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					8                         THE ANNALS OF UNIVERSITY “DUNĂREA DE JOS “ OF GALAŢI
                                     FASCICLE VIII, 2005, ISSN 1221-4590

                        SPUR GEARS
          Laurentia ANDREI, Gabriel ANDREI, Alexandru EPUREANU,
                          Iulian Gabriel BÎRSAN
                              The University “Dunarea de Jos” of Galati, Romania

                 The paper gives an overview of a non-standard spur gear whose geometry is
              defined by both tooth curvature and variable height along the gear face-width. The
              gears are mainly designed for plastic gears, in order to enhance their transmissible
              power. Virtual models are used to investigate gear mesh, tooth deflections and
              strength, and a comparison to standard spur gears is drawn. Due to the complex
              gear geometry, a cutting process is appropriate for the gear manufacture.

              KEYWORDS: non-standard curved face width spur gear, plastic gear, gear
              performances, gear manufacture

               1. INTRODUCTION                            the gear transmissible power level; it also enhances
                                                          lubrication under operating conditions, but reduces
     The conventional plastic spur gears are              the gear manufacture possibilities.
continuously being investigated in order to increase            The non-standard gear geometry and mesh are
their transmissible power level, either by developing     investigated by both numerical method and solid
performing materials, such as nanostructured              modeling technique. They enable the tooth flanks,
composites, or by modifying the gear tooth geometry.      along the gear face width, to be drawn and compared
     The curved facewidth spur gears are not popular      to the standard involute shape. Studies on virtual
for gear industry and not much has been published on      models enable further analysis to be developed such
their performances and manufacture, to our                as tooth bending resistance and deflection, modify-
knowledge. The advantages of these gears, compared        cations in sliding velocity, tooth generation errors.
to standard spur gears are [1]:                                 The simulation of the gear generation, based on
- high contact ratio,                                     a simple kinematics, enables the first attempt in gear
- higher bending resistance and reduced contact           manufacture. Virtual gears are used to manufacture
stresses,                                                 the gear prototype, by the selective laser sintering as
- better meshing in plane misalignment conditions,        a material incress manufacturing technique. Injection
and                                                       moulding is the traditional technique for plastic gear
- there are no axial forces as are inherent in helical    manufacture. Unfortunately, the complexity of the
gears.                                                    shape of the curved face width gear, with modified
       Against these advantages there are limitations:    geometry, makes the design of a die almost
- the difficulty in gear design due to the complex        impossible. Therefore, it was decided to cut the gear
tooth geometry compared to conventional designs,          on a traditional milling machine, with specially
- the difficulty in gear train mounting and               designed equipment and tools.
- the sensitivity to center distance variations.                The tooth geometry precision and quality are
       The gears described in this paper have a           investigated as they are essential in gear operating
modified geometry, controlled by two parameters: the      conditions. Experimental tests carried out by the
radius of the tooth curvature along the gear face width   authors on the running curved face width spur gears,
and the reduction on gear tooth height towards the        with modified geometry, are focused on the gear
gear face width ends. This non-standard gear is           thermal behaviour and noise.
specially designed for plastic gear, less sensitive to          This paper resumes the significant theoretical
variations in tooth profile geometry than their metal     and experimental investigations on the non-standard
counterparts. This modified tooth geometry increases      gear geometry and mesh.
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                                               FASCICLE VIII, 2005, ISSN 1221-4590

2. THEORETICAL INVESTIGATIONS                                        Simulations of gear generation are also
    ON GEAR PERFORMANCES                                        developed using the solid modeling technique [3].
                                                                     Several tools are “designed”, with similar shape
                                                                but different geometrical parameters, shown in figure
              2.1. Non-Standard Gear Generation                 3: Rg - the radius of the generating circle varies from
                           Process                              16 mm to 28 mm, for a 24 mm gear face width, and β
                                                                - the tool axis inclination is considered at 0 - 25°.
      Gear performances are developed on virtual                AutoLISP routines are used for the curved spur gear
gears, using the traditional conjugate surface                  generation process simulation and a representation of
generation theory as well as the solid modeling                 the entire gear is produced (fig. 4).
techniques. Simulations of gear generation consider
the following kinematics:
- the tool performs the rotational motion about its
inclined axis;
- the gear blank is rotated about its axis and is
provided with translational motion, tangential to the
base circle of the gear. A special device provides the
rolling motion, required for the involute tooth flank
profile generation;
 - a simple indexing motion is used to generate all the                          a)                        b)
concave teeth flanks and then the convex flanks,
using a different cutter.                                               Fig. 3. Illustrating the virtual tools for the
      A numerical computation [2], based on the                         tooth convex (a) and concave (b) flanks.
conjugate surface generation theory, enables to
produce the gear tooth forms in several sections along
the gear face width (fig. 1), as well as the line of
action (fig. 2); h indicates the distance from gear
centre. The following design specification is
considered: 2 mm modulus, 30 the number of teeth,
24 mm gear face width, 25° tool axis inclination and
20 mm is the radius of the generating circle. Figure 1
shows that the generated tooth profile is of involute
form except at the extreme ends of the gear face. The
straight lines of action, shown in figure 2, indicate the
gear conjugate motions.
                                                                    Fig. 4. Illustrating the virtual gear blank with two
                                                                                   generated teeth [3].
 y [mm]

