In case of breakdown gear wheel or gears in the gearbox of any mechanism or machine, there is a need to create a drawing using the “old” part, and sometimes using fragments of debris, to make a new wheel and/or gear. This article will be useful to those...
Who has to restore gears in the absence of working drawings for failed parts?
Usually for a turner and milling machine everything required dimensions can be obtained using measurements with a caliper. Requiring closer attention, the so-called mating dimensions - dimensions that determine the connection with other parts of the assembly - can be specified by the diameter of the shaft on which the wheel is mounted and by the size of the key or keyway shaft The situation is more complicated with the parameters for the gear milling machine. In this article we will determine not only the gear module, I will try to outline general order determination of all the main parameters of the ring gears based on the results of measurements of worn samples of gears and wheels.
We “arm ourselves” with a caliper, an inclinometer, or at least a protractor, a ruler and the MS Excel program, which will help to quickly perform routine and sometimes difficult calculations, and we begin work.
As usual, I will cover the topic using examples, which we will consider first cylindrical straight teeth external gear transmission, and then helical.
Calculations gears There are several articles on this site: “”, “”, “”. They contain pictures indicating the parameters used in this article. This article continues the topic and is intended to reveal the algorithm of actions during repair and restoration work, that is, work that is reverse to design work.
Calculations can be performed in MS Excel or in the OOo Calc program from the Open Office package.
You can read about the rules for formatting Excel sheet cells, which are used in the articles of this blog, on the page « ».
Calculation of the parameters of the wheel and gear of a spur transmission.
Initially, we assume that the gear and gear have involute tooth profiles and were manufactured with the parameters of the original contour in accordance with GOST 13755-81. This GOST regulates the three main (for our task) parameters of the initial contour for modules larger than 1 mm. (For modules less than 1 mm, the initial contour is specified in GOST 9587-81; modules less than 1 mm are recommended for use only in kinematic, that is, not power transmissions.)
To correctly calculate the gear parameters, measurements of both gears and wheels are necessary!
Initial data and measurements:
We start filling out the table in Excel with the parameters of the original contour.
1. Profile angle of the original contour α write in degrees
to cell D3: 20
2. Tooth head height coefficient h a* enter
to cell D4: 1
3. Transmission radial clearance coefficient c* we enter
to cell D5: 0,25
In the USSR and Russia, 90% of gears in general mechanical engineering were manufactured with precisely these parameters, which made it possible to use a unified gear-cutting tool. Of course, gears with Novikov gearing were manufactured and special initial contours were used in the automotive industry, but still most gears were designed and manufactured with a contour in accordance with GOST 13755-81.
4. Wheel tooth type (gearing type) T write down
to cell D6: 1
T=1 – with external teeth on the wheel
T=-1 – with internal teeth on the wheel (internal gear transmission)
5. Center transmission distance a w in mm we measure along the gearbox housing and enter the value
to cell D7: 80,0
A number of gear spacings have been standardized. You can compare the measured value with the values in the series shown in the note in cell C7. A coincidence is not necessary, but highly likely.
6-9. Gear parameters: number of teeth z 1 , d a 1 And d f 1 in mm, angle of inclination of teeth on the surface of the vertices β a 1 in degrees we count and measure with calipers and inclinometers on the original sample and write accordingly
to cell D8: 16
to cell D9: 37,6
to cell D10: 28,7
to cell D11: 0,0
10-13. Wheel parameters: number of teeth z 2 , diameters of the tops and bottoms of the teeth d a 2 And d f 2 in mm, angle of inclination of teeth on the cylinder of vertices β a 2 in degrees we determine in the same way - according to the original sample of the wheel - and write accordingly
to cell D12: 63
to cell D13: 130,3
to cell D14: 121,4
to cell D11: 0,0
Please note: tooth angles β a 1 And β a 2 - these are the angles measured on the cylindrical surfaces of the tops of the teeth!!!
We measure diameters as accurately as possible! For wheels with an even number of teeth, this is easier if the tips are not jammed. For wheels with an odd number of teeth, when measuring, remember that the dimensions shown by the caliper are slightly smaller than the actual diameters of the protrusions!!! We take several measurements and write the most reliable values, from our point of view, into the table.
