FI56581C - GRUPP AV KUGGHJULSVAEXLAR - Google Patents

Description

rr ^ FTl [B] (11) ADVERTISEMENT crtfil '' UTLÄGGNINGSSKRIFT 3030 1 qSjgSsm C Patent granted 11 C2 1930 (45) Patent caeddelat ^ ^ (51) Kv.lk. * / lnt.CI. * P Ί6 H 1/20 FINLAND I - FI N LAN D (21) P * tenttlhakemu * - p * t * ntan »eknlnj 3291/70 (22) Hakemisplivi - Ansttknlngtdag 07.12.70 (23) AlkupilvS— Glltighetsdag 07.12.70 (41) Tullut Public - Bllvlt offantllg 12.09.71

Patent · and the National Board of Registration / 44) Date of issue and hearing publication—

Patent- och registerstyrelsen 'Ansdkan utlagd och utl.skrlften publlcerad 31.10.79 (32) (33) (31) Pyydetty etuoikeus — Bagird prlorltat 11.03.70

Belgium-Belgium (BE) PV U99T1 (71) S.A. Hansen Transmissions International NV, in the network HTI, 2520 Edegem, Antwerp, Belgium-Belgium (BE) (72) David Hansen, Antwerp, Belgium-Belgium (BE) (7 ^) Leitzinger Qy (5H) Group of gears - Grupp av kugghjulsväxlar The present invention relates to a group of n-gears with at least n different, increasing wheelbases which meet the requirements for rational and productive prefabrication, comfort considerations and user interests and requirements. The group in question is designed in such a way that each gearbox in a given group corresponds as closely as possible to the specific wishes of the user.

The advantages of rational prefabrication for the manufacturer are well known. The user can select a suitable line changer from the given group that best meets the wishes so that the components of the changer are not undersized with respect to each other and that oversizing is kept to a minimum.

These options lead the manufacturer, first, to pre-select a manufacturing program determined by a well-considered choice of minimum and maximum size; second, to find a sensible serial law between the two boundaries of the first program; third, to decide on the number of sizes considered sufficient to meet market requirements.

The manufacturer's problem is to economically produce each gear in the appeal group. Each gear mainly comprises a housing and gears. The problem is now, within the framework of the choice made, to find a solution that allows the optimal use of the same housings and the same gears in as many combinations as possible that meet practical requirements, and that no component in the exchanger is unnecessarily oversized.

In other words, the group must be designed in such a way that, although it consists of a prefabricated material, each exchanger is as close as possible to the exchanger that would have been chosen if each case had been calculated separately.

These requirements impose certain conditions on the prefabrication of both the housing and the gears. The group of gears according to the invention is therefore characterized by precisely defined rules for selecting the wheelbase and, if necessary, the gear pitch, on the one hand, for selecting the appropriate wheelbases and thus also the gears according to these steps.

For clarity, the next most recent wheelbase at each gear in the series is referred to as the "specific wheelbase".

The specific wheelbase of the derailleur may be repeated in the other gears of the series as the first or second wheelbase, so that the number of wheelbases with different absolute values may be very close to the number of derailleurs in the group in question without being smaller.

The group of gearboxes according to the invention is characterized in that in the group of each gearbox the absolute values of the distance between the last axle, i. characteristic axis spacing, form a discontinuous geometric series whose successive values form a continuous geometric series.

According to an embodiment of the invention, all the primary and total reduction ratios of said gears are part of the same geometric series.

For the sake of clarity, a model program for pre-rolling a group of gears according to the invention, which is only an example of the invention, is used as an import.

In the accompanying drawings 3, S6581, Figs. 1-10 schematically show laterally the respective groups of successive exchangers; Fig. 11 shows a table showing a selection of characteristic axle spacings in the present embodiment; Fig. 12 is a schematic perspective view of a gear gear parallel to its input and output axes; Fig. 13 is a schematic perspective view of a pinion gear exchanger with perpendicular input and output axes; Fig. 1U is a schematic perspective view of a gear changer with motors built thereon, the shaft of which forms the main shaft of the gearbox.

In the selected example, the group comprises gears with helical gears and three wheelbases of different size, increasing in size, the third wheelbase being called the characteristic wheelbase. The number of gears A, B, C, D, E, F, G, H, K, L (Figures 1 to 10) in the group n is 10, while the number of different wheelbases in the group in question is n + 2 = 12, denoted by the series aQQ, aQ, a ^ a2, a ^ ... a1Q. The number of characteristic wheelbases is also 10 and each characteristic wheelbase, i. a ^ - a ^, may be the first, second or third, wheelbase in the group changers. As shown in the table of Fig. 11, the wheelbases aQQ to a1Q are used 1, 3, 3, 5, 3, 2, 2, 1, 1 and 1 times, respectively, which means that about 30 wheelbases are obtained from twelve different wheelbases.

