CN108856908A - The gear hobbing machine-tooled method and device of space beveloid gear pair - Google Patents
The gear hobbing machine-tooled method and device of space beveloid gear pair Download PDFInfo
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- CN108856908A CN108856908A CN201810734547.2A CN201810734547A CN108856908A CN 108856908 A CN108856908 A CN 108856908A CN 201810734547 A CN201810734547 A CN 201810734547A CN 108856908 A CN108856908 A CN 108856908A
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23F—MAKING GEARS OR TOOTHED RACKS
- B23F5/00—Making straight gear teeth involving moving a tool relatively to a workpiece with a rolling-off or an enveloping motion with respect to the gear teeth to be made
- B23F5/20—Making straight gear teeth involving moving a tool relatively to a workpiece with a rolling-off or an enveloping motion with respect to the gear teeth to be made by milling
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23F—MAKING GEARS OR TOOTHED RACKS
- B23F5/00—Making straight gear teeth involving moving a tool relatively to a workpiece with a rolling-off or an enveloping motion with respect to the gear teeth to be made
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Abstract
The present invention relates to beveloid gear processing technique fields, specifically one kind can effectively improve gear teeth processing efficiency, reduce the gear hobbing machine-tooled method and device of the space beveloid gear pair of processing cost, it is characterized in that initially setting up the relative positional relationship of cutter and workpiece, the transformation relation between each coordinate system is then obtained by coordinate transform；Secondly according to the difference of hobboing cutter helicoid, select knife face equation, obtain the tooth surface equation that hobboing cutter is capable of processing out, the machined parameters of gear hobbing are calculated again, the present invention processes high-precision external toothing noninvolute beveloid gears using existing gear cutting machine, produce noninvolute beveloid gears retarder at lower cost, while to overcoming the involute beveloid gear there is particularly important realistic meaning due to the inherent defect that bearing capacity is low, service life is short, bearing capacity is low caused by point contact engagement etc..
Description
Technical field：
The present invention relates to beveloid gear processing technique field, specifically one kind can effectively improve gear teeth processing effect
Rate reduces the gear hobbing machine-tooled method and device of the space beveloid gear pair of processing cost.
Background technique：
Gear drive is one of the important kind of drive of machinery industry.Beveloid gear wheel tooth outline is similar to bevel gear, therefore
Drive gap can be eliminated by axial movement, realize precision drive.With the development of machinery industry, gear is passed in engineering
Dynamic requirement is higher and higher, and beveloid gear has been gradually applied in various industries due to its various advantage.
It is processed when use the methods of roll flute or gear shaping processing beveloid gear during the processing and manufacturing of beveloid gear
Journey is discontinuous, and low efficiency, precision cannot be guaranteed, and the cost of single-piece can be very high, and cutter versatility is not strong.And if special from design
Beveloid gear processing is carried out with the angle of machining tool, will lead to conventional gears machining tool cannot be effectively utilized,
Processing and manufacturing cost can be not only improved, and equally very complicated for the development process of beveloid gear specialized working machine tool of machine.
Summary of the invention：
The present invention is directed to shortcoming and defect existing in the prior art, and gear teeth processing effect can be effectively improved by proposing one kind
Rate reduces the gear hobbing machine-tooled method and device of the space beveloid gear pair of processing cost.
