DESIGN OF AN AUTOMOTIVE DIFFERENTIAL WITH REDUCTIONRATIO GREATER THAN 6
Sumair Sunny1 , Siddhesh Ozarkar 2, Sunny Pawar 3
1Maharashtra Institute of Technology, Maharashtra, India
2Maharashtra Institute of Technology, Maharashtra, India
3Maharashtra Institute of Technology, Maharashtra, India
Abstract
Commonly found automobile differentials have a reduction ratio of 6 at max. This is because designing an automotive differential to position with the limited space available. Furthermore, increasing the size of the differential may lead to excessive undesired weight. Most on-road vehicles have differentials with reductions of 3 or 4. Commercially speaking, finding a differential with a reduction greater than 6 is close to impossible. Most manufacturers would introduce an additional single speed gearbox however this would over complicate the design and increase servicing costs. The aim of this paper is to design a differential with a reduction ratio greater than 6. The paper includes all the calculations as well as a strength based analysis performed on Altair-Hypermesh, to prove the success of the design.
Keywords: Worm, differential, over-running, self-locking, bevel, gear, bearing, reduction ratio
1.INTRODUCTION
We shall now design a differential using a worm gear reduction around the miter gear set. This is inspired from the “Napier Worm Gear Drive” invented by the British “Napier & sons” before the First World War. The company was later consumed by “English Electric” however their concept of a worm drive seems very promising.
1.1 Input Parameters Input power: 5.8913 kW
Input Speed: 4100 rpm
Input Torque: 13.7231 Nm
Reduction Ratio Reqd.: 7:1
1.2 Design Objective
To design a differential offering a reduction ratio of 7 (7:1). It reduces output speed 7 times and multiplies output torque 7 times.
2. DESIGN OF INNER BEVEL SET [2]
2.1 Constraints for Inner Bevel Set
Miter Gears: Pitch geometry (D) = 80 mm
Pitch cone Angle (φ) = 45°
Back cone Angle (β) = 45°
Pressure Angle (ψ) = 20°
Module (m) = 4 mm
Velocity Ratio (G) = 1 (1:1)
2.2 Sizing of Inner Bevel Set Pitch Cone Distance (AO):
Face Width (b):
Height of Addendum (ha):
Height of Dedendum (hf):
Mean Radius (Rmean):
Minimum Number of Teeth on Pinion (Zmin):
Actual Number of Teeth (Zact):
2.3 Force Analysis of Inner Bevel Set Torque acting on Bevel Set (T) = 96.0617Nm =96061.7Nmm Speed of rotation of Bevel Set = 585.7143 rpm
Radial Force on Pinion (FR): FR = FTtan(ψ)cos(φ)
FR = FTtan(20)cos(45)
FR = 742.649 N
∴ FR =FA =742.649 N (MITER GEAR)
Pitch Line Velocity (Vm):
Equivalent Teeth on Pinion (Zep):
2.4 Material Selection Alloy Steel - 15Ni4Cr1 Sut = 1500 N/mmBHN = 650
This selection is based on the design of worm gears as well. The aim is to use as few different materials so as to be able to make maximum use of recyclable metal scrap. The worm is case hardened alloy steel (15Ni4Cr1) and worm wheel (which should be always be made of a more ductile material than worm) is made of Phosphor Bronze.[1] The scrap material can be collected, melted and recast into machinable billets. This reduces cost of waste. We shall consider a factor of safety of 1.5
2.5 Stress Based Analysis of Inner Bevel Set Beam Strength (Sb):
Ratio Factor (Q):
Load Stress Factor (K):
Wear Strength (Sw):
Tolerance Factor (ɸp):
Error (ep) considering IS Grade 5:
Total Error (e): e = (ep + eg)*1000
e = 0.01483 mm
Deformation Factor (C): C = 11500*e
C = 11500 * (0.0148)
C = 169.08 N/mm
Incremental Dynamic Load (Fd):
Fd = 1295.79 N
Effective Load (Feff ): Feff = FTmax + Fd
Feff = 3463.22+ 1295.79 = 4759.026 N
Factor of Safety in Bending:
Factor of Safety in Wear:
Shear Stress on Hollow Bevel Drive Shaft: Inner Diameter (di) = 27 mm
Outer Diameter (do) = 35 mm
Permissible Shear stress (τper)
DESIGN IS PERMISSIBLE
2.6 Bevel Shaft Spline Calculation
Permissible pressure on splines = 6.5 N/mm2 (Internal splines)
Major Diameter of Splines (Ds) = 27 mm
Minor Diameter of Splines (ds) = 23 mm
Number of Splines = 24
Minimum Length of Hub (L):
2.7 Selection of Bearings for Bevel Drive Shafts Due to positioning of all the Miter gears, radial forces cancel out, but axial forces double,
Total axial Force (P) = 2 * Fa P = 2 * 742.649 P = 1485.3 N
Let us select Ball Bearings. Consider L10 as 850 million revolutions and a load factor of 1.4,
C = 19697.66 N
C = 19.7 kN
d = 35 (shaft O.D.)