If this repetition in the use of wheelbases is advantageous, even more so in the manner in which the range of associated torques is stabilized. This amount of the range of characteristic torques of the gearboxes in the group in question so as to better meet the requirements of the user, and also the way in which these wheelbases are selected to match the wheelbases used as specific wheelbases in order to obtain as favorable a force balance as possible.

To make this easier to understand, the group of ten absolute values of the ten characteristic wheelbases a1 to a1Q can be thought of as forming a geometric series in which the common ratio h is the variable itself, i. geometric discontinuous series, and the successive values of h form the correct geometric series with a constant ratio of p. The values of a. ^ - h ^ and p are calculated as a function of the characteristic torques of different sizes, which are within the knowledge of professionals skilled in the manufacture and sale of each gear.

The series of wheelbases a ^ - a ^^ is shown as follows, taking into account that a ^ is a certain wheelbase of the group in question: u 56581 * 1; Ä2 * W a3 “a2’ ^ 2 * ai "ai-l * hi-l '·· an" an-l, hn-l

With respect to the series of variable relations h, it is presented in the following given that there is some particular variable relationship in the group: hl * h2 β hl, p * h3 “h2, pi * ··· hi" hi-l * Pi * ·· hn- i = hn-2 * P ^ which can also be written: 2 i-1 n «o hj ^ i h2 * h ^ .p; h3 = i ^ .p; h ^ p; ... h ^» l ^. p (3)

Considering the values of h in series (l) as a function of the wheelbase a, we obtain from the series: V -Γ (M and hn_! * T-2- (5) 1 ai n 1 an-l

From the series (3) the following relation is obtained: * λ / ^ f <6>

Combining sets (1) and (2), it is obtained that the value of some wheelbase a ^ can be calculated from the ratio il (t-lMi-2) (7) .. - .p 2 This shows that any person skilled in the art can easily apply the essential feature, i.e. note that in a group the absolute values of the eigen-axis intervals a ^ ... a ^ ... a ^ form a geometrically discontinuous series whose variable relation h1§ hg ... hn-1 itself follows the law of a continuous geometric series with a y-ratio p.

The following relationship can be derived between the surface width of the gear and the wheelbase a: b - K ^ a * (8) which applies to all gears in the group in question and where for a given reduction ratio K ^ and e there are constants which can be determined experimentally in the manufacture of gears such that these gears can be produced with the required accuracy.

On the other hand, in order to approach the "optimal conditions" mentioned in this presentation, the characteristic torques of successive sizes are chosen so that they are equal to the last wheelbase of the exchanger, i. characteristic wheelbase, characteristic torques. Moreover, as much as possible has been done to bring these 5 56561 torques close together, calculated as a function of surface strength and strength, while acknowledging the fact that the characteristic torque is determined by calculating the surface strength.

Under these conditions, the characteristic torque T calculated according to a known calculation method (e.g., the method presented by A.G.M.A .: American Gear Manufacturers Association) can be expressed by the ratio: T = K2. af. bg (9) where 1 <2 is a constant exponent for all characteristic torques and is a function of the reduction ratio and rotational speed of the raw material and the secondary shaft; a is the wheelbase, b is the surface width of the gears, f and g are constant.

The characteristic torque ti of a given characteristic axis spacing a ^ can be written according to the relations (8) and (9): T. = K,. a.m (10) created where K 1 and m are constants and K 3 = K 2. and m = f + e. g In this way, a series of characteristic torques can be set along a series of axis spacing so that the terms of both series correspond to each other at a time. From the relationship between (10) and a ^ it is found that a series of characteristic torques is, as well as a series of characteristic axis spacing, a geometric series in which the series has identical properties.