The present invention can be achieved by the following measures：
A kind of gear hobbing machine-tooled method of space beveloid gear pair, it is characterised in that include the following steps：
Step 1：The relative positional relationship of cutter and workpiece is established, wherein coordinate system S0(O0-x0,y0,z0) it is fixed coordinates
System is S with the coordinate system that hobboing cutter connects firmly1(O1-x1,y1,z1), it is S with the coordinate system that workpiece connects firmly2(O2-x2,y2,z2), coordinate
It is S1Not only around itself z2Axis rotation, while there are also the translational motion of horizontal and vertical directions, movement speed is respectively v1With
v2, O when initial0H=a, if when the angle that hobboing cutter turns over isWhen, the distance that hobboing cutter moves horizontally is l1, the distance that vertically moves
For l2, correspond to O0H=l1+ a, HO1=l2, the angle that workpiece turns over isIt is obtained between each coordinate system by coordinate transform
Transformation relation is as follows：
The transformation relation needed is as follows：
Step 2：According to the difference of hobboing cutter helicoid, knife face equation is selected, obtains the tooth surface equation that hobboing cutter is capable of processing out,
When processing method is the movement using the normal section shape of hobboing cutter to simulate rack cutter, straight sided normal worm ZN-worm hobboing cutter is selected
Knife face equation is calculated, and directly the helicoid of wealthy worm hob is formed by a straight edge line to the normal direction, straight edge line equation
It can be write as：
E in formula --- the distance of dynamic point M to G point, e=GM (mm), r0Expression and the tangent cylindrical radius of bus, point of contact is
G point；α --- bus inclination angle (°), according to the normal profile angle α of normal directly wide worm screwnIt can be asked with the helical angle λ of worm screw, sin α=
sinαncosλ；
The coordinate expressions in right hand helix face are
θ in formula --- variable element indicates helicoid bus from starting around z0The angle that axis turns over meets right-hand rule (°)；
P --- helix parameter, p=lead pz/2π.Indicate bus around z0When axis often turns over 1 degree, along the distance of axis rising
(mm)；
Then in hobboing cutter coordinate system S1(O1-x1,y1,z1) in three components of helicoid normal vector for indicating be：
Normal vector is acquired in coordinate system S using formula (2)0(o0-x0,y0,z0) in each component be：
If contact point K is in coordinate system S0In coordinate value be (x, y, z), for gear hobbing cutter, movement velocity can be indicated
For：
The speed of workpiece is represented by：
Then the relative velocity at contact K point is：
Screw can be analyzed to around the rotation of own axes and moving along axis, if in terms of shaft section,
Screw is equivalent to rack gear and translates along axis, is p for helix parameter, and angular speed isGear hobbing cutter, translational velocity
For-p ω1, previous movement is movement of the hobboing cutter helical tooth flank along its own, does not influence engaging for hobboing cutter and workpiece, therefore formula
(9) abbreviation is：
According to two face conditionalsThe meshing condition equation for obtaining hobboing cutter and workpiece is：
nx(v2tanδ+ω2y)+ny(pω1sinΣ-ω2x)+nz(v2-pω1Cos Σ)=0 (11)
It can be obtained by transformation matrix of coordinates formula (2) and formula (3) in coordinate system S2Represented hobboing cutter helicoid equation is down
Simultaneous equations (11), (12) can obtain the tooth surface equation that hobboing cutter is capable of processing out；
Step 3：The machined parameters for calculating gear hobbing, in the basic parameter of known required processing gear, wherein each parameter meter
It is as follows to calculate formula：
The number of teeth is z, and movement taper is δn, modulus mn, pressure angle αn,Established angle is Γ,Hobboing cutter helix angle is λ, and index plane helical angle is β, and pitch plane helical angle is β1, Gear taper is δ, transmission ratio
The above method of the present invention is the calculating using Machine-settings when straight sided normal worm ZN-worm hobboing cutter processing beveloid gear
Method, if the hobboing cutter used is straight sided axial worm hobboing cutter, the geometrical feature of this hobboing cutter is that its axial truncatus is straight
Line, so, without the concern for the helicoid lift angle λ of hobboing cutter, being calculated more when considering the relative position of hobboing cutter and processed gear
It is simple.
The invention also provides a kind of gear hobbing machining set-ups of space beveloid gear pair, are equipped with workbench and grinding carriage
Swivel base, it is characterised in that being equipped with workbench is tilting, and the angle of table inclination is equal to the production type tooth of ground beveloid gear
Cone angle δ, so that workpiece be made on workbench to tilt the angle δ relative to own axes.
