Worm Gear Design: Gear Parameter and Description

Worm Gear Design: Gear Parameter and Description - In the previous article we have explained some of the gear transmission systems such as spur gear, helical gear and bevel gear. If we will connect two parallel shafts, we can use a spur gear or a helical gear. (Read more: spur gear design) (Read more: helical gear design) If we will connect two mutually perpendicular shafts (right angle), we can use a bevel gear. (Read more: bevel gear design)

In this article we will explain about the worm gear. Worm gear is always paired with a worm screw in the transmission system. We can use worm screw and worm gear, when shaft are at right angle and need more reduction in speed between the driving and driven shafts. Couple worm gear is consisting of a worm has an external threaded and a worm gear associated with worms.

What is a worm screw and worm gear?

A worm screw is a cylinder on which is cut single or multiple start acme-type thread. The angle of this thread ranges from a 14,5 to 30o pressure angle. As the angle of the worm increases, the greater of pressure angle must on the side of the thread.

The teeth on a worm gear are machined on a peripheral groove which has a radius equal to half the root diameter of the worm. The drive ratio between a worm and worm gear assembly is one to the number of teeth in the worm gear. The worm which meshes with the worm gear may be a single or multiple start thread. A worm with a double start thread will revolve the worm gear twice as fast as a worm with a single start thread and the same pitch. Thus if worm gear had 50 teeth, the ratio would be 50:1, providing the worm had a single start thread. If it had a double start thread, the ratio would be 50:2 or 25:1.

Based on the above understanding, we can know the advantages and disadvantages of worm gear transmission. Among its advantages are very prominent on his worm gear is smooth and almost without sound, as well as allowing large transmission ratio. Reduction ratio can reach 1/100. However its disadvantages, we can not reverse the direction of transmission of the worm gear to increase the rotation of the worm wheel to the worm screw. This sort of thing will 'lock itself' because the worm screw will stop rotation turn of the worm gear. Another disadvantage of the worm gear is a low efficiency, especially if the pitch angle is small.

Worm screw and worm gear parameter

The standard measure of the worm screw is outside diameter, pitch diameter, root diameter, pitch screw, pitch module, axial module and pitch angle. The standard measure of the worm gear is outside diameter, pitch diameter, throat diameter, root diameter, normal module, arch gear radius and arch gear angle. Worm screw and worm gear is an integral gear paired, so that some of its parameters must have the same dimension is normal module, addendum, dedendum and whole depth. Another important measure as a basis for gear calculation is shaft distance and clearance. This measure will decide the amount of friction between the worm screw and worm gear.

Such as generally gears, module is the main measure of gears that will decide the size of the gear. Worm screw and worm gear pairs must have the same module size. Worm gear is using the normal module that has the same module profile with the generally gears as to spur gear, helical gear and bevel gear. The worm screw is using the axial module that has a trapezoidal screw profile. The relationship between the normal module and the axial module is affected by the pitch angle. If m_n is normal module, m_s is module axial and g is pitch angle then, relations between them are:

We can also calculate the module value by shaft axial distance (a) and the teeth number of worm gear (Z) is through the formula:

In the production process of worm screw, don’t know the term of module, however using the pitch screw. Pitch screw is the distance between two peaks screw in one full turn. If the screw number of worm more than two (z> 2) then the distance between the peaks screw nearby called pitch modules. If the screw number of worm equal to one (z = 1) then pitch screw equal to the pitch module. If m_s is the axial module, g is the pitch angle, z is the screw number of worm, p_m is pitch module and p_s is a pitch screw, the equation between them are:

That is a description about Worm Gear Design: Gear Parameter and Description. If you find misconceptions in the worm gear formula, please give me correction in the comment box.

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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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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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V-Belt Selection Guide: V-belt Sizes, Types and Safety

V-Belt Selection Guide: V-belt Sizes, Types and Safety - Belts are made of rubber with a cotton cloth core or the like as reinforcing the greatest tensile force. Use as v-belt transmission has the following advantages:

• A portion of the belt is twisted in the pulleys experience a wide arc so that grow large section to provide a large friction.
• The friction force also increases due to the influence of the wedge-shaped which generate a large transmission power of relatively low stress.
• It has a slip to avoid damaging an electric motor.
• It can be used in a large transmission ratio and the distance closest to the shaft.

V-belt is a standard part so easy to find in stores or belt manufacturer's dealers. The machine designer simply chooses the type and size of the belt as required by the machine. V-belt selection is determined by the length and type of the cross section of the belt relative to the power and speed are transmitted. Once selected, the belt also remains to be tested for safety by the power capacity and the speed of the belt.

Determined of v-belt types

V-belt has a trapezoidal section with a variety of sizes, from small to large, ie, type A, type B, type C, type D and type E. The v-belt types sections selected based motor  power and driver shaft speed by the following curve.

