Contenu connexe Similaire à RockCrusherProject (20) 2. Abstract:
This project will cover the design of a rock crusher, consisting of a mechanism that transfers the
mechanical energy to the jaw, and a gearbox to increase the torque applied to the mechanism.
Components of the mechanism and gearbox will be designed to account for fatigue and have an
infinite life where applicable. A successful design was created meeting the overall requirements
of the assignment to safely operate under the intended use.
Body:
Procedure gears:
Getting Started:
To start the gear design process, the first thing to be done is to determine what the overall
dimensions of the gearbox or transmission case should or can be. In this design we are making
a reverted gear compound gear train. This will keep the space of the gearbox minimal. In this
case the dimensions given are the crank and the main motor gear have to be 1000 mm apart
exactly and the overall width has to be less than 1200 mm from gear tip to gear tip. The gear
reduction ratio was a given parameter where a 1 to 10 reduction was needed. With that
information known it is possible to come up with the circle diameters to make the design fit into
the case parameters. In this case, to make a 1 to 10 reduction, a 1/2 and a 1/5 reduction were
used to create the overall 1/10 reduction. So, to maximize the gear size for strength given the
large amounts of torque they will be subject to, the overall dimensions of the gears 14 are:
160mm, 800mm, 320mm, and 640mm respectively. Gears 1 and 2 have a face width of 151mm
and gears 3 and 4 have a 226mm face width after all analysis was done. Now that the sizes are
known and the wanted output torque is known, by back stepping the torques through the shafts
and running them through the gear diameters you can find the various minimum and maximum
torques for the gears.
Gear Information:
With the torques and the diameters known the design process can be started. A pressure angle
of 20 was used, it is also one of the two standard pressure angles to pick from. The first step
that was taken in this process is assuming how many teeth gear one will have (the first pinion).
To start, 16 was picked for no particular reason just to have a starting point. After guessing and
checking through the whole process it was figured to be 17. With the number of pinion teeth
known the number of teeth on the gear connected to this pinion can be found. With the diameter
known and the teeth known the diametral pitch along with the pitch circles can be determined.
From those, the base pitch, gear ratio, addendum, contact action, and length of action can be
found. The face width may also now be determined, Norton states a nominal value of 12/pitch
diameter, this can be played with to adjust the surface fatigue safety factor.
3. Bending:
With the contact ratio and numbers of teeth for the gear and pinion, the bending geometry
factors, J’s using table 1210, can be found. Using the correct angular velocity for the gear set
being designed, calculating the pitch line velocity and comparing it to the max, the larger of the
two is used. There are two parameters needed, A and B, to get Vmax. These parameters will be
used in other correction factors. Next, is the loading on the gears. Two torques will be needed
the maximum and minimum for the gear set being designed. The gear quality was set to 11 due
to the fact that an automobile transmission is 1012 and a similar design quality was desired.
Bending Correction Factors:
Six correction factors need to be found:
1) Dynamic factor: this factor involves the parameters A and B as well as Vmax and or Vt
whichever is larger to calculate and the quality of gear which has to be taken into consideration
here.
2) Load distribution factor: use table 1216 in Norton to get this
3) Application factor: use table 1217 in Norton to get this use common sense to apply the
factor
4) Size factor: this is mainly 1 unless otherwise specified
5) Rim thickness factor: a solid gear was chosen so in this case it is 1
6) Idler factor: in this case no idler gears are used so 1
With the loads known and the correction factors calculated the corrected bending stress can be
found.
Surface stresses:
Now, surface stresses must be taken into account and there will be three correction factors:
1) Surface geometry factor: there is three parts to this that need to be calculated.
2) Elastic Coefficient: use Table 1218 if the material is on there. If not there is an equation
available.
3) Surface finish factor: this is mainly 1 unless otherwise specified.
Now calculate the corrected.