The gear hobbing machining set-up inclined angle of medium plain emery wheel frame swivel base of beveloid gear pair in space of the present invention is equal to quilt
It is ground the helixangleβ of beveloid gear；The revolution and translational motion of workpiece keep stringent generating motion relationship.
The gear hobbing machining set-up of beveloid gear pair in space of the present invention during the work time, though grinding straight-tooth or
Helical teeth beveloid gear, in practical grinding process, the adjusting parameter of lathe only includes δ, β and kinematic parameter ω1。
The present invention processes high-precision external toothing noninvolute beveloid gears using existing gear cutting machine, compared with
Produce noninvolute beveloid gears retarder under low cost, while to overcoming involute beveloid gear to lead due to point contact engagement
The inherent defect that the bearing capacity of cause is low, service life is short, bearing capacity is low etc. has particularly important realistic meaning.
Detailed description of the invention：
Attached drawing 1 is beveloid gear Principle of Grinding and Cutting schematic diagram.
Attached drawing 2 is that scheme schematic diagram is ground in the 3 of beveloid gear, and wherein Fig. 2 a is table inclination formula, and Fig. 2 b is column
Tilting, Fig. 2 c are NC Interpolation formula.
Attached drawing 3 is structural schematic diagram of the invention.
Attached drawing 4 is that rolling cut beveloid gear moves schematic diagram in the present invention.
Attached drawing 5 is gear hobbing location diagram in the present invention.
Attached drawing 6 is hobboing cutter helicoid bus position view in the present invention.
Attached drawing 7 is the mobile positional diagram with rotation in the present invention.
Attached drawing 8 is the movement position relation schematic diagram of rotation and rotation in the present invention.
Attached drawing 9 is that hobboing cutter moves schematic diagram in the present invention.
Attached drawing 10 is that hobboing cutter translates schematic diagram in the present invention.
Specific embodiment：
It is bright to this law with reference to the accompanying drawing to be further described.
According to the generating grinding principle of beveloid gear, thicken tooth the invention proposes the space that one kind can be ground beveloid gear
The gear hobbing machining set-up of wheel set can realize the number of beveloid gear by adjusting the inclination angle of gear grinder with cone-shaped grinding wheel workbench
Control grinding.
Gear grinder with cone-shaped grinding wheel is the theory of engagement according to gear and rack gear, with generating intermittent grinding involute flank
's.When being ground beveloid gear, the movement of conical wheel is with the flank of tooth of imaginary rack gear and by roll flute crop rotation gear motion, to transform into
The involute helicoid of the gear teeth.Such as Fig. 1, in order to form the helical angle and cone angle of beveloid gear, by axis of workpiece in xoz plane introversion
While an oblique angle δ, make grinding wheel axis at the tilted angle β of yoz plane.When roll flute, grinding wheel is around its axis with angular speed
ω0It turns round and together with gliding mass along speed v0Make reciprocating stroke movement in direction；In order to grind the flank of the entire gear teeth, workpiece is around it
Axis is with angular velocity omega1It turns round and with speed v1It translates to form generating motion along y-axis.
According to the generating grinding principle of beveloid gear and the analysis of machine tool structure, the tooth that thickens is ground with gear grinder with cone-shaped grinding wheel
Wheel has 3 kinds of different schemes, as shown in Figure 2.
When being ground beveloid gear in view of traditional numerical control gear grinder with cone-shaped grinding wheel, it is necessary to be become by moving interpolation with being formed
The cone angle of thick gear, and when grinding helical teeth beveloid gear, the flank profil arranged on left and right sides flank of tooth must be divided to two using different adjusting parameters
Secondary grinding.The invention proposes the structure of lathe is designed to table inclination formula, at this time the adjusting parameter of lathe and grinding tooth
Parameter is equal to each other, that is, is equal to counterpart rack parameter when beveloid gear design, and the adjustment of the flank profil arranged on left and right sides flank of tooth
Parameter is identical, and clamped one time adjusts the accurate grinding that left and right lateral tooth flank can be realized.Fig. 3 is machine tool structure fortune in the present invention
Dynamic relational graph.