Calculation results:
14. Preliminary m values The engagement module is determined based on the results of gear measurements m 1 and gear m 2 in mm respectively
in cell D17: =D9/(D8/COS (D20/180*PI())+2*D4)=2,089
m 1 = d a1 /(z 1 /cos (β 1 )+2*(h a * ))
and in cell D18: =D13/(D12/COS (D21/180*PI())+2*D4)=2,005
m 2 = d a2 /(z 2 /cos (β 2 )+2*(h a * ))
The gear module plays the role of a universal scale factor that determines both the dimensions of the teeth and the overall dimensions of the wheel and gear.
We compare the obtained values with the values from the standard series of modules, a fragment of which is given in the note to cell C19.
The resulting calculated values are, as a rule, very close to one of the values of the standard series. We make the assumption that the desired gear and pinion module m in mm is equal to one of these values and enter it
to cell D19: 2,000
15. Preliminary values at The angle of the teeth inclination is determined based on the results of gear measurementsβ 1 and gearβ 2 in degrees respectively
in cell D20: =ASIN (D8*D19/D9*TAN (D11/180*PI()))=0,0000
β 1 =arcsin(z 1 *m *tg (β a1 ) / d a1 )
and in cell D21: =ASIN (D12*D19/D13*TAN (D15/180*PI()))=0,0000
β 2 =arcsin(z 2 *m *tg (β a2 ) / d a2 )
We make the assumption that the desired angle of inclination of the teeth β in degrees is equal to the measured and recalculated values and write down
to cell D22: 0,0000
16. Preliminary values the equalization displacement coefficient is calculated based on the results of gear measurements Δy 1 and gear Δy 2 respectively
in cell D23: =2*D4+D5- (D9-D10)/(2*D19) =0,025
Δy 1 =2*(h a * )+(c* ) — (d a1 -d f1 )/(2*m )
and in cell D24: =2*D4+D5- (D13-D14)/(2*D19) = 0,025
Δy 2 =2*(h a * )+(c * ) - (d a 2 — d f 2 )/(2* m )
We analyze the obtained calculated values, and decision made about the value of the equalization bias coefficient Δy write down
to cell D25: 0,025
17,18. Gear pitch diameters d 1 cogwheel d 2 in mm we calculate accordingly
in cell D26: =D19*D8/COS (D22/180*PI()) =32,000
d 1 = m * z 1 / cos(β )
and in cell D27: =D19*D12/COS (D22/180*PI()) =126,000
d 2 = m * z 2 / cos(β )
19. Pitch center distance a in mm we calculate
in cell D28: =(D27+D6*D26)/2 =79,000
a = (d 2 + T * d 1 )/ 2
20. Profile angle α t We calculate in degrees
in cell D29: =ATAN (TAN (D3/180*PI())/COS (D22/180*PI()))/PI()*180=20,0000
α t =arctg(tg(α)/cos(β ))
21. Engagement angle α tw We calculate in degrees
in cell D30: =ACOS (D28*COS (D29/180*PI())/D7)/PI()*180=21,8831
α tw =arccos(a *cos (α t )/a w )
22,23. Gear displacement coefficients x 1 and wheels x 2 determine accordingly
in cell D31: =(D9-D26)/(2*D19) -D4+D25 =0,425
x 1 =(d a 1 — d 1 )/(2* m ) — (h a * )+ Δy
and in cell D32: =(D13-D27)/(2*D19) -D4+D25 =0,100
x 2 =(d a 2 — d 1 )/(2* m ) — (h a * )+ Δy
24,25. Sum (difference) displacement coefficient x Σ(d) calculate to check the correctness of previous calculations using two formulas, respectively
in cell D33: =D31+D6*D32 =0,525
x Σ (d) = x 1 +T*x 2
and in cell D34: =(D12+D6*D8)*((TAN (D30/180*PI()) - (D30/180*PI())) - (TAN (D29/180*PI()) - (D29/180* PI())))/(2*TAN (D3/180*PI()))=0,523
x Σ(d) = (z 2 + T * z 1 )*(inv(α tw ) — inv(α t ))/(2* tg(α ))
The values calculated using different formulas differ very slightly! We believe that the found values of the gear and pinion module, as well as the displacement coefficients, are determined correctly!
