[summary of the invention]
For the problems referred to above, method and products thereof based on mathematical modeling macroprogram processing hindley worm provided by the invention, solves in existing hindley worm process that production cost is high, manufacturing process is complicated, the uppity problem of machining accuracy.
The present invention is achieved by the following technical solutions, and a kind of method based on mathematical modeling macroprogram processing hindley worm, is characterized in that, comprise the following steps:
S11: the mathematical modeling setting up hindley worm reference circle, outside circle, root circle respectively;
S12: the mathematical modeling setting up hindley worm profile geometry according to the mathematical modeling of step S11 foundation;
S13: above-mentioned mathematical modeling being written as Digit Control Machine Tool can be other code;
S14: the above-mentioned code write is input in Digit Control Machine Tool;
S15: adopt thread turning principle to realize the successively matching of segment threaded line and process hindley worm.
Especially, the Mathematical Modeling in described step S11 is set up according to following formula:
$\left\{\begin{array}{c}x=r\mathrm{cos}\mathrm{\θ}\\ y=r\mathrm{sin}\mathrm{\θ}\end{array}\right.---\left(1\right)$
x
^{2}+y
^{2}＝r
^{2} (2)
Wherein, the coordinate of coordinate system in x, y mathematical modeling, r is radius of a circle, and θ is the angle that the point (x, y) on circle is formed with coordinate origin and x-axis, i.e. central angle, is just getting counterclockwise, gets negative clockwise.
Especially, the Mathematical Modeling in described step S12 is set up according to following formula:
Wherein, formula (3) is the modeling formula of flank profil line on the right side of hindley worm flank profil, formula (4) for the modeling formula of flank profil line on the left of hindley worm flank profil, x, y, z be the coordinate of coordinate system in mathematical modeling, r is radius of a circle,
β be cutter when tooth profile centerline and reference circle intersection point, the angle that flank profil line is formed with horizontal direction, i.e. flank profil center profile angle.
The present invention also provides a kind of hindley worm adopting said method to process.
Compared to prior art, method based on mathematical modeling macroprogram processing hindley worm provided by the invention and products thereof, first by setting up hindley worm reference circle, outside circle, the mathematical modeling of root circle, secondly the mathematical modeling of hindley worm profile geometry is set up according to above mathematical modeling, then set up mathematical modeling is written as by macroprogram code that Digit Control Machine Tool can identify and this code is imported in numerically controlled lathe, finally in Digit Control Machine Tool, adopt thread turning principle to realize the successively matching of segment threaded line and process hindley worm.Adopt processing method provided by the present invention, not only shorten the production cycle, reduce production cost, and have that machining accuracy is high, the simple advantage of manufacturing process.
[detailed description of the invention]
In order to make object of the present invention, technical scheme and advantage clearly understand, below in conjunction with drawings and Examples, the present invention is described in more detail, and the present invention explains for straight wide hindley worm.