The series of characteristic torques T can be written as follows, taking into account that there is a certain characteristic torque taken from the series - Tn:

Tl * T2 = Tlkl ’T3 = T2k2’ * * * * Ti = Ti-rki-l »· * * 5 Tn = Tn-l * kn-l (11)

By comparing the characteristic wheelbases (1) with the series and taking into account the ratio (10), we can write: k. = H., M (12) ι-l l-l 6 56561

A series of variable relations k is, like series (2), a geometric series.

thus obtained as follows: formula (12) becomes k ^ = formula (3) becomes h- = h, ^ 3a thus k._ - (p) m.-

from formula (12) we get h ^ m = my ^ s ^ χ ~ \ I

by denoting q = pm where q is a constant \ m / or, p - \ / q (13) can also be written finally: ki = k. ^ 1'1 (14) which indicates that the series of relations k is a geometric series.

A series of variable ratios k is expressed as follows, taking into account that k ^ represents some particular relationship from the series kl »k2 = k1q ·, k3 = k2q; ... ki = k ^ q; ...; kn_x = kn_2q (15) or also k ^, k2 - k ^ q, ... k3 - k ^ q, ... k ^ - k- ^ q '> »· ·» 1 - ^ 1 ^ (16)

Taking into account the ratio (16) can be Jdrjjo 5 = X / ^ tl7)

Combining a series of torques R (11) and ratios k (16) gives: (i-1) (i-2) (18)

Ti - hV'1 '»2

When i = n, the relation (18) becomes: (n-1) (n-2) = T k "'h 2 <19)' n 'lKl q of which 7

Cn-1) (n-2) / - 56581 2 / T „q = -V / -r-r (20) V Tlkl

By replacing q with (17)

It will be appreciated that, taking the above alternatives as a starting point, the numerical values of the characteristic wheelbases as well as the characteristic torques can be determined from the above expressions.

It is also noted that the choice of alternatives is important.

It is a function of the manufacturing program. As an example, it is observed that the applicant is e.g. designed a complete program to prefabricate a series of ten medium-capacity derailleurs with a minimum capacity of 90 mkg and the largest with a characteristic torque of 7000 mkg.

In the group in question, as already mentioned, it has been determined from the outset that T ^ = 90 mkg and T ^ q = 7000 mkg.

Based on the experimental data, the relationship between the minimum torque and the next torque has been confirmed.

On the other hand, taking into account the best fit conditions, it is known that the characteristic torque Tn of size n is approximately 1.3 times the characteristic torque of size n-1, which gives the following ratio: 8 565 * 1

T

τ = £ - = k css 1.3

Vl n 1

The ratio k 1, which is the ratio between two successive characteristic torques, thus varies - from the above application - in a continuous and known manner from one extreme value to the other extreme value.

By choosing the values k ^ = 2 and k ^^ »1.3, the series of relations k is a convergent series.

From the ratio (21), where T1, Tn, k1 and kn-1 are known from the alternatives taken, the value of n can be calculated.

Since a fraction is usually obtained for the number n, the nearest integer is chosen for the number of sizes. Subsequently, this calculation in the opposite direction gives the exact value of k, and this is chosen instead of the initially estimated value.

The value of n gives a value of 10.11.

From this it can be calculated that ten sizes must be used and the exact value is calculated for the ratio k. = 1.316.

n-1

If, according to the example, the following values are known: e = 0.9 f = 1.96 g = 0.9 the ratios (8), (9) and (10) become respectively: b = Κχ a ° * 9 T = K2 a 1 , 96 b ° '9 T. »K, a.2 * 77 l 3 i When determining the values of the constants K ^ and K2, the values of the terms h ^, k ^, p and q can be calculated from the expressions (3), (16), ( 13) and (20), while a series of axelines and a series of characteristic torques T are easily determined by expressions (7) and (18), respectively.

The values of successive characteristic torques T thus form a geometric series whose ratio K is itself a variable.

In said discontinuous geometric series, there are nine terms in a variable relationship, the first and last of which are predetermined. As already mentioned in connection with the properties of the central axis spacings, the different values of the ratios of said geometric discontinuous series change according to the continuous geometric series itself, the constant ratio of which is expressed by the expression: V Τχ χ 29

After the necessary numerical investments have been made, we obtain: - a series of variable ratios k kl k2 k3 kU k5 k6 k7 k8 k9 2 1,898 1,801 1,709 1,622 1,539 l, l + 6l 1,386 1,316 - a series of characteristic torques T (mkg) T1 T2 T3 Tl + T5 T6 T7 T8 T9 T10 90 180 3k2 615 1,050 1,700 2,620 3,830 5,320 7,000 7,800 15,600 30,000 1 + 3,000 91,000 11 + 7,000 228,000 332,000 1 + 62,000 610,000 series of specific axis spacing a (mm) 1 2 3 1+ 5 6 7 8 9 10 111 ll + 3 180 222 269 321 375 1 + 30 1 + 81 + 535 These are theoretical values that are rounded when making manufacturing drawings.