                                                                               2.2. Gear Tooth Geometry
                                                                      Several non-standard gears are generated, with
                                                                the above design specification, in order to investigate
                    h=1mm           h=6mm     h=11mm
                                                                the variation of some tooth geometrical parameters
          0                                            x [mm]
                                                                such as the maximum base circle radius Rb, the
                                                                maximum dedendum circle radius Rf and the
                    Fig. 1. Tooth profiles along                maximum pressure angle α, recorded at the end of
                      the gear face width [2].                  the gear face width, as they influence the gear
                                                                meshing condition (table 1).
     y [mm]

                                                                                                                 Table 1
                  h=1mm                                          Rg [mm]/β [°]        Rb [mm]    Rf [mm]        α[°]
                                                                      16 / 5           29.17       27.94         13.5
                                                                      20 / 5           28.82       27.83        16.12
          0                                                           24 / 5           28.65       27.77        17.25
              0                                     x [mm]            28 / 5           28.55        27.7        17.90
                    Fig. 2. Lines of action along                     28 / 2           28.41       27.65        18.74
                      the gear face width [2].                        28 / 8           28.69       27.78        17.00
                                       FASCICLE VIII, 2005, ISSN 1221-4590

           start of mesh         3° gear rotational angle     8° gear rotational angle    13° gear rotational angle

17° gear rotational angle      20° gear rotational angle     22° gear rotational angle        27° gear rotational angle

                                 Fig. 5. Illustrating the path of contact during gear mesh.

      It is noticed that, for the same tool axis inclina-    - the line of contact is a spatial curve, with a variable
tion, the decrease in the gear generating circle leads       curvature during the gear mesh;
to an increase of the dedendum circle radius,                - there are points along the line of action where three
implying a decrease in gear backlash – for Rg = 16           tooth pairs are in contact, showing the high gear
mm, the gear backlash is reduced to 0.06 mm which            contact ratio;
definitely implies gear interference. Also, the tooth        - a longer contact is specific to the gear tooth, a
flanks exhibits the involute profile on 70% of its           consequence of both the tooth curvature and the
height compared to 85% in the case of the standard           increase of gear base circle radius. Compared to its
tooth. The pressure angle also decreases leading to a        ideal value of 20.3°, calculated for the standard spur
decrease in plastic gear resistance to wear, as it is        gear, the gear rotational angle, for a single tooth
shown [4].                                                   contact, is increased to 27°.
      For the same value of the generating circle
radius, the increase in the tool axis inclination
increases the dedendum circle radius and decreases                    2.4. Gear Bending Resistance
the pressure angle, damaging the gear operating
conditions. A limited increase in the tool axis                    Curved face width spur gears are modeled using
inclination should be considered for each tooth              COSMOS/M, version 2.5, set to the following
curvature, so that the gear mesh avoids interference.        geometrical parameters: modulus 2 mm, 30 teeth and
                                                             24 mm face width. Poisson’s ratio for the plastic
                  2.3. Gear Mesh                             material used in the gear manufacture, ERTALON
                                                             66SA, is 0.3 and the tensile modulus of elasticity is
       The solid modeling technique also enables the         3450 MPa. The gear 3D model consists of SOLID
gear path of contact to be produced. Figure 5                elements - 8 vertex per solid and 3 possible
illustrates the path of contact on the pinion tooth          translational motions per vertex [5].
convex flank, in a theoretical mesh of a gear train                As a first step, the load is applied successively
with the contact ratio equal to 1 and 60 mm center           on the concave and convex flanks of the pinion tooth.
distance. The gears have been generated with a               A gear geometry is considered at 20 mm the
geometry defined by 20 mm generating circle radius           generating circle radius and at 0° the tool axis
and 5° the tool axis inclination. The gears contact          inclination. For an applied load of 4 Nm, the tooth
starts at the beginning of the theoretical line of action,   bending resistance analysis shows that:
specific to the gear center section, where the tooth         - the maximum von Mises stresses, recorded on the
flank exhibits the ideal involute; an interference,          tooth concave flank, is of 14.82 N/mm2 occurring on
produced by an additional gear rotational angle of           limited areas close to the gear face ends, while most
0.01°, is used.                                              of the tooth exhibits a medium of 5-7 N/mm2 stresses;
       The analysis of the gear path of contact shows        - the maximum Von Mises stresses, recorded on the
the peculiarities of the modified curved face width          tooth convex flank, decrease significantly by 32%
gear mesh:
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                                       FASCICLE VIII, 2005, ISSN 1221-4590