Calculation of the parameters of the wheel and gear of a helical gear.
Let's move on to the example with a helical gear and repeat all the steps that we did in the previous section.
It is practically very difficult to measure the angle of inclination of the teeth with the required accuracy using a protractor or protractor. I usually rolled the wheel and gear on a sheet of paper and then made preliminary measurements with an accuracy of a degree or more using the protractor prints of the drawing board's dividing head... In the example below, I measured: β a 1 =19 ° andβ a 2 =17,5 °.
Once again, I draw your attention to the fact that the angles of inclination of the teeth on the apex cylinder β a 1 Andβ a 2 - this is not an angleβ , involved in all major transmission calculations!!! Cornerβ is the angle of inclination of the teeth on the cylinder pitch diameter(for transmission without offset).
Due to the small values of the calculated displacement coefficients, it is appropriate to assume that the transmission was performed without displacement of the producing contours of the pinion and gear wheel.
Let's use the Excel service “Parameter Selection”. I wrote in detail and with pictures about this service at one time.
In the main menu of Excel, select “Tools” - “Select parameter” and fill in the window that appears:
Set in cell: $ D$33
Meaning: 0
Changing the value of a cell: $ D$22
And click OK.
We get the result β =17,1462 °, x Σ(d) =0, x 1 =0,003≈0, x 2 =-0,003≈0!
The transmission was most likely made without displacement, the module of the gear wheel and pinion, as well as the angle of inclination of the teeth, we have determined, we can make drawings!
Important notes.
Displacement of the original contour when cutting teeth is used to restore worn surfaces of wheel teeth, reduce the depth of penetration on gear shafts, to increase the load capacity of a gear transmission, to perform transmission with a given center distance not equal to the pitch distance, to eliminate undercutting of the legs of gear teeth and tooth heads wheels with internal teeth.
There are altitude correction ( x Σ(d) = 0 ) and angular ( x Σ(d) ≠ 0 ).
Displacement of the generating circuit in practice is usually used in the manufacture of spur gears and very rarely helical gears. This is due to the fact that in terms of bending strength, an oblique tooth is stronger than a straight one, and the required interaxial distance can be ensured by an appropriate angle of inclination of the teeth. If height correction is rarely used for helical gears, then angular correction is almost never used.
Helical gears operate smoother and quieter than straight gears. As already mentioned, oblique teeth have higher bending strength and a given interaxial distance can be ensured by the angle of inclination of the teeth and without resorting to displacement of the generating circuit. However, in gears with helical teeth, additional axial loads appear on the shaft bearings, and the wheel diameters have larger size than straight teeth with the same number of teeth and module. Helical wheels are less technologically advanced to manufacture, especially wheels with internal teeth.
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Gear racks and gears.
Rack and pinion transmission - special case gear transmission, widely used in machine tools and mechanisms for transmitting rotational motion and converting angular speeds and torque.
Gear drives are available with straight teeth for low to medium speed applications, and helical teeth for medium to high speed applications or when greater precision is required.
Rack-and-pinion transmissions have become widespread in mechanical engineering thanks to good combination load, dynamic and accuracy characteristics. They are distinguished by their reliability, simplicity of design and ease of installation.
Manufacturer Chiaravalli supplies modular pitch gears M1-M1.5-M2-M2.5-M3-M4-M5-M6. As additional elements In transmissions, pairs of bevel gears can be used in conjunction with rack-and-pinion transmissions. Gears are made of steel S45UNI7845. All supplied components are distinguished by a traditionally high European level of performance. Precision ground rack and pinion pairs are individually selected and custom fitted. High-precision bevel gears with spiral (palloid) teeth undergo several stages of grinding and finishing lapping.
Bevel gears
This type of gears is divided into several types, differing in the shape of the tooth line:
Bevel gears, for example, are used in addition to automobile differentials in various gearboxes ( bevel gear) for taps, drying drums ( bevel gear drying drum), crushers (bevel gear for the crusher), to drive the conveyor belt (belt conveyor gear). Rotation transmission based on a bevel gear with a circular tooth ( circular tooth gear) has high driving performance, namely quiet operation, high load capacity for engagement and high smoothness.
