Computers and Technology No Comments


1. Problem Statement

2. Assumptions and data.

3. Calculation method and variables used

4. Calculations

5. Experimental Data

6. Materials [4]

7. Conclusion

8. Bibliography

1. Problem Statement

The problem under study is to evaluate the performance of brake used Colchester Student 1800 lathe located in the machine shop tools, National University of Colombia at Medellin. The function of the brake is to stop the machine in a possible emergency, therefore its use is not constant, as it would be the brakes of a car.

Description of Mechanism

The brake actuation mechanism is performed by mechanical means through a lever (2 bars) see appendix 1, the operator applies a force of approximately 40 Kg and is assumed direction perpendicular to the line AC (Figure 1).

Fig 1. scheme braking mechanism.

The force is transmitted to the bar in direction BC, which raises and allow the contact of the pulp against the pulley and thus achieve the aim of machine stop due to friction between the two materials.

The force exerted by the spring is neglected because it is very small compared to that made by the operator, the only function of the brake spring is to return to its initial position.

Braking requirements and critical conditions.

The safety brake must be stopped in a relatively short time, to make an estimate of this time, and in general to evaluate the brake, the masses should be considered to be slow at some point, for this critical conditions are chosen in which could be on the move around.

These conditions may occur when the part to be machined is as large as possible to allow the winch technology restrictions.

We analyze the brake with the largest piece and longest that can be mounted on the mandrel and assuming that it operates with maximum speed (1800 RPM), the piece has dimensions of 0.2 m in diameter and 0.42 m long.

To these conditions must masses gears of the gearbox, and inertia of the elements shown in Figure 2.

Also in this figure schematically shows the environment where the problem arises, in a schematic way shows the mechanism, the braking requirements and in turn arises in the different gears scheme involved with each other in order to obtain a red wherein the combination of the spindle axis (S-axis) rotates at 1800 RPM.

The number of teeth of each gear, and additional information is presented below in item 2. assumptions and data and can be seen in Annex 2.

General Scheme

Figure 2 Scheme of the elements to consider when evaluating the brake system.

As seen in this figure the motor transmits power from the drive pulley (pulley 1) to the driven pulley (pulley 2. Pulley which is directly braking), this power driven pulley transmits the axis B for the case of 1800 RPM transmits power through the gear teeth 33 C of the axis D by means of gear teeth 28 H, shaft D through gear transmits F E de33 teeth through the axis X of gear teeth 28. The axis E transmitted via the gear teeth and of the imaginary axis 37 via the gear 24 tooth J.

The imaginary axis name because as a shaft on which the gears are mounted J, K and L, but in reality there is no such axis, ie these gears J, K and L are not joined to shaft D , but it slide on at a different speed.

The dummy shaft transmits power through the gear teeth 44 K S axis (chuck shaft) by means of gear teeth 54 O of the shaft S transmits via the gear teeth 43 M of the shaft via the gear H Q of teeth 35 which is nothing more than an intermediate gear used for the G turn in the same direction as the axis S as shown in Annexes catalogs Q gear face width is quite large because it is a highly worked gear.

The H axis transmits through Q gear teeth of the shaft 35 via the gear G S of teeth 43, the shaft transmits G via the gear teeth 55 R from the axis R by means of gear teeth 96 U of the shaft I transmits via the gear teeth T of the shaft 35 and threads progress through the gear teeth of 90 V, this shaft enters a gear train manager automatic advancement longitudinal and transverse carriages which are not considered in the evaluation by the difficulty of access to the gears.

2. Assumptions and data.

* Assuming that it is operating without automatic lathe and not considered to be performing a tapping operation therefore not taken into account for the gearbox bolt pattern and progress bar, because when this plotting, cutting is a factor that helps the time to stop the machine, its angular velocity is very low, and access to this gearbox was not possible due to the complexity in which it is mounted.

* Not considered gears U and V (see general diagram Figure 2) and annex 2 since these gears are made of a lyre plastic type with very low density, therefore the inertia of the axis G, I and axis pattern also despises.

* Neglect the inertia of the axes.