Selecting Double Row Ball bearings from SKF catalogue:[4]
3. DESIGN OF WORM & WORM WHEEL [2]
3.1 Constraints for Worm Gears
Centre distance (X) = 105 mm
Velocity ratio (V.R.) = 7 (7:1)
Number of starts on worm (Zw) = 4
Normal pressure angle (ψr) = 20
3.2 Sizing of Worm & Worm Wheel Number of Teeth on Worm Wheel (Zg):
Zg = VR * Zw = 7 * 4 = 28 teeth
Lead Angle of Worm (λ):[5]
Helix Angle of Worm Wheel (φ):
Helix Angle of Worm
Preliminary Worm Diameter
Preliminary Worm Wheel Diameter
DG = 2(x) - Dw =2(105)- 42 = 168 mm
Circular Pitch (Pc ):
Axial pitch = Circular Pitch Pa = Pc = 18.9 mm
∴Taking modulus as 6
Actual circular pitch = Actual axial pitch = π = 3.14 * 6 = 18.84
Actual wheel diameter (Dgactual) Dgactual = m * Zg = 6 * 28 = 168 mm (P.C.D.)
Actual worm diameter (Dwactual) Dwactual= 2(x) Dg(actual)
Dw= 2(105) 168 Dw= 42 mm (P.C.D.)
Diametral Quotient (q):
Face Width (b) (of Worm Gear):
Lead of Worm (L): L = Zw* Pa(actual)
L = 4 * 18.9 L = 75.36 mm
Normal Module (Mn): Mn = M *cosλ= 6 * cos(27.61) = 5.3 mm = 6 mm
Height of the addendum (ha) = 1 * Mn= 6 mm
Height of the dedendum (hf) = 1.25 * Mn = 7.5 mm
Clearance (CL) = hf*ha = 1.5 mm
Length of worm (Lw)
3.3 Material Selection & Force Analysis of Worm & Worm Wheel
Speed of worm (Nw) = 4100 rpm
Speed of worm wheel (Ng) = 585.71 rpm
Pitch Line Velocity of Worm Wheel (V):
Velocity Factor (CV):
We know that for 20 involute teeth from Lewis factor (y ′ ):
Material Selection
Worm threads are subjected to fluctuating stresses and a large number of stress cycles. Therefore surface endurance strength is an important criterion in the selection of worm material.
The core of the worm should be kept ductile and tough to ensure maximum energy absorption. The worms are therefore made of case hardened steel with a surface hardness of 60 HRC and a case depth of 0.75 to 4.5 mm.
We have chosen a Nickel-Chromium alloy steel: 15Ni4Cr1[1]
The magnitude of contact stresses on the worm wheel teeth is the same as that on the worm threads.
However the number of stress cycles is reduced by a factor equal to the speed reduction. The worm wheel cannot be accurately generated byhobbing process. The final profile and finish of the worm wheel teeth is the result of plastic deformation during initial stages of service. Therefore the
worm wheel material should be soft and conformable.
Phosphor Bronze with a surface hardness of 90 to 120 BHN, is widely used for the worm gear. Phosphor Bronze worm wheel are sand cast, sand cast and chilled or centrifugally cast. Phosphor Bronze is costly and in case of worm wheel with large dimensions, only the outer rim is made of Phosphor Bronze. It is then bolted into the cast iron wheel. There are two reasons for using dissimilar or heterogeneous materials for worms and worm wheel:
(i) The coefficient of friction is reduced.
(ii) The conformability of worm wheel with respect to the worm is improved.
Worm Material
15Ni4Cr1 (Case Hardened)
Sut=1500 N/mm2 BHN = 650
Allowable Bending stress (σallowable):
Worm Wheel Material Phosphor Bronze
Sut = 240 N/mm2 BHN = 70
Load stress factor (k) = 0.55 N/mm
Check for Tangential Load Transmitted (FT):
FT = 80 *0.538 * 35 * π * 6 * 0.121
FT = 3447.08 N
Power transmitted due to tangential load (PT)
Since this is more than the power to be transmitted, DESIGN IS SAFE
Check for Dynamic Load (FD):
Power transmitted due to dynamic load (PD)
Since this is more than the power to be transmitted, DESIGN IS SAFE Check for Static Load
Flexural Endurance limit (Fc) Fc = 1.75(BHN)
Fc = 1.75(70) Fc = 122.5 N/mm2
Static load (Fs) Fs= Fc * b * π * m * y ′
Fs= 122.5 * 35 * π * 6 * 0.121 Fs= 9808.575 N
Power transmitted due to static load (PS)
Since this is more than the power to be transmitted,DESIGN IS SAFE.