Straight tooth gear (spur gear) is the most common of all types gear wheels. Teeth straight tooth gears are in radial planes, and the contact line of the teeth of both spur gears is parallel to the axis of rotation. Axes first and second straight tooth gears are located strictly parallel. Spur gears ( spur gears) have a lower torque limit than helical and herringbone gears.
Helical gear in its manufacturing process it is more labor-intensive than a spur gear due to the specific shape of the teeth. Means, helical gear manufacturing requires an even more careful approach. In principle, helical gears can be called an improved type of gear with straight teeth.
Circular Tooth Bevel Gears used in various machines and mechanisms in many industries. Manufacturing of such circular tooth gears, perhaps in enterprises that are equipped with appropriate technological equipment and qualified personnel.
Gear
Gears
Gear, gear- the main part of a gear transmission in the form of a disk with teeth on a cylindrical or conical surface that mesh with the teeth of another gear. In mechanical engineering, it is customary to call a small gear with fewer teeth gear, and the big one is a wheel. However, all gears are often called gears.
Gears are usually used in pairs with different numbers teeth in order to convert the torque and number of revolutions of the input and output shafts. A wheel to which torque is supplied externally is called leading, and the wheel from which the moment is removed is slave. If the drive wheel diameter less, then the torque of the driven wheel increases due to proportional decrease rotation speed, and vice versa. In accordance with the gear ratio, an increase in torque will cause a proportional decrease in the angular speed of rotation of the driven gear, and their product - mechanical power - will remain unchanged. This relationship is valid only for the ideal case, which does not take into account friction losses and other effects characteristic of real devices.
Movement of the point of contact of the teeth with the involute profile;
left - driving, right - driven wheel
Spur gears
Gear parameters
Transverse tooth profile
The profile of wheel teeth usually has an involute lateral shape. However, there are gears with a circular tooth profile (Novikov gear with one and two lines of engagement) and with a cycloidal one. In addition, ratchet mechanisms use gears with an asymmetrical tooth profile.
Involute gear parameters:
- m- wheel module. The engagement modulus is a linear quantity in π times less than the circumferential pitch P or the ratio of the pitch along any concentric circle of the gear to π , that is, the module is the number of millimeters of diameter per tooth. The dark and light wheels have the same module. The most important parameter, standardized, is determined from the strength calculation of gears. The more loaded the transmission, the higher the module value. All other parameters are expressed through it. The module is measured in millimeters, calculated by the formula:
- z- number of wheel teeth
- p- tooth pitch (marked in lilac)
- d- diameter of the pitch circle (marked in yellow)
- d a- diameter of the circle of the vertices of the dark wheel (marked in red)
- d b- diameter of the main circle - involute (marked in green)
- d f- diameter of the circle of the dark wheel depressions (marked in blue)
- h aP +h fP- height of the dark wheel tooth, x+h aP +h fP- light wheel tooth height
In mechanical engineering, certain values of the gear module are accepted m for ease of manufacture and replacement of gears, which are integers or numbers with decimal: 0,5 ; 0,7 ; 1 ; 1,25 ; 1,5 ; 1,75 ; 2 ; 2,5 ; 3 ; 3,5 ; 4 ; 4,5 ; 5 and so on until 50 .
Tooth head height - h aP and the height of the tooth stem - h fP- in the case of the so-called zero gear (made without offset, gear with "zero" teeth)(the displacement of the cutting rack, cutting the teeth, closer or further to the workpiece, and the displacement closer to the workpiece is called negative offset, and the displacement further from the workpiece is called. positive) correspond to the module m as follows: h aP = m; h fP = 1.25 m, that is:
From this we obtain that the tooth height h(not indicated in the figure):
In general, it is clear from the figure that the diameter of the circle of the vertices d a greater than the diameter of the circle of the depressions d f to double tooth height h. Based on all this, if you need to practically determine the module m gear, without the necessary data for calculations (except for the number of teeth z), then it is necessary to accurately measure its outer diameter d a and divide the result by the number of teeth z plus 2:
Longitudinal line of the tooth
Gear wheel from a clock mechanism
Gears are classified depending on the shape of the longitudinal line of the tooth into:
- straight teeth
- helical
- chevron
Spur wheels
Spur gears are the most common type of gears. The teeth are located in radial planes, and the contact line of the teeth of both gears is parallel to the axis of rotation. In this case, the axes of both gears must also be located strictly parallel. Spur gears have the lowest cost, but at the same time, the maximum torque of such wheels is lower than helical and chevron gears.
