JPS6224316B2 - - Google Patents

Description

[Detailed description of the invention]

This invention is suitable for automobiles, motorcycles, etc.
The present invention relates to an engine suspension method that can effectively block transmission of engine vibrations to a vehicle body. In devices such as automobiles and motorcycles that use an engine as a power source, it is necessary to prevent engine vibrations from being transmitted to supporting objects such as the vehicle body. In ordinary front-engine, rear-wheel-drive automobiles, the crankshaft is vertically arranged in the longitudinal direction, and in many motorcycles, the crankshaft is horizontally arranged in the transverse direction. In such vehicles, the engine is usually mounted so that the engine's main axis of inertia in the longitudinal direction forms an angle of 10° to 30° with the horizontal plane. Here, the principal axis of inertia is a straight line passing through the center of gravity of the engine, and refers to the straight line where the inertia factor is minimum, the straight line where it is maximum, and the straight line orthogonal to these straight lines. In addition, the periodic forced external force generated in the engine is
In the above-mentioned vertically mounted automobile engine, torque fluctuations occur mainly around the crankshaft. Furthermore, in the case of a horizontally mounted motorcycle engine having an in-line two-cylinder 180° crank or an in-line three-cylinder 120° crank, the main periodic forced external force is an unbalanced inertia couple around the longitudinal axis. The unbalanced inertia couple here refers to the fact that the center axes of each cylinder are not on the same straight line, so the inertia force created by the reciprocating mass of the piston, etc. of one cylinder is the inertia force created by the reciprocating mass of the other cylinder. A couple that cannot be balanced and remains. In such cases, under certain conditions, the engine is supported elastically so that the principal axis of elasticity is appropriately inclined with respect to the principal axis of inertia of the engine, and dynamic coupling due to the product of inertia and static coupling due to the product of elasticity are achieved. The inventor found that by making good use of coupling, it is possible to reduce the resonance point of the engine caused by the main periodic forced external force to only one. This invention was made based on this idea, and is applied to engines where the inertia couple around the engine's longitudinal axis is the main forced external force, effectively blocking the transmission of engine vibration to the vehicle body. This provides a method for suspending an engine that is possible. In order to achieve this objective, this invention makes the center of gravity of the engine substantially coincide with the elastic center, and also makes the lateral principal axis of inertia of the engine substantially coincide with the lateral elastic principal axis, so that when the engine is supported by an elastic body, Of the six eigenvectors of the six-degree-of-freedom equation of motion, five eigenvectors are all orthogonal to the direction of the main forced external force. The engine support point is placed near the plane passing through the elastic principal axis x ^* and the horizontal elastic principal axis y ^* , and the structure is such that the restoring moment around the torque roll axis is smaller than other restoring moments. be. This invention will be explained in detail below. First, the basic principle of this invention will be summarized and explained. FIGS. 1A and 1B are diagrams showing the coordinate systems of a vertically installed automobile engine and a horizontally installed motorcycle engine, respectively. In these figures, x,
y, z are the stationary orthogonal coordinates whose origin is the center of gravity G of the engine, ξ, η, ζ are the principal axes of inertia of this engine,
Furthermore, x ^* , y ^* , and z ^* in Figure B represent principal axes of elasticity. It is now assumed that the center of elasticity is made to coincide with the center of gravity G of the engine, and that both the principal axis of inertia in the lateral direction η and the principal axis of elasticity in the lateral direction y ^* of the engine are made to coincide with the y-axis of the stationary coordinate system. In this case,
The principal axis of elasticity ^x in the longitudinal direction
For example, in the above-mentioned automobile and motorcycle engines, rotational vibrations due to torque fluctuations and unbalanced inertia couples can be reduced to only the rotational vibrations around the axis of one torque roll (described later). I can do it. Therefore, such forced external force does not induce rotational vibration in the direction orthogonal to the torque roll axis or any translational vibration. According to this idea, it is only necessary to reduce the restoring moment around the torque roll axis so that the resonant rotational speed around this axis is below the engine's normal rotational speed, and then reduce the restoring moment in other directions as necessary. It is possible to increase the natural frequency by increasing the oscillation frequency. Therefore, for example, in the case of a motorcycle engine, it is necessary to create a suspension system that has a sufficient vibration damping function while minimizing engine displacement in response to the longitudinal tensile force caused by the drive chain running between the rear wheel sprocket and the rear wheel sprocket. It becomes possible to obtain the device. Next, this principle will be explained in more detail. Generally, the equation of motion of a rigid body in an elastically supported six-degree-of-freedom system is expressed by the following equation. Here, x, y, and z are the displacements in the x, y, and z-axis directions on the right-handed orthogonal coordinate system when the center of gravity G of the rigid body is the origin, and φ, θ, and ψ are the rotations around the x, y, and z axes. angle (right-handed thread direction is positive; see Figure 1 B), m and I
are the mass and inertia factor of the rigid body, and K and f are the restoring coefficient and forced external force, respectively. The three assumptions mentioned above are: (1) The center of gravity G of the engine is aligned with the center of elasticity, (2) The principal axis of inertia η and the principal axis of elasticity y ^* are both aligned with the y-axis, and (3) The principal axis of inertia ξ is The engine is positioned according to the assumption that it makes an angle α with the x-axis, and that the principal axis of elasticity x ^* makes an angle β with the x-axis. Further, assuming that the only forced external force is the inertia couple f, and applying the reciprocity theorem, equation (1) becomes as follows. split this up In other words, translational vibration and rotational vibration are uncoupled,
Furthermore, pitching θ is also uncoupled. Therefore, if we further divide equation (3), we get Therefore, this problem involves rolling φ and yawing ψ
It can be considered as a vibration of a two-degree-of-freedom system.
As a solution of this equation (4) in complex number representation, , and the forced external force as f=F=e ^iwt , and by substituting these into equation (4), the following equation is obtained. the right side