Check for Wear Load Wear load max = DG * b * K
Fw=168 * 35 * 0.55
Fw=3234 N
Power transmitted due to wear load (Pw)
Since this is more than the power to be transmitted, DESIGN IS SAFE Rubbing Velocity(Vs):
From graph of coefficient of friction v/s rubbing speed, we find that the coefficient of friction corresponding to rubbing velocity of 10.17m/s = 0.02(μ)
Friction Angle (ɸF):
Overall Efficiency of Worm and Worm Wheel (η):
3.4 Self-Locking or Over-Running?
In general, the worm is the driver and the worm wheel is the driven member and the reverse motion is not possible. This is called “self-locking”drive,because the worm wheel cannot drive the worm. As for screw threads, the criterion for self-locking is a relationship between the coefficient of friction and lead angle. A worm gear drive is said to be self-locking if the coefficient of friction is greater than the tangent of lead angle, i.e. the friction angle is more than the lead angle. This can be written as
There is another term,reversible or over running or ‘back driving’worm gear drive.In this type of drive,the worm and the worm wheel can drive each other. In general the worm is the driver and the worm wheel is the driven member. If the driven machinery has large inertia and if the driving power supply is cut off suddenly, the worm is freely driven by the worm wheel. This prevents damage to the drive and source of power. A worm gear drive is said to be reversible if the coefficient of friction is less than tangent of the lead angle i.e. the friction angle is less than the lead angle. This can be written as
Thus the system is “OVER RUNNING”
3.5 Strength Rating of Worm & Worm Wheel
Table -2: Strength Rating Factors
T = 17.65 * Xb * Sb * m * b * DG * cosλ
Maximum torque on worm (Twmax)
Twmax= 17.65 * 0.18 * 35.32 * 6 * 35 * 168 * cos(27.61) = 3508368.71 Nmm
Maximum torque on worm wheel (Tgmax)
Tgmax = 17.65 * 0.32 * 5 * 6 * 35 * 168 * cos(27.61) = 882941.67 Nmm
Considering lesser of the two; Power transmitting capacity based on beam strength,
Since this is greater than the power to be transmitted, design is safe.
3.6 Wear Rating of Worm & Worm Wheel
Table -3: Wear Rating Factors
Permissible Torque on worm (Twmax)
Twmax= 18.64 * 0.065 * 6.19 * 1.05 * (168) 1.8 * 6 = 478571.87Nmm
Permissible Torque on worm wheel (Tgmax)
Tgmax= 18.64 * 0.13 * 1.06 * 1.05 * (168)1.8 * 6 = 163905.07 Nmm
Considering lesser of the two, power transmitting capacity
P = 10.05 kW
Since this is greater than the power to be transmitted, design is safe.
3.7 Temperature Rise & Design Considering Max. Permissible Overload
Heat Generated due to Power Losses (Qg): Qg= (1 -η) * power input
Qg= (1-0.95) * 5891.3 Qg= 276.412 W
Projected Area of Worm (Aw):
Projected Area of Worm Wheel (AG):
Total Projected Area (ATOTAL):
ATOTAL = Aw + AG = 1384.74 + 22155.842 = 23540.58mm2= 0.02354058 m2
Thermal conductivity (K): 378 W/m20 C
Temperature Rise(δT):
The temperature must not show a rise greater than (δT), and temperature of lubrication oil should be maintained at less than or around so that the viscosity index is maintained, (considering a mineral oil).
Also if the oil gets too hot, viscosity will drop, but also due to higher temperature seals may get damaged.
