A transmission provides speed and torque conversions from a power source to an output source using gear ratios. They are used in many places but its highest field application lie in the field of automobiles. Here the transmission does the work of transmitting the output of the internal combustion engine to the drive wheel. These kinds of engines operate at very high rotational speed. The function of the transmission is to lower the higher engine speed to the slower wheel speed as a result increasing the torque.
Transmission holds a wide range of applications such as mining, construction, industrial etc. but here in this report we will focus more on the motor application of it. The transmission is connected to the crankshaft of the engine. There is also a torque convertor whose application is explained further on in the report. Transmission is usually made of aluminum due to low weight application. It usually consists of 3 components: Main shaft, Counter shaft and an Idler shaft.
The one which extends outside the case in both directions is the main shaft. Whereas the one which is towards the engine is the input shaft and the one which is towards the rear axle is the output shaft. The shaft is suspended by the main bearing or locking system and is divided towards the input end. At the point of division there is a pilot bearing which holds the shaft together. The gears are free to turn relative to the main shaft exception is there when engaged by clutches.
Automatic transmission is one in which the gear ratios change automatically as movement is experienced by the car. Automatic transmission now is available on nearly all the vehicles, from light weight to heavy weight. This has definitely increased comfort in driving, since no shifting of gears is required. This transmission is highly used in US, Middle East. Manual transmission is very much preferred in countries like India, Japan and other eastern countries of Asia.
We all might be aware about the different modes in an automatic transmission. There is a lever which is to be moved in order to shift the gear mode. The order generally is P, R, N, D and L. Here is a brief overview about it:
Park (P): In this mode the transmission gets locked so as to stop the car from any further movement in any direction. A hand brake is used to lock the rear wheels so as to prevent them from moving, this habit does increase the life of the transmission and park pin mechanism as P mode plus the hand brake on an inclined surface reduces the undue stress on the parking pin. Only thing to be kept in mind while using this gear mode is that the car should be at a complete stop before shifting to this mode.
Reverse (R): This mode makes the car drive backwards in simple terms. For this mode to come into operation a complete halt is required after which only the gear can be changed to R. Another important feature which is related to this mode is that the reverse mode can be function or the gear can be changed only when the brakes are applied, this not only assures safety but also reduces the chances of damaging the transmission.
Neutral (N): This mode is when the transmission is disconnected from the wheels which allow free movement. Apart from park mode this is the only mode in which a car can be started.
Drive (D): This mode allows the car to move ahead and accelerate depending on various ranges of gears. There is an option called over drive (OD). In this, D locks the automatic overdrive off. OD is engaged under low speeds or acceleration about 60-75 km/h.
Parts and Operation:
Automatic transmission is formed of several parts which are relative to each other's functioning. But here are a few of them which are the most important components which are labeled in the picture below:
Dynamometer testing: Ensures trouble free performance
Parts inspection: all the parts are checked so as to assure proper function of each individual equipment or part.
Shafts: explained on previous page.
Valve bodies: It is the main control center of the hydraulic system that receives fluid that is pressurized by the main pump which is operated by the fluid coupling/torque converter. The pressure is regulated which is then used to run a network of spring-loaded valves, check balls and servo pistons. In order to select the ratio for the gear set the valves utilize the pressure from the pump and also the pressure from the output side of the central governor. Different set of valves open and close when there is change in pressure difference as the engine speed changes. The valve indirectly controls the operation of the planetary gear set to select the optimum gear ratio for the current operating conditions. In modern automatic transmission these valves are controlled by electro mechanical servos which are in control by the Engine Management System or separate transmission controller.
Hydraulic and Lubricating Oil: They are also called as automatic transmission fluid (ATF). They are used for lubrication, preventing corrosion, and also to provide hydraulic medium to convey mechanical power. They are basically made from refined petroleum and further processed in order to provide properties such as smooth power transmission and increase service life. ATF needs to be periodically changed as the vehicle ages.
Torque convertor: It basically connects the engine to the transmission. This can also be called a stator seeing its coupling nature. It can also be defined as the one which takes the place of a clutch in a manual transmission. This allows the engine to keep running even at rest. Its function is to provide multiplication of torque even at low gears or engine speed.
The difference in automatic transmission in general is a common knowledge that is known to everyone. There are basically two differences:
Automatic transmission does not have a clutch pedal
The gear shift in automatic transmission is not done by the driver; it is done automatically once the gear has been engaged in the drive mode.
