Gear insertion machining is a gear processing method that has many advantages and is irreplaceable. In the helical gear cutting process, while the workpiece helical gear is being developed, the additional rotation must be performed to form the helical tooth profile surface with the axial feed motion of the gear shaping cutter, that is, the rotary motion of the workpiece helical gear is It is a synthesis of motion and additional rotation. Therefore, the realization of additional rotation is the key to the technical processing of helical gear insertion. The existing cutting method adds a differential drive chain between the upper and lower reciprocating motion of the pinion cutter and the additional rotation of the workpiece spindle, and the two are linked to ensure that the pinion cutter spindle moves up/down by a spiral. The wire lead, the workpiece helical gear spindle is exactly rotated one revolution, and the additional rotation direction of the workpiece helical gear spindle is reversed in the upward/downward movement of the gear shaping cutter. In actual machining, the additional rotational speed of the helical gear of the workpiece tends to be greater than the speed of its development, so that the helical gear of the workpiece changes its rotational direction continuously and with high frequency as the upper and lower reciprocating motion of the shaping cutter. This high frequency forward and reverse will cause torsional vibration of the helical gear of the workpiece, affecting the smoothness of the machining, resulting in reduced machining accuracy. To this end, this paper proposes a helical gear skipping insertion processing method, which can better solve the above problems.
1 Principle of helical gear skipping cutting process In the development of helical gear cutting, the tangential speed of the workpiece helical gear and the gear shaping cutter is equal (the workpiece helical gear section curve and the gear shaping section curve remain pure Rolling), so in order to discuss the convenience of the problem, the following assumptions can be made: 1) the additional rotation is realized by the helical gear of the workpiece; 2) the rotary motion of the shaping cutter is only reciprocating up and down, the helical gear of the workpiece has only additional rotation, and the shaping cutter The rake face is perpendicular to the axis of the pinion cutter. The principle of helical gear skipping.
The difference between the helical gear skipping and the existing cutting method is that when the gear shaping tool has finished the tooth groove a1c1, the gear shaping tool does not return to the next rotation direction by changing the rotation direction of the workpiece spindle by the rotation Δω1. Starting point a2 of the tooth groove, but changing the additional rotational speed Δω1 of the workpiece helical gear to Δω2 (Δω1 and Δω2 in the same direction), skipping the n slots to the starting point an 1 of the n 1th slot; on the next working stroke, the workpiece The additional rotational speed of the helical gear is restored to Δω1, and the nth first slot an 1cn is processed, and the workpiece helical gear is added.
The workpiece helical gear rotates once, and the slots a1c1, an 1cn 1 , a2n 1 , c2n 1 , etc. are processed once, and then the machining of a2c2, an 2cn 2, a2n 2c2n 2 and the like are sequentially processed; when the workpiece helical gear rotates n weeks, all The cogging is processed again.
It can be seen from the above analysis that during the whole machining process, the workpiece helical gear only has the change of the rotational speed without the change of the rotation direction, so the positive and negative rotation phenomenon of the workpiece helical gear main shaft does not occur, and the torsional vibration problem of the workpiece helical gear main shaft will be obtained. Significant improvement.
2 Mathematical model of the tooth skipping machining motion According to the above-mentioned tooth skipping machining principle, in the working stroke of the gear shaping cutter, the motion relationship of the workpiece helical gear is ωcrωcg Δω1(1) where the synthetic moving speed of the ωcr workpiece helical gear is ωcg the workpiece helical gear The rotational speed of the developing motion Δω1 The additional rotational speed of the workpiece helical gear at the working stroke can be seen from Fig. 1. The additional rotational speed Δω1 of the helical gear of the workpiece at the working stroke is determined by its helix angle β, and the relationship is as follows: Δω12vtanβmZc(2) v The axial feed motion speed of the shaper knife β The helical angle of the workpiece helical gear m The modulus of the workpiece helical gear Zc The number of teeth of the workpiece helical gear According to the principle of development, the development motion of the workpiece helical gear and the shaper cutter satisfies the following relationship :ωcgωbgZbZc(3) In the equation, the rotational speed of the ωbg shaper knife Zb is the return stroke of the gear shaping cutter. The movement relationship of the workpiece helical gear is ωcrωcg Δω2 (4) The additional rotation Δω2 is not only related to the helix angle β And also related to the number of skipping teeth n, the relational expression is Δω22vtanβ'mZc(5)tanβ'mnπB-tanβ(6) where the tooth width of the workpiece helical gear is substituted by the formula (5) (6) Available: Δω22vmZcmnπB-tanβ(7)3 Selection of the number of skipping teeth n In the skipping tooth cutting process, the selection of the number of skipping teeth n is very critical.