Since the system normally only produces a temperature rise of up to and max. permissible rise is normally to be kept under we can allow overloading conditions, so long as temperature rise is below
In other words the system can tolerate an overload of 11%
Design of Worm Shaft Considering Overload: Percentage Overload = 11%
Torque acting on worm gear (Tg)
Torque Acting on Worm Shaft (Ts):
Tangential Force on Worm (FTWORM):
Axial Force on Worm (FAWORM):
Radial Force on Worm (FRWORM):
Bending Moment: Bending moment due to Radial Force in vertical Plane: (considering distance between bearings equal to Dg)
Bending moment due to Axial Force in vertical Plane
Total bending moment in vertical plane = 19401.5579 + 13333.6767 = 32735.2346 Nmm Bending moment due to Tangential Force in Horizontal direction:
Resultant Bending Moment On Shaft:
Equivalent Torsional Moment (Teqv):
Inner Diameter (di) = 21.85 mm Outer Diameter (do) = 30 mm
Permissible Shear Stress (τper)
Consider a factor of safety of 3,
3.8 Worm Drive Shaft Spline Calculations
Permissible pressure on splines = 6.5 N/mm2
Major Diameter of Splines (Ds) = 21.81 mm
Minor Diameter of Splines (ds) = 19.35 mm
Number of Splines = 13
Minimum Length Of Hub (L):
3.9 Selection of Bearings for Worm Drive Shafts[2]
FR = 461.94 N FA = 1269.87 N
Shaft OD = 30 mm P = XVFR + YFA
V =1 (where V = race rotation factor)
Y = 1.46 X = 0.56
P =(0.56*1*461.94) + (1.46*1269.87) P = 2112.7 N
Consider L10 as life of 300 million revolutions
∴ Bearing selected is from SKF Catalogue: [4]
Table -4: Designation Number 4206 ATN9
4.IMAGES OF THE WORM DIFFERENTIAL
Fig -1: Square Dimensions (mm)
Fig -2: Exploded view of Worm Differential
Fig -3: Worm Differential Assembly
5. STRENGTH BASED ANALYSIS
Given the complicated geometry of the teeth on worm wheel & threads on worm, it is difficult to calculate the actual deflection on their surfaces upon maximum load condition. [3]To simplify our task and save us from performing huge matrix calculations, we can use Altair Hypermeshto mesh and analyze the stresses & deflections of individual parts.
Fig -4: Maximum Von Mises Stress on Worm: 9.46 N/mm2
Fig -5: Maximum Deflection of Worm: 6.278 *10 -3mm
Fig -6: Max. V. M. Stress on Worm Wheel: 41.24 N/mm2
Fig -7: Max. Deflection of Worm Wheel: 2.014 *10-2 mm
Fig -8: Max. . M. Stress on Miter Gear: 7.909 N/mm2
Fig -9: Max. Deflection of Miter Gear: 2.256 *10-2 mm
T able -5: Summary of Stresses & Deflection
From the table above it can be seen that the stresses incurred by the parts are less than the permissible limit. The deflections are of the order of 10-2 & 10-3 mm and hence can be considered negligible. Thus the DESIGN IS SAFE.
6. ADVANTAGES & DISADVANTAGES
6.1 Advantages
Compact.
Light weight.
Reduction ratio of even 20:1 is possible by this method.
Worm shaft is placed higher in this arrangement near the underbelly of the chassis thus less prone to damage.
Entire structure is centralized in terms of mass & since C.G. is in the center the positioning is easier.
The entire differential offers rotational flexibility about the drive axle axis thus the worm shaft can be tilted at any angle without any trouble or complications. This will not affect the design calculations nor increase design complexity.
The entire enclosure floats around the mechanism. Once disconnected from its mounting, both the shells can come apart offering maintenance worker complete access to the mechanism from any angle.
Design is very simple and has good serviceability.
6.2 Disadvantages
Limited efficiency at best up to 95%.
Due to poorer efficiency, temperature rise must be within permissible limits or else seals may get damaged. Also excessive temperature could lead to tooth failure due to seizure.
The entire system is made of two metals.The worm wheel normally has to be made of a more conformable metal (such as Phosphor Bronze). This may increase costs.
If the gearing size requirement is larger (for increased torque transmitting capacity), height increases.
Since the worm wheel is made out of phosphor bronze, whose wear strength is not as high as that of alloy steels, the frequency of replacement of worn out parts may be greater.
7. SCOPE FOR IMPROVEMENT
The efficiency mainly gets influenced by the velocity ratio as well as the worm Pitch Circle Diameter (P.C.D.). The lower the velocity ratio and greater the size of the worm P.C.D. the more efficient the system becomes. This in turn reduces power lost as heat as well as the overall heat dissipation requirements of the system.
Since phosphor bronze is an expensive alloy and it has a greater tendency to wear, the best way to save money would be to cast only the outer half of the worm wheel from phosphor bronze and then bolt it onto a cheaper cast iron inner wheel. The miter gears will then be pivoted on the pin shaft made of grey cast iron which is much cheaper. This way less phosphor bronze is consumed per unit of production, reducing material cost. But at the same time the mating surface will have to be machined so this increases production time and cost slightly.
The pivoted bevel gears need not be of the same dimensions as those mounted on the drive axles. They can be of smaller size, thus reducing weight even further &/or making system more compact.
8. CONCLUSION
Overall, the worm gear differential seams viable for heavy, load-carrying vehicles used for construction and material transportation as well as public transport such as buses. The worm gear drive with a very high torque transmitting requirement will have a bigger P.C.D. of worm and wheel, and the overall height may become too much for a consumer vehicle. However for small reduction ratios the system can be made even more compact as mentioned above, hence permitting use in consumer vehicles.
REFERENCES
[1]. Design Data Hand Book PSG Coimbatore.