Though both automatic and manual transmissions accomplish the same thing, but their mode of operation is completely different.
Purpose of an Automatic Transmission
Automatic transmission's job is like any other transmission, it allows the engine to operate in its narrow range of speeds while providing a wide range of output speeds.
The most important difference between automatic and manual transmission is that in a manual transmission the various gear ratios are achieved by locking and unlocking different set of gears to the output shaft. But when we see in automatic transmission, the same is achieved by using the same set of gears (planetary gear set).
The Planetary Gear set
In any automatic transmission we can find the following things inside it:
Planetary gear set
Bands to lock the gear set
Set of wet-plate clutches to lock other parts of the gear set
Hydraulic system that controls the clutches and bands
Gear pump to move the transmission fluid
Planetary gear set is the heart of automatic transmission; it is this component that creates different gear ratios that the transmission produces.
Planetary gear sets has the following components:
Planetary Gear set Ratios
Considering a planetary gear set with ring gear having 72 teeth and sung ear having 30 teeth, lots of different gear ratios can be obtained:
Planet Carrier (C)
1 + R/S
Planet Carrier (C)
1 / (1 + S/R)
Planet Carrier (C)
If any two of the three components lock up it will lock the whole device in the ratio of 1:1. If we observe the first gear ratio we see that it is reduction i.e. the output speed is slower than the input speed. From the second gear ratio we observe that it is overdrive since the output speed is more than the input speed. The last gear ratio is reduction again with only difference that the output direction is reversed.
Compound Planetary Gear set
In this kind of automatic transmission, it uses a compound planetary gear set, which although it looks like a single planetary gear set but is composed of two planetary gear sets. It has two sun gears and two sets of planets, but as output of the transmission it has only one ring gear.
Clutches and Bands in an Automatic Transmission
Clutches are the components that connect to the gears by the torque converter and change their ratios. All the gear shifts are triggered by a series of events with different clutches and engaging and disengaging.
Bands are made of steel that wrap around sections of the gear train and connect to the housing. It holds the sun gear in the planetary gear set. It is controlled by hydraulic cylinders inside the case of the transmission. The hydraulic system controls which bands and clutches are energized at any moment of time.
Automatic Transmissions: Hydraulics, Pumps and the Governor
Pump: They are called gear pump and usually located in the cover of the transmission. Its purpose is to maintain the circulation of transmission fluid in the transmission system. The fluid is drawn from the sump that at the bottom of the transmission and feeds it to the hydraulic system. It also feeds this fluid to the transmission cooler and the torque converter also.
It receives its rotational power from the torque converter as the inner gear of the pump is connected to the housing of the torque converter, thus the speed of the pump is the same as that of the engine.
Governor: Governor is a device that tells the transmission the speed of the engine at which it is going. It is connected to the output shaft, so its speed is same as that of the car. The governor on the valve mechanism which is spring-loaded and it opens proportional to the speed at which the governor is spinning. It receives fluid from the pump through the output shaft. More the speed of the car is, more the governor valve will open and higher the pressure of the fluid it lets through.
Electronically Controlled Transmissions
As technology is advancing and everything is getting automated, so are the transmissions. In electronically controlled transmission the hydraulic circuit is controlled by an electric solenoid. This electronic control allows advanced control schemes and simplifies the complete hydraulic system.
This type of transmissions has elaborate control schemes. They can monitor vehicle speed and throttle position, the transmission controller can monitor the speed and also it has control for the anti-lock braking system.
In electronically controlled transmissions using control strategy based on fuzzy logic - programming control systems using human-type reasoning, they can do lots of things like:
The transmission will automatically downshift when going downhill thus preventing the wear of the brakes.
When driving on a slippery surface it up shifts when brakes are applied to help in reducing the braking torque applied by the engine
When driving on a winding road it inhibits the upshift when going into a turn
Continuously Variable Transmission:
A transmission or a system which makes it possible to achieve smooth and step less ratio changes or infinite number of gear ratios within a limit. When compared to other transmissions it holds an upper hand because other transmissions allow very few different and selected gear ratios. In the CVT, its flexibility allows the driving shaft to maintain a constant angular velocity over different range of output velocities. As a result there is a provision for better fuel economy when compared to other transmissions by allowing the engine to run at its most effective RPM for a wide range of vehicle speeds. This also widens the scope of performance of the vehicle as the engine is allowed to turn at the RPM where it produces peak power. This power is usually higher than the RPM that achieves peak efficiency.
