Gear

The machine element is a gear wheel with teeth evenly distributed over the circumference. Two or more paired together gears form a gear train. It is used mainly for transmission between two rotations or a rotation and a linear movement (pairing of a gear with a rack ). Gear drive form the largest group among the transmissions. They are form-fitting, and thus slip.

If the gear ratio on a small scale to be constant, that is, from the previous engagement to engagement of the next tooth in the gaps of the mating gear, the first gear law is observed. The form-fit is not lost, if it is ensured that the subsequent tooth is already engaged before the engagement of the preceding tooth breaks off (second teeth Act).

The shape of the teeth is basically arbitrary in compliance with the laws teeth. But is selected on an engagement surface shape determines the shape of the engagement surface on the mating gear. In practice, we restrict ourselves to tooth shapes ( hence geometrically simple rewritable) can be easily produced. The most widely used have the involute and the cycloidal each with its own advantages in use.

In addition to pure tooth pairs in gear drives, there are pairings between chain links and teeth of gear wheels in chain transmissions. Here engage the chain links (for example, a bicycle chain ) in the tooth gaps (for example, a sprocket and a sprocket on a bicycle ). In a synchronous belt drive, the chain is replaced by a belt with teeth ( toothed belt) (for example, for driving the cam shaft in four-stroke engines ).

• 4.1 Rolling gear
• 4.2 helical

• 5.1 involute
• 5.2 cycloidal
• 5.3 pinion gearing
• 5.4 Wildhaber - Novikov gearing

• 7.1 General
• 7.2 Check of bevel gears
• 7.3 Checking of spur gears

General

The wheels of a gear train rotate with the shafts to which they are attached, or rotate on axes on which they are stored.

The wheel space is designed so that the teeth engage with each other, and thus the rotation of one gear wheel is transferred to the other. In the pairing of two externally toothed wheels, the rotational direction is reversed. If this is not desired, a third gear is disposed between any desired size. The wheels are of different size, the rotation speed is increased or decreased, the torque is reduced or increased ( the change gear ratio ).

History

In the ancient Egyptian Göpeln one finds the oldest form of the gear, a wooden wheel, in the circumferential you put pegs stretched. The role was already in use among the Assyrians and was adopted by the Egyptians, the combination of these roles by means of rope led to the famous tackle. A direct connection of these roles has been 330 BC by Aristotle mentioned, secured the application of gears at Heron of Alexandria, handed down by Vitruvius. Ktesibios used around 250 BC at his water meter a bar which was busy with cogs, as Philo of Byzantium around 230 BC at two apparatuses gears. The most significant artifact today for the application of gears in antiquity is the Antikythera mechanism from about 100 BC

Since the 9th century took place in Europe, the use of gears in watermills, from the 12th century in windmills. In manuscripts Leonardo Da Vinci can be found around 1500 gears in various applications.

Georgius Agricola was in 1556 in his De re metallica libri XII for the first time on the use of gears made ​​of iron. However, an iron gear is shown in Xi'an in Shaanxi Museum of History, which is supposed to be about 2000 years old.

Initially, little attention to the proper shape of the teeth. According to Christiaan Huygens and Gottfried Wilhelm Leibniz the Danish astronomer Ole Rømer recommended by the 1674 epi- cycloid as tooth shape. Probably he had come on the building of his planetariums, eg Jovilabium at the Paris Academie des Sciences. Written evidence no longer exists. A first thorough mathematical investigation of these gears described the Academician Philippe de la Hire (1640-1718) to 1694 Traite des epicycloides (published in 1730). This epicycloidal gear shape ensures a smooth movement of the gears in a uniform sliding friction. These were installed in a targeted movements. John Smeaton in 1759 developed its own form, followed by Leonhard Euler, who in 1760 proposed the involute tooth form for. The development of the steam engine in the 18th century led to an increasing need for gears, since the power to be transmitted continuously rose and gears made of metal instead of the current had to be made ​​of wood. 1820 invented Joseph Woollams the helical gear and herringbone (double helical gears ) ( English patent No. 4477 of 20 June 1820), James White built in 1824 from a differential gear. 1829 presented Clavet ago a tooth planing machine, because the machine tool industry in the 19th century required an increase in accuracy of the teeth. The first practical machine for milling geradverzahnter spur gears built in 1887 G. Grant. 1897 H. PFauter developed in Chemnitz from a universal machine with which also worm and helical gears were finished.

Types of gears

• Spur gear and rack

Inner -toothed (red) and externally toothed spur

Rack and pinion

Spur

The spur gear (or Cylindrical ) is the most commonly used gear. A cylindrical disc is splined on its periphery. The axes of a spur gear and its mating gear ( spur gear or spline shaft end ) are parallel, it develops a spur gear. We distinguish external and internal gear.