Method based on mathematical modeling macroprogram processing hindley worm provided by the invention, comprises the following steps:
S11: the Mathematical Modeling setting up hindley worm reference circle, outside circle, root circle respectively, (i.e. hindley worm roughing),
The reference circle of hindley worm profile of tooth, outside circle, root circle are all the circular arcs of rule, then on flank profil line arbitrfary point all on circle, therefore the point forming flank profile can be obtained by the equation of circle, refers to Fig. 1, if the center of circle is at coordinate origin, take up an official post at circle and get 1 P, point P is designated as (x, y), and radius is r, the intersection point of radius r and X-axis positive axis is P0, if OP
_{0}by the angle ∠ P counterclockwise rotating to OP position and formed
_{0}oP=θ, according to trigonometric function definition, the function that the abscissa x, the ordinate y that put P can represent with θ, namely
The parametric equation of circle:
$\left\{\begin{array}{c}x=r\mathrm{cos}\mathrm{\θ}\\ y=r\mathrm{sin}\mathrm{\θ}\end{array}\right.---\left(1\right)$
Normal equation by the known circle of (1) formula: x
^{2}+ y
^{2}=r
^{2}(2)
Wherein, the coordinate of coordinate system in x, y mathematical modeling, r is radius of a circle, and θ is the angle that the point (x, y) on circle is formed with coordinate origin and x-axis, i.e. central angle, is just getting counterclockwise, gets negative clockwise.Worm screw shaped profile turning cutter reasonably can be selected to carry out roughing hindley worm according to the feature of processing parts by formula (1), (2);
S12: the mathematical modeling (namely Tooth Surface for Enveloping Worm with Straight Line Generatrix repaiies type fine finishining) setting up hindley worm profile geometry according to the mathematical modeling of step S11 foundation,
Refer to Fig. 2 and Fig. 3, L
_{1}be reference circle of worm center of circle O and with the vertical line of worm screw axial line, L
_{2}be the round heart O of calibration and intersected at the straight line of an E with worm screw flank profil center, L
_{1}with L
_{2}angle be θ, cross straight line L
_{2}make straight line L
_{1}' //L
_{1}l
_{2}meet at a B, a some E makes horizontal linear AD and meets at right side flank profil line in a D excessively, extends DE and L
_{1}' meet at an A, cross some D and make CD ⊥ AD, cross some E and make BE ⊥ EC, then in polygon ABCDE, there is following relation: because L
_{1}' //L
_{1}l
_{2}, namely think ∠ L
_{1}oL
_{2}=θ=∠ ABE (i.e. α), again because ∠ ABE (i.e. α)+∠ BEA=90 °, ∠ BEC=90 °, ∠ BEA+ ∠ BEC+ ∠ CED=180 °, so draw ∠ CED (i.e. β)=∠ ABE (i.e. α)=∠ L
_{1}oL
_{2}=θ, CD=CESin θ, DE=CECos θ,
Because straight line L
_{2}be the central axis of worm screw lathe tool, so will process profile geometry by worm screw lathe tool, a demand goes out the Mathematical Modeling of both sides tooth curve, is namely by straight line L by the coordinate of any point in (1) formula and Fig. 2 known right side flank profil line
_{2}increase ED length in X-direction, increase CD length in the Y direction, otherwise any point on the flank profil line of left side can be obtained, then have:
Right side flank profil line:
Left side flank profil line:
Wherein, x, y, z is the coordinate of coordinate system in mathematical modeling, and r is radius of a circle,
β is that cutter is at tooth profile centerline L
_{2}during with reference circle intersection point E, the angle that flank profil line is formed with horizontal direction, i.e. flank profil center profile angle.
Using formula (3), (4) can carry out flank of tooth fine finishining by left and right offset tool to rough machined hindley worm and the flank of tooth repaiies type;
S13: it can be other code that above-mentioned mathematical modeling is written as Digit Control Machine Tool by macroprogram;
S14: the above-mentioned code write is input in Digit Control Machine Tool;
S15: because hindley worm helical pitch is large, turning cutting tool is greatly stressed in turning process, therefore the present invention is according to the principle of thread turning, adopt the little amount of feeding and cutting depth successively matching to process profile geometry and the worm screw degree of depth, namely adopt thread turning principle to realize the successively matching of segment threaded line and process hindley worm.
When processing hindley worm, according to the mathematical modeling set up, then mathematical modeling being written as by macroprogram the code that Digit Control Machine Tool can identify, afterwards code being input in Digit Control Machine Tool, by segment threaded line gradually matching process worm screw; When using macroprogram numerical control turning hindley worm, cutter is bus all the time with reference circle according to the parametric variable of assignment, successively increase progressively turnery processing worm screw according to cutting depth, therefore in NC Machining Process, the less machining accuracy of numerical value of the cutting depth variable assignments of macroprogram is higher.It should be noted that hindley worm is by the matching gradually of segment threaded line when turning, so the helical pitch of every layer of turning changes along with the change of cutting depth when turning hindley worm.