Since the inclined angle of platen is equal to the counterpart rack cone angle δ of ground beveloid gear, grinding carriage swivel base
Inclined angle is equal to the helixangleβ of ground beveloid gear；Meanwhile be guarantee the flank of tooth correct grinding, the revolution of workpiece and
Translational motion should keep stringent generating motion relationship.Therefore, no matter grinding straight-tooth or helical teeth beveloid gear, were actually ground
Cheng Zhong, the adjusting parameter of lathe only include δ, β and kinematic parameter ω1。
The invention also provides a kind of gear hobbing machine-tooled methods of space beveloid gear pair, with reference to the accompanying drawing, to this hair
It is bright to be further described：
According to the basic principle of spatial conjugate it is found that in common hobbing process, there are two independent kinematic parameters, therefore rolls
Tooth movement is the gear motion of double freedom, and the helical tooth flank of the helicoid of hobboing cutter and workpiece is point contact in hobbing process,
The process for deriving workpiece tooth surface equation according to the theory of engagement is as follows：
(a) type of hobboing cutter, such as involute helicoid worm hobboing cutter or straight sided axial worm hobboing cutter are selected, corresponding rolling is established
Knife helicoid equation；(b) the coordinate system transformation relationship between hobboing cutter and workpiece is established, the hobboing cutter side under workpiece coordinate system is obtained
Journey expression formula, and derive according to meshing condition formula the flank engagement equation of hobboing cutter and workpiece；(c) hobboing cutter is solved in different moments
Mesh equation, be updated in the hobboing cutter helicoid equation under workpiece coordinate system, obtain the engagement of different moments, different location
Point, and then the tooth profile of workpiece is obtained, and solve end face section shape.
According to the forming process of involute beveloid gear it is found that imaginary rack cutter is basic rack, then hobboing cutter can be with
It is processed according to the motion profile of rack gear, imaginary rack gear opposite piece will not only have a helical angle, also tilt one
A cone angle, then also will more movements accordingly during hobboing cutter processes beveloid gear.By taking dextrorotation gear as an example, Fig. 4 is
The movement schematic diagram of rolling cut dextrorotation beveloid gear, the axis of workpiece blank is vertical, and microcephaly is upward, axis of workpiece and hobboing cutter axis
Angle is Σ, and the movement of hobboing cutter is exactly the forming process progress rolling cut according to beveloid gear.In gear hobbing, main movement process packet
It includes：The rotary motion ω of hobboing cutter1, the rotary motion ω of workpiece2, feed motion v of the hobboing cutter along axis of workpiece direction2, hobboing cutter is along work
The feed motion v of part radial direction1.Since the feed motion of hobboing cutter includes both direction, therefore there are a cones for the gear cut out
Angle sets the drift angle between imaginary rack gear index plane and Gear axis here as δ, and the movement velocity in gear hobbing campaign is formed
Movement cone angle be δn, two cone angles are not same angles.Movement cone angle needs to be derived by relative motion relation
When processing gear, two direction moving movement proportionate relationships of hobboing cutter can be determined by movement cone angle, and be rotated
There is corresponding gear ratio relation between movement.In this way, in gear hobbing campaign each kinematic parameter can by gear parameter come
Opening relationships formula.
Motion process by analyzing gear hobbing can establish the relative positional relationship of cutter and workpiece, as shown in figure 5, in figure
Coordinate system S0(O0-x0,y0,z0) it is fixed coordinate system, it is S with the coordinate system that hobboing cutter connects firmly1(O1-x1,y1,z1), it is connected firmly with workpiece
Coordinate system be S2(O2-x2,y2,z2).Coordinate system S1Not only around itself z2Axis rotation, while there are also horizontal and vertical directionss
Translational motion, movement speed is respectively v1And v2.O when initial0H=a, if when the angle that hobboing cutter turns over isWhen, hobboing cutter is horizontal
Mobile distance is l1, the distance vertically moved is l2, correspond to O0H=l1+ a, HO1=l2, the angle that workpiece turns over isIt is logical
The transformation relation crossed between the available each coordinate system of coordinate transform is as follows：
For hobboing cutter, hobboing cutter curved surface is helicoid, hobboing cutter can be divided into involute helicoid worm according to the difference of helicoid
Hobboing cutter, straight sided axial worm hobboing cutter and straight sided normal worm ZN-worm hobboing cutter etc., and the processing method selected herein mainly application rolling
The normal section shape of knife simulates the movement of rack cutter, so the knife face equation of straight sided normal worm ZN-worm hobboing cutter is selected to be counted
It calculates.
