Piston Motion Patterns

4.3   Piston Motion Patterns

From the above analysis of the velocity diagram, the following conclusions about piston motion patterns can be drawn.

(1) The piston velocity diagram consists of two triangles: a right triangle for the power-stroke velocity diagram, and a general (non-right) triangle for the return-stroke velocity diagram.

(2) Because the power stroke equals the return stroke, the areas of the two triangles must be equal.

(3) The velocity during the return-stroke braking phase and the power-stroke phase follows a single straight line in the velocity diagram. This is because after the piston valve switches on the return stroke, during the return-stroke braking phase and the power-stroke phase, the valve remains in the same position and the force on the piston is the same.

(4) A key principle for hydraulic rock breaker design: in all feasible designs, the piston maximum velocity v_m (impact energy W_H) and cycle time T (impact frequency f_H) must be constants, because they are specified by the design task and cannot be changed.

(5) Kinematics parameters: return-stroke acceleration distance S_j, return-stroke acceleration time T₂^′, and maximum return-stroke velocity v_mo are all highly useful for controlling the hydraulic rock breaker, because they are all right at the valve switching point on the return stroke. For stroke-feedback hydraulic rock breakers, S_j is the basis for determining the feedback hole position and is very useful for hydraulic rock breaker design. As for T₂^′ and v_mo, no hydraulic rock breaker products currently use these two parameters to control the breaker, but the method is feasible and worth researching.

(6) Comparing all feasible designs from a kinematics perspective (i.e. point P and point F at different positions), v_m and T are the same in all designs. The only difference is the ratio of T₁ to T₂ in T (P is on ME), as well as the resulting different maximum return-stroke velocities v_mo.

Based on the above analysis, if a design is viewed from a kinematics perspective, since v_m and T are both determined by performance parameters, the designer has very little freedom left. A so-called design is simply a matter of correctly distributing T₁ and T₂ within T while keeping v_m and T fixed — nothing more. In this way, hydraulic rock breaker design becomes very simple: just split the piston motion cycle T in two, and you get a feasible design. But the determination of this split ratio involves considerable technical depth, including the optimisation design problem. Once the split ratio is determined, the entire design is fully determined. So the power-stroke time ratio α is the one parameter that can represent a feasible design and has universal applicability.

The power-stroke time ratio α is also commonly called the kinematic characteristic coefficient. Because kinematic characteristic coefficient α is dimensionless and expresses the kinematics characteristics, it is defined as an abstract design variable; each of its specific values represents a design, and its expressed characteristics are fully applicable to hydraulic rock breakers of all sizes and models.

The research above shows that all kinematic parameters are functions of α; likewise, dynamics parameters, structural parameters, etc., can all be expressed as functions of α. So what other properties does α itself have, and what is its range of values? From Fig. 4-1 and Eq. (4.5), the following can be clearly seen:

1) When T₁ = 0, α = 0; this is shown in Fig. 4-1 by point P coinciding with point E. The area of △ENK, i.e. stroke S = 0; a zero-stroke motion (α = 0) does not exist in reality — S = 0 has no physical meaning.

2) When v_mo = v_m, from Eq. (4.6), α = 0.5. In Fig. 4-1 this is shown by point P coinciding with point M; point K exactly bisects the O–E line, i.e. T₁ = ½T. In Fig. 4-1 point F coincides with point O, giving T₂^′ = 0, i.e. the return-stroke acceleration time is zero — this is also impossible and has no physical meaning.

3) When the return-stroke acceleration time equals the return-stroke braking time, i.e. T₂^′ = T₂^″, the return-stroke velocity diagram is obviously an isosceles triangle. The kinematic characteristic coefficient for this special-form velocity diagram is α = 0.4142. From Fig. 4-1, α = 0.4142 can be derived without difficulty. This result also has applications when studying nitrogen-explosive hydraulic rock breakers.

From this it is clear that the range of α is 0 to 0.5; and since α = 0 and α = 0.5 both have no physical meaning, it must be that 0 < α < 0.5. The optimal abstract design variable obtained from different optimisation objectives must also satisfy 0 < α_u < 0.5.