* Both the materials of the gears, as the piece to be machined, the pulleys, the wheel and the mandrel, made considered a steel alloy with an average density of r = 7850 Kg / m ^ 3

It is assumed that an operation is performed so that the occasional brake temperature part, contrary to the case of periodic operation in which there remains a residual heat that influences a new braking operation, therefore the temperature is not a factor in the design of this brake.

* The initial data are some geometric measurements shown in Figures 1 and 2, the shaft speed S of 1800 RPM.

* The operator can exert a force of approximately 45 Kg = 441.45 N

* The coating material for molded asbestos whose coefficient of friction acting molten iron or steel is in the range of 0.2 to 0.5 dry. For this range is calculated with a coefficient of 0.3.

* The three-phase motor and 3 Hp 1750 RPM.

* The input data are summarized in Table 1.

* Modules are assumed equal for all gears equal to 2 mm.

De = Dp + 2 * Mod

De = Z * + 2 * Mod Mod

De = Mod (Z +2)

Mod = De / (Z +2) Equation 1

Measuring the outer diameter of a gear (gear general scheme Q See Figure 2)

De = 74 mm

ZQ = 35

Applying equation must Mod = 2 (and it is assumed that all the gears have the same module)

From: Outside Diameter

ZQ: number of gear teeth Q

Mod: module gear

Dp: gear pitch diameter

Z: number of teeth

L: face width of a gear

TABLE 1. Number of teeth and face width of each gear.

3. Calculation method and variables used


The general method is to find a stopping time, to get to this and other results are used methods such as dynamic analysis of the system, energy conservation, which can be synthesized in applying methods of design books Machines as Norton [1] and Shigley [2], and the help of documents or collections of different techniques teachers who have worked the issue.

Since the equation for the inertia is similar for all the elements, in particular for gears, these are tabulated in Table 1, using the Microsoft Excel program.


As seen in Figure 2. nomenclados gears have been systematically, using the letters of the alphabet, and for each gear corresponds a letter and a number of teeth (see Table 1).

The geometric variables are obtained directly from the physical model and other construction are obtained.

4. Calculations

Kinematic analysis

It has:

Taking this relationship, there is the angular velocity of each axis in terms of the angular speed given axis (shaft S = 1800 RPM)

as these relationships are needed in the 1654 RPM motor, this is a very rough acceptable as it should be 1750 RPM, can be lost in the transmission system, assumptions and approximations errors or slip of the webbing, although this is not so intense.

Inertia calculation on each axis

General equation of inertia

To calculate the inertia of the gears is constructed the following equation:

m = (p d ^ 2 * L * j steel) / 4 Equation 2

I = (m * (d / 2) ^ 2) / 2 Equation 3

Replacing equation 2 into equation 3 we have:

I = (P * L * j * d ^ 4 steel) / 32 Equation 4

d = Z * Mod Equation 5

replacing equation 5 into equation 4, using as the value modulo 0.02 m and the density of the steel and 7850 Kg / m ^ 3 we have the following equation for the mass inertia of the gears according to the number and width of teeth Face L:

I = (3.92 10 ^ -9) * p * L * Z ^ 4 Equation 6

Results According Equations of inertia

Based on Equation 6 is constructed in Table 2 where it appears pinion identification, the number of teeth, and the face width of each gear inertia calculated in Excel. It also calculates the inertia for pulleys and wheel discs as if they were solid.

Table 2. Calculation of the inertia of the gears.

* Inertia Axis B






I = Imotor driveshaft + + Ipolea driving Ivolante

The momentum provided by the engine is taken from a catalog of SIEMENS [3], this catalog was achieved in the documentation center, it shows who has several years of use so their is no bibliography. This catalog indicates that the inertia for a motor.