[0] and The eigenvalues of this equation (5) are ω ₁ , ω ₂ , and the eigenvector is shall be. Here, U ² 〓 and U ² 〓 represent vector φ and ψ components of the second mode. Find the condition under which U ¹ 〓U ² 〓 = 0 when ω ₁ ≠ ω ₂ . The following two equations must hold according to the orthogonality condition. From equations (6) and (7), U ¹ 〓=0 and U ² 〓=0 do not hold at the same time, so U ¹ 〓U ² 〓=0 means either U ¹ 〓 or U ² 〓. is equivalent to becoming 0. Since subscripts 1 and 2 are interchangeable, U ² ==0
Let us consider the conditions under which . In this case, from the properties of the normalized vector, becomes. (1) First, consider the case where I _zx =0. Assuming that U ¹ 〓U ² 〓=0 holds true, equation (6)
The following equation by substituting equation (8) That is, U ¹ 〓I _z =0 must hold. Since I _z ≠ 0, U ¹ = 0, so By substituting equations (8) and (9) into equation (7), we get Therefore, ∴K〓〓=0 must be true. Conversely, if K〓〓=0, then (7)
From the formula always holds true. From this, the linearly independent eigenvectors are

【formula】

[Formula], and in this case, U ¹ 〓U ² 〓=0 certainly holds true. Therefore, K〓〓〓=0 is a necessary and sufficient condition for U ¹ 〓U ² 〓=0. (2) Next, consider the case where I _zx ≠0. (6) Equation × K〓〓 + (7) Equation × I When calculating _zx , Therefore, (I _x K〓〓〓〓〓〓〓+I _zx K〓〓〓)U ¹ 〓U ² 〓+(I _z K〓〓〓 +I _zx K〓〓)U ¹ 〓U ² 〓=0 ...(10) U ¹ 〓U ² If 〓=0 holds true, equation (10) becomes (I _z K〓〓〓+I _zx K〓〓)U ¹ 〓U ² 〓=0
...(11) Equation (6) and Equation (8)

