DE4407696A1 - Temperature compensated gearwheels in gearbox - Google Patents

Abstract

The shaping of the gear teeth and positioning of the gearwheels takes into account the meshing position at operating temperature for optimum torque transfer and long life. Each pair of wheels has basic effective diameters for its gear teeth and the point of contact between the teeth moves with temperature changes. The design takes into account the different thermal expansions of the different materials of the gearwheels and of the gearbox housing as well as the design of the bearings e.g. roller bearings, taper bearings, etc.

Description

The invention relates to a spur gear according to Preamble of claim 1.

In a known spur gear (G. Niemann H. Winter "Machine elements" volume II, second, completely reworked Edition, corrected reprint, Springer-Verlag Berlin Heidelberg New York Tokyo 1985, Sn. 84, 85) is the influence of Warming up on the operating backlash when determining the Tooth thickness dimensions taken into account. Will this Helical gearbox to achieve a lower weight Gearbox made of cast aluminum or magnesium used, are the higher thermal expansions compared to steel or cast iron and their effects on the bearings must be taken into account (p. 296).

From Dubbel "Taschenbuch für den Maschinenbau", 17th new edition tete edition, 1990, Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona, Sn. G115 to G121 the gear geometry, in particular the Involute teeth known.

Flan occur in spur gearboxes of the type mentioned at the beginning damage, which is a consequence of the "flash temperature". In DIN 3990 becomes a flank to avoid this flank damage Correction in the form of a head relief is proposed. It has however, showed that this measure is not sufficient.

The object underlying the invention is essentially Chen in a spur gearbox of the type mentioned  Way to effectively prevent the occurrence of flank damage the.

The task explained is advantageous with the kenn Drawing features of claim 1 solved.

In the spur gear according to the invention results in Normal temperature a falling head involute - and it is the manufacturing condition. This will interfere with something conditions at normal temperature accepted. By the Erwär The gearbox changes to the operating temperature Involute, so that under these conditions there is no rolling There is interference in the intervention.

Through the invention, the life of the spur gear increased, so that warranty and goodwill costs are reduced.

Details of the invention follow from the following Description in connection with the drawing. In the drawing mean

Fig. 1 is a schematic representation of the invention, relevant parameters of the tooth geometry of a gear pair with involute teeth of a spur gear train at room temperature,

Fig. 2 shows the gear geometry of Fig. 1 at operating temperature, and

Fig. 3 is a schematic comparison of the flank engagement at room temperature on the one hand and the operating temperature on the other hand, the toothing geometry of Fig. 1 on an enlarged scale.

Many physical changes under the influence of temperature Sizes such as B. the dimensions of the body.  

Solid bodies expand proportionally with increasing temperature out. The expansion depends on the type of material and on the temperature increase d. H. Temperature difference.

From thermal theory is for the linear expansion of a body known dependency:

δ 1 = α _* l1 _* δt

in which:

δ t = t1-t2 temperature difference
l1 = length of the body at temperature t1
l2 = length of the body at temperature t2
δ 1 = l1-l2 change in length
α = substance-dependent expansion coefficient

The expansion with increasing temperature must be where larger tem fluctuations in temperature occur.

When using different materials you have to pay attention to the different expansion coefficients.

The known gearbox calculations relate to the room temperature. The influence of the operating temperature is with these theoretically neglected. Measurements on gearboxes used gave operating temperatures of 130 ° C to 160 ° C, d. H. a considerable temperature difference of approx. 110 ° C.

The drawing quality of the gears and the housing results in used gear optimal rolling of the gear pairs. The dimensional changes under the influence of temperature however not considered.

Axle bends, tooth constraints, etc. are neglected and only the changes in the transmission with temperature fluctuations analyzed, we get:

• - the change in the base circle diameter  
• - the change of the center distance by two factors:
  • a) linear change in the housing center distance
  • b) dimensional change in the distance between the supported axles.

The change in the bearing distance is important if for Gears and housing different materials with under different expansion coefficients are used, such as. B. Steel and aluminum and in addition, when storing the Shaft tapered roller bearings can be used. The difference between Aluminum housing and steel shaft lead to an axial play of the shaft in the housing.

If the axle bearings are made with tapered roller bearings, then that works Axial play due to the taper angle of the tapered roller bearings in the Ratio 1: 4 or 1: 3 in the radial play.

The comparison of the operating pressure angle of a pair of wheels different temperatures takes into account all dimensional changes to changes in this rolling parameter ters.

So a change in the engagement conditions can be observed under the influence of temperature (graphical representation of the flank engagement F1 / F2 at room temperature and the flank engagement F'1 / F'2 at operating temperature in Fig. 3).

In particular, it should be noted that the two we significant influencing factors, base circle and center distance changes partially compensate, d. H. they don't always work negatively affects the engagement of the pair of wheels.