By using a continuously variable transmission, operating in the optimum RPM also provides benefits like lower fuel consumption, Less green house gas emission and better performance. It is also considered as a jerk free transmission. In automatic transmission, even though it's a minimum jerk, we do experience a slight jerk when the gear is changed.
In the past, CVT usage was very much limited by the engine size; more powerful output was made possible by increasing the strength of the belt, but was ignored due to better materials. CVT presently is being used by many large scale manufacturers, Subaru, Nissan, Toyota are to name a few.
As we know the manual or automatic gearboxes have about 4, 5 or 6 cogs. As the cog's smaller, the higher the gear, it's possible to achieve higher vehicle speed for any number of engine revolutions. Whereas in CVT a cone shaped gear mechanism is used. This includes a strong belt wrapped around which takes the drive from the car's engine. As the throttle is pushed by the driver the vehicle speed increases and the belt moves down the cone in order to vary the diameter which results in higher gearing. Hence we call it infinite number of gear ratios as it depends on the belt's position on the cone.
Ford engine with CVT
In CVT, there are no gearbox with a set of gears, that means they don't have interlocking-toothed wheels. Ingenious pulley system is one of the most common CVT type. This allows an infinite variability between the highest to lowest gears without any shifts.
DIFFERENT TYPES OF CVTS
1) Pulley Based CVT
A CVT basically consist of:
A rubber belt.
A variable input driving pulley.
An output driven pulley.
As mentioned above the three components are the key to the functioning of the technology. CVTs also include microprocessors; sensors etc. but the 3 mentioned above are the Key elements.
This is the most vital and important part of the CVT. A 20 degree cone facing each other is a component of each pulley. The groove between the two cones consists of the V- Belt or rubber belt. The belt can be of different material as well. A V-belt or rubber belt is preferred as it improves the belt's frictional grip.
As the diameter increases the two cones of the pulley go far apart. The belt goes lower in the groove; the radius of the belt loop gets smaller as it goes around the pulley. Whereas when the diameter decreases, the cones of the pulley come closer. The radius of the belt loop gets bigger in the groove as it goes around the pulley.
This type of Pulley always comes in pairs. One of the pulleys is called driving pulley and its connected to the crankshaft of the engine. It is also called Input pulley since it's here where the energy from engine is transmitted to the transmission. The other pulley is called driven pulley, this transfers energy to drive shaft and the first pulley is responsible in turning it.
To understand the above diagram in a better way it's very important to define what pitch radius means. It can be defined as the distance between the centres of the pulleys to where the belt makes contact in the groove.
The pulleys keep increasing and reducing the radius so as to keep the belt tight. As the radii are changed relatively to one another, they create infinite number of gear ratios. For instance, if the pitch radius is small on the driving pulley and larger on the other, this results to a decrease in the rotational speed of the driven pulley, in other words Lower gear. Similarly, when the pitch radius is large on the driving pulley and small on the driven pulley, this results to increase in the rotational speed of the driven pulley, also known as higher gear.
2) Toroidal CVT
Toroidal CVTs is another type of this system which replaces the original pulley and belt system discussed earlier. It consists of discs and power rollers as its components.
Although the components are different, the operation of toroidal CVT is the same as compared to belt-and-pulley system. The working of it is explained briefly below:
The driving pulley is one disc that connects to the engine
The driven pulley is another disc that connects to the drive shaft
Instead of the belt, there are rollers or wheels located between the discs which transmit power from one disc to another.
The wheels are capable of rotating along two axes i.e. they spin around the horizontal axis and tilt in or out around the vertical axis. This two axes rotation allows the wheels to touch the discs in different areas.
For speed reduction in this system and an increase in torque, the wheels must contact the driven disc near the rim, when they were earlier in contact with the driving disc near the center. This results in the reduction of speed and is considered low gear. For overdrive gear, the wheels must contact the driven disc near the centre, when they were earlier in contact with the driving disc near the rim. This results in the increase of speed. Thus a simple tilt of wheels results in gear changes, providing smooth and nearly instantaneous ratio changes.