The teeth are mostly straight ( parallel to the axis ), diagonally ( helical gear ) or as a double helical toothing. For double helical gears, a distinction between those with or without undercut as a true herringbone.

The tooth profile based on an involute curve.

Rack

The rack is a spur gear with an infinitely large diameter. A rack gear is formed by the combination of a toothed rack with a spur gear. The movement of the rack in a straight line and is limited by the finite length. In typical applications, a reciprocation takes place.

An unusually long, composed of many individual pieces rack is the Tooth rail of a rack railway.

Ellipsenrad

Most gear train consist of round gears or from wheel bodies with circular pitch lines. When the driving gear rotates smoothly, also the driven gear rotates evenly. Example of a non-uniformly be translated, and thus consisting of non-circular gear wheels gear is a Ellipsenrad transmission. A Ellipsenrad is a non-circular spur gear.

If two similar and similarly large ellipse wheels combined, the center distance is constant. The wheels turn each round one of its ellipse foci. The ratio varies over one revolution around the mean i = 1 there is only one wheel elliptical, a wheel has to be mounted on a swing axis. Be used such gears as in weaving. Better known is an elliptical chainring in the chain drive some bikes.

• Pinion and crown wheel

Crown wheel gear: spindle gear ( spur gear, top) and crown wheel ( below)

Bevel gear

The axes of bevel gears are not parallel but intersect. Most of the intersection angle is 90 °. The basic shape is a truncated cone, whose outer surface is splined. In two paired with one another bevel gears whose peaks coincide. The teeth extend mostly just in the direction of the generating lines, the so-called hypoid they are arcuate.

The tooth height profile of bevel gears corresponds to a Oktoide.

In spiral bevel gears, a distinction is mainly as follows:

- Circular arc teeth with non-constant tooth height ( Gleason )

- Circular arc teeth with constant tooth height ( Kurvex )

- Cyclo- palloid gearing ® (ringing mountain )

- Palloid gearing ® (ringing mountain )

Traditional production methods:

- Kegelradhobelmaschinen for straight and helical bevel gear ( finishing after hardening by lapping )

- Bevel with soft and hard machining cutter heads for Klingelnberg cyclo-palloid ® Spiral bevel gears

- Bevel with so-called " Christmas tree " palloid cutters for Klingelnberg Palloid ® Spiral bevel gears ( finishing after hardening by lapping )

- Kegelradfräs and Kegelradschleifmaschinen for Gleason Circular Arc Spiral bevel gears.

Bevel are still successfully used in mass production. The 5 -axis milling for the series, in which usually small modules and diameter are interlinked, because of the high manufacturing time in small tooth gaps not economical.

New production methods:

For large bevel gears and small numbers of the 5 -axis milling is elected for 5 -axis simultaneous machining centers capable with non-profiled standard tools in the soft and hard machining meanwhile increased.

The key for a successful production result is a precise calculation of the 3D tooth shape. The Kegelradzahnprofil based on a Oktoide ( as in the conventional production on Bevel ), however, on an involute spur gears ( as in the conventional production of hobbing and shaping machines ).

Simplified calculated bevel gear based on a replacement front wheel in the normal section with evolventischem tooth profile have a different tooth shape with reduced root strength by 10-28 % without axial offset and 45% for off-axis. [ Diss Hünecke, TU Dresden ]. Likewise, it has been shown that " involute bevel gear sets " have a significantly poorer smoothness.

In the preparation method " 5 -axis milling " are not usually necessary correction loops for finish machining to achieve a proper support image. Through professional TCA tooth contact analysis, the contact pattern is already in interpretation of the bevel gear by a Laufprüfsimulation based on 3D models theoretically " unrolled " / tested and evaluated. , The contact pattern does not cover the technical specifications, the contact pattern will be adjusted before production begins by data change in the interpretation. The wear pattern on the bevel gear manufactured corresponds congruently at once to the simulated wear pattern on the basis of volume models of wheel and pinion. Subsequent adjustment work are normally not required.

Crown

A gear with face gear is a bevel gear and a variant of the bevel gear. It was formerly often than a bevel gear used ( see Figure: crown-gear made ​​of wood). The crown gear, the teeth are mounted on the circular surface of a cylinder. It forms together with a spur gear, a crown-gear.

• Worm wheel and worm

Worm wheel and worm

A made up of worm wheel and worm worm gear is in addition to other gear used when the waves cross, but do not cut. Another feature is the relatively high ratio.

