm (which is the driving member) is usually of a cylindrical form having threads of the same shape as that of an involute rack
Type of Worms
Type of Worm Gears
Nomenclature Axial Pitch (Pa)
Nomenclature Lead and lead angle
Nomenclature Tooth Pressure Angle
High Efficiency
Nomenclature Normal Pitch
Nomenclature Helix Angle Velocity Ratio
Nomenclature
Nomenclature
Proportion of Worms
Proportion of Worms
Proportion of Worm Gears
Efficiency of Worm Gearing
Efficiency of Worm Gearing
Efficiency of Worm Gearing
Strength of Worm Gear Teeth
Strength of Worm Gear Teeth
Wear Tooth Load for Worm Gear
Wear Tooth Load for Worm Gear
Thermal Rating of Worm Gearing
Thermal Rating of Worm Gearing
Forces Acting on Worm Gears
Forces Acting on Worm Gears
Design of Worm Gearing Given Power Transmitted, Speed, Velocity, Ratio and The Centre Distance Between The Shafts
Determined Lead Angle, Lead and Number of Threads on The Worm
Design of Worm Gearing
Design of Worm Gearing
Contoh Soal 1
Contoh Soal 1
Contoh Soal 2
Contoh Soal 2