Helical wheels
Helical gears are an improved version of spur gears. Their teeth are located at an angle to the axis of rotation, and their shape forms part of a spiral.
- Advantages:
- The engagement of such wheels occurs more smoothly than straight teeth and with less noise.
- The contact area is increased compared to spur gear, thus, the maximum torque transmitted by the gear pair is also greater.
- Disadvantages helical wheels The following factors can be considered:
- When a helical gear operates, a mechanical force arises directed along the axis, which necessitates the use of thrust bearings to install the shaft;
- An increase in the friction area of the teeth (which causes additional power losses due to heating), which is compensated by the use of special lubricants.
In general, helical gears are used in mechanisms that require the transmission of high torque at high speeds, or have strict noise restrictions.
Chevron wheels
Chevron wheels
The teeth of such wheels are made in the form of the letter “V” (or they are obtained by joining two helical wheels with opposing teeth). Transmissions based on such gears are usually called “chevron”.
Chevron wheels solve the problem of axial force. The axial forces of both halves of such a wheel are mutually compensated, so there is no need to install the shafts on thrust bearings. In this case, the transmission is self-aligning in the axial direction, which is why in gearboxes with chevron wheels one of the shafts is mounted on floating supports (usually on bearings with short cylindrical rollers).
Internal gears
When there are strict restrictions on dimensions, in planetary mechanisms, in gear pumps with internal gearing, in the drive of a tank turret, wheels with ring gear, sliced with inside. The driving and driven wheels rotate in one direction. In such a transmission there are less friction losses, that is, higher efficiency.
Sector wheels
A sector wheel is a part of any type of regular wheel. Such wheels are used in cases where the link does not need to rotate a full turn, and therefore you can save on its dimensions.
Wheels with circular teeth
A transmission based on wheels with circular teeth (Novikov Transmission) has even higher driving performance than helical ones - high load capacity of engagement, high smoothness and quiet operation. However, they are limited in application due to reduced, under the same conditions, efficiency and service life; such wheels are noticeably more difficult to produce. Their line of teeth is a circle of radius, selected for certain requirements. The contact of the tooth surfaces occurs at one point on the engagement line, located parallel to the wheel axes.
Bevel gears
Conical wheels in the dam gate drive
In many machines, the implementation of the required movements of the mechanism is associated with the need to transmit rotation from one shaft to another, provided that the axes of these shafts intersect. In such cases, bevel gears are used. There are types of bevel wheels that differ in the shape of the tooth lines: with straight, tangential, circular and curved teeth. Straight-tooth bevel wheels, for example, are used in automotive final drives, used to transfer torque from the engine to the wheels.
Rack and pinion transmission
Literature
- Ed. Skorokhodova E. A. General technical reference book. - M.: Mechanical Engineering, 1982. - P. 416.
- Gulia N. V., Klokov V. G., Yurkov S. A. Machine parts. - M.: Publishing center "Academy", 2004. - P. 416. - ISBN 5-7695-1384-5
- Bogdanov V.N., Malezhik I.F., Verkhola A.P. et al. Reference Guide to Drawing. - M.: Mechanical Engineering, 1989. - P. 438-480. - 864 p. - Technical Translator's Guide
Link gear mechanism, which has a closed system of teeth and ensures continuous movement of another link (wheel, worm, rack) ... Big Encyclopedic Dictionary
GEAR- the main gear part (see) in the form of a disk with closed system teeth, which meshes with the teeth of another wheel (rack), which ensures continuous movement of the wheel (worm, rack) ... Big Polytechnic Encyclopedia
gear- 3.14 gear wheel: A solid part or assembly unit, which is a gear unit with a closed system of teeth that ensures continuous movement of another gear unit (wheel). 3.15
Information:
Pitch error ± 0.02 mm.
Accuracy class 9.
Manufactured in accordance with DIN 3962/63/67.