The worm may be a helical gear in the simplest case. To line instead of reaching only point of contact between the teeth in the gear, the tooth flanks of the worm wheel are hollow.

The teeth on the little worm is similar to a thread. The worm is like a spur gear with a few very oblique teeth schraubförmig wound around the cylinder. One turn corresponds to a tooth. Wherein the thread-like enveloped gear teeth is non-cylindrical. The cylinder is fitted and adapts to the curvature of the worm gear on.

Basic types of gear transmission

The gear drive can be subdivided in rolling contact and helical according to the position of the axes and the engaged wheels.

Rolling contact

• Hypoid

When rolled gear, the axes either parallel ( spur gear ), or intersect ( bevel gear ). Scroll on the motion transmission imaginary rolling cylinder or Wälzkegel - without slipping - from each other. Sliding takes place only on the contacting tooth surfaces in the profile plane of the teeth instead of ( Wälzgleiten ). The teeth touch each other in lines.

Helical

In helical gears, the axes are parallel to each other, neither, nor do they intersect. The touching teeth glide in addition perpendicular to the profile plane (sliding perpendicular to the profile plane is the typical movement in the screw thread ). helical gear are

• The helical gear, with the pairing of two of helical spur gears ( point contact in Achslot )
• The worm gear with the pairing of a worm gear and a worm ( line contact ) and
• The hypoid gears with the pairing of two screws bevel gears ( point contact outside the Achslotes ).

Types of toothing

Involute

• Use: for the drive from the rapids to slow or vice versa ( eg, car, machine ), most important of gearing
• Slight normalization
• Pairs of wheels can be driven around left and right at the same friction
• Relatively low backlash gearing
• Insensitive to the axial distance, as the contact line is a straight line
• The pitch point only rolling friction; going away from the pitch increasingly sliding friction
• By the convex tooth shape creates a high surface pressure, which is a disadvantage in durability.
• Manufacture of the gears is relatively simple and inexpensive

Cycloidal

The flank of a tooth is above the pitch point a Epicycloid and below a hypocycloid.

• Usage: When driving from slow to fast (eg mechanically driven watches).
• For a drive from slow to fast, there is less friction than with involute.
• Larger gear ratios on a small space is possible, because the teeth are narrower at the foot than with the involute.
• Pure rolling friction only possible above a certain minimum number of teeth of the smaller driven wheel.
• Normalization difficult because the tooth shape relative to the involute in addition depends on the number of teeth of the smaller driven pulley. So you need to get perfect engagement and friction conditions, construct the teeth of a pair of wheels specifically to each other. In watchmaking normalization compromises have been made.
• Larger backlash (dust- compatible ).
• No forward-reverse rotation available. That is rotational movement in one direction only makes sense possible. (Because much larger backlash than the involute and due to different friction conditions for different directions of rotation )
• Only be lubricated wheel bearings, the wheels themselves are operated dry to prevent dirt accumulation.
• The depth of engagement is more critical than the involute. In the watchmaking the mathematically determined distance as the ideal is not sufficient. He will ( be felt needs ) in addition empirically adjusted.

Rack and pinion gearing

The rack and pinion gearing is a special case of the cycloid: rolling circle and rolling circle are equal.

• Use: for example, old mill wheels, Black Forest clocks, racks, roller chains
• Application largely displaced by the involute and cycloid. Earlier advantages of this tooth was the ease of manufacture of wheels. In addition, a sufficiently accurate division was easy to reach by means of a drilling template.

The teeth may be straight, ie parallel to the axis, at an angle ( helical gear ) or be designed as a curved toothing. The size of the teeth is determined as a module. The mating gear must have an interlinking of the same module.

Wildhaber - Novikov gearing

The Wildhaber - Novikov gearing is a circular arc teeth.

• Use: in spur gear teeth ( running gears ).
• Convex, semi-circular teeth engage in similarly designed concave gaps. The theoretical radius of the tooth and tooth gap is the same, but in practice the radius of the tooth gap is made ​​slightly larger.
• There can be no transverse contact ratio can be realized, for uniform motion transmission helical gears with a overlap ratio > 1 is required. The pressure angle is constant in each gear position, so that the tooth force does not change its direction.
• Advantageous effect of the design-related good osculation of tooth and tooth gap. Further advantages are the good bearing capacity (higher than involute ), in uniform wear ( slight relative movement of the edges to each other) and in the low- noise and vibration behavior.
• Critically, these teeth are in geometrical variations such as pitch and tooth alignment errors as well as center distance and Achsneigungsabweichungen.
• The manufacturing cost is large because different gear cutting tools are required for the wheel and the mating gear.