              a)                                       b)                                         c)

                   Fig. 6. Illustrating the Von Mises stresses specific to curved face width gear (a),
                                    double helical gear (b) and standard spur gear (c).

compared to the previous stresses values, and occur           maximum stresses are by 27% higher than in case of
on a large area along the tooth dedendum, on the              standard spur gear, the stresses are distributed on
opposite flank.                                               limited areas where the load is not as high as it has
      As regarding the tooth displacements, it is found       theoretically been considered. The double helical gear
out that the recorded displacement is reduced by              is also convenient regarding the bending resistance,
31.5% when load is applied on the tooth convex                but the recorded maximum stresses exceed by more
flank. The maximum displacement of 35…40 µm                   than 100% the specific values for the curved spur
occurs on the entire tooth length, while the maximum          gear.
displacement of 50…60 µm, recorded when load is                     A third analysis on non-standard gear bending
applied on the tooth concave flank, moves to limited          resistance is focused on the influence of the gear
areas near the gear face ends.                                tooth modified geometry on the Von Mises stresses
      Generally the pinion is the first one to fail in a      and tooth deflections. Figure 7 shows the variation of
plastic gear train [6]; therefore, the previous analysis      the tooth bending stresses versus the tool axis
is important in the attempt of improving the pinion           inclination – the tooth height respectively, for a
behaviour through a convenient mounting, i.e. the             chosen 20 mm radius of the generating circle. It is
load should be applied on the pinion tooth concave            noticed that the maximum stresses increase with the
flanks. Both the tooth stresses and displacements are         reduction in tooth height along the gear face width,
lower than those specific to convex flanks, ignoring          but it is recorded on extremely reduced areas close to
the highest values recorded in limited areas at the end       the tooth tip; moreover, the areas are reduced by the
of gear face width – analysing the gear path of               increase in tool axis inclination. A similar distribution
contact, the load acting on this areas is much reduced        of the bending stresses is exhibited by each tooth
than the theoretical one, considered in finite element        geometry – the most affected is the unload tooth
analysis.                                                     flank, at the tooth dedendum, and the limited sections
      Secondly, a comparison of the standard and              of the loaded tooth flanks.
non-standard gear bending resistance is developed.                  The tooth maximum displacement is recorded
Loads are applied on the tooth concave flanks, related        for β = 0° and decreases with the increase in the tool
to a torque of 4 Nm, in the assumption of having two          axis inclination (the reduction in tooth height). The
teeth in contact. Analysing the illustrations from            maximum tooth displacement is specific to the gear
figure 6, concerning the maximum Von Mises                    center, where the tooth has the standard involute
stresses as well as the stresses distribution, it is          profile.
noticed that:                                                       Figure 8 shows the variation of the tooth ben-
- on the standard spur gear tooth (fig. 6c), the              ding stresses versus the generating circle radius – the
maximum stresses are constant, at about 8 N/mm2.              tooth curvature on the gear face width respectively,
The maximum stresses are developed on a large area            for a chosen 5° the tool axis inclination. It is noticed
on the tooth dedendum, along the gear face width;             that the increase in the radius of the tooth curvature
- on the curved face width spur gear tooth (fig. 6a),         decreases the maximum Von Mises stresses and
the maximum stresses increase to 11 N/mm2, but they           extends the area they occur along the gear face width
are distributed on reduced areas close to the gear            – a distribution specific to the spur gear. For reduced
ends;                                                         values of the generating circle radius, the bending
- on the double helical gear tooth (fig. 6b), the             stresses are not induced in the unload tooth flank. The
maximum stresses are concentrated in gear center              maximum tooth displacement is recorded for Rg = 16
sections (35 N/mm2) and towards the gear face width           mm and occurs at the gear face ends, where the
end sections (24 N/mm2), on extremely reduced areas.          applied load is not as high as theoretically considered.
      In conclusion, the non-standard gear, with a            Increasing the radius of the tooth curvature, the
constant tooth height, has a higher bending resistance        maximum tooth displacement rapidly decreases, but it
than its standard counterparts. Even the recorded             extends along the entire tooth length.
12                                                          THE ANNALS OF UNIVERSITY “DUNĂREA DE JOS “ OF GALAŢI
                                                                       FASCICLE VIII, 2005, ISSN 1221-4590