Engagement angle 20°.
Material: steel C45
The advantages of the offered gears are:
- accuracy of geometry and dimensions;
- strength and wear resistance;
- high quality surface treatment;
- reduced noise level;
- full compliance with standards;
- long service life.
The range includes the most popular spur and spur gears. The products are in demand in mechanical engineering and are also used in various industrial and household mechanisms. Gears are manufactured with a hub from wear-resistant alloys in various standard sizes in accordance with GOST and international standards.
Types of gears and their features
The main elements of a gear transmission are cylindrical or conical parts with a toothed surface. In the mechanisms, several gears interact, engaging the teeth with each other and providing torque conversion.
Elements are also classified according to tooth geometry into spur, helical and chevron. Straight tooth gears are the most popular type of gears. In this case, the contact line is parallel to the axis of rotation. Such products are cheaper to manufacture, but have lower torque compared to other types. Helical wheels are characterized by quieter and smoother running, but require careful lubrication.
Operation of spur gear Gear(gear)- the main part of a gear transmission in the form of a disk with teeth on a cylindrical or conical surface that mesh with the teeth of another gear. In mechanical engineering, it is customary to call a small drive gear, regardless of the number of teeth gear, and the large driven one is a wheel. However, all gears are often called gears.
Gears are usually used in pairs with different numbers of teeth to convert torque and output shaft speed. The wheel to which the torque is supplied from the outside is called the driving wheel, and the wheel from which the torque is removed is called the driven wheel. If the diameter of the drive wheel is smaller, then the torque of the driven wheel increases due to a proportional decrease in the rotation speed, and vice versa. According to gear ratio, an increase in torque will cause a proportional decrease in the angular speed of rotation of the driven gear, and their product - mechanical work - will remain unchanged. This relationship is valid for the ideal case, which does not take into account friction losses and other effects characteristic of real devices.
Transverse tooth profile
The wheel tooth profile usually has an involute side shape. However, there are gears with a circular tooth profile (Novikov gear with one and two lines of engagement) and with a cycloidal one. In addition, ratchet mechanisms use gears with an asymmetrical tooth profile.
Involute gear parameters:
- m- wheel module, dark and light wheels have the same module. The most important parameter, standardized, is determined from the strength calculation of gears. The more loaded the transmission, the higher the module value. All other parameters are expressed through it. The module is measured in millimeters and is calculated using the formula:
- z- number of wheel teeth
- p- tooth pitch (marked in purple)
- d- diameter of the pitch circle (marked in yellow)
- d a- diameter of the circle of the vertices of the dark wheel (marked in red)
- d b- diameter of the initial circle (marked in green)
- d f- diameter of the circle of the dark wheel depressions (marked in blue)
- h aP +h fP- height of the dark wheel tooth, x+h aP +h fP- light wheel tooth height
Spur wheels Spur gears are the most common type of gears. The teeth are a continuation of the radii, and the contact line of the teeth of both gears is parallel to the axis of rotation. In this case, the axes of both gears must also be located strictly parallel.
- When a helical gear operates, a mechanical moment arises directed along the axis, which necessitates the use of thrust bearings to install the shaft;
- An increase in the friction area of the teeth (which causes additional power losses due to heating), which is compensated by the use of special lubricants.
Double helical wheels (chevrons)
Double helical wheels solve the problem axial moment. The teeth of such wheels are made in the form of the letter “V” (or they are obtained by joining two helical wheels with opposing teeth). The axial moments of both halves of such a wheel are mutually compensated, so there is no need to install axles and shafts in special bearings. Transmissions based on such gears are usually called “chevron”.
Internal gears
When there are strict restrictions on dimensions, in planetary mechanisms, in gear pumps with internal gearing, in the drive of a tank turret, wheels with a ring gear cut from the inside are used. The driving and driven wheels rotate in one direction. In such a transmission there are less friction losses, that is, higher efficiency.
Sector wheels
A sector wheel is a part of any type of regular wheel. Such wheels are used in cases where the link does not need to rotate a full turn, and therefore you can save on its dimensions.