[2]. Design of Machine Elements, 3rd Edition, V.B.
Bhandari, McGraw Hill Publications.
[3]. Practical Finite Element Analysis,Nitin S Gokhale,
Sanjay S Deshpande,Sanjeev V Bedekar, Anand N Thite,
Finite to Infinite Publications.
[4]. www.skf.com
[5]. A Textbook of Machine Design R S Khurmi, J K Gupta
汽车差速器减速比大于6的设计
Sumair Sunny1，Siddhesh Ozarkar2，阳光帕瓦尔3
技术，马哈拉施特拉邦，印度1Maharashtra研究所
技术，马哈拉施特拉邦，印度2Maharashtra研究所
技术，马哈拉施特拉邦，印度3Maharashtra研究所
摘要：常见的汽车差速器在最大有6的减速比上。这是因为在设计汽车差速器与现有的有限空间中的位置。此外，增加了差分的大小可能会导致不希望的过高的重量。大多数公路上的车辆有差异为3或4。市售的减少而言，找到一个差分与减少大于6几乎是不可能的。大多数制造商将推出一个额外的单速变速箱然而，这会在复杂的设计，增加维修成本。本文的目的是设计具有减少比大于6，这篇文章包括所有的计算，以及对牵牛星-HYPERMESH执行基于强度分析的差分，以证明该设计的成功。
关键词：蜗杆/微分/过运行/自锁/伞/齿轮/轴承/减速比
1.简介
我们现在使用的设计围绕着人字齿轮组蜗轮减速差。这是从“纳皮尔蜗轮传动”，由英国“纳皮尔父子”的第一次世界大战之前发明的启发。该公司后来被“英国电器”但是消耗的一个蜗杆传动的概念似乎非常有前途.
1.1输入参数 输入功率：5.8913千瓦
输入转速：4100转
输入扭矩：13.7231牛米
减速比REQD：7：1
1.2设计目标
设计一个差动提供的7（7：1）的压缩比。它减少了输出速度7倍，乘以输出转矩7倍。
内斜面SET OF2.设计[2]
2.1约束的内斜面设置人字齿轮：
间距几何（D）=80毫米
节锥角（φ）=45度
背锥角（β）=45°
压力角（ψ）=20°
模块（米）=4毫米
速度比（G）= 1（1：1）
2.2浆纱内斜面设置间距锥的距离（AO）：
AO = 56.67 mm
表面宽度（B）：
附录（公顷）的高度：
齿根（HF）的高度：
平均半径（RMEAN）：
牙齿上的小齿轮（因此Zmin）最小数量：
牙齿（数Zact）的实际数量：
2.3内斜角设定的扭矩作用在锥套装（T）的受力分析=96.0617Nm=96061.7Nmm
锥设置的旋转速度=585.7143转
径向力的齿轮（FR）：FR = FTtan（ψ）COS（φ）
FR = FTtan（20）COS（45）
FR=742.649ñ
∴FR= FA=742.649 N（MITER GEAR）
节线速度（VM）：
在齿轮（番）相当于牙齿：
2.4材料选择 合金钢 - 15Ni4Cr1 SUT=1500牛顿/平方毫米 BHN=650
这种选择是基于蜗轮设计为好。这样做的目的是用尽可能少的不同的材料，从而能够最大限度地利用可回收金属废料。该蜗杆是表面硬化合金钢（15Ni4Cr1）和蜗轮（应始终作了较为韧性材料比蜗杆）是由磷青铜的。[1]该废料可以被收集，熔化重铸可加工成钢坯。这减少了浪费成本。我们应考虑1.5的安全系数
2.5内锥套装束强度2.5基于应力分析（SB）：
比率因数（Q）：
荷载应力系数（K）：
穿强度（SW）：
服务因子（嘉）=1
负荷集中系数（公里）=1.2
最大切向力（FTmax） FTmax= Ka*Km*FT=1*1.2*2886.020 = 3463.22N
糖耐量因子（ɸp）：
错误（EP）考虑的是5级：
总误差（E）：e = (ep + eg)*1000
e = 0.01483 mm
变形系数（C）： C = 11500*e
C = 11500 * (0.0148)
C = 169.08 N/mm
增量动态负载（FD）：
Fd = 1295.79 N
有效载荷（FEFF）
Feff = FTmax + Fd
Feff = 3463.22+ 1295.79 = 4759.026 N