Geometric dimensions of spur gears

With suitably chosen for ratio number of teeth and the module of the pitch circle diameter is determined. The tip diameter is about two head heights of the teeth larger, the root diameter by two foot heights smaller. Typical values ​​for head and foot height are and.

From these requirements, the three circle diameter can be calculated as follows:

For internally toothed ring gears of the equation is to be noted when using that the number of teeth is negative and thus has negative diameter. The root diameter of the ring gear is greater in magnitude than the tip diameter.

The pitch of the teeth is the distance from tooth center to tooth center on the pitch circle (also called pitch ):

Measure the distance (center distance ) of the axes of the paired together externally toothed wheels 1 and 2 indicate the following equations:

The module for cylindrical gears should be selected according to DIN 780-1.

All information is valid only for gears without profile shift, ie uncorrected gears.

Check of gears

General

The Inspection of gears is very extensive and depends on the type of gear. In the gear testing the various determinants of gears by means of conventional length and angle measuring method and special gear measurement methods are determined. For safety- critical applications such as X-ray or scan at the manufacturing end testing material testing method with particle accelerators are used.

Check of bevel gears

The check of bevel gears is mainly by overflow checking. Using a running testing machine, the bevel gear to be tested is contacted with a master gear engaged and shifted in Sollachsabstand, Sollachswinkel and target rotational speed. It is simulated in the transmission actually the subsequent function.

The quality of the bevel gear is judged by the resulting contact pattern, the noise during the running test and the backlash.

In the course of testing, a distinction between Zweiflankenwälzprüfungen and Einflankenwälzprüfungen.

Additional checks are still the concentricity inspection by Roundness and the tooth thickness testing with tooth thickness gauges. The rapid development of test methods can also be seen in the Kegelradprüfung. The use of coordinate measuring machines has also come to the Kegelradprüfung big impact. With appropriate software, the topography of the bevel gear is determined, calculated the contact pattern and backlash and simulated. Correction values ​​are transmitted directly to the Bevel Gear (closed-loop ).

In traditional manufacturing to Bevel there is always more or less large deviations between the theoretical calculations and the practical milling result. In 5- axis milling for 5-axis machining centers simultaneously enabled generally accounts for such subsequent corrections, since due to the preparation method corresponds to the milling and thus position and size of the contact pattern at first the calculation.

Check of spur gears

The basis for the examination of the spur gears to DIN 3960 / 3961st

Depending on the quality requirements, there are different test methods. In the double flank of the specimen is free of play brought and passed with a movably mounted master gear is engaged.

The resulting center distance are recorded and evaluated as Zweiflankenwälzabweichung and Zweiflankenwälzsprung. Only sum of deviations is given, that is, failure causes are partly difficult to see. The master gear must be geometry related with the test match. For gears with high quality requirements, this method is less suitable. The rolling test can be perfectly integrated into production processes. Similar to the double flank is the procedure of Einflankenwälzprüfung. Advantage of this test method is the assignment of the deviations from the right or left flank. The determination of the single failure of a spur gear is the safest and most accurate method for determining the quality.

With special Verzahnungsmeßmaschinen and also with coordinate measuring machines and the appropriate software profile, flank, and pitch deviations as well as the tooth width are determined and evaluated in the report. This measurement process is automatic. From the measured deviations, the teeth of the gear tooth quality can be determined. A targeted correction of the machine is then possible.

The direct measurement of the tooth thickness is not possible. It is measured in practice to determine the tooth thickness, the tooth width or dimension through two inserted into opposite tooth spaces measuring rolls. For the production of spur gears are the designer usually before the tooth width or Roll.

Production

The preparation of gear wheels can in principle be carried out in four ways

• Urformend (casting, sintering)
• Transformative ( forging, pressing, pulling, rolling, punching)
• Machining (see below)
• Freeform milling / 5 -axis milling

Archetype end procedures are usually used for less heavily loaded gears, these methods can often be implemented cost-effectively (eg casting or drawing of plastic gears, sintering or stamping on metal gears, where it does not depend on high accuracy ). Cutting and forming methods are used in highly loaded gears used here also greater accuracies can be achieved (important when it comes to noise running or small backlash, for example ).

The main cutting methods are:

• With geometrically defined cutting edge Wälzhobeln
• Hobbing
• Hobbing, milling profile
• Shaping
• Skiving
• Profile rooms
• Scrape

• Rolling or profile grinding
• Honing
• Lapping
• Freeform milling / 5 -axis milling

During profile milling or grinding the cutting edge already has the exact shape of the tooth flank. With a hobbing tool having generally straight edge of the forming machine is carried out so that it " rolls " with the tooth flank to be produced. The material removal takes place only at a point or on a line. Here can be a tool for many different gear geometries are used, the kinematics and thus the control of the machine is relatively complicated. In the profile method requires a large number of different tools or must the wheel before they are used only bring ( " train " the grinding wheel ) in the shape of the tooth flank. Generating method can be carried out continuously, i.e., the entire gear can be manufactured in one continuous movement (e.g., by a helical milling cutter ). Profile method always work in the indexing method, it can therefore only one tooth gap be made ​​, after which the work gear is rotated through a gap.