The helicoid of normal directly wide worm hob is formed by a straight edge line, so it belongs to prolate involute spiral
A kind of form in face derives the helicoid equation of normal directly wide worm screw below according to the forming process of prolate involute helicoid,
Its bus initial position is as shown in fig. 6, r in figure0It indicates and the tangent cylindrical radius of bus, point of contact is G point.It is closed according to geometry
System, straight edge line equation can be write as：
E in formula --- the distance of dynamic point M to G point, e=GM (mm), α --- bus inclination angle (°), according to the method for normal directly exterior feature worm screw
To profile angle αnIt can be asked with the helical angle λ of worm screw, sin α=sin αncosλ。
For processing dextrorotation gear, hobboing cutter is right hand helix serrated knife, turns round the available dextrorotation spiral shell of formula according to vector
The coordinate expressions of radial facing are：
(4), θ in formula --- variable element indicates helicoid bus from starting around z0The angle that axis turns over, meets right-hand rule
(°)；P --- helix parameter, p=lead pz/2π.Indicate bus around z0When axis often turns over 1 degree, along the distance (mm) of axis rising.
According to the conventional method for seeking surface normal in higher mathematics, can find out in hobboing cutter coordinate system S1(O1-x1,y1,z1)
Three components of the helicoid normal vector of middle expression are
It can be in the hope of normal vector in coordinate system S using formula (2)0(o0-x0,y0,z0) in each component be：
If contact point K is in coordinate system S0In coordinate value be (x, y, z), as shown in Fig. 2, for gear hobbing cutter, movement
Speed is represented by：
The speed of workpiece can be expressed as：
Then the relative velocity at contact K point is：
Screw can be decomposed into around the rotation of own axes and moving along axis, if in terms of shaft section,
Then screw is equivalent to rack gear and translates along axis, is p for helix parameter, and angular speed isGear hobbing cutter, translation speed
Degree is-p ω1, previous movement is movement of the hobboing cutter helical tooth flank along its own, does not influence engaging for hobboing cutter and workpiece.Therefore
Formula (9) can be with abbreviation：
According to two face conditionalsThe meshing condition equation of available hobboing cutter and workpiece is nx
(v2tanδ+ω2y)+ny(pω1sinΣ-ω2x)+nz(v2-pω1Cos Σ)=0 (11)
It is available in coordinate system S by transformation matrix of coordinates formula (2) and formula (3)2Represented hobboing cutter helicoid equation is down
Simultaneous equations (11), (12) can obtain the tooth surface equation that hobboing cutter is capable of processing out.