          Von Mises stresses [N/mm ]

                                       40                                                                                laser beam
                                                           helical gear

                                       20                          width gear
                                                       curved face

                                                       standard spur gear
                                       10                                                    4

                                                                                             5                                             6
                                                5     10     15      20     25      30
                                                            The tool axis inclination [°]
                                                                                                    Fig. 9. Gear manufacture by SLS [8].
                                          Fig. 7. The influence of the tool axis
                                       inclination on the tooth bending resistance.
 Von Mises stresses [N/mm ]

                                                                 helical gear

                                       20                           ed f
                                                                          width ge
                                                      standard spur gear           ar

                                               5     10     15     20     25      30
                                               The radius of the generating circle [mm]                Fig. 10. Curved face width gear
                                                                                                        with modified geometry [8].
                                Fig. 8. The influence of the generating circle
                                   radius on the tooth bending resistance.                        Figure 10 illustrates a pair of the designed non-
                                                                                            standard gears, manufactured by SLS. The relatively
                                        3.    NON-STANDARD GEAR                             poor accuracy of the tooth flank is caused by the
                                               MANUFACTURE                                  particular simulation of the gear generation – the
                                                                                            increment of the rolling motion was limited by the
                                                                                            extremely large size of the file – as well as by the
                                        3.1. Gear Manufacture by DCM                        relatively low precision of the manufacture
       The authors used the selective laser sintering
(SLS), as a material incress manufacturing technique,
to form the solid three-dimensional non-standard                                                       3.2. Gear Cutting Process
gear [7]. Figure 9 shows a schematic representation
of the process.                                                                                   The curved face width gear, with modified
       The unsintered nylon powder 2, from the                                              geometry, is designed to be manufactured on FUS
powder feed 1, is preheated to a temperature close to                                       250 milling machine. Based on the kinematics
its melting point and flatted by a leveling drum 4 into                                     presented in 2.1, the cutting process requires special
the part cylinder 3. Here, the selective solidification                                     equipment, in order to provide both the rolling and
happens by further heating, up to the sintering tempe-                                      the dividing motions, and special tools [8] (fig. 11).
rature, by means of the XY controlled pulsed laser                                                The plastic gear blank 1 and a metal spur gear 2,
beam 5. The powder grains being melt and stocked                                            with the same module and number of teeth, form an
together, the base plate moves down slowly and a                                            opposite set. The blank is fitted on the shaft 9 by two
new layer of powder is spread across the surface. The                                       specific bushing 14 and pin 11, which enable the gear
powder that is not scanned by the laser is unaffected                                       being generated to be further tested on a special rig
and remains in place to support the next layer of                                           [5]. The screw 12 overcomes an additional blank
powder. The gear shape is built in a discrete way,                                          rotational motion due to the exerted cutting forces.
with a point-to-point 2D layer technique. At the end                                              The gear being generated is connected to both
of the building process, the entire cake of sintered                                        the machine-tool table, by the shaft 9 and the bearing
and unsintered powder is allowed to cool down and                                           block 13, and the spindle support, by the following
is lifted out of the machine. Then the loose powder is                                      elements: shaft 9 - metal spur gear 2 - barrel 4 - band
shaken off and the sintered gear is free.                                                   5 – wedge slide 8.
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                                        FASCICLE VIII, 2005, ISSN 1221-4590

                      13             7                         8



    12                                                         4           5         4              6      8

    14                                                         3
    1                                                          2
                            Fig. 11. A schematic presentation of the specific equipment [8].