Bending Fatigue:
Using table 1225 and the hardness of the material chosen, bending fatigue can be found from
the uncorrected fatigue strength
There will be 3 factors for calculating the bending fatigue strength:
1) Life factor: use table 1224 to find the equation to use. It will be related to the hardness.
2) Temperature factor: use the formula given.
3) Reliability factor: use table 1219 to find.
6. beams. For the analysis the material needed to have correction factors added to the theoretical
strengths. There were five correction factors to be calculated:
● Loading For a bending case a loading factor or 1 was used, for the axial case a loading
factor of 0.70 was used.
● Size The size was determined by an equivalent diameter, since the geometry is square
instead of round.
● Surface finish The surface was selected as a hot rolled surface.
● Temperature The jaw will never see a temperature above 450 degrees C so a value of 1
was selected.
● Reliability A reliability of 90% was chosen because of the purpose of the machine and it
is not necessary to have a real high reliability.
Once the correction factors were applied to the material, the infinite life safety factor could be
determined. The safety factor was determined from case 3 to be conservative in this design.
The final value of the safety factor for the bending beam was calculated to be 2.134. Finite
element analysis was used to confirm the maximum bending stress location and to analyze
other key areas on the beam.
Plate design:
The plate that is attached to the face of the jaw was chosen to have a material of 4140
quenched and tempered steel @ 400 degrees. This specific material was chosen because it has
very high yield and tensile strengths, the hardness of this material is also 510HB. There are no
impact forces considered in this design and all the forces are distributed across the whole plate.
The depth on the plate was taken to be 20mm deep. This material also shows impact, and
abrasive resistance properties. Even if occasionally something harder than the typical rock does
enter the crusher, this plate will produce a long part life.
Procedure for Shaft Design and analysis:
Design Procedure:
The main drive shaft within the gearbox was designed in order to withstand a fluctuating torque
and moment produced from a gear. This is with the assumption that the end of the shaft with
the crank attached does not create any sort of bending moments. With this understanding, the
shaft was set up in a simply supported fashion, with the bearings being the supports and the
gear creating the forces between the bearings. Furthermore, the shaft will be designed with a
step to reduce deflections between the bearings and reduce vibrational effects. The thickest
part of the shaft, the part of the shaft between the two bearings, was designed first. This area of
the shaft was designed to withstand the stress concentrations due to a keyway under bending
and shear stresses. Deflections were also analyzed to ensure the gears would properly operate
without failure. The step in the shaft would experience shear stress due to torsion, which is the
areas the bearings attach. Therefore, stress concentration factors for the steps were used to
determine a suitable diameter at these bearing locations under shear stress. This allowed for
7. the determinations of bearings. The final diameter needed was the diameter of the shaft where
the crank is attached. This part of the shaft would experience stresses only due to torsion, and
would contain stress concentrations from a keyway. Once these calculations concluded,
torsional deflections, and the stresses produced on the shaft through a press fits were analyzed.
Analysis:
The fluctuating forces produced by the gear were determined from the known fluctuating torque,
with the maximum force being 43.232 kN and the minimum force of 36.581 kN. The distance
between the bearings is 0.5 meters, and the gear is placed 0.35 meters from the bearing
nearest the drive crank. With the forces determined, the reaction forces at each bearing is
calculated. This is used to find the location of the maximum moment, and critical locations for
analysis. The maximum moment occurs at the location of the gear is referenced in equation 8:
shaft design page 2. With these large forces in mind, the material chosen for the shaft is 1040
steel quenched and tempered at 400 degrees Fahrenheit. The shaft will be ground to a surface
finish of 0.8 microns to 1.6 microns. The mean moment is calculated to be 4.539 kNm and the
alternating moment is 0.349 kNm. The mean torque is 12 kNm and the alternating torque is 1
kNm. To determine the correct endurance limit C factors had to be determined. The C factors
are listed below:
● Loading C factor of 1 since there is only bending and torsional loading.
● Size Equation 6.7b aided in determination, factor of 0.74 found.