安全弯曲的因素：
在戴安全系数：
剪应力空心锥传动轴：内径（DI）=27毫米
外径（办）=35毫米
允许剪切应力（τper）
设计是允许的
2.6锥轴花键计算 在花键允许压力=6.5牛顿/平方毫米（内花键）的样条（DS）大直径=27毫米,样条的小直径（DS）=23毫米,样条数=24,集线器（L）的最小长度：
2.7选择轴承圆锥传动轴。由于所有的人字齿轮的定位，径向力抵消，但轴向力双，总的轴向力（P）=2*发 P = 2 * 742.649 P = 1485.3 N
让我们选择球轴承。考虑L10850万转和1.4的负载率，
C = 19697.66 N
C = 19.7 kN
d = 35（轴外径）
选择双列球轴承SKF的目录：[4]
窗体顶端
表-1：指定编号4207 ATN9
窗体底端
3.蜗轮与蜗杆砂轮设计[2]
3.1约束的蜗轮 中心的距离（X）=105毫米
速度比（V.R.）= 7（7：1）
开始在蜗杆数（ZW）=4
正常压力角（ψr）=20
对蜗轮齿的蜗轮蜗杆轮数3.2浆纱（ZG）：ZG= VR*度Zw=7*4=28的牙齿
蜗杆（λ）的导角：[5]
蜗轮的螺旋角（φ）：
蜗杆螺旋角
初步蜗杆直径
初步蜗轮直径 DG = 2(x) - Dw =2(105)- 42 = 168 mm
圆形的间距（PC）：
轴间距=间距通知 Pa = Pc = 18.9 mm
∴Taking模量为6
实际的循环间距=实际轴间距=π=3.14*6=18.84
实际车轮直径（Dgactual） Dgactual= M * ZG=6*28= 168毫米（P.C.D.）
实际的蜗杆直径（Dwactual） Dwactual=2（x）的DG（实际）
DW= 2（105）168 DW= 42毫米（P.C.D.）
直径商数（Q）：
脸部宽度（B）（蜗轮）：
蜗杆（L）铅：L =度Zw*帕（实际） L = 4 * 18.9 L = 75.36 mm
普通模块（锰） Mn = M *cosλ= 6 * cos(27.61) = 5.3 mm = 6 mm
增编的高度（HA）=1 * Mn= 6 mm
齿根（HF）的高度=1.25* Mn=7.5毫米
清除率（CL）=hf*ha =1.5毫米
蜗杆的长度（LW）
蜗轮蜗杆砂轮3.3材料选择与力分析
蜗杆的速度（NW）=4100 RPM
蜗轮的速度（NG）=585.71转
蜗轮节线速度（V）：
速度系数（CV）：
我们知道，20渐开线齿刘易斯因子（Y'）：
材料选择:蜗杆螺纹经受波动的应力和大量的应力循环。因此表面耐久强度是蜗杆材料的选择的一个重要标准。该蜗杆的核心应保持韧性和强硬的，以确保最大的能量吸收。因此，蜗杆制成表面硬化钢60 HRC的表面硬度和0.75至4.5毫米的情况下，深度。我们选择镍铬合金结构钢：15Ni4Cr1[1]接触应力对蜗轮齿的大小相同，在蜗杆螺纹。然而应力循环的数目是由等于速度减少一个因子减小。蜗轮不能准确地生成byhobbing过程。蜗轮齿的最终轮廓和光洁度是塑性变形的过程中的服务的初始阶段的结果。因此，蜗轮材料应柔软舒适。磷青铜为90的表面硬度为120 BHN，被广泛用于蜗轮。磷青铜蜗轮是砂型铸造，砂型铸造和冰鲜或离心浇铸。磷青铜是昂贵的，如果蜗轮与大尺寸的，只有外缘是由磷青铜的。它然后用螺栓连接到铸铁轮。有两个理由使用异种或异质材料蜗杆和蜗轮：
（ⅰ）摩擦系数被降低。
（ⅱ）蜗轮相对于蜗杆的贴合性得以提高。
蜗杆材料 15Ni4Cr1（表面硬化） Sut=1500 N/mm2 BHN = 650
允许弯曲应力（σallowable）：
蜗轮材料 磷青铜
Sut = 240 N/mm BHN = 70
荷载应力系数（K）= 0.55 N/mm
检查切向负载发送（FT）：
FT = 80 *0.538 * 35 * π * 6 * 0.121
FT = 3447.08 N
功率发送，由于切向负荷（PT）的
由于这是以上所述的功率要发射，设计是安全检查动态负载（FD）：
功率发送，由于动态负载（PD）的
由于这是以上所述的功率要发射，设计是安全检查静负荷
弯曲疲劳极限（FC） Fc = 1.75(BHN)
Fc = 1.75(70)
Fc = 122.5 N/mm2
静载（FS） Fs= Fc * b * π * m * y ′
Fs= 122.5 * 35 * π * 6 * 0.121