                        3                          4                                 Rg

                                 Fig. 12. The tool heading configuration and position
                                      related to the machine milling spindle [8].

       The translational motion of the milling table 10       the cutters show straight lines for the imaginary rack-
is transmitted to the entire equipment, including the         cutters flanks, with zero pressure angle, necessary to
barrel 4 which simultaneously induces the rotational          generate an involute tooth profile in all sections
motion for the gear set, thus the required rolling            along the gear face width.
motion necessary for the gear tooth involute profile
generation. A proper rolling motion is assured if the                   4. EXPERIMENTAL TESTS
outside diameter of the barrel (Db) is equal to the gear
base circle diameter, calculated in the gear centre                 A number of plastic curved face width gear,
section. At one stage, one gear tooth flank is                with modified geometry, were cut to the following
generated. The blank and the standard gear 2 are then         specifications: gear modulus = 2 mm, number of teeth
simply dividing; the pin 7 initially disengages the           = 30, gear face with = 24 mm, the radius of the
system rolling motion.                                        generating circle = 20 mm, the tool axis inclination =
       Variations of tooth geometry are generated by          25°.
different tool-headings. Figure 12 shows a schematic                Investigations on gear flanks are focused on the
illustration of the cutter heading 1 with its inclined        tooth profile precision and on the flank surface
axis (β) related to the milling spindle direction. The        quality. In concern to gear running behaviour, with no
cutter 3 is located and accurately positioned into the        lubrication, measurements of the gear temperature
cutter heading 1 by special screws 4. The translation         and noise are developed.
of the cutter, along its axis, is controlled by the guide
pin 2 and enables the variation of the radius of the                     4.1. Tooth Profile Precision
generating circle (Rg). The limitation of the designed
cutter heading is that the tool axis inclination cannot             The tooth profile is investigated using a
be varied and the generation of new gear geometries,          Coordinate Measuring Machine. A comparison to the
relative to the variation of the tooth height, requires       standard involute shows that [2, 9]:
new cutter headings.                                          - at gear center, the tooth has the standard involute
       Two different cutters are used for the tooth           profile, as expected due to the gear kinematics;
convex and concave sides. The normal sections of
                                      FASCICLE VIII, 2005, ISSN 1221-4590

- in sections away from the gear center, the tooth          measurements showed that the run-out errors of the
profile is slightly changed; it gets close to a different   curved face width spur gears were quite large and
involute, specific to a base circle whose radius is Rbi≠    they would lead to an effective reduction of the
Rb – a consequence of both the tool axis inclination        center distance and non-uniform wear on the tooth
and tool cutting edge geometrical configuration.            rear face.

            4.2. Tooth Surface Quality                                                                                     98°

      The tooth flank surface roughness is measured                                     90                       90°
on a Talysurf machine and the data is exported to the                                                      82°
3D mapping program Toposurf which produces a
topographical map of the investigated area (fig. 13)
and is able to calculate the physical and statistic

                                                               Temperature [°C]
roughness parameters in sections along the gear face                                    60
width and along the tooth height.
      It is found out that, along the gear face width,                                  50
the flanks roughness is appropriate, considering the
manufacturing conditions: a single point cutter is                                      40
generating the tooth flank; there is no cooling liquid
during the gear manufacture as the cutting forces,                                      30
                                                                                                                                         N = 1500 revs/min
specific to plastics, were considered relatively low.
                                                                                        20                                               N = 1000 revs/min
The manufacturing conditions influence mainly the                                                                                         N = 500 revs/min
tooth surface roughness along the gear height.                                                                                               = the predicted
                                                                                                                                         surface temperature

                                                                                                      0        10       20        30   40     50         60
                                                                                                                                   Time [min]

                                                                                       Fig. 14. Temperature of CFW spur gears as a
                                                                                                function of speed [10].