Wheels with circular teeth
A transmission based on wheels with circular teeth (Novikov Transmission) has even higher driving performance than helical ones - high load capacity of engagement, high smoothness and quiet operation. However, they are limited in their use by reduced, under the same conditions, efficiency and service life; such wheels are noticeably more difficult to produce. Their line of teeth is a circle of radius, selected for certain requirements. The contact of the tooth surfaces occurs at one point on the engagement line, located parallel to the wheel axes.
Bevel gears
Rack and pinion transmission
Crown wheels
A crown wheel is a special type of wheel whose teeth are located on the side surface. Such a wheel is usually connected to a regular spur wheel, or to a drum made of rods (lantern wheel), as in a tower clock. Manufacturing of gears
Run-in method
Currently, it is the most technologically advanced, and therefore the most widespread, method of manufacturing gears. In the manufacture of gears, tools such as a comb, hob cutter and cutter can be used.
Run-in method using a comb
In addition to the comb as cutting tool use a hob cutter. In this case, a worm gear occurs between the workpiece and the cutter.
Run-in method using a cutter
Gears are also chiseled on gear shaping machines using special cutters. A gear shaper is a gear wheel equipped with cutting edges. Since it is usually impossible to cut off the entire metal layer at once, processing is carried out in several stages. During processing, the tool makes a reciprocating movement relative to the workpiece. After each double stroke, the workpiece and the tool rotate relative to their axes by one step. Thus, the tool and the workpiece seem to “run” against each other. After the workpiece has made a full revolution, the cutter makes a feed motion towards the workpiece. This process continues until the entire required layer of metal is removed.
Copy method (Divide method)
A disc or finger cutter is used to cut one tooth cavity of the gear. The cutting edge of the tool is shaped like this depression. After cutting one cavity, the workpiece is rotated one angular step using a dividing device, and the cutting operation is repeated. The method was used at the beginning of the 20th century. The disadvantage of this method is its low accuracy: the cavities of a wheel made using this method are very different from each other.
Manufacturing of bevel wheels
The manufacturing technology of bevel wheels is closely related to the geometry of the side surfaces and tooth profiles. The method of copying the shaped profile of a tool to form a profile on a bevel wheel cannot be used, since the dimensions of the cavity of the bevel wheel change as it approaches the apex of the cone. In this regard, tools such as a modular disc cutter, a finger cutter, or a shaped grinding wheel can only be used for rough cutting of cavities or for the formation of wheel cavities no higher than the eighth degree of accuracy. To cut more precise bevel wheels, use the method of running in the machine engagement of the cut workpiece with an imaginary producing wheel. Side surfaces producing wheels are formed due to the movement of the cutting edges of the tool during the main cutting movement, which ensures cutting off the allowance. Tools with a straight blade became more widespread. With a straight main movement, a straight blade forms a flat producing surface. Such a surface cannot form an involute conical surface with spherical involute profiles. The resulting conjugate conical surfaces, which differ from involute surfaces, are called quasi-involute.
Mistakes in gear design
Tooth trimming
According to the properties of involute gearing, the straight part of the initial generating contour of the gear rack and the involute part of the tooth profile of the cut wheel touch only on the machine gearing line. Beyond this line, the original generating contour intersects the involute profile of the wheel tooth, which leads to the cutting of the tooth at the base, and the cavity between the teeth of the cut wheel becomes wider. Trimming reduces the involute part of the tooth profile (which leads to a reduction in the duration of engagement of each pair of teeth of the designed gear) and weakens the tooth in its dangerous section. Therefore, pruning is unacceptable. To prevent undercutting from occurring, geometric restrictions are imposed on the wheel design, from which the minimum number of teeth is determined at which they will not be undercut. For a standard tool, this number is 17. Undercutting can also be avoided by using a gear manufacturing method other than the running-in method. However, even in this case, the conditions for the minimum number of teeth must be observed, otherwise the depressions between the teeth of the smaller wheel will turn out to be so tight that the teeth of the larger wheel of the manufactured gear will not have enough space for their movement and the gear will jam.
Sharpening the tooth
As the tool offset increases, the tooth thickness will decrease. This leads to sharpening of the teeth. The risk of sharpening is especially high for wheels with a small number of teeth (less than 17). To prevent chipping of the top of a pointed tooth, the displacement of the tool is limited from above.