Fs= 9808.575 N
功率发送由于静载荷（PS）的
由于这是以上所述的功率要发射，设计是安全。检查磨损负荷
穿负荷最大= DG* B* K Fw=168 * 35 * 0.55 Fw=3234 N
传送由于磨损负载功率（PW）
由于这是以上所述的功率要发射，设计是安全摩擦速度（Vs）：
摩擦速度
从摩擦V / S的摩擦速度的系数的曲线图，我们发现，摩擦系数对应于摩擦10.17米/ s的速度= 0.02（μ）内摩擦角（ɸF）：
蜗杆蜗轮（η）的总体效率：
3.4自锁或超转？
在一般情况下，蜗杆是驾驶员和蜗轮是从动构件和反向运动是不可能的。这就是所谓的“自锁”的驱动，因为蜗轮不能驱动蜗杆。至于螺纹，该标准自锁是摩擦和超前角的系数之间的关系。蜗轮传动被说成是自锁，如果摩擦系数大于导角的正切，即摩擦角大于导程角。这可以写成
还有另外一个长期的，可逆的或通过跑步或“回driving'worm齿轮drive.In这种类型的驱动器，蜗杆和蜗轮可以驱动对方。在一般的蜗杆是驾驶员和蜗轮是从动构件。如果驱动机械具有较大的惯性，如果驱动电源突然中断，该蜗杆通过蜗轮自由驱动。这样可以防止损坏驱动器和动力源泉。蜗轮传动据说是可逆如果摩擦系数小于所述导程角的正切即摩擦角小于导程角。这可以写成
因此，该系统是“超跑”
3.5强度蜗轮蜗杆砂轮评级
表-2：实力评级的因素
蜗杆 车轮
速度因子（预算外）
弯曲应力（SB） 0.18
35.32 0.32
5
T = 17.65 * Xb * Sb * m * b * DG * cosλ
在蜗杆最大扭矩（Twmax）
Twmax= 17.65 * 0.18 * 35.32 * 6 * 35 * 168 * cos(27.61) = 3508368.71 Nmm
在蜗轮最大扭矩（Tgmax）
Tgmax = 17.65 * 0.32 * 5 * 6 * 35 * 168 * cos(27.61) = 882941.67 Nmm
考虑较小两者;基于波束强度送电能力，
由于这是大于功率要发射，设计是安全的。蜗轮蜗杆砂轮磨损3.6额定
表-3：戴评级因素
蜗杆 蜗轮
速度系数（XC）
表面应力因子（SC）
ZONE因子（YZ） 0.065
6.19
1.05 0.13
1.06
1.05
在蜗杆允许转矩 (Twmax) Twmax= 18.64 * 0.065 * 6.19 * 1.05 * (168) 1.8 * 6 = 478571.87Nmm
在蜗轮容许转矩(Tgmax) Tgmax= 18.64 * 0.13 * 1.06 * 1.05 * (168)1.8 * 6 = 163905.07 Nmm
考虑较小的两个，电力传输能力
P = 10.05 kW
由于这是大于功率要发射，设计是安全的。
3.7温升与设计考虑最大。允许过载产生的热量，由于功率损耗量（Qg）：
Qg= (1 -η) *电源输入 Qg= (1-0.95) * 5891.3 Qg= 276.412 W
蜗杆（AW）的投影面积：
蜗轮投影面积（AG）：
总投影面积（ATOTAL）：
ATOTAL = Aw + AG = 1384.74 + 22155.842 = 23540.58mm2= 0.02354058 m2
热导率（K）：378 W/m20 C
温度(δT):
温度必须不显示的上升比（ΔT）以上，并应保持润滑油的温度保持在小于或周围，以使粘度指数保持不变，（考虑矿物油）。此外，如果油变得太热，粘度就会下降，而且由于较高温度的密封可能会损坏。由于系统通常只产生高达和最大温度上升。允许的上升通常被保持在我们可以允许超载的条件，只要温度上升低于最大允许过载换句话说，系统可以容忍的11％的过载.蜗杆轴的设计考虑过载：超载率= 11％
力矩作用于蜗轮（TG）
扭矩作用于蜗杆（TS）：
切向力的蜗杆（FTWORM）：
轴向力的蜗杆（FAWORM）：
径向力的蜗杆（FRWORM）：
弯矩：弯矩由于径向力在垂直平面：（考虑轴承等于DG之间的距离）
弯矩由于轴向力在垂直平面
在竖直平面内总弯矩=19401.5579+13333.6767=32735.2346 NMM
弯矩由于切向力在水平方向：
产生的弯矩轴：
等效扭矩（Teqv）：
内径（DI）=21.85毫米 外径（办）=30毫米
允许剪应力（τper）
考虑3安全系数，