Gears are often hardened after Gear. The tooth flanks are thus resistant to wear, in particular to the so-called pitting, and the gear wheel bears heavier loads and lasts longer. However arises in hardening hardening distortion, so the edges must be finished after hardening by grinding to achieve the desired tooth quality in general.

Another editing option is eroding. Small gears are also etched (similar to lithography) or electrolytically produced.

For several years, the free-form milling and 5 -axis milling is often being used on machining centers for individual part production or small quantities. The basic idea is based on the realization that a gear ultimately nothing more than a form - comparable from the tool and mold making - but with complex gear geometry. For this purpose, non-profiled, detached from the mesh data of the workpiece, independent of solid carbide tools are used. Typical accounts for gear cutting tools such as hobs and side milling cutters, cutting wheels, wood combs and planing steels, knife heads with Kegelradverzahnungsmesser, Bevel, etc. Schneckenradwälzfräser.

In principle, different gear types on the same 5 -axis simultaneous machining center capable in the soft and hard machining ( / - 62 HRC) are produced. The 5 -axis simultaneous capability ensures that for the finishing of helical gears and spiral gears non-profiled end mills can be used instead of a lengthy wise milling means of a ball mill.

Design / CAD: For gear production on machining centers are contrary to the usual 2D drawing data and Maschineneinstelldatenblättern for gear cutting machines requires highly accurate 3D models of computation.

Instead of consuming manual CAD designs based on points clouds of gear measurement data, meantime, there are convenient calculation software modules, eg for spur gears and bevel gears. However, to be preferred is a gear software that includes not only the mathematical calculation, a kinematic Herstellsimulation. This ensures that a complete tooth profile edition consisting of the tooth tip, tooth flanks and tooth root is generated analogously to manufacturing with conventional gear cutting tools. The cutting result on the machining center is comparable to a machined workpiece on hobbing, shaping and bevel gear in the case. A manual construction of the tooth root radii means you should definitely avoid Moreover, since this involves risks with regard to the tooth root, an unintended edge reduction and an increased risk of collision, especially in spiral bevel gears.

In terms Kegelradsoftware is considered that bevel gears have a tooth profile of a Oktoide. In contrast, spur gears based on an involute.

It should be noted that various Kegelradsoftwaremodule are available that work with a simplified calculation of an involute profile. If one calculates the full Kegelradgeometrie place on a Oktoide based on a replacement spur gear with involute profile, there is a modified tooth profile with a lower tooth root! ( Influencing factors are, Zahnfußdicke, bending lever arm, root fillet radius at 30 ° tangent, ...) [ Hünecke, Diss TU Dresden ]

Bevel gear sets that are designed and manufactured in deviation from a Oktoide, do not correspond to the traditional interpretation and production on Bevel.

" Oktoidale " calculated bevel gear sets correspond to the production yield of conventionally employed Bevel (ringing Mountain, Gleason, Oerlikon, WMW, etc.).

Milling programming: For milling programming is used, a separate CAM software in the rule that sets the focus on the milling of free-form surfaces and therefore can be excellently used for tooth profiles. This has the advantage of greater flexibility. Depending on the nature of the work, the gear module and the resulting size of the tooth gap individual milling strategies for efficient and productive roughing, tooth root and finishing can be selected. Although a combined CAD / CAM software works easily on first sight, but on second view takes a tremendous amount of efficiency.

It should be noted that the modulus of the field is not limited in 5- axis milling on machining centers, so that a suitably chosen for tooth gap milling strategy makes sense.

Gear quality

According to DIN 3961, there are 12 teeth qualities that can be achieved with different production methods, with 1 being the finest and the coarsest 12 tooth quality is.

Production methods:

• Honed quality 1-6
• Ground quality 2-7
• Scraped quality 5-7, (cold rolled)
• Quality 5-9 hobbed, wälzgehobelt, wälzgestoßen
• Quality 7-12 milled form, form encountered
• Quality stamped 8-12, pressed, sintered, injected

Types of damage

The following damages may occur:

• Pitting (pitting )
• Tooth fracture, usually in the area of the tooth root
• Micropitting (micro- pitting )
• Food
• Wear ( at slow speed )