                                                                                                     140                136°

                                                                                  Temperature [°C]

     Fig. 13. Showing a 3D map of the tooth concave
                    flank surface [8].                                                               80

              4.3. Gear Temperature                                                                                                          T = 15 Nm
                                                                                                                                             T = 12 Nm
      The curved face width spur gear temperature is                                                                                          T = 9 Nm
                                                                                                                                                 = the predicted
measured [10] using the test rig designed by Walton                                                  20                                      surface temperature
[11], to investigate the wear of polymer and
composite gears. The test rig also enables the gear                                                   0
temperature to be measured using an infrared                                                               0        5        10      15   20     25          30
                                                                                                                                      Time [min]
thermocouple placed 5 mm away from the test gear,
after the gear comes out of mesh. Suitable computer
data-based monitoring and data logging systems                      Fig. 15. Temperature of CFW spur gears as a
allow continuous measurement of the average surface                            function of torque [10].
temperature of the gear in operating conditions.
      Figure 14 shows the significant influence of                Figure 15 shows that the increase in torque
speed on gear temperature - a torque of 6 Nm is             does not influence the increase in gear temperature
applied to the non-standard pinion. There are several       significantly and the recorded maximum surface
reasons for the rapid increase in gear temperature: the     temperature is lower than its predicted temperature –
tooth flank surface finish and a definite evidence of       a speed of 500 rev/min is considered. The extremely
contact on the rear face – the transmission error           high rate of the temperature rise is also explained by
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                                                                                 FASCICLE VIII, 2005, ISSN 1221-4590

the tooth flank surface finish and running errors; in                                                      Figure 17 shows the influence of the applied
addition, the mechanical hysteresys losses, caused by                                                 torque on gear noise at 1000 rev/min speed. It can be
the viscoelastic nature of polymers, should be                                                        seen that the noise amplitude decreases with torque.
considered.                                                                                           This is explained by the reduction in friction forces,
      Other tests were carried out, at higher torques,                                                as for plastics the coefficient of friction decreases
but the gears were not allowed to run for too long in                                                 with load, so there is less excitation for gear teeth.
order to avoid the overheating. The gears failed at 25                                                Also, the increase in temperature modifies the
Nm while a similar standard spur gear train would                                                     flexibility of the teeth and the transmission error is
fail at about 15 Nm. The failure was caused by the                                                    changed.
high temperatures induced that affected the gear                                                            The main reason for the higher value of the
mesh rather than by excessive wear.                                                                   non-standard spur gear noise is the manufacturing
                                                                                                      process leading to important transmission errors and
                                                      4.4. Gear Noise                                 rough tooth flank surface that induces high friction
                                                                                                      forces. It is noticed that the temperature for curved
     The non-standard gear noise is recorded using                                                    face width gears are extremely sensitive with respect
the above mentioned test rig; a small microphone is                                                   to gears speed. The higher the speed, the higher the
positioned in front of the gear train at exactly 50 mm                                                rate of gear temperature increase; consequently, more
away from the meshing point. The microphone is held                                                   deflection occurs.
at the end of a long aluminum tube, clad in pipe
insulation, which helps to isolate it from                                                                          5. CONCLUSIONS
mechanically transmitted vibrations. The micro-
phone is connected to a standard PC computer that is                                                         A non-standard geometry is specially designed
running a program called Creative Wave Studio. This                                                   for the plastic spur gears in order to increase their
samples the microphone signals and gives a plot of                                                    transmissible power level. The gear tooth has a
noise pressure level against time.                                                                    circular shape along the gear face width and a
     Figure 16 shows the influence of gear speed on                                                   variable tooth height, decreasing to the gear end
noise (sound pressure in kN/m2), at a low torque of 5                                                 sections.
Nm for speeds of 500 and 1500 rev/min. It can be                                                             Based on a simple specific kinematics, the gear
seen that the noise amplitude increases with speed,                                                   generation process is simulated both with numerical
due to the increase in tooth collisions. A similar                                                    and solid modeling methods. Investigations on gear
standard spur gear is quieter than the CFW gear, as                                                   tooth geometry show that the tooth flank is an
recorded, and reaches lower surface temperature.                                                      involute or near involute in all locations around the
                                                                                                      face width.
                      130                                                                                    Simulation of the gear mesh enables the path of
Sound pressure [dB]

                                         spur gear
                                         CFW gear               47 C      50 C       60 C             contact to be produced and the increased contact
                                                                                                      ratio, compared to the standard spur gears, is proven.
                                                                                     52 C
                                                                                                             The finite element analysis was used for the
                                         35 C             37 C            43 C
                      100                                                                             non-standard gear bending resistance study. The
                                                                                                      double curvature of the gear tooth as well as the
                           90            33 C
                                                                                                      reduced tooth height decrease the recorded Von
                           80                                                                         Mises stresses and locate the maximum stresses on
                                                                                                      limited areas towards the end sections of the gear
                                 0              500            1000      1500       2000       2500   face width.
                                                                                 Speed [revs/min]            Based on the virtual gear, produced by the solid
                                Fig. 16. Sound pressure level versus speed,                           modeling method, the curved face width spur gear
                                           for a 5 Nm torque [8].                                     prototype is manufactured by selective laser
                                                                                                      sintering. Due to the difficulty of a moulding die
                                                                                     spur gear
                                                                                                      design, the gears are then cut on a conventional
         Sound pressure [dB]