Substitute [formula] and Similarly, from equation (7) From formulas (11) and (13), K〓〓≠0, U ¹ 〓U ² 〓≠0 Therefore, formula (11) is I _z K〓〓＋I _zx K〓〓=0
...(14) Conversely, when (14) holds, I _zx , I
_z , K〓〓≠0, so K〓〓≠0,
From formula (10) (I _x K〓〓〓+I _zx K〓〓)U ¹ 〓U ² 〓=0
...(15) Here, if we assume that I _x K〓〓+I _zx K〓〓=0 (16), then K〓〓≠0, so I _x = −K〓〓〓/K〓〓 I _zx ...(16)' From formula (14), I _z = -K〓〓/K〓〓I _zx ...(14)' Substitute formulas (14)' and (16)' into formula (5). hand Letting the determinant of the matrix on the left side be 0, (K〓〓+ω ² I _zx ) (K〓〓K〓〓/K〓ψ〓−1)
=0 Therefore, the eigenvalue becomes a multiple root, contradicting the first assumption that ω ₁ ≠ ω ² . Therefore, since equations (14) and (16) cannot hold simultaneously, it must be I _x K〓〓+I _zx K〓〓≠0. At this time, from equation (15), U ¹ 〓U ² 〓=0 must hold true. Therefore, equation (14) is a necessary and sufficient condition for U ¹ 〓U ² 〓=0. Also, since I _z ≠ 0 and K 〓 ≠ 0, we transform equation (14) to get I _zx /I _z = −K 〓 〓 / K 〓 〓...(
17) This also satisfies the conditional expression K〓〓=0 found when I _zx =0. Therefore, if I _zx = 0 and I
To summarize the conditional expression when _zx ≠0, ω ₁ ≠ω
The necessary and sufficient condition for U ¹ 〓U ² 〓=0 when ₂ is expressed by equation (17). Next, the relationship between the angles α and β formed by the principal axis of inertia ξ and the principal axis of elasticity x ^* with the x-axis is determined. For this purpose, coordinate transformation is used. When converting the inertia factors on the principal axes of inertia ξ, η, ζ to the inertia factors on the stationary coordinate system x, y, z, the following equation holds true. Therefore, I _x = I〓cos ² α+I〓sin ² α …(20) I _z =I〓sin ² α+I〓cos ² α …(21) I _zx (I〓−I〓)sinαcosα ……(22 ) Here, I〓 and I〓 represent the inertia rates (principal inertia rates) on the principal axes of inertia ξ and ζ. For completely similar restoration coefficients, the following equation holds. K = K ^* = cos ² β + K ^* = sin ² β ...... (23) K = = K ^* = sin ² β + K ^* = cos ² β ... (24) K = = - (K ^{* =} - K ^* 〓)sinβcosβ
...(25) Here, K ^* 〓 and K ^* 〓 are the elastic principal axes x ^* and z, respectively.
^* This is the restoration factor above. Substituting equations (21), (22), and (24) and (25) into equation (17), we get (I〓−I〓) sin αcosα/I〓sin ² α+I〓cos ² α=(K〓 ₋ K〓) sinβc
osβ/K〓sin ² β+K〓cos ² β where R=I _zx /I _z , I〓/I〓=p, K〓/K
If we set 〓=q, then R=(p-1)tanα/ptan ² α+1=(q-
1) tanβ/qtan ² β+1...(26) According to the principle explained in detail above, for p, α, and R, which are determined from the characteristics of the engine itself and the mounting angle, q and β that satisfy equation (26) are If selected, U ¹ 〓U ² 〓=0 holds true. That is, since either U ¹ 〓 or U ² 〓 becomes 0, this vibration system has only one resonance point with respect to the forced external force f 〓. If this resonant frequency is kept out of the engine's normal rotational speed range, the vibration damping function will be improved. FIG. 2 is a graph showing the relationship between q and β, with R as a parameter, based on equation (26).
Therefore, if R is determined from the characteristics of the engine, q and β can be determined from this graph. As is clear from equation (26), this graph also shows the relationship between p and α when q is replaced with p and β is replaced with α. Therefore, if β and q are predetermined depending on the engine suspension method or the characteristics of the elastic member, the relationship between p and α is determined based on this graph, and the suspension angle and engine inertia factor are determined according to this relationship. The specifications should be determined so as to satisfy the following. Next, the torque roll shaft will be explained. This becomes the axis of rotation when the engine performs rotational vibration when a forced external force f around the x-axis is applied. First, the eigenvalues (natural angular frequencies) and eigenvectors (vibration modes) are expressed in six degrees of freedom as follows. Note that [U] ^T represents a transposed vector. ω ₁ , [U ¹ ] ^T = [000u ¹ 〓0U ¹ 〓] ω ₂ , [U ² ] ^T = [000001] ω ₃ , [U ³ ] ^T = [000010] ω ₄ , [U ⁴ ] ^T = [010000] ω ₅ , [U ⁵ ] ^T = [U ⁵ _x 0U ⁵ _z 000] ω ₆ , [U ⁶ ] ^T = [U ⁶ _x 0U ⁶ _z 000] Based on this, the frequency response function from φ to φ H〓
To find 〓, H〓〓=Φ/F〓=〓〓〓〓U〓U〓〓/m〓(ω〓 ₂₋ 〓 ² )=(U〓)/m ₁ (ω ₁ ² −ω ² )...
...(27) Here m〓 is the equivalent mass of mode r. Moreover, ^the frequency response function H〓〓 from φ to ψ ^is as _follows : ω ₁ ² −ω ² )…
...(28) From equations (27) and (28), Φ:Ψ=H〓〓:H〓〓=U ¹ 〓:U ¹ 〓=I _z :I _zx =1:R (from equation (12)) and Become. This holds true regardless of frequency, indicating that the axis of rotation of the response to F is fixed. This rotating shaft is the torque roll shaft. Next, the relationship between the inclination δ of the torque roll axis and α and β is determined. -R=tanδ into (26), tanδ=(1-p)tanα/ptan ² α+1=(1
-q) tanβ/qtan ² β+1 This is tan(α-δ)=tanα-tanδ/1+tan
By substituting αtanδ, tan(α−δ)=ptanα tan(β−δ)=qtanβ