The machined parameters for carrying out gear hobbing below calculate：
(1) relative speed relationship：Processing beveloid gear needs lathe while including four movements, and two movements and two turn
Dynamic, each movement connects each other.Consider the relationship between two movement first, movement speed and move can be between cone angle
Establish following relationship
During analyzing gear hobbing process, the whether movement of hobboing cutter or the rotation of hobboing cutter, workpiece can all have accordingly
Rotation, can establish the relational expression between rotation and movement speed according to relative motion relation is
ω2=i1ω1+k2v2 (14)
I in formula1--- engaged transmission ratio,k2--- the ratio of workpiece rotational frequency and hobboing cutter movement speed in differential motion
Value, the related (mm with gear structure to be processed-1)。
The movement for considering hobboing cutter first, since the movement of hobboing cutter includes moving in parallel and vertically moving, and move in parallel only
It is the modification coefficient for influencing gear not on coaxial cross-section, the rotation with workpiece is without directly contacting, so need to only consider that hobboing cutter is vertical
Relationship between the rotation of mobile and workpiece.Fig. 7 is the relative motion relation figure of workpiece and cutter on pitch circle, is moved down on hobboing cutter
It is dynamic, translational velocity v2, the corresponding velocity of rotation of workpiece is ω2。
The gear helical angle being located on pitch plane is β1, the pitch radius of work gear to be added is r, when hobboing cutter moves t moment
Afterwards, blank and hobboing cutter move at dotted line, and contact point is C point, and motion conditions are as shown in fig. 6-7.In triangle Δ AOC, OC
=v2T, OA=ω2AOC=90 ° of rt, ∠.It is available according to geometrical relationship
Therefore when hobboing cutter does not rotate, the differential motion relationship of hobboing cutter and workpiece is
And when hobboing cutter only rotates, the movement relation of hobboing cutter and workpiece can be assumed to be turbine and worm movement, work as workpiece
When rotation, corresponds to hobboing cutter and also make rotating motion accordingly, relative motion position is as in Figure 3-5.If the spiral liter of hobboing cutter
Angle is λ, and helix parameter p, hobboing cutter established angle is the angle Γ of axis and horizontal plane, and the revolving speed of workpiece is ω at this time2, hobboing cutter turn
Speed is ω1.After hobboing cutter rotates t moment, the angle θ is had rotated, the mobile distance in corresponding hobboing cutter face is
OC=p θ=p ω1t (17)
Workpiece flank of tooth move distance is
OA=ω2rt (18)
Therefore it is available according to movement relation, when hobboing cutter does not move, the transmission ratio of hobboing cutter and workpiece is
So the movement velocity relationship of hobboing cutter and workpiece is when hobboing cutter processes gear
2) relative positional relationship
It is also true according to the difference of gear parameter to be processed after movement velocity relationship during determining gear hobbing process
Fixed corresponding hobboing cutter parameter and established angle etc., below analyze the relative position of hobboing cutter and workpiece.Work gear to be added has five
A known parameters, as shown in table 1.
1 Basic parameters of gear of table
Hobboing cutter processes the movement relation of involute beveloid gear as shown in fig. 6, hobboing cutter is doing translational motion along straight line AB
While around own axis, the cone angle of workpiece to be added is δ, and the movement cone angle of hobboing cutter is δn, straight line BC and processed gear
Pitch cylinder it is tangent, point of contact be D point.It, should according to motion conditions it is found that the motion profile of hobboing cutter axis is an inclined plane
Plane is parallel with the imaginary index plane of rack gear, if plane M1For the index plane of imaginary rack gear, straight line l is hobboing cutter axis in figure
In plane M1On projection, then the established angle Γ of hobboing cutter can be obtained according to the geometrical relationship of diagram
By Fig. 9 it will also be appreciated that the index plane helical angle of counterpart rack is β, i.e., gear teeth to be processed is in plane M1On
Tooth form helical angle, if the helix angle of hobboing cutter is λ, the angle γ between hobboing cutter axis and straight line BC can pass through geometrical relationship
It is expressed as
Therefore the helix angle of hobboing cutter can be expressed as
The pitch circle spiral arrived used in the process of the index plane helixangleβ and consideration gear hobbing process of lower surface analysis counterpart rack
Angle beta1Relationship between (see Fig. 8).Pitch circle helixangleβ1It is the tooth form inclination angle when hobboing cutter only does mobile, specific movement relation is such as
Shown in Figure 10, when hobboing cutter moves to A point by B point, the distance of workpiece pitch cylinder rotation is BD, so β1It can be expressed as
It is available according to geometrical relationship
The parameter asked is needed mainly to have movement taper δ when processing beveloid gearn, pitch plane helixangleβ1, hobboing cutter established angle Γ
And speed transmission ratio can be calculated in the basic parameter of known required processing gear according to the calculation formula that table 2 gives
Corresponding machined parameters.