As previously stated, each gear in the series in question comprises not only one or two wheelbases of the characteristic wheelbase selected from the series of characteristic wheelbases shown above.

When looking at a gear, the permissible capacities of the gears connected to it can be compared with each other and the most economical gear is, of course, obtained when the different specific capacities are as close to each other as possible and strive for equality. Moreover, in this case, it is avoided as much as possible that one gearbox becomes oversized in relation to another.

With respect to torque values, it can be said that the most economical gear is obtained when the last torque value of the previous wheelbase is as close as possible - but not less - to the characteristic torque value of the specific wheelbase transmission in a given gear divided by the reduction ratio used for this wheelbase.

10 56581

The wheelbase of the countries is progressing in the same way. The reduction ratio of the last wheelbase plays an important role in setting the criterion for equilibrium or the internal economy of the gearbox, where different ratios are possible.

On the other hand, when gears are used repeatedly, gears that are used at wheelbases other than the specific wheelbase are selected from a series of specific wheelbases. Since in order to form a sufficient range of gears, this group must follow a special law (geometric discontinuous series), it is understood that the "technique" of this choice must also take into account said law while being somewhat flexible.

If the "reduced torque" is called the torque in a smaller gear with a specific wheelbase, the characteristic torque of which is, of course, in the torque-non-torque wheel, it may be written:

T

T - r Rr where T is the reduced torque described above Γ T is the characteristic torque of the last wheelbase R is one of the selected reduction ratios of the last wheelbase.

2 *

Since this ratio can vary between R and R, the following equations are obtained: r min r max '' m m T - · = - * - and T. - = - = -

r max R w r min R

r min r max

The selection of the wheelbase from a series of characteristic wheelbases shall be made in such a way that its torque Τ 'is as close as possible - but not less - to the reduced torque T

r max

Thus T · ^ T

r max

It should be noted that the absolute value of the reduction ratio R plays an important role in determining the selection criterion, and that the ratio Rr max measures the imbalance of the capacities introduced into the gear unit. ** r min

R

The fact that the ratio r max is kept to a minimum is therefore directly aimed at

R

r min to maintain the internal harmony or internal economy of the exchanger by avoiding excessive deviations from the starting point in question, which is the result of a reasonable balance between the R and the amine axis distances obtained, r min

The table in Figure 11 illustrates the application of the above.

11 56581

While not essential, it is highly desirable for the same group (or “only group”) to have discount ratios for gearboxes of all sizes. In the light of these considerations, it is also desirable in practice to introduce as figures values which are commonly used, that is to say, normalized figures, that is to say, 'standard figures'.

In the present case, the so-called R 20 series applies (see Recommendation No U97, International Standardization Organization).

It should be noted that it is sufficient if the primary reduction ratios (i.e. implemented at a certain wheelbase) are part of said series R20, so that the total reduction ratios (obtained by combining the primary ratios) are also part of the same series.

However, the aggregation of primary ratios to obtain overall ratios is regulated - in this case - by the repeated use of the same gears in a group of gears (rationalization that reduces the number of different gears, resulting in an "overall" economy). This repetitive use is governed by the "law of selectivity of the specific axis spacing", which itself is the result of the search for a balance of capacities in each gearbox (which tends to achieve an internal, i.e. inherent, economy).

In addition to the above conditions, the desired result (i.e., a ratio range that is complete and the same for each size) must be achieved by rationally selecting the primary reduction ratios for each wheelbase from a set of standard figures. Thus, it seems that with this problem in mind and when a set of standard figures is available, the most economical solution must be sought.

This solution is based on the fact that the differences between the order numbers of the reduction ratios for the same wheelbase must be different from the differences in the adjacent wheelbases.

It should be remembered that the standard numbers R 20 form a geometric series in which the ratio 8 is> 20 / - 8 -V 10 * 1.12 · ..

The numbers in this series that are taken into account are obtained by taking the positive total power from the ratio s.

More specifically, if it is written that the corresponding terms are obtained by the expression sn (n is the exponent "sequence number"), each sequence number is naturally corresponding to the term in the series R 20 and consequently the discount ratio.

The table on page Ib gives the ratio: sequence number / reduction ratio for the ratio 1 to 100.