[Table] Table 1 shows the relationship of α, β, and δ with respect to p and q. Next, the natural frequencies ω ₁ and ω ₂ are determined. Substituting equation (12) and then substituting equations (20), (21), and (22), m ₁ = I〓I〓(I〓sin ² α+I〓cos ² α)/I
〓sin ² α+I〓cos ² α……(29) Also, Substituting equation (13), and then (23), (24), (25)
Substituting the formula, k ₁ =K〓K〓(K〓sin ² β+K〓cos ² β)/K
〓sin ² β+K〓cos ² β……(30) From equations (29) and (30), ω ₁ ² =K〓K〓(I〓sin ² α+I〓cos ² α)(K〓sin ² β+K〓cos ² β)/I〓I〓(I〓
sin ² α+I〓cos ² α)K〓sin ² β+K〓cos ² β)……(31) On the other hand, From equations (32) and (33), ω ₂ ² = K〓sin ² β+K〓cos ² β/I〓s
in ² α+I〓cos ² α……(34) (31) According to the formula (34) The procedure for designing using the above results will be explained. First, if the specifications of the engine to be installed and its mounting angle are determined in advance, p and α
is decided. Therefore, R is calculated using equation (26), and q and β are selected using the graph shown in FIG. At this time, consider the required natural frequency ratio for each combination of q and β using equation (35), calculate ω ₁ directly from equation (31) or indirectly from equation (34), and write K ^* 〓. decide. That is, K ^* 〓 is determined so that ω ₁ is equal to or lower than the engine's normal frequency. It is sufficient to determine other restoring coefficients based on K ^* 〓, q, etc. obtained in this manner, select support points and support methods for the engine in accordance with these, and suspend the engine elastically. Here, the elastic principal axis x ^* usually does not coincide with the torque roll axis, but α and β are relatively small in a typical engine. Therefore, in order to reduce the restoring moment around the torque roll axis, the elastic principal axis x ^*
All you have to do is reduce the restoring moment around it. Next, embodiments of the present invention based on the above concept will be described with reference to the drawings. In all of these embodiments, the present invention is applied to a horizontally mounted engine for a motorcycle. 3A and 3B are a side view and a cross-sectional plan view of the engine support portion of the first embodiment. In this figure, reference numeral 1 denotes an engine, and the engine 1 includes a crankcase 2 and a power transmission mechanism (not shown) such as a transmission, which vibrate together. 3 is a sprocket, and the rotation of the engine 1 is transmitted from this sprocket 3 to a rear wheel (not shown). In other words, this sprocket 3
A chain (not shown) runs between the front wheel and the rear wheel sprocket (not shown). Therefore, when the engine 1 drives the rear wheels, the upper side of the chain is stretched, and a driving reaction force acts on the engine 1 in the direction of arrow 4 in FIG. 3A, that is, in the rearward direction. Similarly, when applying engine braking, the engine tries to be pulled backwards. Reference numeral 5 denotes a front attachment portion, and numeral 6 denotes a rear attachment portion, which are formed integrally with the crankcase 2 so as to protrude forward and rearward from the crankcase 2, respectively. In this embodiment, the front and rear mounting portions 5 and 6 are formed in pairs on the left and right, respectively. An annular rubber cushioning material 7 is attached to each of the mounting portions 5 and 6, and each pair of left and right cushioning materials 7 are arranged coaxially so that their center axes are oriented toward the side of the engine. Further, the center of gravity G of the engine 1 is located on a plane 8 passing through the center of each of the four cushioning materials 7. Note that the elastic principal axis x ^* ,
y ^* exists on this plane 8. 11 is a frame, 12 and 13 are stays, and 14 is a mount bolt. Note that the inertia couple of an engine generally has a rolling component around the x-axis and a yawing component around the z-axis (see FIG. 1B), and the latter is smaller than the former. In the engine 1 in this embodiment, the yawing component is made sufficiently small to be ignored by adjusting the balance of the crankshaft (not shown). Further, the left-right distance between the front attachment part 5 and the rear attachment part 6 is sufficiently narrower than the interval between the front and rear attachment parts 5 and 6. Furthermore, it is assumed that the center of gravity G and the center of elasticity coincide, and that the principal axis of inertia η and the principal axis of elasticity y ^* both coincide with the y-axis (see FIG. 1B). In this embodiment, an annular buffer material 7 is used, but with this shape, the coefficient of restitution is high in the direction perpendicular to the axis that lies on the plane 8 and passes through the center of the left and right buffer materials 7, 7. , and the restoration coefficient becomes smaller in the direction in which this axis is tilted. Therefore, the plane 8
The restoring coefficient around the upper elastic principal axis x ^* is smaller than the restoring coefficient around the other principal axes y ^* and z ^* . Therefore, while it becomes easy to turn around the main axis x ^* , it becomes difficult to turn around the other main axes y ^* and z ^* .
If the driving reaction force from the chain in the four directions of the arrows does not pass through the center of gravity G, this tensile force will give the engine 1 a yawing force around the z-axis and a force in the pitching direction around the y-axis. Since the coefficient of restoration around the main axes y ^* and z ^* increases, the vibration of the engine 1 decreases. Furthermore, this cushioning material 7
The hardness and dimensions of the material may be determined according to the procedure described above. FIGS. 4A and 4B are a side view and a rear view showing the second embodiment, and although not shown, the engine 1 is shown in the third embodiment.
It is supported by a frame in the same position as shown in the figure. In this embodiment, the number of rear mounting portions 6 is one. Therefore, since the width of the cushioning material 7 of the rear mounting portion 6 that crosses the elastic main axis x ^* can be reduced, it is possible to reduce only the restoring moment around the main axis x ^* . In the above embodiment, the engine 1 has its crankshaft balanced so that only the rolling around the stationary coordinate axis x acts as a forced external force, and the engine support point is set on the plane 8, that is, transversely to the principal axis of elasticity x ^* in the longitudinal direction. Since it is arranged on a plane passing through the principal axis of elasticity y ^* in the direction, it more closely conforms to the theory and provides extremely good vibration isolation. It is clear that this invention can be applied not only to motorcycles and automobiles, but also to any engine that satisfies certain conditions. As described above, this invention arranges an engine in which the inertia couple around the axis in the longitudinal direction is the main forced external force so as to satisfy certain conditions, and furthermore, the restoring moment around the axis of the torque roll is used as the restoring moment in the other direction. Since it is configured so that it is smaller than the moment,
Transmission of engine vibration to the vehicle body can be effectively blocked. Furthermore, when applied to a motorcycle engine, movement of the engine due to the drive reaction force of the rear wheel drive chain can be extremely reduced.