3) Hydrostatic CVT
So far we have discussed frictional type of CVTs (pulley-and-V-belt CVT and toroidal CVT). There is one more type of CVT that follows different principle of operation. Hydrostatic CVT functions by varying the fluid flow into the hydrostatic motors using variable displacement pumps. The hydrostatic pump located on the driving side derives its rotational power from the engine. This rotational motion is then used to convert it in to fluid flow. This fluid flow is converted back into rotational motion using a hydrostatic motor located on the driven side.
Sometimes this mode of transmission is coupled with a planetary gear set and clutches to form a hybrid system known as hydro-mechanical transmission. These kinds of transmissions transmit power in three different modes:
At low speed power is transmitted hydraulically
At high speed power is transmitted mechanically
In between these two extremes, the transmission uses hydro mechanical means to transfer power.
These transmissions are very ideal for heavy-duty applications such as agricultural tractors and also for all-terrain vehicles.
4) Infinitely Variable Transmission
Before we understand why an IVT was produced its important to know what IVT constitutes of. The most important components of the IVT are listed below:
Variator: Its function is to create continuous varying ratios.
High regime clutch: This clutch is very different from the one in manual gear. This clutch is engaged for all forward speeds from the second gear onwards only.
Input gear set: This transmits power from the engine to the planet gear in the epicyclic gear train.
Epicyclic gear set: This is responsible for the running engine being connected to the stationary road wheels without any clutch or torque convertor.
Fixed ratio chain: Its function is to take the drive from the output discs and transfer it to the sun gear of the epicyclic gear set and input of the high regime clutch.
This is a type where zero ratio is included in the range of output to input shaft speed. This can also be defined as the higher ratio. A zero output speed or also defined as low gear, with a limited input speed suggest an infinite input to output speed ratio. This infinite value can be approached by a given finite input value with an infinitely variable transmission. This zero output speed can also be a reference to low ratios of output to input speed. This is considered as an extreme in IVTs, which results in neutral or non driving gear limit that implies the output speed is null.
IVTs can be better defined as the combination of planetary gear system with CVT. To go further in its working it's important to know about what CVR is that is continuously variable regulator. In this configuration the CVT is used as a CVR, in which the rotation speed of any one of the three rotators for the planetary gear system is regulated. CVR has a setting which results in the IVT output to be zero. In this setting two of the PGS rotator speeds are the input and output of CVR.
IVTs are better efficiency providers compared to CVT as most of the power comes through planetary gear system and not CVR. As a result the torque transmission capacity is increased.
The explanation given above can be summarized as shown
It is a type of transmission which is based on static friction. This mechanism includes engaging and disengaging certain elements between the driving and driven system. The transmission ratio is changed by varying the linkage geometry within the oscillating elements. The power shifts from input to output when the clutch or ratchet is engaged. This kind of CVT can transfer a large amount of torque because the static friction increases relative to torque as a result avoiding slippage. As the dynamic friction caused by transitional clutch speed changes the efficiency increases. The only problem with Ratcheting CVT is the vibration caused by repetitive transition in speed required in acceleration. This type of mechanism is not much use due to the above mentioned problem but still used in slightly auto mechanized cycles.
PROS AND CONS OF CVT
Much cheaper to manufacture.
Lighter and smaller in size compared to other transmissions.
Absolutely jerk free transmission.
Higher in efficiency and performance.
Not as reliable as Automatic or Manual transmissions.
Not able to cope up with big engine capacities (above 3.5 liters).
CVT Vs Manual Transmission:
CVT has proved to be very much notified and worked upon since its development has been recognized and so have its benefits. Engine here operates at the most optimum regimes and best throttle position. This transmission also meets the extreme power demands.
In order to show that the performance of CVT is better than manual transmission, we can do a simple calculation. We can find out how much time is required to accelerate the car from a complete stop to 100 km/h using a manual transmission. In both the cases we ignore aerodynamics and energy losses.
Firstly, let's take the case of manual transmission:
Let us take a light weight vehicle:
Mass (M): 1250 kg,
Power: 75 cV @ 5700 rpm.