2 machined parameters calculation formula of table
When table 2 is using straight sided normal worm ZN-worm hobboing cutter processing beveloid gear, the calculation method of Machine-settings, if adopted
When hobboing cutter is straight sided axial worm hobboing cutter, the geometrical feature of this hobboing cutter is that its axial truncatus is straight line, so examining
When considering the relative position of hobboing cutter and processed gear, without the concern for the helicoid lift angle λ of hobboing cutter, calculate more simple.
The present invention is by state natural sciences fund (number：51675118) it subsidizes, utilizes existing gear cutting machine
High-precision external toothing noninvolute beveloid gears are processed, produce noninvolute beveloid gears deceleration at lower cost
Device, while since point contact engagement is caused, bearing capacity is low, service life is short, bearing capacity to involute beveloid gear is overcome
Low inherent defect has particularly important realistic meaning.
Claims (4)
1. a kind of gear hobbing machine-tooled method of space beveloid gear pair, it is characterised in that include the following steps：
Step 1：The relative positional relationship of cutter and workpiece is established, wherein coordinate system S0(O0-x0,y0,z0) it is fixed coordinate system, with
The coordinate system that hobboing cutter connects firmly is S1(O1-x1,y1,z1), it is S with the coordinate system that workpiece connects firmly2(O2-x2,y2,z2), coordinate system S1No
Only around itself z2Axis rotation, while there are also the translational motion of horizontal and vertical directions, movement speed is respectively v1And v2, just
The O when beginning0H=a, if when the angle that hobboing cutter turns over isWhen, the distance that hobboing cutter moves horizontally is l1, the distance vertically moved is l2,
Correspond to O0H=l1+ a, HO1=l2, the angle that workpiece turns over isThe transformation between each coordinate system is obtained by coordinate transform
Relationship is as follows：
The transformation relation needed is as follows：
Step 2：According to the difference of hobboing cutter helicoid, knife face equation is selected, obtains the tooth surface equation that hobboing cutter is capable of processing out, when adding
When work method is the movement using the normal section shape of hobboing cutter to simulate rack cutter, the knife face of straight sided normal worm ZN-worm hobboing cutter is selected
Equation is calculated, and directly the helicoid of wealthy worm hob is formed by a straight edge line to the normal direction, and straight edge line equation is writeable
At：
E in formula --- the distance of dynamic point M to G point, e=GM, r0It indicates and the tangent cylindrical radius of bus, point of contact is G point；α——
Bus inclination angle, according to the normal profile angle α of normal directly wide worm screwnIt can be asked with the helical angle λ of worm screw, sin α=sin αncosλ；
The coordinate expressions in right hand helix face are
θ in formula --- variable element indicates helicoid bus from starting around z0The angle that axis turns over, meets right-hand rule；
P --- helix parameter, p=lead pz/2π.Indicate bus around z0When axis often turns over 1 degree, along the distance of axis rising；
Then in hobboing cutter coordinate system S1(O1-x1,y1,z1) in three components of helicoid normal vector for indicating be：
Normal vector is acquired in coordinate system S using formula (2)0(o0-x0,y0,z0) in each component be：
If contact point K is in coordinate system S0In coordinate value be (x, y, z), for gear hobbing cutter, movement velocity is represented by：
The speed of workpiece is represented by：
Then the relative velocity at contact K point is：
Screw can be analyzed to around the rotation of own axes and moving along axis, if in terms of shaft section, spiral
Movement is equivalent to rack gear and translates along axis, is p for helix parameter, and angular speed isGear hobbing cutter, translational velocity be-p
ω1, previous movement is movement of the hobboing cutter helical tooth flank along its own, does not influence engaging for hobboing cutter and workpiece, therefore formula (9) is changed
Letter is：
According to two face conditionalsThe meshing condition equation for obtaining hobboing cutter and workpiece is：
nx(v2tanδ+ω2y)+ny(pω1sinΣ-ω2x)+nz(v2-pω1Cos Σ)=0 (11)
It can be obtained by transformation matrix of coordinates formula (2) and formula (3) in coordinate system S2Represented hobboing cutter helicoid equation is down
Simultaneous equations (11), (12) can obtain the tooth surface equation that hobboing cutter is capable of processing out；
Step 3：The machined parameters for calculating gear hobbing, in the basic parameter of known required processing gear, wherein each parameter calculates public affairs
Formula is as follows：
The number of teeth is z, and movement taper is δn, modulus mn, pressure angle αn,Established angle is Γ,
Hobboing cutter helix angle is λ, and index plane helical angle is β, and pitch plane helical angle is β1,
Gear taper is δ, transmission ratio
2. a kind of gear hobbing machine-tooled method of space beveloid gear pair according to claim 1, it is characterised in that if adopted
Hobboing cutter is straight sided axial worm hobboing cutter, when considering the relative position of hobboing cutter and processed gear, without the concern for hobboing cutter
Helicoid lift angle λ.