If the motor used is 3 HP at 1750 RPM,

I motor = (GD ^ 2) / 4

I motor = 0.0207 / 4

I motor = 0.005175 kg * m ^ 2

I = 0.024217 Kg driveshaft M’2

* I S

I Ipieza axis s = Imandril + + + IN + IM + IO IP

For the 1800 Student Colcherster around the larger piece that can mill has the following dimensions:

Length = 200mm Diameter = 420mm

Steel case:

For the mandrel having:

Figure 3. Dimensions of the mandrel

L1 = 38mm, L2 = 90mm, d1 = 118mm, d2 = 200mm, di = 55mm

For a steel mandrel:

So Ieje S: 0.2342 Kgm’2

Equivalent inertia calculation:

The pulley is located on the axis B is the pulley which is braked by a coating with cross section similar to a trapezoidal see catalog sheave annexes. Therefore it is necessary to replace the whole train of gears, pulleys, the motor, the mandrel, the workpiece and the wheel to a shaft with one equivalent inertia rotating shaft speed to B, it is possible considering the kinetic energies rotation as follows:

replacing the values of the ratios of Clause 4.1 and the inertia found in section 4.2.2 we have:

Calculation of the normal forces depending on the strength of the operator and brake geometry

senq = (0.014/0.21)

q = 3.82

AB bar is two and the direction of forces Fn1 vector is known. Of the sum of moments in the bar ADC, to D, we have:

Figure 4. Free body diagram of the pulley channel

Figure 3. Assemble Band – pulley

Figure 3 illustrates the dimensions of the contact between the pulley and the wafer.

Calculation of the frictional moment

To estimate the friction torque will take a disk radii ro and ri as shown in Figure 4.

Figure 4. Differential contact area on the tablet – pulley

For uniform pressure:

Time: Solving P and substituting:

Due to the inclination of the faces (pulley is a “V”), it is necessary to decompose the frictional moment which brings each face by an angle (see Figure 3):

To wear uniform:


Solving and substituting Pmax

Similarly to what was done for uniform pressure:

is clearly seen as the equation modeling the behavior of the brake disk as if two surfaces, the difference is that they involve an inclination of approximately 16 between what would be the surface of the disc.

If these two formulas are given numerical values, in accordance with paragraph 4.4, the time can be expressed in terms of braking friction and force the operator to do so:

Mf =-0.18635m Fop to wear.

Mf =-0.18683m Fop for uniform pressure.

You can see the resemblance of both theories, almost indifferent to use one or the other.

Braking time

The summation of moments about the axis of the brake when you start to slow down, is:

replacing Mf we have:

braking time depending on the speed at which the shaft is to be braked, the friction coefficient and the force required of the operator.

Given all the assumptions made in section 2. a calculation of the time as well:

m = 0.3

Fop = 441.5 N

w B = 1800 RPM

Tf = 5.9 sec when the largest piece is mounted.

Tf = 3.5 sec when you have assembled part and maximum speed


5. Experimental Data

to get a rough idea of what may be the friction coefficient for the pair of materials under study, we propose a little test that will feature many logical errors and uncertainties, but experience is just as valid to perform.

It involves taking a specific weight (28 Kg – 275N) and let it download on the brake bar, thus simulating the force exerted by the operator simultaneously takes the time it takes for the spindle to stop from a speed of 1800 RPM and without have no part mounted.


It took eight times as follows:


tpromedio = 3064 sec.

This time is replaced in the equation of section 4.6 and is obtained

m = 0.55

6. Materials [4]


The pulley piece serves as support must be made of metallic material to avoid having a high wear and to allow evacuation of heat generated.

In general the support part must comply with the following parameters:

* Have sufficient strength to prevent warping or failures that prevent the normal operation of the brake operating temperatures. It is important to take into account the centrifugal force.

* Have sufficient rigidity to have small deformations

* Having a coefficient of friction with the stable and suitable for coating application.

* Having low wear as they rub through the coating

* Maintain smooth, free and continuous erosion after wear

* No erosions or uneven surfaces on the coating

* Having a low deformation warming effect (low coefficient of expansion)

* Have a good thermal conductivity and specific heat

* Having a low density to limit inertia.

To meet these requirements require among other that the material has a metallographic structure fine, homogeneous and with high transformation temperatures.

To clutch (brake) Dry operating generally used cast iron with lamellar pearlitic matrix thin, with no ferrite, carbides and inclusions. The approximate composition is 3% of carbon, 2% silicon and 0.7% manganese. These mills have a tensile strength half of 225 MPa, hardness of 225 BHN and modulus of 11×104 MPa. The main thermal properties include thermal expansion of 45.9 W / m C, specific heat of 501.6 J / Kg C and density of 7800 kg/m3.