As we know that the transmission ratio=output speed/input speed, Therefore we get the transmission ratios as:
Tr1=0.066, Tr2=0.095, Tr3= 0.14, Tr4=0.19 and Tr5= 0.28
Let's say we want to calculate the car speed on the very first gear at 5700 rpm
So V= 5700 x Tr1 x wheel radius x K1 = 43 Km/hr,
K1= unit conversation factor we can find that out by the following formulae:
K1=(2 x Ï€(rad)/1rot)/(60s/1min) x (1km/1000m)/(1hr/3600s) = 0.3768 min km/m.hr
Let us take a rough diagram of engine's power/torque chart,
Blue line is the torque values which are corresponding to maximum power at 5700rpm
Here the car takes about 12 seconds to accelerate from stationary to 100 km/hr. will full mass it takes about 15.5 seconds. At every instance the torque will be constant and the acceleration as well. Force = Power/Velocity and Acceleration= Force/Mass
Therefore equating both the above formulae's we get,
Acceleration=power/ (Velocity x Mass)
The power produced at 1st gear is 55 kW
So now, Acceleration/Acc1 = 55 kW / (43 km/hr x Mass) x K2 = 3.7 m/s2
K2= (1km/1000m) / (1hr/3600sec) = 3.6 Km.s./m.h
In the same way, Acc2= 2.6m/s2, Acc3= 1.8m/s2, Acc4= 1.4m/s2 and the 5th gear acceleration would not be required since we reach 100 in the 4th gear itself.
Time = total time to attain 100 km/hr
So finally we can say that,
Final.velocity = Initial.velocity + acceleration x Time.
Rearranging the above equation in order to get time.
Time1 = (43km/hr - okm/hr) / (acc1 x K2 ) = 3.2 Seconds.
Similar way Time2, Time 3, Time 4 is found out and total time = 11.9 seconds.
Secondly, Let's compare the above result to that of CVT:
We calculate time to accelerate from stationary to 100 km/hr in CVT, to get maximum acceleration the power should be at the maximum.
In terms of acceleration: Force= Power / Velocity and
Newton's Law: Force = Mass x Acceleration.
Equating the above equations we get Power / Velocity = Mass x Acceleration,
Differentiating wrt time: dv/dt, we get
Velocity x Mass x dv/dt / Power = 1,
Êƒ the equations on RHS and LHS, that is
Êƒ (Velocity x Mass / Power ) dv = Êƒ 1 dt
Substituting Velocity = 100 Km/hr, Mass = 1250 Kg, Power 75 cV
Therefore we get final CVT time as 8.8 seconds.
By this mere calculations we can conclude that CVT is 33-35% more sufficient and efficient then manual transmission and further on it takes just 75% of the time to accelerate to 100 km/hr when compared to manual transmission.
Steps involved in designing a CVT?
____ = Final Result, ____ = Formulae used.
1. Determination of the highest ratio.
We find the highest ratio so as to achieve maximum speed. We also use a higher ratio so as to achieve or benefit highway fuel economy. Therefore, using the given power, we can find out the vehicle's maximum speed.
Available power (Pt)
Let the engine power be Pe = _______ hp,
The transmission eff which also includes the rolling resistance is Eff: _______%
Pt = Pe x Eff = ________hp = ________w.
At a speed v (m/s), the Thrust force will be Tf = Pt/v = ________/v N
To get the maximum speed we need to know the Drag force, Df.
The Df = Cd x Â½ x r x v2 x A
Cd: drag force coefficient
r: air density = 1.2 [kg/m3]
v: vehicle velocity (m/s)
A: Vehicle's projected frontal area: ________m2
The maximum velocity can be calculated by equating the Thrust force to Drag force (Tf=Df) & solving for the velocity:
v3= Pt / ( Cd x Â½ x r x A )
v.max = _______m/s = ________km/h = ________mph
Let us consider that the maximum power is at ________rpm rpm.MaxP, the wheel diameter is _______ inches
And the Differential ratio Diff.Ratio is ____:1,
The highest ratio (High.Ratio) can be calculated by the equation:
v.max = (rpm.Maxp x 2 x 3.1416/60) x ((wheel.Dia x 0.0254)/2) / (High.Ratio x Diff.Ratio)
High.Ratio = (rpm.MaxP x 2 x 3.1416/60) x ((Wheel.Dia x 0.0254)/2) /
(v.max x Diff.Ratio)
And therefore the High.Ratio = __________
We find highest ratio value in order to optimize the maximum speed.
2. Determining the lowest ratio
2.1 Force as a result of the slope
Let us assume that the car is fully loaded & should start to move uphill.
Now, the vehicle's mass is _______Kg and the maximum load is _______Kg,
The load also includes the weight of passengers.
The slope inclination, (%.Incl), is _______% and the safety factor is _______.
As a result of the slope the forces will be:
F.slope = (mass+load) x 9.81 x (%.Incl/100) x safety / Eff = ________N
2.2 Tangential force available in the tyres:
As we know the maximum engine torque is ________ Nm.