The present invention also provide a kind of basis as above method processing hindley worm, it should be noted that, man-hour is being added to hindley worm, roughing can select shaping worm screw lathe tool, when selecting shaped profile turning cutter roughing, lathe tool angle must be less than flank profil angle, otherwise will produce and cut, owe to cut phenomenon, if Fig. 4 a (i.e. Fig. 4 a1-Fig. 4 a3) is worm screw lathe tool roughing schematic diagram different in hindley worm process; Roughing figure wherein during the rough turn worm screw of Fig. 4 a1 to be point of a knife angle be shaped profile turning cutter of 40 °, the shaped profile turning cutter being 40 ° by Fig. 4 a1 known employing point of a knife angle adds can produce man-hour to be cut, owes to cut phenomenon; Roughing figure when Fig. 4 a2 is groove cutter rough turn worm screw, during by Fig. 4 a2 known employing groove knife processing and forming, cuts, cuts phenomenon less, but the rigidity of groove cutter own is poor without crossing; Fig. 4 a3 is the roughing figure of point of a knife angle when being less than the rough turn worm screw of the shaped profile turning cutter of 40 °, and the shaped profile turning cutter being less than 40 ° by Fig. 4 a3 known employing point of a knife angle adds man-hour, cutting, cutting phenomenon less without crossing; Man-hour is added in flank profil, need reserved enough allowances for finish to carry out the flank of tooth and repair type, if Fig. 4 b (i.e. Fig. 4 b1-Fig. 4 b3) is worm screw lathe tool fine finishining schematic diagram different in hindley worm process, wherein Fig. 4 b1 is that on the left of the fine finishining of left avertence cutter, flank profil repaiies type figure; Fig. 4 b2 is that on the right side of the fine finishining of right avertence cutter, flank profil repaiies type figure; Fig. 4 b3 is that mid-lathe tool fine finishining root circle of worm repaiies type, and from Fig. 4 b3, in order to avoid occurring cutting, owe to cut phenomenon, the point of a knife angle of mid-lathe tool was enough little.Meanwhile, in order to effectively reduce knife, random dental phenomenon, when worm screw turning feed, withdrawing time should introduce one section of raising speed and reduction of speed distance (H=N*P helical pitch, N is positive integer).
Adopt the starting point of numerical control workshop worm screw should determine according to the centre tooth of worm screw, the maximum number of teeth of the worm and wheel engagement that such guarantee processes.During rough turn worm screw, not easily excessive, rotating speed is unsuitable too high for cutting depth, adopts little cutting output slow-speed of revolution turning can effectively ensure crudy and cutting wear.Must first select suitable cutting tool during finish turning hindley worm, as shown in Figure 4, then select less cutting output, finally determine that a suitable rotating speed carries out the flank of tooth and repaiies type.
Below by way of specific embodiment, the present invention is explained, embodiment workpiece blank of the present invention is of a size of φ 50x200mm, material is 45 steel, FANUC Series Oi Mate-TD system is selected in processing, front knife-carrier, using the intersection point of right side and axial line as workpiece coordinate system initial point, the hindley worm reference radius processed is 114.64mm, radius of addendum is 112.28mm, root radius is 117.79mm, modulus m is 3.15, the number of teeth is 73, pressure angle is 20 °, and lead angle is 5.07083 °.