                               120        47 C          68 C                         CFW gear         milling machine. To provide the required kinematics
                                                                         75 C
                                                                                                      of the gear generation process, special tools and
                               110               44 C           70 C                                  equipment are designed.
                               100                                       90 C                                Measurements of the gear tooth profile,
                                                             80 C                85 C
                                           37 C                                             80 C      developed on a CMM, showed the involute or near
                                                                                                      involute tooth profile. The tooth flank surface
                               80                                                                     quality, investigated by a Talysurf machine, is
                                                                                                      reasonable for a cutting process with a single point
                                     0      5           10          15    20     25     30     35     generation process and with no lubrication during
                                                                                   Torque [Nm]        manufacturing.
                                Fig. 17. Sound pressure level versus torque,                                 The temperature of the running non-standard
                                            at 1000 rev/min [8].                                      gear was measured on a specially designed test rig; it
                                        FASCICLE VIII, 2005, ISSN 1221-4590

was found that, due to the gear generation errors and            3. Andrei L., Andrei G., Mereuta E., 2002, Simulation of
                                                                 curved-face-width spur gear generation and mesh using the solid
due to the rough surface of the tooth flank (compared            modelling method, Proc. 10th Int. Conf. on Geometry and
to the standard moulding injected spur gears), the               Graphics, Kiev, Ucraine, Vol. 1, pp. 245-9.
temperature of the CFW gears increases rapidly and               4. Parsons B.N.V., Walton D., Andrei L., Andrei G., 2004, Non-
it is more influenced by an increase in speed rather             Standard Cylindrical Gears, Gear Technology, The Journal of
                                                                 Gear Manufacturing, Randall Publishing, Inc. USA, Nov./Dec, pp
than in the applied load.                                        30-37.
      Measurements of sound pressure level, with                 5. Gafiţeanu M., Poteraşu V. F., Mihalache N., 1987, Elemente
variations in torque and speeds, showed that noise               finite şi de frontieră cu aplicaţii în calculul organelor de maşini, Ed.
level is very much dependent on speed. The curved                Tehnică, Bucureşti.
                                                                 6. Breeds A.R. et al., 1993, Wear behaviour of acetal gear pairs,
gears noise level decreases for high torques, mainly             Wear, 166, pp. 85-91.
as a consequence of the high temperature induced                 7. Kruth J.P., 1991, Material incress manufacturing by rapid
that modifies the tooth stiffness.                               prototyping technique, Annals of the CIRP, vol.40/2, pp. 603-14.
      There are reasons to encourage the curved face             8. Andrei L., 2002, Study of plastic curved face-width spur gear
                                                                 generation and behaviour, PhD Thesis, University “Dunarea de
width spur gear development and its application in               Jos” of Galati.
the gear industry, but the manufacture process should            9. Andrei L., Walton D., Epureanu A., Andrei G., 2003,
be improved. Also, lubrication is recommended for                Experimental assessment of plastic curved face width spur gears
gear operating conditions.                                       behaviour, The Annals of University “Dunărea de Jos” of Galaţi,
                                                                 Fascicle VIII, Tribology, pp. 193-198.
                                                                 10. Andrei L., Epureanu A., Andrei G., Walton D., 2004,
                   REFERENCES                                    Investigation of the thermal behaviour of non-metallic curved face
                                                                 width spur gears, Tribotest, Leaf Coppin, UK, pp. 299-310.
1. Sidorenko A.K., 1984, 70-NKMZ, Mashinostroenie, Moscow.       11. Walton D., Hooke C.J. et. al., 1992, A new look at testing
2. Andrei L., Andrei G., Epureanu Al., Oancea N., Walton D.,     and rating non-metallic gears, 3rd World Congress on Gearing and
2002, Numerical simulation and generation of curved face width   Power transmission, Paris.
gears, Int. J. Machine Tools Manufact., 42, pp. 1-6.

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