When the car just begins to move, the efficiency as a result of cluth slip is _______% (cluth.eff)
The tyres also have tangential forces which can be calculated:
F.tyres = torque x clutch.eff x Low.Ratio x Diff.Ratio /((Wheel.Dia x 0.0254)/2)
2.3 Lowest Ratio
Equating F.slope = F.tyres and isolating Low.Ratio results:
Low.Ratio = F.slope x ((Wheel.Dia x 0.0254)/2)/torque x cluth.eff. Diff.Ratio)
Therefore Low.Ratio = ________:1
3. Adding of an external fixed ratio in order to obtain symmetric ratios:
As calculated earlier: Low.Ratio: _________ & High.Ratio : ________
A V-Belt CVT generates symmetric extreme ratios:
Low.Ratio x Corr.fac = 1/High.Ratio
This is because both pulleys move apart by equal amounts.
Note: Corr.Fac = ____ is correction factor. Lower Corr.fac (0.91-0.99).
We use lower correction factor values so as to lower the whole ratio span within the CVT which is an advantage.
Therefore, after the V-belt CVT we must add a fixed reduction. So that it is possible to have a symmetric ratio in the V-belt CVT.
The fixed reduction ensures that the final ratio span will be exactly from Low.Ratio to High.Ratio.
Therefore, we should add in a final/fixed reduction with a possible ratio of:
K=squareRootOf (Low.RatioxHigh.RatioxCorr.fac) thus K = ________.
Now we can calculate the new CVT's high & Low ratios. There will result from dividing each of initial Low.Ratio and High.Ratio by k.
Hence we can conclude that:
The CVT's symmetric ratios are
Sym.Low.Ratio = ________, and Sym.High.Ratio = ________.
4. Dimensions of the CVT:
4.1 Dimension of the Pulley:
Let's take the smaller diameter (D1) is _________mm
And the bigger is (D2) which will be D1/D2 = Sym.High.Ratio.
Thus D2=D1/Sym.High.Ratio = ________mm.
Specify the pulley groove angle : beta = ________deg.
4.2 Dimension of Belt:
Let the pulleys centre-to-centre distance is a = _________mm.
(Note: It must be greater than ________mm),
Belt_length = 2xa + (PI/2)x(D2+D1) + (D2-D1)/(4xa)
Thus the belt_length = ________mm.
5. High/Low ratio Velocities:
5.1 Lowest ratio velocities:
Driver pulley's rotational speed = ____rpm; (N1);
Driver pulley's rotational speed = ____rpm (N2=N1/Sym.Low.Ratio)
Belt_Speed = ________m/s; ((N1x2xPI/60) x (D1/2))
5.2 Highest ratio velocities:
Driver pulley's rotational speed = _______rpm; (N1);
Driver pulley's rotational speed = ________rpm (N2=N1/Sym.High.Ratio)
Belt_speed = _________m/s; ((N1x2xPI/60)x(D1/2))
6. Forces present:
6.1 The Friction coefficient:
Let the co-eff of friction is mu = _________.
The effective friction co-eff will be calculated by
Mu.eff = mu/sin (beta/2) = __________.
6.2. Belt tensions in the highest ratio:
As we know highest ratio is ________.
Now the driver pulley is D1 = ________mm,
And the driven pulley is D2 = _________mm.
The smallest belt wrap angle is alpha ________deg;
The possible ratio of the belt forces will be T12 = _________.
Belt tension load T1 = __________N,
Belt tension load T2 = __________N.
And the shaft.load = _________N,
Axial clamping.force = ( Pe/Belt_speed)/mu.eff = __________N.
6.3 Belt tensions in the lowest ratio:
As we know the lowest ratio is _________.
Now, we will use D1 = _________ mm for the driver pulley,
And D2 = __________ mm for the driven pulley.
The smalles belt_wrap angle is calculated by
2.acos((D2-D1)/(2xa)), This alpha _________deg.
The possible ratio of belt forces will be e(mu.effxalpha), so T12 = _________,
Belt tension load T1 will be (Pe/Belt_speed)/(1-1/T12) = _________ N,
Belt tension load T2 will be T1/T2 = __________ N.
The shaft load can be computer by:
Therefore, shaft.load = __________N,
Axial clamping force = (Pe/Belt_speed)/mu.eff = ________ N.