3. a kind of dress using the gear hobbing machine-tooled method of space beveloid gear pair as described in any one of claim 1-2
It sets, is equipped with workbench and grinding carriage swivel base, it is characterised in that being equipped with workbench is tilting, and the angle of table inclination is equal to
The production type rack cone δ of ground beveloid gear, so that workpiece be made on workbench to tilt the angle δ relative to own axes.
4. a kind of gear hobbing machining set-up of space beveloid gear pair according to claim 3, it is characterised in that the sky
Between the gear hobbing machining set-up inclined angle of medium plain emery wheel frame swivel base of beveloid gear pair be equal to the helical angle of ground beveloid gear
β；The revolution and translational motion of workpiece keep stringent generating motion relationship.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810734547.2A CN108856908A (en) | 2018-07-06 | 2018-07-06 | The gear hobbing machine-tooled method and device of space beveloid gear pair |
Applications Claiming Priority (1)
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| CN201810734547.2A CN108856908A (en) | 2018-07-06 | 2018-07-06 | The gear hobbing machine-tooled method and device of space beveloid gear pair |
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| CN112935415A (en) * | 2021-03-18 | 2021-06-11 | 重庆大学 | Hobbing and hobbing method for variable-tooth-thickness involute helical gear and hobbing cutter design method |
| CN113001265A (en) * | 2021-03-18 | 2021-06-22 | 常州机电职业技术学院 | Method for determining grinding wheel parameters of tool grinder for grinding spiral groove hob |
| CN113102838A (en) * | 2021-05-18 | 2021-07-13 | 山东大学 | Method for solving working angle of cutter in gear hobbing process |
| CN113478024A (en) * | 2021-06-30 | 2021-10-08 | 大连理工大学 | High-precision involute pure rolling generating device, assembly and application |
| CN113722843A (en) * | 2021-08-01 | 2021-11-30 | 北京工业大学 | Method for calculating residual height of tooth surface of flexible gear hobbing of harmonic reducer |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN112935415A (en) * | 2021-03-18 | 2021-06-11 | 重庆大学 | Hobbing and hobbing method for variable-tooth-thickness involute helical gear and hobbing cutter design method |
| CN113001265A (en) * | 2021-03-18 | 2021-06-22 | 常州机电职业技术学院 | Method for determining grinding wheel parameters of tool grinder for grinding spiral groove hob |
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| CN113102838A (en) * | 2021-05-18 | 2021-07-13 | 山东大学 | Method for solving working angle of cutter in gear hobbing process |
| CN113478024A (en) * | 2021-06-30 | 2021-10-08 | 大连理工大学 | High-precision involute pure rolling generating device, assembly and application |
| CN113722843A (en) * | 2021-08-01 | 2021-11-30 | 北京工业大学 | Method for calculating residual height of tooth surface of flexible gear hobbing of harmonic reducer |
| CN113722843B (en) * | 2021-08-01 | 2023-04-04 | 北京工业大学 | Method for calculating residual height of tooth surface of flexible gear hobbing processing of harmonic reducer |
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