● Surface Equation 6.7b aided in determination, factor of 0.9 found for ground finish.
● TemperatureNo temperature effect, so factor of 1.
● Reliability Reliability of 99.9% so factor used is 0.753.
Corrected endurance limit is found to be 195.33 MPa.
To determine the diameter necessary at the gear, a stress concentration factor of 3 is used for a
keyway. This is for both the shearing and bending stresses to achieve a conservative
approach. The diameter of the shaft necessary at the gear is determined to be 0.112 m with a
safety factor of 3, the shaft diameter at this location is chosen to be 0.130 m in order to reduce
deflections. The step in the shaft to accommodate for bearing mounting only experiences shear
stresses due to torsion, due to the fact that there is no moment present at these locations which
is referenced in equation 8: shaft design page 2. The notch radius at the step locations will be 1
mm, so the stress concentration factor at this location is 3 under torsion to be conservative. The
diameter necessary at this location is 0.112 m with a safety factor of 3, and the diameter chosen
is 0.120 m. The final diameter necessary, is the diameter of the shaft to accommodate the
mounting of the crank. There will be a stress concentration due to a keyway, and the crank will
only experience stresses due to torsion. There will be the same keyway stress concentrations
that were used in determining the diameter of the shaft at the gear. A shaft diameter is
determined to be 0.109 meters at the crank, the diameter chosen at the crank will be 0.120 m.
The maximum torsional deflections along the shaft is found to be 0.231 degrees, which is
suitable for this application. Maximum deflection due to bending is found to be 0.031 mm, which
8. is suitable for proper gear meshing. This is referenced in equation 12: shaft design page 6.
Maximum angular deflection is 0.013 degrees at bearing locations, which is suitable for proper
running of bearings. This is referenced in equation 11: shaft design page 5. Bearing selection
will be described later in the report, but the tolerances were given for the shaft at bearing
locations. An m6 tolerance condition for the shaft at bearing locations was recommended by
SKF. The shaft tolerances will be +35 microns for an upper limit and +13 microns for a lower
limit along the whole shaft. This is seen in the SKF bearing report in figure 19. A safety factor
due to the interference fit for the shaft is found to be 6.625, therefore the shaft will not fail due to
the interference fit. The h4 tolerance class will be used on the area of the shaft located between
the bearings. The total length of the main drive shaft will be 0.866 m. All calculations for the
shaft are found in equations 7 through 13: shaft design pages 1 through 7. Final dimensions and
tolerances of the shaft are referenced in technical drawing 4.
The shaft was analyzed for critical speeds using solidworks, modes 15 were found to make
sure the shaft was not close to its natural resonating frequency. The natural frequency of the
shaft speed is 2 hertz. Therefor the fundamental frequency is significantly higher than the
rotating frequency of the shaft. The shaft will not fail due to critical rotating speeds. The modes
can be seen in Figures 1014.
Table 1: Frequency analysis of main drive shaft
Bearing Selection:
With large shock loads in the radial direction and no axial loads, a cylindrical roller bearing is the
proper bearing for the loading conditions in this case. The maximum radial force either of the
two bearings along the drive shaft will experience is 30.263 kN and the shaft will rotate at 120
rpm. The roller bearing chosen through the SKF bearing calculator tool is a NJ 2324 ECMA
sealed bearing in order to provide high cleanliness. In this application the inner ring will be the
only part of the bearing rotating, with the shaft having a horizontal orientation. This bearing has
a bore diameter of 120 mm, an outside diameter of 260 mm, and a width of 86 mm. Lubrication
determination will be explained later in the report, but the lubrication is a grease with a viscosity
of 500 mm squared per second at 40 degrees Celsius and 32 mm squared per second at 100
degrees Celsius. Under these conditions, SKF gave the bearing a modified L10 life of over
1,000,000 hours. This L10 life is more than suitable for the rock crusher. The power loss due to
the bearing is 30 W. Relubrication intervals are determined to be every 3090 hours, with a
grease quantity of 110 g when replenishing. SKF determined the shaft and housing tolerances
9. if there was to be thermal expansion in the shaft. The shaft tolerance class is m6 and the
housing tolerance class is G7. Referenced in the SKF bearing report in figure 19.