1) hindley worm roughing (made allowance 0.6mm)
O1234; (using formula (2))
G90 G98 G40 G00 X100 Z100；
T0101 M08; (35 ° of worm screw lathe tools)
M03 S400；
G00 X48 Z-77.582; (worm screw turning starting point)
#4=0.1; (cutting depth initial value 0.1mm)
WHILE [#4 LE 6.804] DO2; (if cutting depth initial value >=cutting depth stop value, performs the program between DO2 to END2, otherwise performs END2 program below)
#1=34.619; (Z initial value in circle coordinates system, raising speed feed section gets the integral multiple of helical pitch)
#2=-34.619; (Z stop value in circle coordinates system, reduction of speed withdrawing section gets the integral multiple of helical pitch)
WHILE [#1 GE #2] DO1; (if Z initial value >=Z stop value, performs the program between DO1 to END1, otherwise performs END1 program below)
#5＝9.891*#4/6.804
#3=SQRT [114.64*114.64-#1*#1]; (knowing Y value in circle coordinates system by formula (2))
G32 X [2*#3-#4] Z [#1-112] F [#5]; (each screw chasing degree of depth is #4, and pitch is 9.891mm)
#1=#1-#5; (X change of stride amount in circle coordinates system, each decreasing pitch 1 pitch variation)
END1；
G00 X50; (X-direction withdrawing in workpiece coordinate system, must be greater than the maximum nominal diameter of screw thread, random tooth when preventing withdrawing)
Z-77.582; (Z-direction withdrawing in workpiece coordinate system, move to cutter outside workpiece, must be more than or equal to screw thread loop start, integral multiple pitch)
X48; (X-direction feed in workpiece coordinate system, arrives start position, prevents from starting the random tooth of section)
#4=#4+0.1; (cutting depth increases progressively 0.1mm at every turn)
END2；
G00 X100 Z100；
M09；
M30；
2) hindley worm fine finishining (flank profil repaiies type)
O2345; (right side flank profil repaiies type)
G90 G98 G40 G00 X100 Z100；
T0101 M08; (worm screw right avertence cutter lathe tool)
M03 S400；
G00 X48 Z-77.582; (worm screw turning starting point)
#4=0.1; (cutting depth initial value 0.1mm)
WHILE [#4 LE 6.804] DO2; (if cutting depth initial value >=cutting depth stop value, performs the program between DO2 to END2, otherwise performs END2 program below)
#1=-72.042; (in circle coordinates system, cutting start angle)
#2=-107.958; (in circle coordinates system, cutting termination point)
WHILE [#1 GE#2] DO1; (if initial angle angle value >=termination point, performs the program between DO1 to END1, otherwise performs END1 program below)
#5＝9.891*#4/6.804
#6=(114.64+#4) * sin [#1]+#5/4*sin [#1]; (knowing right side flank profil line Y value in circle coordinates system by formula (3))
#7=(114.64+#4) * cos [#1]+#5/4*cos [#1]; (knowing right side flank profil line X value in circle coordinates system by formula (3))
G32 X [2*#6-#4] Z [#7-112] F [#5]; (each screw chasing degree of depth is #4, and pitch is 9.891mm)
#1=#1-0.1; (angle successively decreases 0.1 ° at every turn)
END1；
G00 X50; (X-direction withdrawing in workpiece coordinate system, must be greater than the maximum nominal diameter of screw thread, random tooth when preventing withdrawing)
Z-77.582; (Z-direction withdrawing in workpiece coordinate system, move to cutter outside workpiece, must be more than or equal to screw thread loop start, integral multiple pitch)
X48; (X-direction feed, arrives start position, prevents from starting the random tooth of section)
#4=#4+0.1; (cutting depth increases progressively 0.1mm at every turn)
END2；
G00 X100 Z100；
M09；
M30；
Adopt same way, using formula (4) can carry out left side flank profil line flank of tooth fine finishining to rough machined hindley worm and the flank of tooth repaiies type, and the product processed as shown in Figure 5.
Compared to prior art, the present invention is directed to processing characteristic and the difficult point of hindley worm, first by setting up the profile geometry Mathematical Modeling of hindley worm, then adopting the principle of thread turning to realize the successively matching of segment threaded line according to Mathematical Modeling and processing profile geometry.Propose the new processing method of hindley worm and machining process, successfully achieve the production and processing on 2 Shaft and NC Machining Test lathes of straight wide hindley worm, there is the advantage that machining accuracy is high, manufacturing process is simple, novel, and adopt the method for the invention and production technology to not only reduce production cost, and shorten the production cycle, and prove the realistic production requirement of the method by specific embodiment.
Should be understood that, for those of ordinary skills, can be improved according to the above description or convert, and all improvement and conversion all should belong to the protection domain of claims of the present invention.