Shaft Design: Shaft Dimension and Strength

Shaft Design: Shaft Dimension and Strength - Shaft is static or dynamic part having a round cross section, which is attached to elements such as gears, pulleys, steering wheel, crank, sprocket and other power transmission elements. Shaft can receive bending load, strength, pressure and torque, either alone or in combination with others.

The word shaft could include the term of axle and spindle. The term of axle more dedicated to the shaft that accepts torque load, while the spindle is dedicated to the reception of the short shaft around. Calculating the shaft load type also depends on the torque and deflection or both.

Torque load of shaft

The torque load occurs at the shaft rotation of the reception of the electric motor. The torque is the ratio of the power requirement and shaft speed by the formula:

Note: 

T = Torque (kg mm)

P_R  = Power Requirement (kW)

n = Shaft Speed (Rpm)

Power requirement is obtained from the power of electric motors after that is multiplied by a correction factor by the following formula:

Note:

P_R  = Power Requirement (kW)

P = Electric Motor Power(kW)

f_c  = Correction Factor

Correction factors have been taken according to the values of use of the transmission power as shown in the following table.

Note:

• Use the correction factor at average power if the shaft load is not constant and the calculated average load. This condition is the cause of the power consumption varies.
• Use the correction factor at maximum power if the calculated maximum loads on the shaft.
• Use the correction factor at normal power if the shaft load is constant or normal load

The shaft diameter with the torque load can be calculated by the equation:

Note:
d = Shaft Diameter (mm)
t  = Shear Stress (kg/mm)
T = Torque (kg mm)
f_T = Torque Factor
f_D = Deflection Factor

Torque factor and deflection factor are selected according to the type of load which is received by the shaft as in the following table:

Note:

• If the shaft certainly not accept a bending load, the deflection factor taken 1,0.
• If the shaft is provided for receiving the bending load, but its value is not known, a deflection factor value corresponding caught in the table above.
• If the shaft directly receives a bending load, and then use the calculation of torque and deflection load of shaft together.

Torque load will cause the deformation in the form of an angle of the torsion shaft. It is calculated by the equation:

Note:
θ      = Torsion angle (o)
T = Torque (Kg mm)
d = Shaft Diameter (mm)
l = Shaft Length (mm)
G = Modulus of Rigidity (Kg/mm2)

Shaft can be declared safe if the torsion angle less than 0,25 degree/m in the normal working conditions. If the calculation results show the value of the torsion angle of more than 0,25 degree/m, it should be redesigned to take a larger shaft diameter.

Bending load of shaft

Bending stress will occur in the static or dynamic shaft gets radial force in a region that has a distance from the fulcrum. Radial force is the force which is perpendicular to the axis of the shaft. The radial force caused by the external load or internal load of shaft.

The external load of shaft is caused by the force received by the machine element is mounted on the shaft like belt tension, gears tangential force, blade shear forces etc. The internal load of shaft is caused by weight of shaft and other component.

Its loads will cause a bending moment that can be calculated using the formula:

Note:

M = Bending Moment (Kg mm)

F = Radial Force or Load (Kg)

l = Distance of Force to Equilibrium Moment  (mm)

If a large number of forces acting on the shaft that the bending moment then be taken into account largest bending moment on the shaft by following equilibrium calculations.

If the static shaft receives a pure bending load, the shaft diameter can be calculated by the equation:

Note:

d = Shaft Diameter (mm)

t  = Shear Stress (kg/mm)

M = Bending Momen(kg mm)

f_D     = Deflection Factor

Bending load will cause the deformation in the form of deflection shaft. It is calculated by the equation:

Note:

y = Deflection (mm)

d = Shaft Diameter (mm)

F = Force (Kg)

l_A, l_B = Distance of Force to Bearing (mm)

l = Distance of Bearing to Bearing (mm)

Shaft can be declared safe if the shaft deflection less than 0,3 (mm/m) in the normal working conditions. If the shaft works in high speed or high precision, the shaft deflection must be less than 0,03 – 0,15 (mm/m). If the calculation results show the value of the deflection shaft of more than standard, it should be redesigned to take a larger shaft diameter.