Bearing Mounting:
As stated above, the housing for the bearings within the frame will be a G7 housing tolerance
class. The housing bore tolerance values will be +69.0 microns as an upper limit and + 17.0
microns as a lower limit, with a nominal diameter of the housing being 260 mm. The outer ring
of the bearing nearest the crank will clamped axially to the housing, and the inner ring will be
located using a sleeve spacer and the flange of the shaft. This bearing will not be the bearing to
account for thermal expansion. The outer ring of the other bearing will be allowed to float within
the housing to account for thermal expansion. This will ensure there will be no axial forces due
to thermal expansion of the shaft. The inner ring of this bearing will be located using a snap ring
and the flange along the shaft. Stress concentration analysis was not needed on the groove for
the snap ring because this area of the shaft is not exposed to any stresses. When inserting the
shaft into bearings, an expansion fit will be used by cooling the shaft through the use of liquid
nitrogen before insertion. There is m6 shaft tolerance values on the shaft where the bearings
attach, which will create an interference fit. The expansion fit will reduce the axial stresses
created on the bearings due to insertion of the shaft. Referenced in the SKF bearing report in
figure 19.
Key Selection Analysis:
The key will fail due to shearing or bearing failure, so analysis was done to ensure the key will
not fail under these conditions. The key material chosen is 1020 hot rolled steel since this is a
softer material than that of the shaft, gear, and crank. Standardized dimensions for the key
were used, the width of the key being 32 mm and the height being 18 mm. A length of 152 mm
is chosen for the key. Both the crank and gear will use the same size key. Analysis was done
on the key using the fluctuating torque created by the gear, which ranged from 13 kNm and 11
kNm. The alternating component of the shear stress is 3.155 MPa and the mean component is
37.856 MPa. The Von Mises alternating stress component is calculated to be 5.464 MPa and
the mean component is 65.568 MPa. To determine the correct endurance limit, C factors must
be determined. The C factors are listed below:
● Loading C factor of 1 since there is only shearing.
● Size Equation 6.7b aided in determination, factor of 1.753 found. Size factor will be
chosen as 1 for a conservative approach.
● Surface Equation 6.7b aided in determination, factor of 0.8 found for machined finish.
● TemperatureNo temperature effect, so factor of 1.
● Reliability Reliability of 99.9% so factor used is 0.753.
Corrected endurance limit is found to be 114.003 MPa. This giving a fatigue life safety factor of
4.526. A safety factor is also needed for bearing failure of the key, which is determined to be
2.524. This value is a suitable to resist bearing failure, and is lower than the safety factor for the
gear, shaft, and crank. Therefore, the key will fail before the shaft, gear, and crank will. In
11.
Procedure for Connecting Rods Design and Analysis:
Design Procedure:
In determining the dimensions for the connecting rods, the rod that experienced the heaviest
loads and most stress was designed initially. By designing for the rod that experienced the worst
case scenario it leads to a more conservative design if the same rod is used in less extreme
loading conditions. Connecting rod 8 experienced maximum compression loads of 110 kN which
would lead to column failure in concentric loading before any other type of failure depending on
the slenderness ratio. With that being said, a buckling analysis was performed to find the
allowable load from a chosen safety factor. The length and thickness were already known from
given dimensions and previous pin dimensions determined. The width was determined by
multiplying the pinhole diameter by 3 in order to use a minimum of onepin diameter of material
between the edge of the hole and the parts outer edge. This was suggested by the book as a
good starting design point. The compressive yield strength was set equal to the tensile yield
strength of the material as a very conservative approach to the buckling analysis.