[Brief explanation of the drawing]

Figure 1 is a diagram showing the coordinate system for the engine, Figure 2 is a graph showing the relationship between q and β based on equation (26), with R as a parameter, and Figure 3 A and B.
4A and 4B are a side view and a cross-sectional view of an engine support portion showing a first embodiment of the present invention, and FIGS. 4A and 4B are a side view and a rear view showing a second embodiment. 1... Engine, x, y, z... Stationary orthogonal coordinates, ξ, η, ζ... Principal axis of inertia, x ^* , y ^* , z ^*
...Elastic principal axis, G...Center of gravity of the engine.

Claims (1)

[Scope of Claims] 1. In an engine in which a major periodic forced external force such as an inertia couple exists around the longitudinal axis of the engine, the center of elasticity is made to approximately coincide with the center of gravity of the engine, and The principal ^axis of inertia η of
The elastic principal axis x* in the longitudinal direction is tilted around the abscissa axis y by an angle β necessary for the two eigenvectors to be perpendicular to the direction of the main forced external force, and the elastic principal axis ^{x* and} the horizontal elastic principal axis y ^* A method for suspending an engine, characterized in that the engine is supported so that a restoring moment about the torque roll axis is smaller than other restoring moments by arranging a support point of the engine near a plane passing through the axis. 2. Claim 1, characterized in that the inclination angle β of the principal axis of elasticity x ^* in the longitudinal direction is determined by the following formula:
Engine suspension method described in Section 1. (p-1) tanα/ptan ² α+1=(q-1)
tanβ/qtan ² β+1 However, p=Iξ/Iζ q=Kφ*/Kψ* Iξ: Inertia factor around the principal axis of inertia ξ in the longitudinal direction Iζ: Inertia factor around the principal axis of inertia ζ in the vertical direction K _x ^* : Inertia factor in the longitudinal direction Restoration moment around elastic principal axis x ^* K _z ^* : Restoration moment around elastic principal axis z ^* in vertical direction α : Inclination angle of principal axis of inertia ξ β : Inclination angle of elastic principal axis x ^*