As already mentioned, the center distance of the gearbox also changes an aluminum housing through two influencing factors:  

1. Linear change in center distance under the influence of temperature

δ 1 = α _*

l1 _*

δ t

δ t = 110 ° C temperature difference between room and operating temperature
α = 23.9 _* 10 ^-6 l / ° C coefficient of expansion f. Alu
l1 = 152 mm center distance in the housing

The center distance thus changes mathematically / theoretically by:

δ l = 0.399 mm

2. Change in center distance through the axial play or radial play

With an axial play α la, due to the length difference of Thermal expansion of the housing and the shaft in the axial direction, there is a radial play δ r of:

δ r = δ la _* tan τ

τ = taper angle of the tapered roller bearings

Practically, this means that from an axial play in the normal case a radial play results with the factor approx. 1: 3. When used The use of an aluminum housing becomes other tapered roller bearings installed and this results in a factor of approx. 1: 4.

Practical procedure:

δ la = δ lG - δ lw

δ la - axial play
δ lG - linear expansion of the housing
δ lw - linear expansion of the shaft

δ lG = αa _* lG δ t

αa = 23.9 _* 10 ^-6 l / ° C expansion coefficient
lG = 498 mm for aluminum

δ lw = αw _* lw _* δ t

αw = 11.5 _* 10 ^-6 l / ° C coefficient of expansion
lw = 509 mm for steel

δ la = 1.309 - 0.644 = 0.665 mm

δ r1 = ¼ _* δ la

δ r1 - radial play in the bearing

δ r1 = 0.166 mm

The effective radial play corresponds to the length ratios between the position of the toothing and the bearing distance, d. H.:

δ r = 0.109 mm

3. Total change in center distance

If the axial play or radial play is both the main and the countershaft is taken into account, then you get the following ge Entire change in center distance:

δ a = δ l + 2 _* δ r

δ a = 0.617 mm

The change in the base circles of the pair of wheels is a linear length extension and is calculated using the following formula:

δ db = α _* db _* δ t

in which:

α = 11.5 _* 10 ^-6 l / ° C coefficient of expansion for steel

The pair of wheels examined in the transmission has the following parameters:

• - for oblique degree I
  db1 = 133.726 mm
  Z1 = 24
• - for slope degree II
  db2 = 139.298 mm
  z2 = 25
• - helix angle
  β = 22 °

With a temperature difference δ t = 110 ° C, the following reasons circle changes calculated:

δ db1 = 0.169 mm
δ db2 = 0.176 mm

The following are parameters from the gear calculation, in fact:

1. Operating pressure angle αwt

db1, 2 - base circles
a - center distance

2. Forehead pressure angle αt

α - pressure angle
β - helix angle
βb - helix angle in the base circle

3. Pressure angle deviation fα

fα = αist - αsoll  

fHα - profile angle deviation
Lα - profile test area

4. Base circle deviation fb
fb = dbist - dbsoll

For the analysis of the engagement relationships of the wheel pair formed two groups of parameters:

The following relationship exists between the parameters of both groups hunger:

d′b1 = db1 + δ db1
d′b2 = db2 + δ db2
a2 = a1 + δ a

The operating pressure angle at room and operating temperature is Consequently:

Are in the equation of the pressure angle at Be drive temperature replaced the parameters d'b1 and d'b2, then this leads to the following relation:

Simply put:

One therefore takes place under the influence of the temperature fluctuation Change of the engagement conditions of the pair of wheels instead. Constant operating pressure angle and with it also identical rolling conditions are in the case examined, d. H. Aluminum Housing and steel wheels only theoretically possible, especially practical a complete compensation of the two influencing factors is not can be done.

The change in the pressure angle can be due to the Value of the factor k can be analyzed.

It follows that the base circle for an optimal design Operating temperature is less than the basic drawing circle.

In this case, the design diameter is larger than that Basic drawing circle.

The calculations do not necessarily have to change the Lead base circle. The same effect can be with a new calculated pressure angle can be achieved.

C. If the value of the coefficient k = 1, then changes the operating pressure angle is not influenced by the loading operating temperature, d. H. the rolling of the gears is optimal.

It is estimated that the vehicle transmission works 90% of its time Lifetime at operating temperature. Taking into account the dimensional Changes in the gear parameters, it is fixed provides that the wheel pairs in known transmissions only Room temperature, d. H. Roll about 10% of the service life optimally.

So that the wheel pairs are calculated with the operating temperature Interference with regard to load transmission and ge pass on noise, a gearbox design at Be operating temperature according to the teaching of the claim suggested.

Example of gearbox design at operating temperature

The example examined relates to a pair of wheels of a Ge drive with aluminum housing.

The parameters of the wheel pair are:  

The difference in the pressure angle relates to that Pair of wheels and can according to the ratio of the base circles of the wheels allocated proportionately.

In the example shown, due to the small sub divide the base circles each half of δαwt one wheel arranges.

Claims (1)

Helical gear unit in which the design value of at least one parameter of the tooth geometry of the involute teeth of a gear pair is corrected to the operating temperature, taking into account the coefficient of thermal expansion, characterized in that a base circle diameter (db1 or db2) or both base circle diameters (db1 and db2) or the intervention angle (α) are corrected under the condition that k ≷ 1, undcos αwt3 = K _* cos αwt1 applies anddb1, db2 the base circle diameter at room temperature
db1 + 6db1, db2 + 6db2 the base circle diameter at operating temperature
a1 the center distance at room temperature
a1 + δa the center distance at operating temperature
αwt1 the operating pressure angle at room temperature
αwt3 indicate the operating pressure angle at operating temperature.