12 56581

The consideration of economics that underlies these considerations can also be expressed in terms of efficiency, which means that for a given number of primary discount ratios must be obtained by combining a set of different values that are as close as possible to an ideal number. In a gear unit with two center distances, this figure is obtained by multiplying the reduction ratios of the two wheelbases by each other.

0 nnnn _R a s__n _R s_ 0 1,0 20 10,0 1 1,12 21 11,2 2 1,25 22 12,5 3 1,1 »23 1» »i * 1,6 2k 16 5 1, 8 25 18 6 2.0 26 20

7 2.2U 27 22, U

8 2,5 28 25 9 2,8 29 28 10 3,15 30 31,5 11 3,55 31 35,5 12 1 », 0 32 1» 0 13 1 *, 5 33 1 * 5 li »5, 0 3l »50 15 5.6 35 56 16 6.3 36 63 17 7.1 37 71 18 8.0 38 80 19 9.0 39 90 _I__Uo_ 100_

Considering the specific case of the characteristic and second last wheelbases of a series of gears, the subject of the present invention, it should be remembered that in order to balance capacities in each of these gears and although each wheelbase has several (usually more than two) predetermined reduction ratios, only two ratios are used if this wheelbase is used as the characteristic wheelbase. This is important to set a practical rule for the optimal choice of discount ratios.

Finally, it should not be forgotten that one of the efforts in the field of discount relations is to avoid gaps or shortcomings in the overall group.

All the above considerations lead to the formulation of a practical rule according to which the selection of the reduction ratios for each wheelbase in a given series of wheelbases is made taking into account the selection of these wheelbases in such a way that the differences between successive reduction ratios are classified in ascending order. , 1, 3 «1» 3. ··) and in series II (... 2, 2, 2, 2, 2 ...) belong respectively to the characteristic wheelbase of one of the gearboxes and the latter to the previous wheelbase.

The number of combinations of different reduction ratios obtained by complying with this rule is equal to the ideal or maximum number, which thus means the minimum number of different gearboxes for the whole area.

In the case of gear changers, said standard figures must, of course, be implemented as discount ratios, i.e. as a ratio of the total number of teeth. This means that the above values are achieved with a certain tolerance that does not affect the basic value of the set rule at all.

Therefore, due to this new concept, especially in setting a freely defined group as a whole and the characteristics of each gear, regardless of the quality of the industry, gears are made available to industry which, due to the relatively small number of different parts, allow not only maximum number of combinations but also almost all required to use medium-sized gears and which have a harmonically distributed range of reduction ratios and which are heavily dimensioned and which do not have any unnecessary oversizing of the components in the gear in relation to another.

It should also be noted that these particular special features brought about by this invention do not present any difficulty in the ability to change the group of gears. These new factors, which determine the absolute values of the characteristic intervals as well as the gears, do not affect the housing, i. in a group of all gears, in external form.

Apparently, looking at the experience gained in the field of gearboxes in the past, it can be estimated that maximum efficiency will be achieved if these rules are applied to gearboxes with a tapered housing, which allows manufacturing and is very well suited to many applications and installation options.

By belonging to a group of gears, which in itself is subject to the laws of interdependence, the object of the invention is essentially bound to the concept of a group of gears itself. However, since each gear, considered alone, has a different advantage in its intrinsic value than the advantages of the group in question, the invention equally applies to each gear in such a stupid case.

Claims (10)

1. Series n gear gears with at least n different, growing axle spacings, can be characterized, that in each group of gears, the absolute value of each individual axle spacing forms, i.e. the specific axis distance, a discontinuous geometric series, whose successive values form a continuous geometric series. 2. A series of gears according to claim 1, characterized in that the absolute values of the n specific axis distances form a discontinuous geometric series, whose successive values h., H ,, ... h of the variable relation form a continuous a geometric series whose constant relation p is obtained from Equation V - v / vT-p '\ / - and each specific axis distance a ^ is obtained from Equation (i-1) (i-2) 2 ai ». hx. P where a ^ and h ^ are selected values. A series of gear gears according to claim 1 or 2, characterized in that the gear wheel width b for each gear pair is obtained from the equation b ae where there is a constant, a is the axis distance of the gearwheel in question and e is a constant exponent to be determined. The gearbox of claim 3, characterized in that for a series of 10 gears, the exponent e is 0.9. 5. A series of gears according to any of the preceding claims, characterized in that for a series of gears, the ratio of a gear's specific torque to the specific torque of the gear set in the series is one in transmitter of a geometry-eerie term, of which two are first term and the constant relations in urea ur