Torque and bending load of shaft together

If the shaft receives the torque and deflection together, the shaft diameter can be calculated by the equation:

Note:
d  = Shaft Diameter (mm)
t = Shear Stress (kg/mm)
M = Bending Moment (kg mm)
T = Torque (kg mm)
f_T  = Torque Factor
f_D = Deflection Factor

Value of bending moment and torque can be calculated by previous equation. Shaft strength can be checked by calculation of torque angle and deflection shaft.

Shaft calculation formulas above is taken from the handbook of Design of Machine Elements by Sularso & Kiyokatsu Suga and Mechanical Engineering Design by Shigley & Mitchel

That is a description about Shaft Design: Shaft Dimension and Strength. If you find misconceptions in the shaft formula, please provide the correction in the comment box.

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Spur Gear Design: Spur Gear Dimension and Strength

Spur Gear Design: Spur Gear Dimension and Strength - Gear transmission classified according to the location of shaft, the direction of rotation, and the teeth formed lines. Spur Gear is a gear of the parallel shaft with teeth aligned in two zones of the cylinder is called "pitch field". Both surfaces of the cylinder are crossing each other with a fixed parallel axis.

Calculation gears are similar, particularly in the spur gear and helical gear. Therefore, Spur gear description will focus more on the basis of mechanical gears size calculations, while for the strength calculation of the gear will be described in more detail in the calculation of helical gear. (Read more: calculation of helical gear)

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Plastic Recycling Machine by Crusher and Pellets Forming System

Plastic Recycling Machine by Crusher and Pellets Forming System - Plastic known since the early 19th century BC and it’s developed after the discovery of resin phenol formaldehyde by Backland, LH in 1909. In the 20th century BC, the development of plastics is increasing since the early issues raw material to processed products, so that the plastic started slowly change the role of metal.

In general, the plastic material can be classified into two types of thermosetting and thermoplastic. The use of thermosetting limited because it can not recycled. This differs from the thermoplastic material can be recycled in demand, especially by the industry average. Plastic recycling process is not much to change the shape and quality of its chemical structure, while the price is much cheaper compared to new plastics. This condition is the reason for the plastics industry uses recycled plastic.

Plastic recycling process is through several stages of crushing process and forming of plastic pellets. Crushing is the shape of the plastic debris of destruction process crashed into a small size using the crushing machine. Forming of plastic pellets is a continuation of crushing process that shredded plastic processing to the form of plastic pellets in the melting process and plastic forming. At this time only the forming process of plastic pellets by high industry and industrial products, while small industries is only able to process up to the level just shredded plastic.

In fact, only shredded plastic is used as a raw material for the manufacture of low quality products, while high-quality products to use a raw material of plastic pellets. Therefore, a combination of crusher and plastic pellets forming in a small industrial scale is required. So, in this article will explain the Plastic Recycling Machine by Crusher and Pellets Forming System.

Construction of Plastic Recycling Machine

The construction of plastic recycling machine can be seen in the image below:

Construction of Plastic Recycling Machine

This machine uses three main systems, i.e., the crusher system, the heat extrusion system and the pellets forming system.

Crusher and Pellets Forming Concept for Plastic Recycling Machine

Crusher concept is used plastic sheet cut through pinch two grooved wheels providing the cutting force. Shear strength of both ends of the wheel truncated plastic case. When the cutting process, the plastic material that has been cut will be pulled downwardly and retracting plastic wheels used above.

Crusher is designed with two grooved wheels rotating in opposite directions to each other and intersects. Rotation of both wheels using the gear transmission spur gears with the same comparison for causing rotation in the opposite direction at the same speed. The size of the slots of the wheel will determine the size of the result of the cut.