Its selection is directly related to the effect and success of the processing method. The selection of the number of skipping teeth must consider the following aspects: 1) In order to ensure the smoothness of helical gear cutting, the working stroke and return of the helical gear of the workpiece in the shaper The additional rotational speeds Δω1 and Δω2 of the stroke should be as close as possible, that is, the values ​​of β' and β should be as close as possible. It can be known from the formula (6) that the number n of skipping teeth should be a rounding value of 2Btanβmπ, that is, nint2Btanβmπ(8)2) There is no common divisor between the number of skipping teeth n and the number of teeth Zc of the workpiece helical gear.
In this way, after the workpiece helical gear rotates for n weeks, all the slots can be processed once, and the gear cutter will return to the starting slot for the next round of cutting, so that some of the slots will not be obtained. Processing situation.
Therefore, if there is no common divisor between n and Zc obtained by equation (8), the number of skipping teeth is n; otherwise, nn±1, until there is no common divisor between n and Zc.
In summary, the number of skipping teeth n does not have a common divisor between the number of teeth Zc of the helical gear of the workpiece except that the formula (8) is satisfied.
4 The example assumes that the number of teeth of the helical gear of the workpiece is Zc40, the modulus is m1.5, the helix angle is β15°, and the tooth width is B20 mm. The number of skipping teeth from equation (8) is nint2×20×tan15°1.
There is a common divisor between the number of 5Ï€2 skipping teeth n2 and Zc, which does not satisfy the selection condition of the number of skipping teeth n. So take nn 1 3 first, there is no common divisor between the number of skipping teeth 3 and Zc, so determine the number of skipping teeth n3.
Bring n3 into equations (2) and (7) respectively, and obtain the additional rotational speed of the workpiece helical gear on the working stroke and return stroke of the shaper: Δω12vtanβmZc≈v112Δω22vmZcmnπB-tanβ≈v137 The amount of change in the rotational speed: δΔωΔω1-Δω2≈ V614 utilizes the existing helical gear cutting method, the rotational speed change of the helical gear main shaft of the workpiece is δΔω′2Δω1≈v56. From the above results, it can be seen that in the skipping tooth cutting process, the workpiece helical gear main shaft is in the working stroke and the return stroke. Not only the change of the direction of rotation, but also the change of the rotational speed is significantly reduced, which is less than the change of the rotational speed of the existing processing method.
5 Conclusions 1) The helical gear skipping insertion machining method Compared with the existing insertion machining method, the change of the rotation direction of the workpiece spindle is only the change of the rotation speed, and the rotation speed variation is greatly reduced. Therefore, the workpiece spindle does not have obvious torsional vibration phenomenon during processing, and the smoothness of the processing is improved, which is beneficial to the improvement of the machining precision.
2) This paper discusses the case of additional rotation by the workpiece spindle. According to the helical gear profile forming principle, the additional rotation can also be realized by the gear shaping spindle. The two are identical in principle, so the jump tooth cutting processing The law is equally valid for the latter.
Nozzle Check Valve
PFA Coating Check Valve,Stainless Steel Check Valve,Non-Slam Check Valve
Butterfly Valve,Check Valve,Gate Valve Co., Ltd. , http://www.fw-valve.com