After performing the buckling analysis for connecting rod 8, since connecting rod 7 would not
experience as much compression and would not buckle before connecting rod 8 if the same
designs were used for each, a fatigue analysis was performed on both connecting rods. The
fatigue analysis was completed for a uniaxial fluctuating stress state where only axial loads
were experienced by the connecting rods. From the fatigue analysis an endurance limit and
safety factor were determined for an infinite life material. A case 3 safety factor was chosen to
be calculated where both alternating and mean stress components can increase under service
conditions but their ratio will remain constant.
Analysis:
After performing the buckling analysis on connecting rod 8, the final dimensions were
determined to be 550 mm long from the center of each pinhole, 30 mm thick, 189 mm wide, with
pinhole diameters of 63 mm. The material selected was machined 1040 steel, quenched and
tempered at 400o
F. We selected a hardened steel with very good material properties in order to
be more conservative. Hardened steel is also compatible with itself in surface wear so it can be
used in practice with the hardened steel pins selected. With a safety factor of 4, the buckling
analysis resulted in an allowable load of 594.322 kN which is much higher than the 110 kN
experienced. This design can also be used in connecting rod 7 conservatively.
After the buckling analysis, fatigue analysis was performed on each connecting rod. The results
for connecting rod 8 give an endurance limit of 126.601 MPa and a safety factor of 5.487.
Fatigue analysis results of connecting rod 7 give the same endurance limit as rod 8 but give a
12. more conservative safety factor of 6.022. Guided solutions to these numbers can be seen in
Equations 2829: Mathcad Pages 12 Connecting Rod Buckling Calculations, Equations 3032:
Mathcad Pages 13 Connecting Rod 8 Fatigue Analysis Calculations, and Equations 3335:
Mathcad Pages 13 Connecting Rod 7 Fatigue Analysis Calculations.
Lubricant Selection:
Once the bearings were selected an appropriate lubricant needed to be chosen. Fortunately,
SKF has a bearing grease selection chart listed on their website in pdf format. Their bearing
grease selection chart lists all their greases, a brief description of each grease along with
applications, temperature ranges, and operating speeds. Fortunately, SKF offers a grease
commonly used with jaw crushers, construction machinery, and vibrating machinery.
The grease chosen is LGEM 2 grease from SKF that has an operating temperature range from
20o
C to 120o
C which is considered a medium temperature range according to SKF. The
operating speed for LGEM 2 grease is listed as very low so it is necessary to check into this and
see if the current application speed is considered very low.
For cylindrical roller bearings very low speeds are considered to be < 30,000. Where n isn * dm
the rotational speed in rpm’s, and is the mean diameter of the bearing (0.5*(D+d)). Thedm
product of for the bearing selected is 22,800 which is lower than 30,000 and considered an * dm
very low operating speed and meetings the specifications for grease LGEM 2.
Grease selection chart and parameter definitions can be seen in figures 16, 17 and 18.
Finite Element Analysis:
Static finite element analysis was used to analyze all parts. For the jaw a static study was done
to verify the maximum bending moment on the face, and the maximum stress magnitude and
location. Both solidworks and singularity functions found the maximum bending moment in the
same location as well as magnitude. An analysis was also performed on both connecting rods in
tension and compression. The analysis showed that both rods under both loading conditions
were not close to yielding. Finite element confirmed that the highest stresses were indeed found
at the pin hole of the connecting rods. The shaft was analyzed for both pure torsion and bending
moments due to the gears. The maximum bending displacement for the shaft was found to .231
degrees which is acceptable for this design. The pure torsion design in the shaft is higher than
what was actually calculated. This could be due to two reasons, the first being that the material
that solidworks does not perfectly match the 1040 QT at 400 degrees.The second is because of
the mounting fixtures; to mount the flywheel there is a resulting fixture at the main shaft output
which, caused a false bending moment causing the stresses to be higher than they actually are.
Finite element should only be used in this case to confirm critical areas under a static loading
condition. All Finite Element Analysis parts can be seen in Figures 39.