When speeds are very high or high stresses are typically used nodular cast iron. Coated sintered carbon steels are used.


assumes that the coating material for this round is possibly asbestos molded, as compared to steel has good friction characteristics, has a very low cost and wide range of applications, see Annex3. Another reason to think that is an asbestos is that the lathe is a machine study relatively old and at that time this was the most common material used today this item is no longer used mainly due to their adverse health effects as agent carcinogen.

Friction linings should have certain properties which enable them to operate properly:

Coefficient of friction:

the friction coefficient is strongly influenced by some operating conditions such as:

* Temperature. Generally the ratio is slightly lower at low temperatures, then take a normal value to fall to a certain critical temperature at which it becomes unstable. Therefore, in no case should reach this temperature operation.

* Rotation speed. In general low friction coefficient with increasing speed. So generally is lower for high slip.

* Pressure: By increasing the pressure generally decreases the coefficient of friction.

* Stay in time: using some materials tend to vary with use their surface and hence the friction coefficient.

Therefore the materials used for the coatings should be possible friction coefficient as constant as possible to the operating conditions and residence time. Additionally given the variations that occur with operating conditions published values for the various materials to be taken as indicative of the dynamic coefficient between. It is therefore recommended that you take to use a safety margin of around 25 to 30%.


It is important that the wear is small to avoid modifications of the drive control and frequent replacements of the coatings.

However it is desirable to renew this wear to surfaces and thus maintain the same constant coefficient should be avoided whenever possible in the entire surface of wear parts which contacts the coating.

The surface condition of coatings must have a continuous surface. So to wear the coat should not be produced erodaciones or uneven surfaces.

The thickness of the coatings to provide wear (1 or 2mm).

Mechanical strength

The coating must be able to withstand and transmit the loads imposed on it during operation as:

* Resistance to centrifugal force: The coating supports considerable centrifugal forces that try to undo it. To endure require good mechanical strength, an adequate fixing and mounting and a mass (density) as low as possible. The latter is also important to achieve low moments of inertia.

* Shock resistance: During operation the friction surfaces of the clutch (brake) can collide and break might cause damage to the facility. Thus the materials used must not be fragile.

* Shear strength: Since coatings must transmit torques shear support both its surface and fixation, especially when using rivets.

* Hardness and elasticity: The coating must be strong enough to withstand the pressures which works without being incrustations, not cause wear on the surface of the piece that slides against him and should be adapted to small surface irregularities

Thermal Properties

Because the processes involved in generating heat clutch facings are required to retain the mechanical properties (coefficient of friction, mechanical strength, hardness, etc..) To operating temperatures. Also it is convenient to allow the evacuation of heat from the friction surfaces to avoid excessive local heating.



* Jacket Material: ASBESTOS MOLDING, low cost, maximum pressure of 50 to 150 psi, maximum operating temperature 500 F.

* Friction coefficient: 0.3 (0.2 to 0.5)


* OPERATING UNDER CONDITIONS OF WEAR: Basically the same as if I was not.

* Braking time: Tf = 5.9 sec when the largest piece is mounted.

Tf = 3.5 sec when no piece is mounted and the maximum rotation speed.

The conditions described above are the most critical potential varying any of them immediately braking time will be less.

7. Conclusion

brake in study design has good features, wear theory is similar to the uniform pressure in my opinion the brake satisfactorily fulfills the functions for which it was designed, it has a good selection of materials, the system is not complex , it has a low probability of failure is usually efficient and depending on the level of analysis that is being done, if you give more embarrassing results as the case of an assessment of an accident, you have to have much more rigorous as it have ruled out several things and of course others, which can lead to errors in calculations.

Parameters Evaluated

Braking time: acceptable.

Force from the operator: to perform normal.

Specific power: there was no reference for comparison.

Materials: for the time of its construction, optimal.

Operation wear: acceptable.

Dissipated heat, temperature control: not assessed. Approximate models lack of heat transfer.

8. Bibliography

[1] NORTON. Robert L. machine design. 1999. pag. 959 to 983.

[2] Shigley. Joseph. Mechanical Engineering Design. Mc Graw Hill. Pag 609-629.

[3] SIEMENS. Electric motors and fans. (Documentation center) page 1/15

[4] FRESNEDA, Elisha. Principles of operation of clutches. January 2000.