Examples:
If the belt driven by a motor with a power of 3 kW at a speed of 2000 rpm pulley, then the graph above corresponding the intersection of the power requirement line (blue line) with the speed of driver pulley (red line) is in the region A means that the type of belt is selected by type A.

Determined of v-belt sizes

Once the type of v-belt is known, the following must be known how long the belt is required. In the trade standard, long belt is expressed by v-belt sizes. The v-belt size is units of inches in circumference around length, not decimals and fractions. Before determining the v-belt sizes, the v-belt must be known mm in length using the following calculation:

Note:
L = V-Belt Length (mm)
C = Center Distance (mm)
d = Diameter of driver pulley (mm)
D = Diameter of driven pulley (mm)The v-belt size is obtained by converting the circumference of belt in inch units. Its results are rounded. For example, if you get 24.45 inches then take a belt number is 25.

V-belt safety by power capacity

Belt has a power capacity that can be transmitted. Power capacity issued for each single belt depending on the v-belt type, pulley diameter, speed of the driver pulley and belt marks. Belt manufacturer usually have the belt capacity catalogue. An example of a table for the power capacity of the v-belt type A shown.

Power capacity of v-belt is main value in table and value added suitable of transmission ratio, example if driver pulley speed is 600 rpm, pulley diameter  is 100 mm and transmission ratio is 1,5 so power capacity of v-belt is 0,77 + 0,06 = 0,83 kW.

V-belt safety is sure if belt capacity in the table is greater than the actual belt capacity. The actual belt capacity can be calculated by the following equation:

Note:
Pr = Actual belt capacity (kW)
P = Power requirement (kW)
N = Number of belt
k = Correction factor

The v-belt correction factor is obtained by following table:

Safety of v-belt speed

V-belt safety can be seen from the ability to withstand the transmitted speed. Generally, the belt speed can be provided for every 10 to 20 m/s and up to 25 m/s with a maximum power which can be transmitted is less than 500 kW. This means that the belt can be considered safe, if its speed is less than 25 m/s (v <25 m/s).

That is a description about how to determine of V-Belt Selection Guide: V-belt Sizes. Types and Safety. If you find misconceptions in the v-belt design, please provide the correction in the comment box.

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Helical Gear Design: Helical Gear Dimension and Strength

Helical Gear Design: Helical Gear Dimension and Strength - Helical gears used to move between the axes of rotation are parallel. Helix angle is the same in each gear, but the gear is shifted to the right and the other left. Involutes tooth shape is an expectation. A helix is a theoretical line or path generated on a cylindrical surface by a cutting tool which is fed length-wise at a uniform rate, while the cylinder is also rotated at a uniform rate. Initial bias intersection gear teeth are something that has become a more teeth line in the communion of the teeth.

Helical gear design includes the standard dimensions and strength. Standard dimensions are pitch diameter, outside diameter, root diameter and whole depth. The helical gear strength is the ability to withstand the deflection load and surface pressure.

Standard dimension of helical gear

Main gear dimensions are often expressed by the number of teeth (T) and the normal module (M) for the metric. Multiplying two variables leads to what is called the pitch diameter. In helical gears, the value of the pitch diameter is affected by the helix angle with the following relationship:

Note:

D = Pitch diameter (mm)

M = Normal module

T = Number of teeth

ß = Helix angle (o) 

How to determine outside diameter, root diameter, addendum, dedendum and whole depth are equal to spur gear calculation. (Read more : Spur Gear Calculation)

Helical gear strength by deflection load

Deflection load occurs due to the tangential force acting on the tooth surface. Tangential force is the force acting in the direction of rotation of the gear to a point on the pitch circle. Tangential force can be calculated by the following equation:

Note:

Ft = Tangential force (Kg)

Pe = Power estimation (Kw)

V = Velocity (m/s)

Velocity of helical gear can be calculated by the following equation:

Note:

V = Velocity (m/s)

n = Rotation speed (rpm)

D = Pitch diameter (mm)

Deflection load caused by the tangential force should not exceed a bending load per unit width on the sides of the permissible bending stress so that the wheels do not have a broken tooth. Deflection load can be calculated based on the Lewis equation, which is the basis for the gear design which is:

Note:

Fb = Deflection load per unit width (kg/mm)

Sd = Deflection stress (kg/mm2)

M = Normal module

Y = Gear factor

fv = Velocity factor

Helical gear strength by surface load

If the pressure between the surfaces of the tooth is too large, the teeth wear out rapidly. Furthermore, the tooth surface may be damaged because of the repeated fatigue load. Therefore, the pressure on the surface of the tooth or the surface load capacity must be limited. The surface pressure does not exceed the surface load per unit width. The surface load is calculated based on the Hertz theory that the decline in the equation can be obtained by the following equation.

Note:

Fs = Surface load per unit width (kg/mm)

fv = Velocity factor

Sc = Contact stress (kg/mm2)

D1 = Pitch diameter of pinion (mm)

T1 = Number of teeth of pinion

T2 = Number of teeth of gear

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

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