Pellets forming concept consists in heating the raw materials to melt by means of an electric heating element placed outside the pipe. This heating process is performed in several steps along the pipe is pressed by a rotating screw extrusion as a result of the power transmitted by the electric motor so that the first material has a melting point moved to the end the pipe. At the end of the melted plastic tubes come through a round hole in the form of a continuous plastic mold and a certain period of his forming will be cut to a standard of pellets size.

That is a description about the Plastic Recycling Machine by Crusher and Pellets Forming System. If you find misconceptions in this post, please provide the correction in the comment box.

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Bevel Gear Design: Bevel Gear Dimension and Strength

Bevel Gear Design: Bevel Gear Dimension and Strength - Bevel gear is used to transmit power from one shaft to another shaft axes intersect. In general, the shaft bevel gear is formed at a 90 degree angle with a different number of teeth, but under certain conditions, this gear may be made at any size angle and tooth profile of the helix. Therefore, in addition also the bevel gear terms such as known:

1. Bevel gear, when two shaft are located at an angle with their axial lines intersecting at 90 degrees.
2. Miter gear, when the shafts are at right angles and the gears are of the same size
3. Angular bevel gear, when connecting the shaft angle is smaller or larger than 90 degrees.
4. Hypoid gear, when modified bevel gear having helical teeth.

Standard parameters of bevel gear are pitch diameter, module, number of teeth, whole depth, face angle, pitch angle, cutting angle and outside diameter. Parameter of bevel gear can be seen in the image below.

Determined of pitch diameter, module and number of teeth for bevel gear

Calculation of pitch diameter, module and number of teeth for bevel gear, miter gear and angular bevel gear of the same as the calculation of spur gear using the following equation: (Read more : calculation of spur gear)

Note:

D = Pitch diameter (mm)

M = Normal module

T = Number of teeth

Although calculation of pitch diameter, module and number of teeth for hypoid gear follow the calculation of helical gear using the following equation: (Read more: calculation of helical gear)

Note:

D = Pitch diameter (mm)

M = Normal module

T = Number of teeth

b = Helix angle or Hypoid angle (degree)

Determined of whole depth for bevel gear

Whole Depth is the height of teeth which is the sum of addendum and dedendum, or by the following formula:

Note :

H = Whole Depth (mm)

Ad = Addendum (mm)

Dd = Dedendum (mm)

x = Coefficient of tooth change

T1 = Number of teeth of gear

T2 = Number of teeth of pinion

Value of the coefficient of tooth change is different for bevel gears and pinion. Addendum to the pinion is greater than the bevel gear while dedendum to the pinion actually less than the bevel gear so that the value of x1 = x and x2 = - x.

Determined of pitch angle for bevel gear

If shaft angle (Σ) is smaller than 90 degree, so pitch angle for bevel gear and pinion can be calculated by the formula:

Note:

Δ1 = Pitch angle of gear (degree)

Δ1 = Pitch angle of pinion (degree)

If the shaft angle (Δ) is equal to 90 degrees, so pitch angle for bevel gear and pinion can be calculated by the formula:

Determined of face angle for bevel gear

Note:

Δ = Pitch angle (degree)

Δf = Face angle (degree)

θa = Addendum angle (degree)

Ad = Addendum (mm)

R = Pitch bevel length (mm)

D = Pitch diameter (mm)

Determined of cutting angle for bevel gear

Note:

Δ = Pitch angle (degree)

Δc = Cutting angle (degree)

θd = Dedendum angle (degree)

Dd = Dedendum (mm)

R = Pitch bevel length (mm)

D = Pitch diameter (mm)

Determined of outside diameter for bevel gear

Note:

Do = Outside diameter (mm)

D = Pitch diameter (mm)

Ad = Addendum (mm)

Δ = Pitch angle (degree)

That is a description about Bevel Gear Design: Bevel Gear Dimension and Strength. If you find misconceptions in the bevel gear formula, please provide the correction in the comment box.

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