3.8蜗杆传动轴花键计算 在花键允许压力=6.5牛顿/平方毫米
花键大径（DS）=21.81毫米
样条的小直径（DS）=19.35毫米 样条数=13
最小长度中枢（L）：
3.9选择轴承的蜗杆传动轴[2] FR = 461.94 N FA = 1269.87 N 轴OD = 30 mm
P = XVFR + YFA V =1 （其中V =种族旋转系数）
Y = 1.46 X = 0.56
P =(0.56*1*461.94) + (1.46*1269.87) P = 2112.7 N
考虑L10为300万转的生活
∴轴承选择是SKF产品目录：[4]
表-4：指定编号4206 ATN9
4.蜗杆差分图像
图-1：方形外形尺寸（mm）
图-2：蜗杆差的分解图
图-3：蜗杆差速器总成
5.基于强度分析
定于蜗轮＆线程上蜗杆的齿的复杂的几何形状，这是难以计算上时的最大负荷条件其表面的实际偏转。 [3]为了简化我们的任务，拯救我们的表演巨大的矩阵计算，我们就可以使用牛郎星Hypermeshto网格和分析应力与单个零件的变形。
图-4：最大von Mises胁迫对蜗杆：9.46 N / mm2的
图-5：6.278*10-3mm：蜗杆的最大挠度
图-6：最大。 V. M.胁迫对蜗轮：41.24 N / mm2的
图-7：最大。蜗轮偏转：2.014*10-2毫米
图-8：最大。。 M.应力斜齿轮上：7.909 N / mm2的
图-9：最大。偏转斜齿轮：2.256*10-2毫米
表-5：应力与变形摘要
分析对象： 力 应力 挠度
蜗杆
蜗轮
人字齿轮 (FT)3447.08
(FA)3447.08
(FT)2886.02 9.46
41.24
7.909
从上面的表中可以看出，所招致的部件的应力小于允许的极限。挠度是10-2＆10-3毫米的量级，因此可以被认为是可忽略不计。这样的设计是安全。
6.利弊
6.1优点
紧凑。
重量轻。
即使减少20：1的比例，可以通过这种方法。
蜗杆轴被放置在较高的这种布置靠近底盘从而不易发生损坏的腹部。
整个结构被集中在大规模的CG＆以来术语是在中心的定位更容易。
整个鉴别提供了有关驱动桥轴因而蜗杆轴可以在任何角度倾斜没有任何麻烦或并发症转动灵活。这不会影响设计计算，也提高了设计的复杂性。
整个机箱周围浮动机制。一旦从它的安装断开连接，无论是弹可分开来提供维修工人完全访问从任何角度的机制。
设计是很简单的，并具有良好的耐用性。
6.2缺点
有限效率充其量高达95％。
由于较差的效率，温升必须在允许的范围内，否则密封件可能会损坏。另外温度过高可能会导致牙齿失败因癫痫发作。
整个系统由两个metals.The蜗轮通常必须被制成一个更适形的金属（如磷青铜）的。这可能会增加成本。
如果传动装置尺寸的要求是大的（对于增加的扭矩传递容量），高度增加而增加。
由于蜗轮是做出来的磷青铜，它的磨损强度不一样高合金钢的，更换磨损零件的频率可能会更大。
7.改进的余地
效率主要被由速度比以及蜗轮节圆直径（PCD）的影响。越低的速度比和更大的蜗杆PCD的大小的更有效的系统变得。这反过来又降低了功率失去作为热量以及该系统的总的热耗散要求。
由于磷青铜是一种昂贵的合金，它有一个更大的趋势穿，省钱的最佳方式是将铸从磷青铜蜗轮的只有外一半，然后用螺栓它放到一个更便宜的铸铁内轮。斜切齿轮将被转动的销轴制成灰铸铁中的哪一个要便宜得多。这样，少磷青铜单位产量所消耗，降低了材料成本。但在同一时间的配合表面将具有被加工，以便这增加了生产时间和成本略。
枢转锥齿轮不必是相同的尺寸与安装在驱动轴的。它们可以是更小的尺寸，从而减少甚至进一步的重量及/或使系统更紧凑。
8.结论
总体而言，蜗轮齿轮差速器接缝可行的用于建筑和材料运输以及公共交通，比如公交车重，载重车辆。蜗轮驱动以非常高的扭矩传递的要求将具有更大的PCD虫和车轮，总体高度可能会变得太大了消费者车辆。然而，对于小的减速比，如上所述，因此，允许在消费者的车辆使用该系统可更加紧凑。
参考
[1]设计数据旧书哥印拜陀PSG。
[2]机械元件，第3版，VB设计
班达里，麦格劳希尔出版。
[3]实用的有限元分析，尼廷S戈卡莱，
桑杰S德什潘德，Sanjeev V Bedekar，阿南德ñThite，
有限到无限出版物。
[4] www.skf.com
[5]一本教科书机械设计RS Khurmi的，JK·古普塔
