Kinematics Study of Hydraulic Rock Breakers

4.1   Kinematic Characteristics and Characteristic Coefficient α

This section mainly studies the geometric nature and characteristics of hydraulic rock breaker piston motion, so that piston motion becomes more rational and proceeds according to the motion pattern we specify, achieving the best motion results.

To study hydraulic rock breaker piston kinematics, two conditions must be clearly established:

(1) The velocity of the piston when it strikes the chisel tail must be guaranteed to reach the specified maximum velocity v_m. In other words, when studying kinematics, v_m is a constant; no matter what pattern the piston follows, its velocity when striking the chisel tail must be the specified maximum velocity v_m. Only in this way can the hydraulic rock breaker achieve the required impact energy W_H.

(2) The piston motion cycle T is also a constant, thereby ensuring the impact frequency f_H of the hydraulic rock breaker.

Fig. 4-1 shows the linearised piston working velocity diagram. Point M has coordinates (v_m, 0); point E has coordinates (0, T); point N has coordinates (−v_m, T). Connecting points M and E forms triangle △MOE in the v–t coordinate system, whose two right-angle sides are respectively the maximum velocity of piston motion to the impact point and the piston motion cycle T. Taking any point P(v_mo, T₂^′) on line ME, and connecting PO and PN, then PN intersects the t-axis at K. Point K on the time axis divides the piston motion cycle T into two parts: T₁ and T₂. Clearly T₁ + T₂ = T, forming two triangles △OPK and △ENK.

It is easy to show that the areas of these two triangles are equal, i.e. △OPK = △ENK, giving v_moT₂ / 2 = v_mT₁ / 2. Clearly, in the v–t diagram, the area enclosed by △OPK is the piston return stroke, and the area enclosed by △ENK is the piston power stroke. The power stroke equals the return stroke — this is a given. In other words, curve O–P–K represents the piston velocity variation on the return stroke; curve K–N–E represents the piston velocity variation on the power stroke.

Curve O–P–K–N–E represents the piston velocity variation during motion cycle T. The piston starts the return stroke from impact point O where it contacted the chisel tail, accelerating from v = 0 to point P — valve switching (when the piston velocity reaches the maximum return-stroke velocity v_mo) — the piston starts to decelerate, and its speed gradually drops to v = 0, reaching top dead center (end of return stroke). The piston then starts power-stroke acceleration; when the velocity increases to v = v_m, it strikes the chisel tail exactly, and the velocity immediately drops to zero (v = 0), and the piston returns to the starting point of its motion, completing one cycle.

It must be pointed out that when the maximum velocity and cycle of the hydraulic rock breaker piston are both fixed, the maximum return-stroke velocity v_mo must fall on the M–E auxiliary line, i.e. at point P. One can imagine that there are infinitely many points P on line M–E, which means infinitely many maximum return-stroke velocities v_mo, i.e. infinitely many piston cycle motion curves — the piston has infinitely many motion patterns to choose from. We must of course choose the optimal motion pattern. This is the optimisation design problem to be studied in later chapters.

A deeper examination of the piston motion pattern can be made by analysing Fig. 4-1. To do this, from △MOE ∞ △PFE we get:

v_m / v_mo = T / (T₁ + T₂^″)                                                           (4.1)

From △PFK ∞ △ENK:

v_m / v_mo = T₁ / T₂^″                                                                   (4.2)

Therefore:

T / (T₁ + T₂^″) = T₁ / T₂^″                                                           (4.3)

After rearranging:

T₁ / T = v_mo / (v_m + v_mo)                                                           (4.4)

From Eq. (4.1) it can be clearly seen: given fixed piston motion cycle T and maximum velocity v_m, the so-called different motion patterns have different velocity variation curves; the distinguishing characteristic is expressed as different values of maximum return-stroke velocity v_mo and power-stroke time T₁. Therefore, these two parameters carry the property of characterising a particular hydraulic rock breaker's motion characteristics.

But our objective cannot be limited to a single specific hydraulic rock breaker; we need to go further and find a more abstract characteristic index applicable to all hydraulic rock breakers. This abstract characteristic index applies to all hydraulic rock breakers (hydraulic impact mechanisms) and expresses their motion characteristics and operating performance.

In Eq. (4.1), let:

α = T₁ / T                                                                                   

Then the power-stroke time is:

T₁ = αT                                                                               (4.5)

Substituting into Eq. (4.4):

α = v_mo / (v_m + v_mo)                                                                 (4.6)

Combining Fig. 4-1 and Eqs. (4.5) and (4.6), it is easy to see that α is a ratio and a variable — dimensionless. For a hydraulic rock breaker with fixed performance requirements, T is constant, determined by frequency f_H. So α necessarily changes with the change of T₁, while T₁ changes with the position of point P. The closer point P is to point M, the larger T₁ is and the larger α is. Conversely, the closer point P is to point E, the smaller T₁ is and the smaller α is. The same conclusion can be reached from Eq. (4.3). In the equation v_mo is a variable while v_m is a constant determined by impact energy. So α varies with v_mo, while v_mo varies with the position of point P. The closer point P is to point M, the larger v_mo is and the larger α is, and vice versa.

Therefore, the following understanding is reached: given fixed v_m and T, the magnitude of v_mo can specifically represent the motion characteristics of the piston, while α as a variable abstractly represents the motion characteristics of all hydraulic rock breaker pistons. For this reason, we define α as the kinematic characteristic coefficient of the hydraulic rock breaker. For certain optimisation requirements on a hydraulic rock breaker, α must have a corresponding optimal value α_u.